{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60176,"title":"Find the number of diagonals in a n sided polygon.","description":"Find the number of diagonals in a n sided polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 21px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 10.5px; transform-origin: 407px 10.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of diagonals in a n sided polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = count_diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =12;\r\ny_correct =54;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =4;\r\ny_correct =2;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =3;\r\ny_correct =0;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3469688,"edited_by":3469688,"edited_at":"2024-05-02T19:23:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2024-05-02T19:23:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-02T18:52:26.000Z","updated_at":"2026-03-15T05:04:28.000Z","published_at":"2024-05-02T19:23:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of diagonals in a n sided polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52854,"title":"Poly2mask, drawpolygon or patch","description":"Recently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\r\nvertexes coordinates is given as follow:\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nTips: patch is the answer!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evertexes coordinates is given as follow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex = [0 1 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey = [0 0 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTips: patch is the answer!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Output = Plot_polygon(x,y)\r\nbw = poly2mask(x,y,256,256);\r\nimshow(bw)\r\n\r\nmy_vertices = [x;y];\r\nh = drawpolygon('Position',my_vertices,'LineWidth',1,'Color','cyan');\r\n\r\npatch(x,y,'cyan')\r\n\r\nOutput = 'poly2mask';\r\nend","test_suite":"%%\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nassert(isequal(Plot_polygon(x,y),'patch'));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1133393,"edited_by":427930,"edited_at":"2024-07-08T18:22:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-03T05:53:41.000Z","updated_at":"2026-03-02T13:59:55.000Z","published_at":"2021-10-03T05:53:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evertexes coordinates is given as follow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = [0 1 1 0];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [0 0 1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTips: patch is the answer!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43034,"title":"angle in regular polygon","description":"Make a function which returns measure of interior angle in x-side regular polygon. x is as input.\r\nPlease pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\r\n\r\nif x=3 its triangle and angle is 60 degrees\r\nx=4 -\u003e angle = 90 degrees","description_html":"\u003cp\u003eMake a function which returns measure of interior angle in x-side regular polygon. x is as input.\r\nPlease pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\u003c/p\u003e\u003cp\u003eif x=3 its triangle and angle is 60 degrees\r\nx=4 -\u0026gt; angle = 90 degrees\u003c/p\u003e","function_template":"function y = pol_angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 60;\r\nassert(isequal(pol_angle(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 90;\r\nassert(isequal(pol_angle(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 108;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 120;\r\nassert(isequal(pol_angle(x),y_correct))","published":true,"deleted":false,"likes_count":28,"comments_count":0,"created_by":90955,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":215,"test_suite_updated_at":"2016-10-07T08:18:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T08:26:32.000Z","updated_at":"2026-02-16T12:26:33.000Z","published_at":"2016-10-05T08:26:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function which returns measure of interior angle in x-side regular polygon. x is as input. Please pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif x=3 its triangle and angle is 60 degrees x=4 -\u0026gt; angle = 90 degrees\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45178,"title":"An n-sided regular polygon is drawn within a circle whose radius is 'r', what will be the area of the polygon?","description":"area of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003earea of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=poly(n,r)\r\ny=n\r\nend","test_suite":"\r\n%%\r\nn = 6;\r\nr = 6;\r\ny_correct = 93.5307;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 8;\r\nr = 6;\r\ny_correct = 101.8234;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 11;\r\nr = 7;\r\ny_correct = 145.7027;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 13;\r\nr = 13;\r\ny_correct = 510.4984;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2021-12-25T10:22:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-10-18T23:23:26.000Z","updated_at":"2026-02-18T09:44:32.000Z","published_at":"2019-10-18T23:55:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45196,"title":"Determine whether a given point is inside or outside a polygon","description":"A closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\r\nIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\r\nHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361px 8px; transform-origin: 361px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function InOut = inOrOut(p,r)\r\n% inOrOut() Determines whether point r is inside (InOut = 1) or \r\n% outside (InOut = 0) polygon p\r\n    InOut = 0;\r\nend\r\n","test_suite":"p = [0,0; 0,100; 5,10; 10,100; 15,20; 20,100; 25,30; 30,100; ...\r\n    35,40; 40,100; 45,50; 50,100; 50,0; 0,0];\r\n%%\r\nr = [44.28, 60.99];\r\np = [0,0; 0,100; 5,10; 10,100; 15,20; 20,100; 25,30; 30,100; ...\r\n    35,40; 40,100; 45,50; 50,100; 50,0; 0,0];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [38.33, 57.67];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [0.98, 23.99];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [27.07, 95.94];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [ -7.45, 7.14];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [43.19, 2.87];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [19.39, 16.79];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [48.72, 71.27];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [-6.42, 68.20];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [20.03, 47.11];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":8580,"edited_by":223089,"edited_at":"2022-09-09T08:55:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":"2022-09-09T08:55:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-11-06T23:11:51.000Z","updated_at":"2026-01-23T09:40:37.000Z","published_at":"2019-11-06T23:20:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; 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sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation 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the pentagon (with the minimum number of triangles)","description":"Problem statement\r\n\r\nAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V, corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\r\n\r\nV = [1           0            0;\r\n     cos(2*pi/5) sin(2*pi/5)  0;\r\n     cos(4*pi/5) sin(4*pi/5)  0;\r\n     cos(4*pi/5) sin(-4*pi/5) 0;\r\n     cos(2*pi/5) sin(-2*pi/5) 0];\r\n\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, F. The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nTip\r\nBeware to avoid self intersecting triangles.\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1278.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 639.2px; transform-origin: 408px 639.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.525px 8px; transform-origin: 327.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.09167px 8px; transform-origin: 6.09167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eV = [1           0            0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(2*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(4*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(-4*pi/5) 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.5px; tab-size: 4; transform-origin: 127.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(-2*pi/5) 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.442px 8px; transform-origin: 384.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 169.75px; text-align: left; transform-origin: 385px 169.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"445\" height=\"334\" style=\"vertical-align: baseline;width: 445px;height: 334px\" 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AhAUx7lAlow8mJbOyhW3AARL6AL5GWr/DkyPxAUgZPs/pyb5+YgAaVG5AAB5ELpAHlQuAEDSrB0BmVG5AACps7cM5ETlAgDkROgCqVO5AAAZsLcMZEPlAgDkwd4ykAeVCwCQDaELZEDlAgBkSegCiVK5AAA5cUEXSJ3KBQDIjL1lIGkqFwAgP0IXSJfKBQDIm9AF0qJyAQCy5IIukCiVCwCQK3vLQIpULgAAQhdIh8oFAMiYvWUgOSoXACBv9paBtKhcAIDsCV0gISoXAIAOQheInMoFAMAFXSAdKhcAgFH2loEkqFwAAPYRukD8VC4AABMRukCcVC4AAB1c0AUip3IBABjL3jIQM5ULAEB3QheIjcoFAGAce8tAtFQuAAATsbcMxEnlAgDQhdAFIqRyAQDogdAFIqFyAQDozgVdIDYqFwCASdlbBqKicgEAmIrQBeKhcgEA6IfQBcKmcgEA6IELukAkVC4AAL2xtwzEQOUCANA/oQuESuUCANAze8tA8FQuAAD9sLcMhE3lAgDQJ6ELBEzlAgAwAKELBEblAgDQPxd0gVCpXAAApsXeMhAklQsAwHQJXSA8KhcAgDIIXSAMKhcAgAG4oAsERuUCADAYe8tASFQuAADlEbpA01QuAAADs7cMBEPlAgBQBnvLQBhULgAAJRG6QABULgAAFRC6QENULgAA5XFBF2iaygUAoFT2loFGqVwAAMomdIHmqFwAAKokdIF6qVwAACrggi7QEJULAEA17C0DTVC5AABUT+gCdVG5AABUxt4yUDuVCwBAlewtA/VSuQAAVEzoAjVSuQAA1EjoAhVTuQAAVM8FXaAuKhcAgFrYWwZqoXIBAKid0AUqo3IBAKhL596y0AWqoXIBAKiRC7pAxVQuAAD1ckEXqJLKBQCgOUIXKJvKBQCgdvaWgcqoXAAAmmBvGaiGygUAoCFCF6iAygUAIABCFyiJygUAoDku6AJlU7kAADTK3jJQKpULAEAwhC4wMJULAEDTOveWhS4wGJULAEAAXNAFSqJyAQAIgwu6QBlULgAA4RG6wHSpXAAAgmFvGRiYygUAICT2loHBqFwAAAIjdIEBqFwAAAImdIE+qVwAAMLjgi4wXSoXAIAg2VsGpkXlAgAQPKEL9EzlAgAQqs69ZaEL9EblAgAQMBd0gT6pXAAAwuaCLtAPlQsAQDyELjAVlQsAQPDsLQM9U7kAAMTA3jLQG5ULAEAkhC7QA5ULAECEhC7QhcoFACAeLugCU1G5AABExd4yMCmVCwBAtIQuMI7KBQAgNvaWge5ULgAAEbK3DHShcgEAiJPQBSaicgEAiJ/QBfZRuQAARMsFXWAclQsAQMzsLQNjqVwAACIndIEOKhcAgIQIXcieygUAIH4u6AL7qFwAAJJgbxkYpXIBAEiO0IWMqVwAAFJhbxlQuQAAJMXeMmRP5QIAkBahC3lTuQAApEvoQn5ULgAAyXFBFzKmcgEASJG9ZciVygUAIFFCF7KkcgEAyIDQhWyoXAAA0uWCLuRH5QIAkDR7y5AZlQsAQDaELmRA5QIAkDp7y5ATlQsAQAbsLUM2VC4AAHkQupAHlQsAQH6ELqRL5QIAkA0XdCEDKhcAgJzYW4bUqVwAADIjdCFpKhcAgIwJXUiOygUAID8u6EK6VC4AAFmytwyJUrkAAGRP6EJCVC4AALmytwwpUrkAAGTM3jIkR+UCAJA3oQtpUbkAALCP0IX4qVwAALLngi4kROUCAIC9ZUiHygUAgFFCF5KgcgEAYByhC9FSuQAAsI8LuhA/lQsAAB3sLUPkVC4AAHQhdCFCKhcAAMaytwwxU7kAADCOvWWIlsoFAICJCF2Ik8oFAICpCF2Ih8oFAIAuXNCFCKlcAADozt4yxEblAgDApIQuREXlAgBAz4QuBE/lAgDAVFzQhXioXAAA6IG9ZYiEygUAgD4JXQiYygUAgN7YW4YYqFwAAOiZvWUInsoFAIB+CF0Im8oFAIDpEroQHpULAAB9ckEXAqZyAQCgf/aWIVQqFwAApkXoQpBULgAADEzoQjBULgAATJcLuhAelQsAAAOwtwyBUbkAAFASoQsBULkAADAYe8sQEpULAAADs7cMwVC5AABQBqELYVC5AABQNqELzVG5AABQEhd0IQAqFwAAymNvGZqmcgEAoFRCFxqlcgEAoDJCF2qncgEAoGwu6EJzVC4AAFTA3jI0ROUCAEDFhC7USOUCAEA17C1DE1QuAABUxt4y1E7lAgBAlYQu1EvlAgBAXYQuVE/lAgBAxVzQhRqpXAAAqJ69ZaiLygUAgFoIXaiFygUAgNoJXaiMygUAgLq4oAvVU7kAAFAje8tQMZULAAANEbpQAZULAAD1srcMVVK5AABQO3vLUBmVCwAATRC6UA2VCwAATRO6UB6VCwAADXFBFyqgcgEAoDn2lqFsKhcAAMIgdKEMKhcAABrVubcsdGFgKhcAAJrmgi6UR+UCAEAAXNCFkqhcAAAIjNCFAahcAAAIg71lKIPKBQCAYNhbhoGpXAAACInQhcGoXAAACJXQhf6pXAAACIwLujAAlQsAAOGxtwzTpXIBACBsQhf6oXIBACBInXvLQhd6pnIBACBULuhC/1QuAAAEzAVd6JPKBQCASAhd6IHKBQCAsNlbhn6oXAAACJ69ZeiZygUAgBgIXeiNygUAgNgIXehO5QIAQCRc0IUeqFwAAIiHvWWYisoFAIA4CV2YiMoFAICodO4tC10YR+UCAEBsXNCF7lQuAABEyAVd6ELlAgBA5IQudFC5AAAQJ3vLMBGVCwAA0bK3DOOoXAAAiJnQhbFULgAApELogsoFAIDouaALHVQuAADEz94y7KNyAQAgLUKXvKlcAABIgr1lGKVyAQAgFfaWQeUCAEBSKg7d97///Xv27Nm+fXv7awiPygUAgESVHbojIyM33XTTjBkz2l9DkFQuAACkpZoLurNnz77rrruOP/749tcQKpULAADJKXtvef78+ffdd98ZZ5zR/hoCpnIBACBF5YXuihUr1q9ff8opp7S/hrCpXAAASN10Q/eEE05Yu3btTTfdNHfu3NaX11133X//+9/iWxAslQsAAIka+ILuqlWrTj311NbDSy+9dM4551xyySXFewiZygUAgHQNvLf82muvfetb3zruuONuvfXW9isIm8oFAIA89B+6v/nNbxYuXHjFFVfs2LGj/QqCp3IBACBpA+wtP/TQQ9u2bWt/AZFQuQAAkLqy/2EhCJnKBQCADAhdsqFyAQAgA1de2X44+OD2AyRK5QIAQOokLjlRuQAAkLT9iQt5ULkAAJAHB7nkQeUCAEC67CqTH5ULAACJsqtMllQuAACkzkEuOVG5AACQIrvK5ErlAgBAciQuGVO5AACQFtdxyZvKBQCARDnIJUsqFwAAElLxrvK8efMOPvjgww8/vP01hEflAgBAKlzHBZULAACJcB0XRqlcAABIi4Nc8qZyAQAgfnaVYR+VCwAAkbOrDB1ULgAApMJBLqhcAACIm11lGEvlAgBAtCQujKNyAQAgTq7jwkRULgAARM5BLnRQuQAAECG7ytCFygUAgNjYVYbuVC4AAESlM3Ed5MI4KhcAAOIkcWEiKhcAAOLhOi5MReUCAEAkXMeFHqhcAACIjYNc6E7lAgBADOwqQ29ULgAABE/iQs9ULgAAhM11XOiHygUAgEg4yIUeqFwAAAiYXWXok8oFAIBQ2VWG/qlcAAAIUmfiOsiFnqlcAAAIm8SFfqhcAAAIj+u4MF0qFwAAAuM6LgxA5QIAQKgc5EL/VC4AAITErjIMRuUCAEAwJC4MTOUCAEAYXMeFMqhcAAAIjINcGIDKBQCAANhVhpKoXAAAaJpdZSiPygUAgEZ1Jq6DXBiYygUAgDBIXCiDygUAgOa4jgtlU7kAANAQ13GhAioXAACa5iAXyqNyAQCgCXaVoRoqFwAAaidxoTIqFwAA6uU6LlRJ5QIAQEMc5EIFVC4AANTIrjJUTOUCAEBd7CpD9VQuAADUzkEuVEblAgBALewqQy1ULgAAVE/iQl1ULgAAVMx1XKiRygUAgLo4yIXqqVwAAKiSXWWol8oFAIDKSFyoncoFAIBquI4LTVC5AABQMQe5UCOVCwAAFbCrDA1RuQAAUDa7ytAclQsAAJVxkAu1U7kAAFAqu8rQKJULAADlkbjQNJULAAAlcR0XAqByAQCgbA5yoTkqFwAAymBXGcKgcgEAYGASF4KhcgEAYDCu40JIVC4AAJTEQS4EQOUCAMAA7CpDYFQuAABMl11lCI/KBQCAgTnIhWCoXAAAmBa7yhAklQsAAP2TuBAqlQsAAH1yHRcCpnIBAGC6HORCeFQuAAD0w64yhE3lAgBAzyQuBE/lAgBAb1zHhRioXAAA6JODXAiYygUAgB7YVYZIqFwAAJiKXWWIh8oFAICeOciF4KlcAACYlF1liIrKBQCA7iQuxEblAgBAF67jQoRULgAATMVBLsRD5QIAwETsKkOcVC4AAIwjcSFaKhcAAMZyHRdipnIBAKALB7kQIZULAAAd7CpD5FQuAADsY1cZ4qdyAQBgHAe5EC2VCwAAo+wqQxJULgAASFxIh8oFACB7ruNCQlQuAADs4yAX4qdyAQDIm11lSIvKBQAgYxIXkqNyAQDIleu4kCKVCwBA9hzkQkJULgAAWbKrDIlSuQAA5MeuMqRL5QIAkDEHuZAclQsAQGbsKkPSVC4AADmRuJA6lQsAQDZcx4UMqFwAAPLjIBfSpXIBAMiDXWXIg8oFACADEheyoXIBAEid67iQE5ULAEA2HORCBlQuAABJs6sMmVG5AACky64y5EflAgCQAQe5kA2VCwBAouwqQ5ZULgAAKZK4kCuVCwBAclzHhYypXAAA0uUgF/KjcgEASItdZcibygUAICESF7KncgEASIXruIDKBQAgQQ5yIWMqFwCAJNhVBkapXAAA4mdXGdhH5QIAkBAHuZA9lQsAQOTsKgMdVC4AADGTuMBYKhcA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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.092px 8px; transform-origin: 131.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBeware to avoid self intersecting triangles.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_pentagon()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct1 = [1 2 3;\r\n              1 3 4;\r\n              1 4 5];\r\n\r\nT_correct2 = [2 3 4;\r\n              2 4 5;\r\n              2 5 1];\r\n\r\nT_correct3 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct4 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct5 = [5 1 2;\r\n              5 2 3;\r\n              5 3 4];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct2,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct3,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct4,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct5,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_pentagon.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":149128,"edited_by":149128,"edited_at":"2025-08-13T05:29:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2025-08-13T05:29:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T12:59:46.000Z","updated_at":"2026-02-10T17:07:57.000Z","published_at":"2025-07-23T15:54:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[V = [1           0            0;\\n     cos(2*pi/5) sin(2*pi/5)  0;\\n     cos(4*pi/5) sin(4*pi/5)  0;\\n     cos(4*pi/5) sin(-4*pi/5) 0;\\n     cos(2*pi/5) sin(-2*pi/5) 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"445\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeware to avoid self intersecting triangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh 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many ways?","description":"Create a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?","description_html":"\u003cp\u003eCreate a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?\u003c/p\u003e","function_template":"function y = how_many(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 2;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 6;\r\ny_correct = 14;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 8;\r\ny_correct = 132;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 9;\r\ny_correct = 429;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 12;\r\ny_correct = 16796;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 15;\r\ny_correct = 742900;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct =  477638700;\r\nassert(isequal( how_many(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-30T20:37:23.000Z","updated_at":"2026-03-14T18:50:24.000Z","published_at":"2020-01-30T20:38:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56413,"title":"how to determine is a point is inside, on or outside a polygon?","description":"design function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(232, 230, 227); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(232, 230, 227); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 84px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 42px; transform-origin: 407px 42px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003edesign function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function dist = pointPolygonTest(contour,point,meatureDist)\r\n% Brief: how to determine is a point is inside, on or outside a polygon?\r\n% Details:\r\n%    The function determines whether the point is inside a contour, outside, or\r\n% lies on an edge (or coincides with a vertex). It returns positive (inside),\r\n% negative (outside), or zero (on an edge) value, correspondingly. When\r\n% measureDist=false , the return value is +1, -1, and 0, respectively.\r\n% Otherwise, the return value is a signed distance between the point and\r\n% the nearest contour edge.\r\n% \r\n% Syntax:  \r\n%     dist = pointPolygonTest(contour,point,meatureDist)\r\n% \r\n% Inputs:\r\n%    contour - [n,2] size,[double] type,Polygonal order vertices.\r\n%    points - [1,2] size,[double] type,Coordinate points of the query.\r\n%    meatureDist - [1,1] size,[logical] type,Whether meature distances.\r\n%\r\n% Outputs:\r\n%    dist - [m,1] size,[double] type,Description\r\n% \r\n% Example: \r\n%    None\r\n% \r\n% See also: None\r\n\r\narguments\r\n    contour (:,2) {mustBeNumeric}\r\n    point (1,2) {mustBeNumeric}\r\n   meatureDist (1,1) logical = false\r\nend\r\n\r\nassert(size(contour,1)\u003e=3,\"contour at least 3 vertices\");\r\n\r\nend\r\n\r\n","test_suite":"%% test\r\nL = linspace(0,2*pi,6);\r\nxv = cos(L)';\r\nyv = sin(L)';\r\nrng default\r\nxq = randn(250,1);\r\nyq = randn(250,1);\r\npoints = [xq,yq];\r\ndists = inf(size(points,1),1);\r\nfor i = 1:size(points,1)\r\n    dists(i) = pointPolygonTest([xv,yv],points(i,:));% use pointPolygonTest function determine points whether inside polygon \r\n    assert(dists(i)==1||dists(i)==-1||dists(i)==0)\r\nend\r\nassert(sum(dists==1)==80)\r\nassert(sum(dists==0)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":199546,"edited_by":199546,"edited_at":"2022-10-23T11:55:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2022-10-23T11:55:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-23T10:27:43.000Z","updated_at":"2025-10-18T10:21:59.000Z","published_at":"2022-10-23T10:27:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edesign function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42821,"title":"Polygon division","description":"Given the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\r\n\r\n1. The division is done by drawing straight lines between existing vertices.\r\n\r\n2. The triangles are made of existing vertices.\r\n\r\n3. Different orientations of a similar solution are counted as different solutions.\r\n\r\nAssume that n is a positive integer greater than 2.\r\n\r\nExample 1:\r\n\r\nn = 4 (square)\r\n\r\nw = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\r\n\r\nExample 2:\r\n\r\nn = 5 (pentagon)\r\n\r\nw = 5","description_html":"\u003cp\u003eGiven the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\u003c/p\u003e\u003cp\u003e1. The division is done by drawing straight lines between existing vertices.\u003c/p\u003e\u003cp\u003e2. The triangles are made of existing vertices.\u003c/p\u003e\u003cp\u003e3. Different orientations of a similar solution are counted as different solutions.\u003c/p\u003e\u003cp\u003eAssume that n is a positive integer greater than 2.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 4 (square)\u003c/p\u003e\u003cp\u003ew = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 5 (pentagon)\u003c/p\u003e\u003cp\u003ew = 5\u003c/p\u003e","function_template":"function w = polydiv(n)\r\n  w = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('polydiv.m');\r\nassert(isempty(strfind(filetext,'str')))\r\n\r\n%%\r\nn = 3;\r\nw_correct = 1;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 4;\r\nw_correct = 2;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 5;\r\nw_correct = 5;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 8;\r\nw_correct = 132;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 11;\r\nw_correct = 4862;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 15;\r\nw_correct = 742900;\r\nassert(isequal(polydiv(n),w_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2016-04-30T20:32:42.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-24T15:28:47.000Z","updated_at":"2026-01-19T17:32:36.000Z","published_at":"2016-04-24T15:28:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. The division is done by drawing straight lines between existing vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. The triangles are made of existing vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3. Different orientations of a similar solution are counted as different solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that n is a positive integer greater than 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 4 (square)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5 (pentagon)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60999,"title":"Total Area Covered by Overlapping Polygons","description":"Given a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\r\np1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\r\np2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\r\n\r\nThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 617.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.997px 308.778px; transform-origin: 407.997px 308.785px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 425.554px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 212.77px; text-align: left; transform-origin: 385px 212.777px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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rdVq1XVdKWWz2dLT0+vr60cEaefOnbm5uS6X68c//vFpp512rA/le7gvLy8vPz8/mKtH0dXVFeIrjvDoo49WVFSYu0GC3/1u+aTwCSYO+NWvfnXRRReZOMDlcpl4dQkDDng8fX197e3tJm4w/QdCb2+vuQPGJDFIHo8nISHBdxgREdHS0jL8BMMwvv7668cee8zlcnk8nhtuuGHFihWjfiin0xncrWMZ0dEQ++KLLx5+9pXEi9NM3LBv376oqCgTB9x11UW/+p+iaZGRZg3Y9t7rPT095n4SlFKn+IAzrD0Wi8Xc70dl9g8Ec3vsD4mvsjMMQ9N+GKZpmtfrHX5CT0/PwoULn332WYfDsXXr1rq6updeeinkMwEAgSQxSBaLxTAM36HX6w0P/487uenTp69bt2769OlKqWnTpmVmZu7YsSPUKwEAASUxSNHR0U1NTb5Dt9udlJQ0/ISOjo7Nmzf7Dvv7+8PCwkK3DwAQBBKDlJycrJSy2+1KqdbWVofDkZqaqpRqbGzs7u5WSh0+fLikpKStrU0p1dPT895771177bWmTgYAnCiJL2rQNK2srKyoqEjX9ebm5tLS0sjISKVUeXl5VlZWTk5OfHz8Qw89dPPNN8+ePfvzzz+/++67+UtIADDeSQySUiolJaWhoWHEO4e/gnnx4sX8JSQAOJlIfMgOAHAKIkgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEuUHq7Ox89913nU7n8U9rbGzct29faCYBAIJHaJCqq6sXLVpUU1NTWFi4du3aY53W1taWl5fX2NgYym0AgGAIN3vAKAzDKCkpqaqq0nXd5XJlZGRkZ2fHxcWNOO3IkSO///3vIyMjzdgIAAgwiUGqra21Wq26riulbDZbenp6fX390UFas2bN5Zdf3tzcfJwPFR8fP/RGXl5efn5+cPYeU1dXV4ivOEJfX9+BAx5zH9J0uVwmXl0pNWVqdOnTz5g44OABd/iEwRccx/tCDbaBgYHwcDO/2U0fsHvf/tlJ89rb203cYPoPhN7eXnMHjElikDweT0JCgu8wIiKipaVlxDnbtm378MMPX3nllaVLlx7nQ435FFSwHd3RULJYLGecYY2KijJxg1LK3AG/ur/UOHzQxAG11X+NthjLli0zccPevXvPPPPMU3mAUiouLs7c70dl9g8Ec3vsD4lBMgxD0354ckvTNK/XO/yE3t7e4uLiZ54x84+9GC9s06abW8Qvdjh+evrAggULTNzQ3t5u+o9C02Mg/8cxJAbJYrEYhuE79Hq9P/rRj4af8MQTTyQmJnZ0dHR0dLhcrubm5tjYWN+jcwCA8UhikKKjo5uamnyHbrf76quvHn5CVFTUzp07KysrlVK7d++22+1TpkwhSAAwrkkMUnJyslLKbrfPnz+/tbXV4XA89thjSqnGxsbo6OiYmJjly5f7Tl66dOlNN920cOFC0+YCAAJBYpA0TSsrKysqKtJ1vbm5ubS0dOi13eXl5VlZWTk5OWYPBAAEnsQgKaVSUlIaGhpGvLOiouLoM9evXx+SRQCA4BL6mxoAAKcaggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQIN3vAMXV2djqdztjY2Pj4+FFPcDqdnZ2duq7HxcWFdhoAIPCE3iFVV1cvWrSopqamsLBw7dq1R5/w5JNP3n333e+9996vf/3r9evXh34hACCwJN4hGYZRUlJSVVWl67rL5crIyMjOzh5+G9Ta2rpx48a6ujqr1bpv37758+ffdNNNNpvNvMkAgBMl8Q6ptrbWarXquq6Ustls6enp9fX1w08499xzX331VavVqpQ67bTTDMM4cuSIOVsBAAEi8Q7J4/EkJCT4DiMiIlpaWoafoGmaruuGYWzevLmysnLZsmXTpk0b9UP5nn/Ky8vLz88P3uZRdXV1hfiKI/T19R044Nm3b5+JG1wul4lXlzDg4MGDB/oPt7e3m7jB9C9F0wdI2GD6gN7eXnMHjElikAzD0LQfbt00TfN6vUef5nK5+vr6oqOjGxoaCgoKhm6YRnA6nUEc6gdzX3BhsVjOOMMaFRVl4gal1Ck+YPLkyWecbjH9pTcMkLDB3AHm/qnIHxIfsrNYLIZh+A69Xm94+CjhjIqKKigo2LBhw8SJE5977rkQDgQABJ7EIEVHRzc1NfkO3W53UlLS8BN27dq1adMm3+GZZ565d+/e0O0DAASBxCAlJycrpex2u1KqtbXV4XCkpqYqpRobG7u7u5VShmE8/vjju3btUkr961//qq+vz8zMNHUyAOBESXwOSdO0srKyoqIiXdebm5tLS0sjIyOVUuXl5VlZWTk5Oeedd97DDz98ww03JCUl7dixo7CwMCMjw+zVAIATIjFISqmUlJSGhoYR76yoqPC9fcstt9xyyy2hHQUACCKJD9kBAE5BBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIgQbvaAY+rs7HQ6nbGxsfHx8aOe0NbW1t7ebrPZLrroohBvAwAEnNAgVVdXr1q1Ki0tbceOHdnZ2cuXLx9xwooVK7Zs2ZKUlNTS0jJ58uSKigqLxWLKVABAQEgMkmEYJSUlVVVVuq67XK6MjIzs7Oy4uDjfCV988cVf//rXuro6q9WqlLr22murq6tzcnJMWwwAOGESg1RbW2u1WnVdV0rZbLb09PT6+vrhQbJarevXrx+qkVLqnHPO2bNnjylT5ftXd+e+PZ0mDnC5XOrI4VN5AAA/SQySx+NJSEjwHUZERLS0tAw/ISYmJiYmZujtjo6OrVu3FhYWjvqhfM8/5eXl5efnB2fvMXV1dYX4iiPMmjXr9Q2rX99g5oaBgYHwcDO/zEwfoJRa9OST7e3tJg4w/UvR9AESNpg+oLe319wBY5IYJMMwNO2Hl/9pmub1ekc9s6en57bbbrvzzjtnzZo16glOpzMoE/02/MYu9IqLizdu3GjiAKVUe3u7uZ8E0wcI2cAACRtM/14w8er+kPiyb4vFYhiG79Dr9Y76J9zPP//8+uuvLygoONbtEQBgHJEYpOjo6KamJt+h2+1OSkoacY7D4ViyZMkjjzxy++23h3YdACAoJAYpOTlZKWW325VSra2tDocjNTVVKdXY2Njd3a2U6uzsvOuuu5544onLLrvsyJEjR44cGX5HBQAYjyQ+h6RpWllZWVFRka7rzc3NpaWlkZGRSqny8vKsrKycnJzKysqDBw/+9re/9f1Pbr311uLiYvMmAwBOlMQgKaVSUlIaGhpGvLOiomLojfvuu+++++4L+SgAQBBJfMgOAHAKIkgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEIEgAQBEIEgAABEIEgBABIIEABCBIAEARCBIAAARCBIAQASCBAAQgSABAEQgSAAAEQgSAEAEggQAEEFukDo7O999912n03n80+rq6kKzBwAQVEKDVF1dvWjRopqamsLCwrVr1x7rtKeffvrBBx8M5TAAQJCEmz1gFIZhlJSUVFVV6brucrkyMjKys7Pj4uKGn+PxeEpLS2tqaiZPnmzSTABAIEkMUm1trdVq1XVdKWWz2dLT0+vr60cEqby83GazrVy58o9//ONxPlR8fPzQG3l5efn5+UGbPLqurq4QX1HaAAkbTB8gYQMDJGwwfUBvb6+5A8YkMUgejychIcF3GBER0dLSMuKc4uJiTdPsdvvxP9SYT0EF24iOnoIDJGwwfYCEDQyQsMHcAe3t7SZe3R8Sn0MyDEPTfhimaZrX6x1xzvATAAAnAYk/1i0Wi2EYvkOv1xseLvFODgAQQBKDFB0d3dTU5Dt0u91JSUkm7gEAhIDEICUnJyulhp4fam1tdTgcqampSqnGxsbu7m6TxwEAgkPiQ2GappWVlRUVFem63tzcXFpaGhkZqZQqLy/PysrKyckxeyAAIPAkBkkplZKS0tDQMOKdFRUVI94zf/58flMDAJwcJD5kBwA4BREkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgEKYheeOGFU3yAhA2mD5CwgQESNjBgTBMGBwfN3vBf6uzsdDqdsbGx8fHxo54QHx/vdDpDvIoB0jaYPkDCBgZI2MCAMY3XO6Tq6upFixbV1NQUFhauXbvW7DkAgBMVbvaA/4ZhGCUlJVVVVbquu1yujIyM7OzsuLg4s3cBAP574zJItbW1VqtV13WllM1mS09Pr6+vPzpI8+bNO9ajeSHDAAkbTB8gYQMDJGwwd8C8efNMvLo/xmWQPB5PQkKC7zAiIqKlpeXo0+Q/gwcA8BmXzyEZhqFpPyzXNM3r9Zq4BwBw4sZlkCwWi2EYvkOv1xsePi5v9QAAPuMySNHR0U1NTb5Dt9udlJRk4h4AwIkbl0FKTk5WStntdqVUa2urw+FITU01exQA4ISM178Y++GHHxYVFem63tzcvGLFiiuvvNLsRQCAEzJegwQAOMmMy4fsAAAnH4IEABAh7JFHHjF7Q+B1dnZ+9NFHR44ciYyMFHXFurq6GTNmmLWhra3t448/9ng8MTExpgxwOp2ffvqppmlWqzUYA/zZMKSxsTEsLGzy5MkhHuByuZqbm/f8W0REhMViCeWAoQ3/+Mc/vvnmm5/+9KeBvbQ/G0Z8Bvbs2dPf3x/wr4cxPwnt7e3bt2/v6+uLiooK7KX93zD0/RgWFha8b4ejBfVH0Ik7CYNUXV19zz339Pf3b9iwwePx/OIXvxByxaeffnrt2rVLliwxZcOKFSvWrVt36NChV155pbq6+pprrgnsX94ac8CTTz65bt26w4cPP/PMM99///3FF18cwKv7uWFIW1tbbm7uz3/+85/97GchHlBZWXnfffe9+eab1dXV1dXVF1100dlnnx3KAXa7/Y477jh8+PCbb77597///Ze//OWECRMCOGDMDXV1dcuXL6/+t5dffvnIkSMLFiwI2QClVEVFxcMPP9zf3//8889/+eWXGRkZAby6nxtWr179+OOP9/f3//nPf/Z4PKH5pT5B/REUGIMnl4GBgblz57a2tg4ODu7fv3/OnDn//Oc/Tb+i2+2+//77586de8kll5iyYefOnRdccIHb7R46vOaaa15++eVQDmhpafEN+Oabb2bNmrV///4ADvBnw5D+/v7rrrtuwYIF77zzTugH3HvvvS+++GJgr+v/gIGBgdTU1A8//HDoMCsr68033wzxhuHq6urS09N9X5ahGWAYRmJiYktLy+Dg4IEDBxITE3fu3BnAAf5s+Oyzzy644II9e/YMDg4ePnz4sssu++yzzwK7YYRg/wgKlJPtOaRRf++q6VcsLy+32WwrV640a4PVal2/fr3vkYFzzjlnz549oRxw7rnnvvrqq0MDTjvtNMMwjhw5EsAB/mwYsmbNmssvv3zmzJmBvbqfA3bu3Hnuuee6XK6A/+v7M8But5911lm+P4y//vrrAf/7Ev5/Ax46dOiBBx5YsWJFYB+w8mfA4ODgxIkTlVKnn366pmn9/f0BHODPhra2tksvvXTokXOLxZKUlFRTUxPYDSME+0dQoJxsv3HHz9+7GuIrFhcXa5o29Dd5TdkQExPje96oo6Nj69athYWFoRygaZqu64ZhbN68ubKyctmyZdOmTQvgAH82KKW2bdv24YcfvvLKK0uXLg3s1f0ZYBjG119//dhjj7lcLo/Hc8MNN6xYsSKUA9xud2xsbHFx8WuvvRYWFrZs2bI77rgjgAP82eCzYcOGhISESy+9NMQDNE0rKSm588478LEVYAAABJ1JREFUFy5c6HA4cnNz58yZE+INFotl9+7dvsPe3t7hv5wzGIL9IyhQTrY7pND/3lV/rhjsrzb//617enpuu+22O++8c9asWaEf4HK5+vr6oqOjGxoaPB5PAAf4s6G3t7e4uHjNmjWBva7/A3p6ehYuXPjss886HI6tW7fW1dW99NJLoRzQ1tZWU1Nz/vnnNzY2vvTSS88880zAHz/w8yuhr6+voqLid7/7XWCv7ueA7du3T5o0KSoqymq1fvXVV4cOHQrxhrS0tJ6entWrV2/btu25555ramoK9o+pYP8ICpTxsdJ/of+9qxJ+06ufGz7//PPrr7++oKAgsLdH/g+IiooqKCjYsGHDxIkTn3vuuRBveOKJJxITEzs6Oux2+9BrvQL7n3Mec8D06dPXrVs3ffp0pdS0adMyMzN37NgRygFnn332jBkzcnNzlVLx8fGZmZlvvPFGAAf4s2HIW2+9FRsbO3v27MBe3Z8BW7Zs+eSTTyorKxcvXrx+/Xql1MaNG0O8wWq1btq0qaOjY926dd9+++11110X8BdbjlMnW5BC/3tXJfymV382OByOJUuWPPLII7fffnvoB+zatWvTpk2+wzPPPHPv3r0h3hAVFXXw4MHKysrKysrdu3fb7XaHwxHKAR0dHZs3b/Yd9vf3h4WFhXLA1KlThx9qmhbwPzj7+e1gt9szMzMDe2k/B7jd7pkzZ/o+8zNmzOjs7Azxhu++++7gwYNPPfXUpk2b7rrrrvb29rlz5wZ2w3hl9qsqAswwjEsuueT9998fHBxsaWm58MIL9+3bZ8oVP/3006FX0fi8//77QXqJy5gbvv7667lz527ZsqX/3wYGBkI5oKWlJTEx8auvvhocHNy3b19aWtp7770XwAH+bBjuN7/5TcBfZTfmgC+//DIxMXHoxVd79+5NS0urq6sL5YD+/v6UlJQtW7YMDg7u378/PT39gw8+COAAfzYMSU1NHTon4MYcsHPnzgsvvHDoS/HAgQNZWVmbN28O8YY9e/YkJibu3bt3cHDw448/vvjiiw8cOBDYDaMK3o+gQDnZgjQ4OPjBBx+kpaUVFBQkJSUF/FWt/l/xtttuG/HS6qB+NRx/w6pVq2b+p//93/8N5YDBwcHKyso5c+YsWbJkzpw5zzzzTGCv7ucGn2AEyZ8BL7744ty5cwsKCubOnbtx48bQD/joo48WLFiQm5ublJT0pz/9KeAD/NlgGMbMmTO/+eabYFzdnwF/+ctfkpKShk5YuXKlKRuee+65uXPn5uXlLViwIOB/LDgW+UE6aX+56qFDhyZOnBjKp/JCf0WBG44/wOv1ulyun/zkJ4F9qOr/tCEExvwkHD58OKgLx/wMfP/99z/60Y/4f8FisZj4STAMo6+vb9KkScEbMO6ctEECAIwvJ9uLGgAA4xRBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIAJBAgCIQJAAACIQJACACAQJACACQQIAiECQAAAiECQAgAgECQAgAkECAIhAkAAAIhAkAIAIBAkAIML/B/bLq8TsfZ7uAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = lapgon(P)\r\n    A=[];\r\nend","test_suite":"%% Test Case 1\r\nP{1}=[0.2,0.2;0.5,0.2;0.5,0.5;0.2,0.5];\r\nP{2}=[0.4,0.4;0.8,0.4;0.8,0.8;0.4,0.8];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.240000;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 2\r\nP{1}=[0.1783,0.2985;0.3849,0.6214;0.8407,0.8054];\r\nP{2}=[0.1112,0.8761;0.8927,0.4062;0.6089,0.0228];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.244813;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 3\r\nP{1}=[0.5967,0.2763;0.3286,0.2200;0.7586,0.4690];\r\nP{2}=[0.4809,0.5456;0.5589,0.2875;0.5021,0.3001;0.2000,0.7725];\r\nP{3}=[0.4260,0.0843;0.0140,0.4489;0.5535,0.8630;0.4133,0.3718;0.8033,0.0733];\r\nP{4}=[0.0169,0.7757;0.1636,0.9072;0.7480,0.9785;0.2718,0.4179;0.8687,0.2735;0.0599,0.1064];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.459378;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 4\r\ntheta=0:0.01:2*pi;\r\nP{1}(:,1)=0.35*cos(theta)+0.6;\r\nP{1}(:,2)=0.22*sin(theta)+0.5;\r\nP{2}=[0.1083,0.3508;0.7413,0.9426;0.2748,0.0933];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.307282;\r\n\r\nassert(isequal(A,A_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4910069,"edited_by":4910069,"edited_at":"2025-09-12T18:34:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2025-09-12T18:34:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-12T17:15:15.000Z","updated_at":"2026-03-19T16:19:38.000Z","published_at":"2025-09-12T18:28:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" 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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n  y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr 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PCkpKR+/fpNnTr1+PHjxoxksb5/8sknGRkZe/fuHTVq1M9//vPCwsInn3zyrbfeUi/xPp/vrbfemjhx4jfffDNq1Kjx48fX1dWtXr36ySef9Hq9sqfTkc/nW7Nmzc6dO2UPoq/9+/dPnDhxw4YNSUlJEyZM6Natm8J/uevWrZs0aZL2TP7FL37h9XpnzJgxd+7c6upq2aP5TUlJycKFC0+fPt1kvaam5re//e3MmTNramrGjx8/ePDgnJycCRMm7N2714ixfNZRXFw8bty4IUOG7NmzR1txu92jR48eOnTooUOH5M7md4cOHRo6dOjo0aPz8/O1lYqKijlz5iQmJr722mtyZ9PVZ5991rdv38TExJtuuumHH36QPY4uKioqHn300b59+27atKmurs7n850/f/65555LTEx87733ZE/nZwUFBSNHjmz8si0uLr7vvvsGDhy4e/duubP5y/fffz9u3LjExMTExMRt27Y1vsvlcg0cOPDBBx8sLS3VVv75z3/27dv30Ucfraio0HswK+3fv/7664MHD44dO3bQoEHaSkJCwvTp04uKij799FO5s/ndjh07Tp069eCDDyYmJmorYWFhv/zlL2NjY3fu3FlWViZ3PJ2cOnXq1Vdf7d+//09/+lPZs+joyy+/zMnJyczMvOOOOwICAoQQwcHBEydOjIyM3Ldvn2IHLoqKioqLi2+88cb6l21UVNTIkSPLysoM2sPqSTv2Mm7cuKNHjw4YMKDJvT6fb8uWLefOnXvkkUciIyO1xVtvvfX222/Py8s7evSo3uNZqe+7du2qrq5OTU3VXhKafv36xcTE7N69+9y5cxJn87vCwsLY2Nj+/fs3XgwPD+/SpYuskfRWU1OzfPnyU6dOPffcc/UvBiXt3bs3KCho7NixjZ/JAwcO3Ldv36JFi4KCgiTO5ndBQUEOh6O4uLiqqqp+UdugxMTEyJvLPw4ePDh37tygoKDVq1ffcccdTe4tLS3dt29fjx49+vTpU7/ocDiGDh3q9Xq//vprvcezUt8LCwsjIyO1n2tcr3v37mFhYadPn2787FHACy+8sHPnzpSUlMaLX375ZUFBQUJCQnh4uKzB9LNt27aNGzf+6le/ungfpBKfz5efnx8TE3P55Ze/88472ttuCr+/2qdPn9tvv33Hjh2rVq0qKyurra3dunXru+++e8011wwdOlT2dJ0VFBT00EMPbdu2bdiwYRffe+7cueLi4iuuuKJbt26N1y+//HIhxIkTJ/Qezw+/v8kY5eXlzZ5N0bVr1169ep04cUKx/fvFPB7P66+/Hh4efs899zTe96nB4/EsW7Zs+PDhDzzwgGIHKJooLy8vLCysrq5+6aWXXC5XSkpKWlpabm7u6tWrDxw4sHLlSsW+dwkODp47d25MTMzq1atXrlypLd52221z586Nj4+XO1vnDRgwoJXtSFFRUbOHUuPi4iIiIgoLC/UcTQgL9d3n89XU1DR7V2Cglb4L6ZhTp049/fTT+fn5s2fPVmDX00R1dfXKlStLS0ufeeaZsLAwVd9daOzkyZO1tbUffPBBcnKyLXeRrQAABHFJREFUEKKysvKVV15Zt27dn/70pxkzZsiezp9qa2vXr1//17/+NTQ0dMSIEV26dMnNzd22bVtkZOS8efMiIiJkD6ij2traZqsVGBhozBbNMmUMCAhwOJr/16iurs7gYQx2/PjxyZMn79q1a9q0aQ8//LB6m/etW7du3Lhx+vTp11xzjexZjDNt2jQt7kKIsLCwxx57rFevXjk5OWfPnpU7mH99/PHHv//975OTk3NyclasWLFkyZLt27dPmDAhOzt79erVPuXObG5Me+/h4nXtpCkDBrBM38PDw3v06HHxekVFxYkTJ6Kjo1V94/Hzzz/PzMzMz8+fN29eVlZWcHCw7In87Pjx4wsXLrz11lsnTJggexYjaDuV4ODgpKSkxuvR0dFXXXVVcXGxSkcaa2pqNm/eHBQUNH369KioKG0xLCzsqaeeuuaaa/7973+XlJTInVBXsbGxzX6DcurUqbKysp49e+o9gGWOzwghfvKTn3i93h9++GHgwIH1i2fPnq2srIyJiQkNDZU4mx58Pl92dvaLL77YpUuXP/7xj7fccot6O3chxLFjxwoKCgoKCjZv3tzkrrS0tCuuuGLDhg3N/tNuUeHh4QkJCTU1NRdf3aPed6JVVVXFxcXBwcFNXp5hYWHR0dEej6elg65q0N4d9Hg8FRUVjUP/ww8/CCF69eql9wBW6ntycnJwcHBubm7j0h04cKCoqGjIkCHq7d+3bt364osv9ujRY9WqVddee63scfTSs2fPzMzMxivV1dWfffZZZWXl6NGjL7/8cvX+5U5NTV23bl1OTs7IkSPrn8kej+fYsWN9+vTp2rWr3PH8KDQ0NDo6Wqt84/XKysri4mKHw6HklqVeRERE//799+zZ8+2339bvUWpqar744ovIyMjrrrtO9wn0voDKj06ePJmenj5kyJD6y94Uvn51z549Q4YMaXz9qn14vd6JEycqfP2q2+2+5ZZbhgwZsmPHDm1Fuzg5KSlJvetXN23alJSU9MADDxQXF2sr58+ff+2115KSkubPn68diVbDG2+8cfH1q9r12I2/fCOvX7XS/j0uLm7atGkzZ86cNGnSTTfd1KVLl5ycnPLy8tmzZze+fEABNTU1f/nLX7ST+idPntzk3uTk5FdffVXJU+BtIiEh4fnnn585c+bDDz+ckpISHx+fm5t78uTJUaNG3X333bKn87MxY8ZMnDhx7dq1N91007BhwyIjI10uV0FBwaBBg6ZOnar2/l0IkZaWNn78+A8++CA9PX348OEFBQW7du267LLLHn/88bCwML0/u5X6LoRIT0+PjY1dtGjR9u3b6+rqevfuPXPmzDFjxij2LCkuLtYu3S4vLy8vL29yr9Pp9Cl91oEd3HzzzRs2bFi8eLHL5XK5XPHx8fPmzZswYYIBr3mDBQcHz58//4Ybbli5cuWnn35aW1sbHx//3HPPTZw4Ue2TIzXal9+vX781a9Zs3LgxJCRkxIgRL7zwQv3PHdFVAKUAACVZ5vxIAEC7/H9xqHu+j/zRZwAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61091,"title":"Slicing a 4-pointed star polygon","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \r\nGiven (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where\r\nin the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;\r\nin the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;\r\nand so on, until last slice of the 4-pointed star polygon;\r\nin the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.\r\nHint: The slices of the 4-pointed star polygon are not congruent among each other.\r\ninput: (A, h)\r\noutput: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 840.862px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 420.425px; transform-origin: 408px 420.431px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e does not exceed the circle's area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e otherwise;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=9)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the circle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_star(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [3 1; 6.75 1; 10.5 1; 13.5 1; 16.5 1; 20.25 0; 24 0; 27 0; 6.25 5];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [3.75 1; 9 1; 14.25 1; 18 1; 21.75 1; 27 1; 32.25 1; 36 1; 12.25 8];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('slicing_star.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [7.75 1; 17 1; 26.25 1; 34 1; 41.75 1; 51 0; 60.25 0; 68 0; 13.69 5];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [9.5 1; 22.25 1; 35 1; 44.5 1; 54 1; 66.75 1; 79.5 1; 89 0; 26.01 7];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-08T13:42:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-03T13:58:16.000Z","updated_at":"2025-12-19T15:03:36.000Z","published_at":"2025-12-08T13:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not exceed the circle's area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=9)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the circle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/r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you in or are you out?","description":"Given vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \"true\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\r\n\r\nExample:\r\n\r\n % The specified point is the center of the unit square:\r\n xv = [0 1 1 0];\r\n yv = [0 0 1 1];\r\n X = 0.5;\r\n Y = 0.5;\r\n\r\n inside(xv,yv,X,Y) -----\u003e true\r\n","description_html":"\u003cp\u003eGiven vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \"true\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e % The specified point is the center of the unit square:\r\n xv = [0 1 1 0];\r\n yv = [0 0 1 1];\r\n X = 0.5;\r\n Y = 0.5;\u003c/pre\u003e\u003cpre\u003e inside(xv,yv,X,Y) -----\u003e true\u003c/pre\u003e","function_template":"function tf = inside(xv,yv,X,Y)\r\n  tf = maybe;\r\nend","test_suite":"%%\r\nxv = [0 1 0];\r\nyv = [0 0 1];\r\nX = 0.8;\r\nY = 0.8;\r\ntf_correct = false;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n%%\r\nxv = [0 1 1 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 1 1 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 0.25 0.25 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = false;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 0.25 0.25 0] + 1000;\r\nyv = [0 0 1 1] + 1000;\r\nX = 1000.1;\r\nY = 1000.1;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":384,"test_suite_updated_at":"2012-01-31T14:13:38.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-31T14:13:38.000Z","updated_at":"2026-03-29T20:42:27.000Z","published_at":"2012-01-31T15:52:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \\\"true\\\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % The specified point is the center of the unit square:\\n xv = [0 1 1 0];\\n yv = [0 0 1 1];\\n X = 0.5;\\n Y = 0.5;\\n\\n inside(xv,yv,X,Y) -----\u003e true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":194,"title":"Clockwise or Counterclockwise","description":"Given a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\r\n\r\nThe inputs to this function are two vectors *x* and *y* (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\r\n\r\nThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\r\n\r\nExample:\r\n\r\n  x = [-1,-1,1,1];\r\n  y = [-1,1,1,-1];\r\n\r\ndefines a square, the vertices are listed clockwise\r\n\r\n  d_correct = true;\r\n\r\n","description_html":"\u003cp\u003eGiven a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\u003c/p\u003e\u003cp\u003eThe inputs to this function are two vectors \u003cb\u003ex\u003c/b\u003e and \u003cb\u003ey\u003c/b\u003e (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\u003c/p\u003e\u003cp\u003eThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = [-1,-1,1,1];\r\ny = [-1,1,1,-1];\r\n\u003c/pre\u003e\u003cp\u003edefines a square, the vertices are listed clockwise\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ed_correct = true;\r\n\u003c/pre\u003e","function_template":"function tf = isSortedClockwise(x,y)\r\n  tf = false;\r\nend","test_suite":"%%\r\nx = [-1,-1,1,1];\r\ny = [-1,1,1,-1];\r\nd_correct = true;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-1,-1,-2,-2];\r\ny = [-1,1,1,-1];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-1,-1,-2,-2];\r\ny = [-1,1,1,-1];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-6,-7,-2,1,1,-2];\r\ny = [4,-7,-13,-11,0,5];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-59,-59,-55,-51,-50,-46,-45,-45,-39,-40,-40,-41,-46,-50,-50];\r\ny = [-68,-33, -5,-13,-28,-30,-20,-10, -8,-23,-34,-45,-48,-51,-51];\r\nd_correct = true;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = flip([-59,-59,-55,-51,-50,-46,-45,-45,-39,-40,-40,-41,-46,-50,-50]);\r\ny = flip([-68,-33, -5,-13,-28,-30,-20,-10, -8,-23,-34,-45,-48,-51,-51]);\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [1,1,2,2];\r\ny = [2,1,1,2];\r\nassert(isequal(isSortedClockwise(x,y),false));\r\n\r\n%%\r\nx = flip([1,1,2,2]);\r\ny = flip([2,1,1,2]);\r\nassert(isequal(isSortedClockwise(x,y),true));\r\n\r\n%%\r\nx = [-2,-2,-4,-4];\r\ny = [1,3,1,-1];\r\nassert(isequal(isSortedClockwise(x,y),false));\r\n\r\n%%\r\nx = flip([-2,-2,-4,-4]);\r\ny = flip([1,3,1,-1]);\r\nassert(isequal(isSortedClockwise(x,y),true));\r\n\r\n%%\r\nr=rand(100,15);\r\na=2*pi*rand(100,1);\r\nd=2*(rand(100,1)\u003e.5)-1;\r\nx=r.*cos(a*ones(1,15)+d*2*pi*(0:14)/15)+randn(100,1);\r\ny=r.*sin(a*ones(1,15)+d*2*pi*(0:14)/15)+randn(100,1);\r\nassert(all(arrayfun(@(i)isequal(isSortedClockwise(x(i,:),y(i,:)),d(i)\u003c0),1:100)))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":216,"test_suite_updated_at":"2017-12-04T00:52:18.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-31T06:39:48.000Z","updated_at":"2026-03-31T15:28:48.000Z","published_at":"2012-02-02T02:42:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs to this function are two vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = [-1,-1,1,1];\\ny = [-1,1,1,-1];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003edefines a square, the vertices are listed clockwise\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[d_correct = true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44694,"title":"Monte Carlo integration:  area of a polygon","description":"The area of a polygon (or any plane shape) can be evaluated by \u003chttps://www.mathworks.com/matlabcentral/cody/problems/179 Monte Carlo integration\u003e.  The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape.  That is illustrated schematically below for a circle.  \r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\u003e\u003e\r\n\r\n^\r\n\r\n*Steps:*\r\n\r\n# Define a 2D region within which to sample points.  In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.  \r\n# By a 'random' process generate coordinates of a point within the bounding box.  In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed.  _Other schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon)._\r\n# Determine \u003chttps://www.mathworks.com/matlabcentral/cody/problems/198 whether the sampled point is inside or outside the polygon\u003e.  _Due to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null._  \r\n# Repeat steps 2–3 |N| times.  \r\n# Based upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.  \r\n\r\nInputs to your function will be |N|, the number of points to sample, and |polygonX| \u0026 |polygonY|, which together constitute \u003chttps://www.mathworks.com/matlabcentral/cody/problems/194 an ordered list of polygon vertices\u003e.  |N| will always be a positive integer.  |polygonX| \u0026 |polygonY| will always describe a single, continuous outline;  however, the polygon may be self-intersecting.  \r\n\r\nFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant.  A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\u003e\u003e\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\u003e\u003e\r\n\r\n^\r\n\r\nEXAMPLE\r\n\r\n % Input\r\n N = 1000\r\n polygonX = [1 0 -1  0]\r\n polygonY = [0 1  0 -1]\r\n % Output\r\n A = 2.036\r\n\r\nExplanation:  the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°.  The exact area is hence 2.  As the value of |N| is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon).  \r\nOf course, if the code were run again then a slightly different value of |A| would probably be returned, such as |A|=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.  ","description_html":"\u003cp\u003eThe area of a polygon (or any plane shape) can be evaluated by \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/179\"\u003eMonte Carlo integration\u003c/a\u003e.  The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape.  That is illustrated schematically below for a circle.\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003e\u003cb\u003eSteps:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eDefine a 2D region within which to sample points.  In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/li\u003e\u003cli\u003eBy a 'random' process generate coordinates of a point within the bounding box.  In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed.  \u003ci\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/i\u003e\u003c/li\u003e\u003cli\u003eDetermine \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/198\"\u003ewhether the sampled point is inside or outside the polygon\u003c/a\u003e.  \u003ci\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/i\u003e\u003c/li\u003e\u003cli\u003eRepeat steps 2–3 \u003ctt\u003eN\u003c/tt\u003e times.\u003c/li\u003e\u003cli\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eInputs to your function will be \u003ctt\u003eN\u003c/tt\u003e, the number of points to sample, and \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e, which together constitute \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/194\"\u003ean ordered list of polygon vertices\u003c/a\u003e.  \u003ctt\u003eN\u003c/tt\u003e will always be a positive integer.  \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e will always describe a single, continuous outline;  however, the polygon may be self-intersecting.\u003c/p\u003e\u003cp\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant.  A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\"\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e % Input\r\n N = 1000\r\n polygonX = [1 0 -1  0]\r\n polygonY = [0 1  0 -1]\r\n % Output\r\n A = 2.036\u003c/pre\u003e\u003cp\u003eExplanation:  the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°.  The exact area is hence 2.  As the value of \u003ctt\u003eN\u003c/tt\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon).  \r\nOf course, if the code were run again then a slightly different value of \u003ctt\u003eA\u003c/tt\u003e would probably be returned, such as \u003ctt\u003eA\u003c/tt\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/p\u003e","function_template":"function A = monteCarloArea(N, polygonX, polygonY)\r\n    % Fun starts here\r\nend\r\n\r\n\r\n% Note:  the Test Suite has been designed to account for variability in outputs. \r\n%        Nevertheless, it is possible that on rare occasions a valid submission \r\n%        might fail the Test Suite in one instance.  \r\n%        If your submission has narrowly failed only one of the test cases, \r\n%        then please try resubmitting it, in case it was just due to 'bad luck'.  ","test_suite":"%% No silly stuff\r\n% This Test Suite can be updated if inappropriate 'hacks' are discovered \r\n% in any submitted solutions, so your submission's status may therefore change over time.  \r\n\r\n% BEGIN EDIT (2019-06-29).  \r\n% Ensure only builtin functions will be called.  \r\n! rm -v fileread.m\r\n! rm -v assert.m\r\n% END OF EDIT (2019-06-29).  \r\n\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'}, 'FileName','monteCarloArea.m')\r\n\r\nRE = regexp(fileread('monteCarloArea.m'), '\\w+', 'match');\r\ntabooWords = {'ans', 'area', 'polyarea'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n    'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n    'Banned word.' char([10 13])];\r\nassert(~any( testResult ), msg)\r\n\r\n\r\n%% Unit square, in first quadrant\r\nNvec = 1 : 7 : 200;\r\npolygonX = [0 1 1 0];\r\npolygonY = [0 0 1 1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 1;\r\nassert( all(areaVec==area_correct) )\r\n\r\n%% 3×3 square, offset from origin, in all four quadrants\r\nNvec = 1 : 19 : 500;\r\npolygonX = [ 1 1 -2 -2];\r\npolygonY = [-1 2  2 -1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 9;\r\nassert( all(areaVec==area_correct) )\r\n\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (1)\r\nN = 1;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (2)\r\nN = 2;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0 2 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (3)\r\nN = 4;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0:4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (1)\r\nN = 100;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (2)\r\nN = 1000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (3)\r\nN = 10000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  large N\r\nN = 100000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 7 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.0016 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.016 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants:  moderate N (1)\r\nN = 100;\r\npolygonX = [ 1 -1  1 -1];\r\npolygonY = [-1  1  1 -1];\r\narea_exact = 2;\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants:  moderate N (2)\r\nN = 10000;\r\nfor j = 1 : 10,\r\n    rVec = 100 * rand(2);\r\n    polygonX = [ 1 -1  1 -1] * rVec(1,1) + rVec(1,2);\r\n    polygonY = [-1  1  1 -1] * rVec(2,1) + rVec(2,2);\r\n    area_exact = 2 * rVec(1,1) * rVec(2,1);\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 12-cornered polygon of unit 'circumradius' centred on origin:  moderate N\r\nN = 1000;\r\npoints = 12;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\npolygonX = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\npolygonY = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\narea_exact = polyarea(polygonX, polygonY);\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% P-cornered polygon of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\nfor j = 1 : 10,\r\n    points = randi([5 100]);\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 100]);\r\n    r = rand();\r\n    polygonX = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    polygonY = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    area_exact = polyarea(polygonX, polygonY);\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 5-pointed star of unit 'circumradius' centred on origin:  moderate N\r\nN = 1000;\r\npoints = 5;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\nx = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\ny = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\npolygonX = x([1:2:end, 2:2:end]);\r\npolygonY = y([1:2:end, 2:2:end]);\r\narea_exact = sqrt(650 - 290* sqrt(5))/4  * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n% http://mathworld.wolfram.com/Pentagram.html\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% 5-pointed star of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\npoints = 5;\r\nfor j = 1 : 10,\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 100]);\r\n    r = rand();\r\n    x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    polygonX = x([1:2:end, 2:2:end]);\r\n    polygonY = y([1:2:end, 2:2:end]);\r\n    area_exact = sqrt(650 - 290* sqrt(5))/4  * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n    % http://mathworld.wolfram.com/Pentagram.html\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% P-pointed star of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\nfor j = 1 : 20,\r\n    points = 3 * randi([3 10]) - 1;\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 30]);\r\n    r = rand();\r\n    x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    polygonX = x([1:3:end, 2:3:end, 3:3:end]);\r\n    polygonY = y([1:3:end, 2:3:end, 3:3:end]);\r\n    \r\n    area_polyarea = polyarea(polygonX, polygonY);                % Incorrect value\r\n    warning('off', 'MATLAB:polyshape:repairedBySimplify')\r\n    area_polyshapeArea1 = area( polyshape(polygonX, polygonY) ); % Incorrect value\r\n    area_polyshapeArea2 = area( polyshape(polygonX, polygonY, 'Simplify',false) );  % Incorrect value\r\n    \r\n    % REFERENCE:  http://web.sonoma.edu/users/w/wilsonst/papers/stars/a-p/default.html\r\n    % Here: a {points/3} star\r\n    k = 3;\r\n    sideLength = circumradius * sind(180/points) * secd(180*(k-1)/points);\r\n    apothem = circumradius * cosd(180*k/points);\r\n    area_exact = points * sideLength * apothem;                  % Correct value\r\n    fprintf('Area estimates from different methods:  \\r\\npolyarea = %4.1f;  polyshape.area = %4.1f or %4.1f;  geometrical analysis = %4.1f\\r\\n', ...\r\n        area_polyarea, area_polyshapeArea1, area_polyshapeArea2, area_exact);\r\n    \r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2019-06-29T13:06:05.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2018-07-02T02:19:05.000Z","updated_at":"2025-09-14T14:22:43.000Z","published_at":"2018-07-02T08:55:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe area of a polygon (or any plane shape) can be evaluated by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/179\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMonte Carlo integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSteps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/198\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ewhether the sampled point is inside or outside the polygon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2–3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs to your function will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of points to sample, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which together constitute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/194\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ean ordered list of polygon vertices\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always be a positive integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026amp; middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Input\\n N = 1000\\n polygonX = [1 0 -1  0]\\n polygonY = [0 1  0 -1]\\n % Output\\n A = 2.036]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). Of course, if the code were run again then a slightly different value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e would probably be returned, such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"},{"id":60924,"title":"Largest Small n-Polygons or Biggest Little Polygon","description":"Largest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has diameter one and that has the largest area among all diameter-one n-gons. (from Wikipedia, MathWorld)\r\nIn the case n = 6, the polygon is called Graham's Biggest Little Hexagon.\r\nFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\r\nImage\r\nThe results for cases where n is 3 to 8 are as follows.\r\n\r\n\r\n\r\nReference program\r\n* https://github.com/tomtkg/Largest-Small-Polygon","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1068px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 534px; transform-origin: 408px 534px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLargest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone and that has the largest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eamong all diameter-one\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-gons. (from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Biggest_little_polygon\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/BiggestLittlePolygon.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMathWorld\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the case n = 6, the polygon is called \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGraham's Biggest Little Hexagon\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 385px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 385px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImage\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results for cases where n is 3 to 8 are as follows.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 269px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 134.5px; text-align: left; transform-origin: 385px 134.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"271\" height=\"263\" style=\"vertical-align: baseline;width: 271px;height: 263px\" 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+jA7O1ur1TY3N/vb32w2d3R0lJWV7dix47XXXvvHf/zH8+fP85wXYDkKXGY4cnTSMFwNA94FqiudnZ2EkG3btvm2FBcXm81mo9G47P51dXXch/n5+WlpaXyEBAjE7ppX5jLDkcOkYSCEQHVlcHBQrVbHxcX5tmRmZhJCzp49G8pbX7ly5emnn44wH0BQtLdYgcsMRw4LFYMQ/NYVu93udrtTUlK4G9VqNSHEarUGfd/Tp0+XlJSUl5dHnBAgEHqLH3qLw6ZJikfPMfDL7z/xzGYzISQjI4O7MSYmhhAyOzsb4B0vXLjQ09Nz4sSJ1atX33bbbffeey9PUQGWYTBNobc4EolqVVVBssE09ZvtuGoN/OD/0kFBQQEhZGFh4YMPPti/f39WVlZRUVHgl+Tm5vp+7u/v9/08MTHBe7ywMRWGIA8hhBDz1PV55xyZWbDOiB8mAKbyLBtm3nmt61PnHbeL0PjA/pcjIqbyLApTUVHhb0+/dYUOuXu9Xu5Gj8dDCImPD/TLFxsbW1RUVFRUlJOT8+KLL7777rtB68r4+Li/pzQaTeDXRhNTYQjyEHJs/G/1W/6vZdvA8OUEsDTMr382f+z8lcSfbRBlmIrxL0dcTOXhhuEet7nnBiTA+EpqaqpKpbp48SJ3o8vlIjdG74Pau3fvLbfc4nQ6QwsMsDLoLeYRFioGHvmtKzExMaWlpTMzM9xTlrGxMXJz53Ggt46JKS4uTkzEgCrwzzrtHp10YGSFR+g5Br4E6jOuqalZWFgYHh72bTGZTHl5eZs2bQrx3c1mM8btQQiYCox36DkGvgSqK2VlZXq9vquriz602WwjIyOtra30odFo1Ol0hw8fpg+9Xu/LL7988uRJ38sPHTpUUVGh0+mESQ7KNTrpsLvmMQEJ7+hFRUwaBhEKMkZ38ODBxsbGlpaW7Oxsg8HQ3t7uqxPj4+NOp9M3z/HCwkJvb+8333zz6quvbt682eFwbN++/YknnhA2PigSTlYE4pvnGDUbIhGkrqxZs6ajo8Nms01PT9fV1dH7V6ja2tqsrCzfNbHY2NjBwcHR0VG3252RkbFhA2YABEEMWOx0kFnsIPKkSYpPVKsGLHbcagphC6mnMD09PT09fen2kpIS7sOYmBhc9QJB0WWGMW+xoHzzHGNqHAgP1osEKUFvcRQkqlXa29ZiAB/ChroCkkG7YDGyEgXa1AT0HEPYUFdAMjBcHzVYqBgigboC0oBlhqOMDuCj5xjCgLoC0jBw6Tus3BVNuE0Swoa6AhIwYLFrkuIxXB9l9DvH1TBYKdQVYB3tLcbJiigwaRiEAXUFWIdlhkWEnmMIA+oKMA3LDItOm5qAhYphRVBXgGnoLRYdeo5hpVBXgF20yRXD9aKjc7qg5xhChLoC7KIjK2KnAEIIqSpIxigLhAh1BRiFqcCYQueQxtUwCAXqCrDI7pofnXTgZIUp6DmGEKGuAIvQW8wg3IEPIUJdAeagt5hZ9LIkTlkgMNQVYI7BNIXeYjah5xhCgboCbMEyw4zzLVQsdhBgF+oKsAVTgbGvqiB59PI1u2te7CDAKNQVYAh6iyWBnlBiAB/8QV0BVlin3aOTDoysSII+a/3opAMD+LAs1BVgBaYCk5BEtQp34IM/qCvAhNFJh901j2WGJYRersSkYbAU6gowAScrkoPbJMEf1BUQH3qLJYr2HON2FlgEdQVERpcZxsmKRFUVJNP5EcQOAgxBXQGRYSowScNCxbAU6gqIic6Pi6nAJE2bmoB5joELdQXEhCtgMoBJw2AR1BUQDW1RRW+xDNABfPQcA4W6AqLBVGCygZ5j4Aqprng8HovFEuI7er1ei8Vy9erVCFKB/A1Y7JqkePQWywb9v4mrYUCC1hWv19vW1tbQ0NDX11ddXX3u3LnA+3d3d2/ZsuXuu+++8847d+/efeHCBf6ignzQ3mKcrMgMFioGKkhzZ1NTk9Vq7e7uJoRUVlbu2bOnq6srPz9/2Z1PnTrV0dHx8MMPb9iw4dSpU5988kl9fX1PT092djb/wUHK0FssS76rYfVJG8TOAmIKdL4yMjJiMBj27dtHH2ZnZ2u12ubmZn/79/b20v1379792muv1dfXu93uI0eO8BwZJA7LDMuYJine7prHKYvCBaornZ2dhJBt27b5thQXF5vNZqPRuHRnj8dTX1+/bt0635bHHnuMEPLtt9/yFhZkAb3FMoaeYyCB68rg4KBarY6Li/NtyczMJIScPXt26c6xsbFbtmzhblm3bt3q1avXrl3LU1SQA9qKiuF6GdOmJqDnWOH81hW73e52u1NSUrgb1Wo1IcRqtYby1levXr1+/XplZWVkCUFW6MiK2ClAWFiaReH81hWz2UwIycjIuGnvmBhCyOzsbChv3dfXV1RUtGPHjsgSgnxgmWGFoLNT42qYYgnVkDM7O/vee++9+eaboeycm5vr+7m/v9/388TEBP/JwsVUGCLBPBMz8wNfXGvQ/sRqdYoeJsqYyhOdMJmx3ve/uPZT799vXxfkIKPALyd0TOVZFKaiosLfnn7/l6elpRFCvF4vd6PH4yGExMcH//fmgQMHnnzySY1GE3RPQsj4+Li/p0J8h+hgKgyRWp6B81eqNv90Y7TawKT15URZdMJ4Exyjl6+VaoL3HCvwywkdU3m4YbjHbe65AQlwHSw1NVWlUl28eJG70eVykRuj9wG8/fbbhYWF5eXlKwkMckaXGUZvsaLQC57oOVYgv3UlJiamtLR0ZmaGe8oyNjZGbu48XurMmTN2u72uro7HlCB16C1WIPQcK1agPuOampqFhYXh4WHfFpPJlJeXt2nTJn8vOXPmzGefffb444/7tszNzX366ae8ZAWJwjLDikXnOR6w2MUOAlEVqK6UlZXp9fquri760GazjYyMtLa20odGo1Gn0x0+fNi3/+nTp5uamubm5p67obm5ubKy8tZbbxXuPwDYh6nAlKyqIHn08jUsVKwoQVo1Dh482NjY2NLSkp2dbTAY2tvbdTodfWp8fNzpdPrmOf7oo48aGxsJIe+88w73HXJycvzNJwZKgN5ihaOnqrgQqihB6sqaNWs6OjpsNtv09HRdXR29f4Wqra3NysryXRPbtWvXrl27BEwKEmSddo9OOp6tyAi+K8iXPmv9//efX2lvW4t/XihESOuvpKenFxUVcYsKVVJSwp3lBWAR/CsVCCGJalVVQTIG8JUD60WCULDMMPhgoWJFQV0BoWC4HnywULGioK6AINBbDIvQUxZcDVMC1BXgH11mGCMrsEhVQTJd1U3sICAs1BXgH5YZhmUlqlXa29biapjsoa4Az6zTbuu0G1OBwbK0qQn0N0TsICAg1BXgGa6AQQCYNEwJUFeAT+gthqCwULHsoa4An7DMMIQCPcfyhroCvMFUYBAiTVI8FiqWMdQV4MfMnHd00oGTFQiRPms9BvDlCnUF+HH6Syd6iyF0uANfxlBXgAfWaffMnBe9xbAimqR4u2t+Yga3ScoN6grwYODSd7/IvEXsFCAx9JTl9JdOsYMAz1BXIFK0YfT2dbgCBiumTU1YFxeDhYplBnUFIoXeYojELzJvwULFMoO6AhFBbzFEaF1cDF2oWOwgwBvUFQgfXWYYJysQIfQcywzqCoSPTgWG3mKIEHqOZQZ1BcI0Oumwu+YxFRjwgl5KxSmLPKCuQJgwbzHwCPMcywnqCoQDywwD7+hCxeg5lgHUFQjHwKXvMFwPvKsqSEbPsQygrsCKHTt/Bb3FIAQsVCwPqCuwMrQfFCMrIBAsVCwDqCuwMhiuB0FhAF8GUFdgBbDMMEQBHcDHQsXShboCK4DheogC3CYpdagrEKoBi50uHyt2EJA/esqCq2EShboCIbG75nGyAtFUVZCMAXyJCqmueDwei8Wyovd1OByzs7NhRQIW0cnwMRUYRA16jqUrSF3xer1tbW0NDQ19fX3V1dXnzp0L+o52u/3QoUPbt283m808hQSR0X82YplhiDJtaoLdNY9TFskJ8s/PpqYmq9Xa3d1NCKmsrNyzZ09XV1d+fr6//b/88suhoaGenh6nE2uLysfApe/qizeInQIUx9dz/JvtaWJngRUIdL4yMjJiMBj27dtHH2ZnZ2u12ubm5gAvyczM3Lt3744dO/jMCKKi7Z4YrgdRaFMT0HMsOYHqSmdnJyFk27Ztvi3FxcVms9loNAZ+U5UKV+HlA8sMg7iqCpIxyiItgerK4OCgWq2Oi4vzbcnMzCSEnD17VvBcwAYsMwyiozNno+dYQvzWFbvd7na7U1JSuBvVajUhxGq1Ch0LWGB3zWOZYWABFiqWFr91hXZzZWRk3LR3TAwhBA3ECoHeYmAE7sCXFiYOGbm5ub6f+/v7fT9PTEyIEWd5TIUhwueZmJn/ctKpT/6J1RrSOktMfT9MhSGM5WEqDAk5T8yc98vJa5/GOW9fJ+BRS6JfTnQsClNRUeFvT7//h9LS0gghXq+Xu9Hj8RBC4uN5vto+Pj7u7ymNRsPvZ0WCqTBE4DyG//yqYfvtKxpZYer7YSoMYSwPU2FIyHnWJbsNpqnSjcL2HEv0y4kObhjucZt7bkACXAdLTU1VqVQXL17kbnS5XOTG6D3I2OikA8sMA2uwULFU+K0rMTExpaWlMzMz3FOWsbExcnPnMcgSeouBTVioWBIC9RnX1NQsLCwMDw/7tphMpry8vE2bNgkfDESD3mJgFj2NxgA+4wLVlbKyMr1e39XVRR/abLaRkZHW1lb60Gg06nS6w4cPL30hPcW5fv0632lBcNZp9+ikAytCArPQc8y+IPNOHjx4cG5urqWlpbOzs7Gxsb29XafT0afGx8edTueieY6npqa6u7sHBwcJIW+99dapU6cEyg0CwTLDwDj0HLMvSMfemjVrOjo6bDbb9PR0XV0dvX+Fqq2tzcrKWnRNLDk5+f7777///vsFCQsCG5102F3zWGYYGKdJih+9fG100oHfVTaFtP5Kenp6UVERt6hQJSUl3FleQOpwsgKSgFMWxmG9SPjBgMWO3mKQCvQcswx1BQi5scwwTlZAQtBzzCzUFSDkRm8xpgIDCcFCxcxCXYEflhnGyQpIjjY1AT3HDEJdAQzXg1T5FioWOwjcBHVF6egKr+jXBImiA/hYqJgpqCtKN3DpO0wFBtKFnmMGoa4o2oDFrkmKR28xSBr9HcbVMHagrigX7S3GyQrIACYNYwrqinJhmWGQDfQcMwV1RaGs0267a16fnSh2EAB+aFMT7K55nLKwAHVFodBbDDKDnmN2oK4oEW3KxHA9yAydMwI9x6JDXVEiLDMMclVVkIxRFtGhrigOlhkGGaNzcuNqmLhQV5SFLjOMkxWQMfQciw51RVnoDSvoLQYZwx34okNdURD0FoNC0Mu8OGURC+qKghhMU+gtBiVAz7G4UFeUAssMg6JgoWIRoa4oBaYCA6XBQsViQV1RBPQWgwLRE3QM4Ecf6or80d5ijKyAAumz1o9OOjCAH2WoK/KHqcBAsRLVKtyBH32oKzI3Oumwu+axzDAoFr38i0nDogl1ReZwsgIKh9skow91Rc7QWwxAbvQc43aWqEFdkS26zDBOVgAIIVUFyXS+CbGDKALqimxhmWEAHyxUHE2oK/JE53PFVGAAPtrUBMxzHB2oK/KEK2AAi2DSsKgRpK54PB6LxSLEO0MoaEsleosBFsFCxdHBc13xer1tbW0NDQ19fX3V1dXnzp3j9/0hFJgKDMAf9BxHAc+Duk1NTVartbu7mxBSWVm5Z8+erq6u/Px8fj8FAhiw2DVJ8egtBlgW/evAmhGC4vN8ZWRkxGAw7Nu3jz7Mzs7WarXNzc08fgQERnuLcbICEAAWKhYan3Wls7OTELJt2zbfluLiYrPZbDQaefwUCAC9xQBB4Q58ofFZVwYHB9VqdVxcnG9LZmYmIeTs2bM8fgr4g2WGAUKkSYq3u+ZxyiIQ3uqK3W53u90pKSncjWq1mhBitVr5+hQIAL3FACFCz7GgeKsrZrOZEJKRkXHTu8fEEEJmZ2f5+hTwh7ZOYrgeIEToORYOExfic3NzfT/39/f7fp6YmBAjzvKYCkOW5Dl27rt789eKeGrI1PfDVBjCWB6mwhBR8+jWed8//02MY+26uBjRwyyLqTyLwlRUVPjbk7e6kpaWRgjxer3cjR6PhxASHx/kH9Hj4+P+ntJoNDyEI+SAQwAAIABJREFU4wlTYQgnj8E0pf9ft5SKfRGMqe+HqTCEsTxMhSGi5vnSM/Wlh1Tl/vi3gy8nAG4Y7nGbe25AeLwOlpqaqlKpLl68yN3ocrnIjdF7EAhdZhi9xQBhQM+xEHirKzExMaWlpTMzM9xTlrGxMXJz5zHwjt6wgt5igDCg51gIfPYZ19TULCwsDA8P+7aYTKa8vLxNmzbx+CnARZcZRm8xQNhotwtOWXjEZ10pKyvT6/VdXV30oc1mGxkZaW1t5fEjYBH0FgNECD3HvON53smDBw/Ozc21tLR0dnY2Nja2t7frdDp+PwJ8sMwwAC/oQsUDFrvYQWSC54vya9as6ejosNls09PTdXV19P4VEMjApe/qizeInQJADqoKko+dv5L0M2/wXSEYQY776enpRUVFKCqCOv2lU5uagJMVAF7QU//hSZfYQeQAh35Jsk67zVPXMbICwCN91nrz1HUM4EcOdUWSBi5994vMW8ROASAriWrVLzJvwQB+5FBXpIfOaPR/J68WOwiA3Ny+ToVJwyKHuiI9WLkLQCDr4mJwm2TkUFckBssMAwiK9hzjalgkUFekBMsMA0RBVUEyXSVP7CBShboiJVhmGCAKEtUq7W1rcTUsbKgrkkFnXcVUYABRoE1NwDzHYUNdkQxMBQYQNZg0LBKoK9JAGx+1qQliBwFQCixUHDbUFWmgIytipwBQlqqCZIyyhAF1RQIMpilMBQYQfXTSMFwNWynUFdbZXfNYZhhALFioOAyoK6xDbzGAiLBQcRhQV5hGb85CbzGAiDRJ8XbXPE5ZQoe6wjT0FgOIDj3HK4W6wi7a4IjhegDR0Z5jLFQcItQVdqG3GIAdVQXJo5evYdKwUKCuMAq9xQBMoT3HGMAPBeoKi6zT7tFJB0ZWAJiCnuMQoa6wCMP1AAxCz3GIUFeYMzrpsLvmMRUYAIPopWlMGhYY6gpzcLICwCycsoQCdYUtAxY7HR4UOwgALI8uVIye4wBQVxiCZYYBJAE9x4GhrjAEvcUAkoCFigNDXWEF7V/EyAqAJGCh4gBQV1iB4XoACcGkYQGgrjABywwDSA4dwEfP8VKoK0zAcD2A5KDn2B/UFfENWOyapHgM1wNIDj1lwdWwRUKtKx6Px2KxrOitHQ7H7OzsyiMpC3qLASStqiAZA/iLBK8rXq+3ra2toaGhr6+vurr63LlzQV9it9sPHTq0fft2s9nMR0g5wzLDAJKGnuOlgh/OmpqarFZrd3c3IaSysnLPnj1dXV35+fn+9v/yyy+HhoZ6enqcTiefSeWI/jOnvniD2EEAIHza1ITRy9es025czaaCnK+MjIwYDIZ9+/bRh9nZ2Vqttrm5OcBLMjMz9+7du2PHDt4yytfApe9QVACkDj3HiwSpK52dnYSQbdu2+bYUFxebzWaj0Rj4hSoVLuwEgWWGAWSDLlSMnmMqSF0ZHBxUq9VxcXG+LZmZmYSQs2fPCptLAbDMMICcVBUkY5SFClRX7Ha72+1OSUnhblSr1YQQq9UqaCzZw1RgADJDZyLH1TASeNyednNlZGRwN8bExBBC+G0gzs3N9f3c39/v+3liYoLHT4kQj2Fm5rwDn/+9QfsTqzX81gamvhzCWB6mwhDG8jAVhjCWJ8IwmbHe97+49lPv329fx89AAMtfTkVFhb89mRgFGR8f9/eURqOJYpAg+Apz7PyVqs1JG7MTI3wfpr4cwlgepsIQxvIwFYYwlifCMN4Ex+jla6Ua3vpxmP1yuMdt7rkB8dUVj8fT29vLfeKee+5JS0sjhHi9Xu52j8dDCImPxwWcMFmn3XbXvL440qICAAzSJMWj5/iHuuJ0Ovfv3899ory8PDU1VaVSXbx4kbvd5XKRG6P3EAaDaQrzFgPIla/n+Dfb08TOIpof6kpiYqLJZOI+ERsbSwgpLS0dGhryer10WIUQMjY2Rm7uPIbQjU46sMwwgLz5FirWR3ytW6J+7AeLvRndWFNTs7CwMDw87NvNZDLl5eVt2rQp2kllAb3FAEqg8IWKg9y/UlZWptfru7q66EObzTYyMtLa2kofGo1GnU53+PDhpS+kozLXr1/nNa20obcYQCHoZQnF3s4SfN7JgwcPzs3NtbS0dHZ2NjY2tre363Q6+tT4+LjT6Vw0z/HU1FR3d/fg4CAh5K233jp16pQQuSXHOu0enXRgZAVAIfRZ6xU7z3HwPuM1a9Z0dHTYbLbp6em6ujrfQAshpLa2Nisra9E1seTk5Pvvv//+++/nP6yUYZlhAEXxrfpVn6S4OQBDXX8lPT29qKiIW1SokpIS7iwvsKzRSYfdNY9lhgEUhV70VuCkYVgvMhpwsgKgQIpdqBh1RXADFjt6iwGUSZkLFaOuCIsuM4yTFQDFogsVK6rnGHVFWLS3GMsMAyiWAhcqRl0REO0yxMkKgMJpUxMU1XOMuiIgXAEDAKK8hYpRV4RCmwvRWwwA5MYAvkJ6jlFXhDJw6TtMBQYAlKJ6jlFXBDFgsWuS4tFbDAA+9JighKthqCv8o73FOFkBgEUUMmkY6gr/6GT46C0GgEUU0nOMusKzH5YZVup6PgAQmDY1we6al/cpC+oKz9BbDAABKKHnGHWFT7SJEMP1ABAAnYNDxj3HqCt8wjLDABCKqoJkGY+yoK7wBssMA0CI6Bzncr0ahrrCD7rMME5WACBEMu45Rl3hB71hBb3FABAiGd+Bj7rCA/QWA0AY6GVz+Z2yoK7wwGCaQm8xAKyUXHuOUVcihWWGASBsdJ7jAYtd7CB8Ql2JFKYCA4BIVBUkj16+JqeFilFXIoLeYgCIEL3gIacBfNSV8NHeYoysAECE9FnrRycdshnAR10JH6YCAwBeJKpVcroDH3UlTFhmGAB4RC+ny2PSMNSVMGG4HgB4JKfbJFFXwoHeYgDgHe05lsHtLKgrK0aXGcbICgDwrqogmc7fIXaQiKCurBiWGQYAgchjoeJQ64rH47FYLCHu7PV6LRbL1atXw03FLjr/KKYCAwCBaFMTpD7PcfC64vV629raGhoa+vr6qqurz507F3j/7u7uLVu23H333Xfeeefu3bsvXLjAU1Qm4AoYAAhKBpOGBb+Y09TUZLVau7u7CSGVlZV79uzp6urKz89fdudTp051dHQ8/PDDGzZsOHXq1CeffFJfX9/T05Odnc1zcDGgtxgAokCbmjB6+dropEOiF0aCnK+MjIwYDIZ9+/bRh9nZ2Vqttrm52d/+vb29dP/du3e/9tpr9fX1brf7yJEjfEYWD3qLASA6JN1zHKSudHZ2EkK2bdvm21JcXGw2m41G49KdPR5PfX39unXrfFsee+wxQsi3337LT1hRnf7SqUmKR28xAEQBPdqc/tIpdpBwBKkrg4ODarU6Li7OtyUzM5MQcvbs2aU7x8bGbtmyhbtl3bp1q1evXrt2LR9RxWR3zZunruNkBQCiRp+1fmJmXooD+IHqit1ud7vdKSkp3I1qtZoQYrVaQ3n3q1evXr9+vbKyMoKETDCYpu5IVaO3GACiJlGtuiNVLcWrYYHqitlsJoRkZGTc9IKYGELI7OxsKO/e19dXVFS0Y8eOCBKKj96mdMftuAIGAFF1+zqV3SW9UxYB/wE+Ozv73nvvvfnmm0H3zM3N9f3c39/v+3liYkKQZCv0/hfX7khVT0z8j9hBbsLIl+PDVB6mwhDG8jAVhjCWh6kwhJCZqcs56pQj/zneoP2J2FkWfzkVFRX+9vyhrng8nt7eXu4T99xzT1paGiHE6/Vyt3s8HkJIfHzwf7wfOHDgySef1Gg0QfccHx/391QoLxfU6KTjpz+NK924wWpViR5mEeQJgKkwhLE8TIUhjOVhKgwhRKPRfEOu2GPXsnCHA/fL4R63uecGxFdXnE7n/v37uU+Ul5enpqaqVKqLFy9yt7tcLnJj9D6At99+u7CwsLy8PJzsLDGYpuqLN4idAgCUq6og+dj5K3RWSrGzhOSHlImJiSaTiftEbGwsIaS0tHRoaMjr9dJhFULI2NgYubnzeKkzZ87Y7fbHH39ckMhRhGWGAUB0voWKpTLZx4/j9rE3oxtramoWFhaGh4d9u5lMpry8vE2bNvl7xzNnznz22WfcojI3N/fpp58KEF5YdJlh9BYDgOj0WeslNGlYkLOqsrIyvV7f1dW1detWQojNZhsZGTl+/Dh91mg0/vrXv/63f/s33w35p0+f3r9/f2Vl5XPPPUe3uN3ukZGR3//+94L9JwiF3l0vlRNPAJAx36pf9UkSuCwf/KB58ODBxsbGlpaW7Oxsg8HQ3t6u0+noU+Pj406n0zfP8UcffdTY2EgIeeedd7jvkJOT428+MWaNTjrsrnl9sUSn5wEAudEkxY9evmaddrN/ZT54XVmzZk1HR4fNZpuenq6rq/MNtBBCamtrs7KyfNfEdu3atWvXLqGSRpeELmUCgBL45jn+zfY0sbMEEer6K+np6UVFRdyiQpWUlHBneZEHLDMMAAyiLWEDFrvYQYLAepHLwLzFAMCmqoLk0cvXGF+oGHVlMfQWAwCzfD3HYgcJBHXlJrS3GCMrAMAs9nuOUVduguF6AGAc+wsVo678CMsMA4Ak0AF8eshiEOrKjzBcDwCS4LtNUuwgy0Nd+cGAxY5lhgFAKugpC5tXw1BXCCHE7prHyQoASEtVQTJddVDsIIuhrhBCiME0hanAAEBaEtUq7W1rGTxlQV0htGNPn42pwABAYrSpCQwuVIy6gt5iAJAqNnuOlV5X0FsMAJKmTU1gredY6XWFjqyInQIAIHxVBclM9Rwruq5gKjAAkAE6aRg7V8OUW1fsrnksMwwA8sDUpGHKrSvoLQYA2WDqDnyF1hV6MxF6iwFANjRJ8Yz0HCu0rhhMU+gtBgA5YafnWIl1ZXTSgWWGAUB+aM+x6AsVK7GuoLcYAOSKhYWKFVdX0FsMADLGwkLFyqorWGYYAGRP9J5jZdUVTAUGALInes+xgurK6KTD7prHVGAAIHv0Ur9Yk4YpqK7gZAUAFELcUxal1JUBix29xQCgHHShYlF6jhVRV7DMMAAokFg9x4qoK+gtBgAFogsVR/9qmPzrCu23w8gKACiQNjUh+j3H8q8rGK4HAMUSZdIwmdcVLDMMAApHB/Cj2XMcal3xeDwWiyXEnb1er8ViuXr1aripeIPhegBQuOj3HAevK16vt62traGhoa+vr7q6+ty5c4H3P3PmzNatW+++++4777yzurr666+/5inqig1Y7JqkeAzXA4DC0SNh1K6GBa8rTU1N//Vf/3X8+PHGxsbf/e53Dz/88BdffOFvZ6PReOLEiRdeeOHNN9/8p3/6p88///y3v/0tr4FDhd5iAACfaE4aFmQV3pGREYPB8Prrr9OH2dnZWq22ubn55MmTy+5vNps7Ojrozzt27Ni9e/f58+d5jBs6LDMMAODj6zmuT9og9GcFOV/p7OwkhGzbts23pbi42Gw2G43GZfevq6vjPszPz09LS4s45IphmWEAgEW0qQnRWag4SF0ZHBxUq9VxcXG+LZmZmYSQs2fPhvLuV65cefrppyPJFx70FgMALBK1nuNAdcVut7vd7pSUFO5GtVpNCLFarUHf+vTp0yUlJeXl5ZElXDHaTofhegCARehCxUL3HAcafjCbzYSQjIwM7saYmBhCyOzsbIAXXrhwoaen58SJE6tXr77tttvuvffewCFyc3N9P/f39/t+npiYCPzCZR079929+WtDqXwrEl4Y4SBPAEyFIYzlYSoMYSwPU2GIMHl067zvn/8m0fOTCMNUVFT421OQYe2CggJCyMLCwgcffLB///6srKyioqIA+4+Pj/t7SqPRrOijDaYp/f+6pVSYi2ArDSM05AmAqTCEsTxMhSGM5WEqDBEmz5eeqVEHCWOwgBuGe9zmnhsQX13xeDy9vb3cJ+655x465O71ernbPR4PISQ+PtBVptjY2KKioqKiopycnBdffPHdd98NXFf4YnfNj046frNdhE4BAACp0GetP3b+inXaLdB4wQ91xel07t+/n/tEeXl5amqqSqW6ePEid7vL5SI3Ru+D2rt376uvvup0OnlKGwR6iwEAgvLdgS9Qz/EPh+DExESTycR9IjY2lhBSWlo6NDTk9XrpsAohZGxsjNzceRxATExMcXFxYmI0+n1/6C0uRm8xAEAQmqT40cvXBDpl+bEfLPZmdGNNTc3CwsLw8LBvN5PJlJeXt2nTphA/wGw2Bx2354XBNIXeYgCAUAjacxzk/pWysjK9Xt/V1UUf2my2kZGR1tZW+tBoNOp0usOHD9OHXq/35Zdf5t6Kf+jQoYqKCp1OJ0Dym2CZYQCAFRFuoeLgQxEHDx5sbGxsaWnJzs42GAzt7e2+OjE+Pu50On3zHC8sLPT29n7zzTevvvrq5s2bHQ7H9u3bn3jiCd5DLzVw6bv6YsEnJwAAkJOqguRj56/Qm1p4fNvg77VmzZqOjg6bzTY9PV1XV+cbaCGE1NbWZmVl+a6JxcbGDg4Ojo6Out3ujIyMDRuidKDHMsMAAGGgl3l4n6Ak1BqVnp6enp6+dHtJSQn3YUxMTBSuenFZp92jk45nKzKC7woAADcToudY8utFYiowAICwCbHql7Tryuikw+6axzLDAABho2cqPE4aJu26gpMVAIAI8X7KIuG6gt5iAABe0J5jvm5nkWpdocsM42QFAIAXVQXJdNaSyN9KqnUFU4EBAPDIt1Bx5G8lybpinXZbp91YZhgAgEfa1AR6dI3wfSRZV3AFDACAd3xNGia9ukKb4dBbDADAOzqAH2HPsfTqysCl7/RZ68VOAQAgQ7z0HEusrgxY7JqkePQWAwAIhB5jI7kaJqW6QnuLcbICACAofdb6SAbwpVRX0FsMABAFEV4Nk0xd+WGZYfQWAwAIT5MUb3fNh3fKIpm6gt5iAICoiaTnmOG6YrUmvP8+GRggN3qLMVwPABA1dB3JH3qOOQfkoJgcqzhwgDz7LCHkp/ShRmMvvUf/+xfFjAQAoDxVBcnW//dpcvgVwjkgk/p60toa4FXs1ZWyssUl0WrVW39PPu0lf/ubOJEAABQpcdc/aZcckMmzz5JjxwIckBm7Dra0qPhYreTBB6MaBgBAycI9ILNUVwYGgly8O3YsxKt7AAAQkQgOyCzVlcFBfvYBAIAIRXBAZml8xWoNuov94zMDex4VPsoyvvnGmeLgZzE1XiBPAEyFIYzlYSoMYSwPU2GIqHm0xi80QXcaGFh2AJ+luhIKjUazXi3KJ692xd4m0kcvC3kCYCoMYSwPU2EIY3mYCkNEzZOojg2+k0az7GaW6oqfiFyJO/+3WDPkJ3pWa1ianB95AmAqDGEsD1NhCGN5mApDxM2Tnx18nx07lt3M0vjK3r3B99HrBY8BAAARHJBZqisaDTl6NNAOzz4byjkNAABEKoIDMkt1hRCi19M77Zfx7LOB7/AEAAA+hXtAZqyuaDSktZX87W8/nl5pNESvJ3/6E4oKAEBUhXtAZmnc3kejIX/6EyHEarVqcOELAEBEKz8gM3a+AgAAEhdqXfF4PBaLZaXv7nA4Lly4sNJXAQCAdAWvK16vt62traGhoa+vr7q6+ty5c6G/e3Nz80MPPRRBPAAAkJjg4ytNTU1Wq7W7u5sQUllZuWfPnq6urvz8/KAvPHnyZH9//y233MJDTAAAkIgg5ysjIyMGg2Hfvn30YXZ2tlarbW5uDvq+X331VU9Pz/bt23nICAAA0hGkrnR2dhJCtm3b5ttSXFxsNpuNRmPgFz7zzDPPP/98TAz6AgAAlCXIcX9wcFCtVsfFxfm2ZGZmEkLOnj0b4FXt7e07d+5EizAAgAIFqit2u93tdqekpHA3qtVqQojV/5z2n3/+uclkqq2t5SkhAABISaBxe7PZTAjJyMjgbqSXtmZnZ5d9icvlamtra29v5y8hAABICc/327/00kuPPvpoYmLiil6Vm5vr+7m/v9/388TEBG/JIsZUGII8ATEVhjCWh6kwhLE8TIUhjOVZFKaiosLfnj/UFY/H09vby33innvuSUtLI4R4vV7udo/HQwiJj49f+l6Dg4Pz8/M6nc53NjM/P08ImZ2dXbVqFXeQZpHx8XF/TzE1SMNUGII8ATEVhjCWh6kwhLE8TIUhjOXhhuEet7nnBsRXV5xO5/79+7lPlJeXp6amqlSqixcvcre7XC5yY/R+kd7e3g8//JDe6cJVVFSk1+s7OjrC+M8AAABp+aGuJCYmmkwm7hOxsbGEkNLS0qGhIa/X6+sYHhsbIzd3Hvs8+OCDu3bt4m5pb2+/dOnSK6+8cuuttwqRHgAAWPPj+AotJIvU1NQMDAwMDw9v3bqVbjGZTHl5eZs2bVq6c2FhYWFhIXfLiRMnrFZreXk5r5kBAIBdQe5fKSsr0+v1XV1d9KHNZhsZGWm9MfO+0WjU6XSHDx8WNiMAAEhH8PvhDx48ODc319LS0tnZ2djY2N7ertPp6FPj4+NOpzOMeY4BAECugvcZr1mzpqOjw2azTU9P19XVcadmqa2tzcrKWvaaGIWxegAApQn1/pX09PT09PSl20tKSnjNAwAA0oZ5IQEAgE+oKwAAwCfUFQAA4BPqCgAA8Al1BQAA+IS6AgAAfEJdAQAAPqGuAAAAn1BXAACAT6grAADAJ9QVAADgE+oKAADwCXUFAAD4hLoCAAB8Ql0BAAA+oa4AAACfUFcAAIBPqCsAAMAn1BUAAOAT6goAAPAJdQUAAPiEugIAAHxCXQEAAD6hrgAAAJ9QVwAAgE+oKwAAwCfUFQAA4BPqCgAA8Al1BQAA+IS6AgAAfAq1rng8HovFImgUAACQAVXQPbxe7wsvvDA2NqbT6YaGhp566qktW7YEfsnVq1d/+ctfLiws0Ic///nP//CHP8TE4NwIAED+gteVpqYmq9Xa3d1NCKmsrNyzZ09XV1d+fn6Alxw9ejQ+Pt738IEHHkBRAQBQiCB1ZWRkxGAwvP766/Rhdna2Vqttbm4+efKkv5dMT0//5S9/GRoa4jMmAABIRJDTiM7OTkLItm3bfFuKi4vNZrPRaPT3kuPHj2/evNl3EQwAABQlSF0ZHBxUq9VxcXG+LZmZmYSQs2fPLrv/zMzM0aNH33jjjY0bNzY3N3/11Vc8ZgUAAPYFqit2u93tdqekpHA3qtVqQojVal32JTabbffu3XfddRchpKenp7KycnBwkLewAADAvEDjK2azmRCSkZHB3UhH4GdnZ5d9SWFhYWFhISHE4XC8/vrrR44cefzxx3t7e+lZDgAAyF7wfrDwJCQkPPXUU2lpaQcOHDhy5Mjzzz8fYOfc3Fzfz/39/b6fJyYmBIoXBqbCEOQJiKkwhLE8TIUhjOVhKgxhLM+iMBUVFf72/KGueDye3t5e7hP33HNPWloaIcTr9XK3ezweQgi3jTiABx544OTJk8PDw4F3Gx8f9/eURqMJ5YOig6kwBHkCYioMYSwPU2EIY3mYCkMYy8MNwz1uc88NiK+uOJ3O/fv3c58oLy9PTU1VqVQXL17kbne5XOTG6H0odu7c+c4776wgOAAASNkPdSUxMdFkMnGfiI2NJYSUlpYODQ15vV7fjY1jY2Pk5s7jIB+gUhUXF/OWFwAA2PZjP1jszejGmpqahYUF7oUsk8mUl5e3adOmED/g448/bmho4DExAACwLMj9K2VlZXq9vquriz602WwjIyOtra30odFo1Ol0hw8f9u3/yCOPtLS0TE9PE0I8Hs9zzz133333Lbr0FroA40LRx1QYgjwBMRWGMJaHqTCEsTxMhSGM5Qk9TPB+sIMHDzY2Nra0tGRnZxsMhvb2dp1OR58aHx93Op3ceY5XrVrV3d3d09OTm5u7evXqxsbGoJNUAgCAnASvK2vWrOno6LDZbNPT03V1ddwZJGtra7OysrjXxNrb261W6+XLl/Py8pKSkgSJDAAADAv1/pX09PT09PSl20tKShZt0Wg0TDXGAQBANGH6egAA4NM/fP/99+ImCHtUHwAAGMG9TVL8ugIAAHKC62AAAMAn1BUAAOAT6goAAPAJdQUAAPiEugIAAHxCXQEAAD6hrgAAAJ9QVwAAgE+oKwAAwCfUFQAA4BNbdcXj8XBXcxFXeGEcDseFCxfEDeP1ei0Wy9WrV3mPwWaeMP5PORyO2dlZgfIsItZv9Uo/V9DvJPQwUfjtZS1PeL/AQhxnwguzFCt1xev1trW1NTQ09PX1VVdXnzt3LuhLrl69WlxcrLth165dXq9XrDA+zc3NDz30EC8xwgtz5syZrVu33n333XfeeWd1dfXXX3/NY5gw8nR3d2/ZsoXm2b17N79/DGH8n7Lb7YcOHdq+fbvZbOYxCV/xRPlcQb+TFYUR9LcljDys/TX58H6cCSNMoCPw92x48skn//mf/5n+/Ne//nXjxo1msznwS373u9+Vchw/flzEMNQHH3yQk5NTVFTEV5KVhvnss88efvjhP/7xjwMDA4899lhOTs6vfvUrHsOsNM/HH39cVlb25ptv9vX10TwbN27861//KkqY77///tKlS8eOHdu+fXtOTs758+f5isFXPFE+V+jvJPQwQv+2rDQPa39NPkIcZ8IIE+AIzERdOX/+fE5OzieffOLb8i//8i9VVVUBXvLtt9/y/v847DDUf//3f//qV7/69a9/zeP/75WGWVRc77777pycHL7ChJHnX//1X//+97/7Hv7Hf/xHTk5OU1OTKGF8/v3f/z0KdSXseKJ8rkDfyYrCCPrbEkYe1v6aKCGOM2GECXwEZuI6WGdnJyFk27Ztvi3FxcVms9loNPp7yfHjxzdv3rywsMBCGOqZZ555/vnnues0Rz9MXV0d92F+fn5aWppYeTweT319/bp163xbHnvsMULIt99+G/0wXCpVqMukRiLseKJ8rkDfSehhhP5tWWkewthfk48Qx5kwwgQ+AjNRVwYHB9VqdVwGqJSgAAAFYElEQVRcnG9LZmYmIeTs2bPL7j8zM3P06NE33nhj48aNzc3NX331lYhhqPb29p07d/K+AHN4YXyuXLny9NNPi5UnNjZ2y5Yt3C3r1q1bvXr12rVrox8m+sSKx9TXEnoYoX9bVppnKXH/miiBjjMrDRP0CCx+XbHb7W63OyUlhbtRrVYTQqxW67Ivsdlsu3fvvuuuuwghPT09lZWVg4ODYoUhhHz++ecmk6m2tpaXDBGG8Tl9+nRJSUl5eTkjeQghV69evX79emVlJQthBCVWPKa+lgjD8PjbEnkeFv6aBDrOhBEm6BE4GhcEAqMtKBkZGdyN9CzPX9djYWFhYWEhIcThcLz++utHjhx5/PHHe3t7aYGNchiXy9XW1tbe3h7hR/MShrpw4UJPT8+JEydWr15922233XvvveLm8enr6ysqKtqxYwcLYQQlVjymvpYIw/D42xJJHkb+moQ7zoQRJugRWPzzlUgkJCQ89dRTra2t169fP3LkiCgZXnrppUcffTQxMVGUT19WQUHBnj17qqurr1+/vn//foH63Fdqdnb2vffee/HFF8UOAhLAzm8LI39NDB5niP8jcLTPVzweT29vL3cLrf+Lbj3xeDyEkPj4+FDe84EHHjh58uTw8HD0wwwODs7Pz+t0Ol9Vn5+fJ4TMzs6uWrWKe7EyCmF8YmNji4qKioqKcnJyXnzxxXfffbeoqCj0JLznoQ4cOPDkk0+Gd2lYiF8bQdEB3ujHE+tzeQ8TyW8Lv3l4+WuKMAyPx5nIwyy19Agc7bridDr379/P3XLvvfeqVKqLFy9yN7pcLnJj4CgUO3fufOedd6Ifpre398MPP+zu7l60vaioSK/Xd3R0RDPMUnv37n311VedTmfoMQTK8/bbbxcWFoZ9eVqgXxvhpKamihJPrM/lN0yEvy2856Ei+WuKMAyPx5nIwyxr0RE42nUlMTHRZDIt2lhaWjo0NOT1en3Nc2NjY+TmprfAVCpVcXFx9MM8+OCDu3bt4m5pb2+/dOnSK6+8cuutt0Y5zFIxMTHFxcXhnTvzmOfMmTN2u/3xxx8PIwbvYaIjJiZGlHhifS6PYSL/beE3D/flYf81RRiGx+NM5GGWtegILML4SuzNCCE1NTULCwvc0yiTyZSXl7dp06YQ3/Pjjz9uaGiIfhj6ryqu5OTkVatWlZeXh3GyLMQ3Yzabwx5p5CXPmTNnPvvsM+5hYm5u7tNPPxUlTDSJFY+pr2WlYfj6beErzyKR/DVFEobf40yEYZa16AjMxLh9WVmZXq/v6uqiD20228jISGtrq28Ho9Go0+kOHz5MHz7yyCMtLS3T09OEEI/H89xzz9133325ubmihBHUisJ4vd6XX3755MmTvmcPHTpUUVGh0+lEyUMIOX36dFNT09zc3HM3NDc3V1ZW8vKPrLD/T9HryNevX488QyTxRPncKH8nKwoj6G/LSvOI/tcUzePMSsMEPQKL32dMHTx4sLGxsaWlJTs722AwtLe3c///jY+PO51O3yybq1at6u7u7unpyc3NXb16dWNj46I7qqIZRmihh1lYWOjt7f3mm29effXVzZs3OxyO7du3P/HEE2Ll+eijjxobGwkhi4a+cnJy8vPzoxyGmpqa+uMf/0h77d96662ZmZmdO3fykiSMeKJ8bvS/kxDDROG3ZUV5RP9rivJxZkVhgh+BeZxhJnJWq9VoNC4sLCx96ty5c2632/fwb3/725///Odvv/2WhTBREGKYhYWFzz777M9//vPly5dZyBMdTIVZKkA8UT5XlO+EqTAh5hH9r4nl/1OBj8D/8P3330etHgIAgOwxMb4CAACy8f8Dh7KH7wgafg8AAAAASUVORK5CYII=\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 385px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 385px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReference program\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e* \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://github.com/tomtkg/Largest-Small-Polygon\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://github.com/tomtkg/Largest-Small-Polygon\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = LSP(n) % Largest Small Polygon (LSP)\r\n    X = [0 0.5; 0.5 0; 0 -0.5; -0.5 0]; % Case n = 4 passed\r\nend","test_suite":"%%\r\nn = 3;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.43301270 - 0.01);\r\n%%\r\nn = 4;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.50000000 - 0.01);\r\n%%\r\nn = 5;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.65716389 - 0.01);\r\n%%\r\nn = 6;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.67498144 - 0.01);\r\n%%\r\nn = 7;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.71974093 - 0.01);\r\n%%\r\nn = 8;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.72686848 - 0.01);\r\n%%\r\nn = 9;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.74561923 - 0.01);\r\n%%\r\nn = 10;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.74913735 - 0.01);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2217275,"edited_by":2217275,"edited_at":"2025-05-18T15:08:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-05-18T08:26:55.000Z","updated_at":"2026-03-13T22:08:20.000Z","published_at":"2025-05-18T08:40:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLargest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eone and that has the largest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eamong all diameter-one\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-gons. (from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Biggest_little_polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/BiggestLittlePolygon.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMathWorld\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the case n = 6, the polygon is called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGraham's Biggest Little Hexagon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results for cases where n is 3 to 8 are as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr 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+3o1yTwNCC3I9WBg2bNhARHNzc+++++6+ffvS0tIMBkPgTTIzM31f9/T0+L4eHR0VfLywMTUMMTbPO5/98P3497uyV4dyLCsBpp4cYmwedoZZO+f9ZuLK247vquSexIedJ4fD1DwLhikrK/O3pt+ucKfcvV4vf6HH4yGi2NjYAN87OjraYDAYDIaMjIznnnvurbfeCtqV4eFhf3clJycH3lZKTA1DzMxz9OyFdetidmWvZmQeDlPDEGPzsDPMbbddPUl0fvIGdi4+ZufJ4TA1D38Y/n6bf2xAAc6vJCQkREVFDQ4O8hdOT0/T9bP3Qe3evfuGG25wu92hDQyKhHMqEIk4fdQ/r1+Jcy0q47crOp2usLDw8uXL/EOWoaEhmn/lcaCH1uny8/Pj4uIinxLYhKhA5NbE6HAaX2UCXWdcWVk5NzfX39/vW2K327OysnJzc0N8dIfDgfP2aoWogFBwhZjKBOpKSUlJcXGxyWTibrpcLqvV2tTUxN202WxGo/HQoUPcTa/X+8ILL5w4ccK3+cGDB8vKyoxGoziTg5wQFRAW0qImQa4Ha2lpqaura2xsTE9PN5vNra2tvk4MDw+73W7f5xzPzc11dXV99913L7300saNGycnJzdv3vzYY4+JOz7IAVEBMeAzxFQjSFdWrVrV1tbmcrnGx8erq6u5969wqqqq0tLSfK+JRUdHWyyW8+fPz8zMpKSk3HILdjrqhKiAeJAWdQjp/StJSUlJSUmLlxcUFPBv6nQ6vOqlbogKiA1pUQH8vUgIFaIC0sC5FqVDVyAkiApICWlRNHQFgkNUQHpIi3KhKxAEogJyQVoUCl2BQBAVkBfSokToCviFqAALkBbFQVdgaYgKsANpURZ0BZaAqABrkBYFQVdgIUQF2IS0KAW6AvMgKsAypEUR0BX4CaIC7ENa2IeuwDWICigF0sI4dAWIEBVQGqSFZegKICqgSEgLs9AVrUNUQLmQFjahK5qGqIDSIS0MQle0C1EBdUBaWIOuaBSiAmqCtDAFXdEiRAXUB2lhB7qiOYgKqBXSwgh0RVsQFVA3pIUF6IqGICqgBUiL7NAVrUBUQDuQFnmhK5qAqIDWIC0yQlfUD1EBbUJa5IKuqByiAlqGtMgCXVEzRAUAaZEeuqJaiAoAB2mRGLqiTogKAB/SIiV0RYUQFYDFkBbJoCtqg6gA+IO0SCOkrng8npGRkRAf0ev1joyMjI2NRTAVhAlRAQgMaZFAkK54vd7m5uba2tru7u6KioqBgYHA63d0dGzatGn79u133nnnjh07zp07J9yoEASiAhAKpEVsUYHvrq+vdzqdHR0dRFReXr5z506TyZSdnb3kyidPnmxra3vooYduueWWkydPfvjhhzU1NZ2dnenp6cIPDvMhKgCh49Jy/qtJs/3iPRvWyz2O2gQ6XrFarWazec+ePdzN9PT0vLy8hoYGf+t3dXVx6+/YsePll1+uqamZmZk5fPiwwCPDIogKwHLhqEU8gbrS3t5OREVFRb4l+fn5DofDZrMtXtnj8dTU1KxZs8a35NFHHyWiS5cuCTYsLAVRAQgP0iKSQF2xWCx6vT4mJsa3JDU1lYj6+voWrxwdHb1p0yb+kjVr1qxcuXL16tUCjQpLQFQAIoG0iMFvVyYmJmZmZuLj4/kL9Xo9ETmdzlAeemxs7MqVK+Xl5ZFNCH4hKgCRQ1oE57crDoeDiFJSUuatrdMR0dTUVCgP3d3dbTAYtmzZEtmEsLR3PvuBEBUAIfjScuoLt9yzqEGQ68HCNjU19fbbb7/22muhrJyZmen7uqenx/f16Oio8JOFi6lh3vnsh/Hx73dlrw7x2FECTD0/TA1DjM3D1DDE0jxr57yzly+99tGn/5p6g9yzXMPOk0OLhikrK/O3pt+uJCYmEpHX6+Uv9Hg8RBQbGxt0ggMHDjz++OPJyclB1ySi4eFhf3eF+AjSYGSYo2cvrFsXsyt7NSPz+DA1D1PDEGPzMDUMMTbP+Iq15yc97Fx8zNSTwx+Gv9/mHxtQgNfBEhISoqKiBgcH+Qunp6fp+tn7AI4dO5aTk1NaWrqcgSEkOKcCIJ41MTqca4mc367odLrCwsLLly/zD1mGhoZo/pXHi50+fXpiYqK6ulrAKYGDqACIDafxIxfoOuPKysq5ubn+/n7fErvdnpWVlZub62+T06dPf/LJJ3v37vUtmZ2d/fjjjwWZVeMQFQBpIC0RCtSVkpKS4uJik8nE3XS5XFartampibtps9mMRuOhQ4d86586daq+vn52dvbp6xoaGsrLy2+66Sbx/gM0AlEBkBLSEokg14O1tLTU1dU1Njamp6ebzebW1laj0cjdNTw87Ha7fZ9z/P7779fV1RHRm2++yX+EjIwMf58nBiFCVACkh88QC1uQrqxataqtrc3lco2Pj1dXV3PvX+FUVVWlpaX5XhPbtm3btm3bRJxUqxAVALkgLeEJ6e+vJCUlGQwGflQ4BQUF/E95AcEhKgDywgtiYcDfi2QXogLAAqRludAVRiEqAOxAWpYFXWERogLAGqQldOgKcxAVADYhLSFCV9iCqACwDGkJBbrCEEQFgH1IS1DoCisQFQClQFoCQ1eYgKgAKAvSEgC6Ij9EBUCJkBZ/0BWZISoAyoW0LAldkROiAqB0SMti6IpsEBUAdUBaFkBX5IGoAKgJ0sKHrsgAUQFQH6TFB12RGqICoFZICwddkRSiAqBuSAuhK1JCVAC0AGlBVySCqABoh8bTgq5IAVEB0BotpwVdER2iAqBNmk0LuiIuRAVAy7SZFnRFRIgKAGgwLeiKWBAVAOBoLS3oiigQFQDg01Ra0BXhISoAsJh20oKuCAxRAQB/NJIWdEVIiAoABKaFtKArgkFUACAUqk8LuiIMRAUAQqfutKArAkBUAGC5VJyWkLri8XhGRkaW9biTk5NTU1NhjaQwiAoAhEetaQnSFa/X29zcXFtb293dXVFRMTAwEPQRJyYmDh48uHnzZofDIdCQ7EJUACASqkxLVOC76+vrnU5nR0cHEZWXl+/cudNkMmVnZ/tb/4svvujt7e3s7HS73QJPyh5EBQAix6Xl/FeTZvvFezasl3scAQQ6XrFarWazec+ePdzN9PT0vLy8hoaGAJukpqbu3r17y5YtQs7IJEQFAISisqOWQF1pb28noqKiIt+S/Px8h8Nhs9kCP2hUVJDDIKVDVABAWGpKS6CuWCwWvV4fExPjW5KamkpEfX19os/FMEQFAMSgmrT47crExMTMzEx8fDx/oV6vJyKn0yn2WMxCVABAPOpIi9+ucFdzpaSkzFtbpyMijVxAvBiiAgBiU0FamDgRkpmZ6fu6p6fH9/Xo6Kgc4yzttT/9fe3af9qVvZqRwzWmnhxibB6mhiHG5mFqGGJsHnaGWTvn/WbiytuO76rknsRnwZNTVlbmb02/XUlMTCQir9fLX+jxeIgoNjY20gHnGx4e9ndXcnKysN8rPEfPXli79p/+61c5cg8yDyNPjg9T8zA1DDE2D1PDEGPzsDPMbbddPUl0fvIGdi4+5j85/P02/9iAArwOlpCQEBUVNTg4yF84PT1N18/eawf38teu7NVyDwIAGhKnj/rn9SuV+IKY367odLrCwsLLly/zD1mGhoZo/pXHqodzKgAglzUxOiWeawl0nXFlZeXc3Fx/f79vid1uz8rKys3NFX8wJiAqACAvJZ7GD9SVkpKS4uJik8nE3XS5XFartampibtps9mMRuOhQ4cWb8gd4ly5ckXoaSWFqAAACxSXliCfO9nS0jI7O9vY2Nje3l5XV9fa2mo0Grm7hoeH3W73gs85vnjxYkdHh8ViIaLXX3/95MmTIs0tNkQFANihrLQEuc541apVbW1tLpdrfHy8urqae/8Kp6qqKi0tbcFrYuvXr7/vvvvuu+8+UYaVCqICAKxR0MdThvT3V5KSkgwGAz8qnIKCAv6nvKgDogIAbFLKUQv+XuQ8iAoAsEwRaUFXfoKoAAD72E8LunINogIASsF4WtAVIkQFAJSG5bSgK4gKACgSs2nRelcQFQBQLjbToumuICoAoHQMpkW7XUFUAEAdWEuLRruCqACAmjCVFi12BVEBAPVhJy2a6wqiAgBqxUhatNUVRAUA1I2FtGioK4gKAGiB7GnRSlcQFQDQDnnToomuICoAoDUypkX9XUFUAECb5EqLyruCqACAlsmSFjV3BVEBAJA+LartCqICAMCROC3q7AqiAgDAJ2VaVNgVRAUAYDHJ0qK2riAqAAD+SJMWVXUFUQEACEyCtKinK4gKAEAoxE6LSrqCqAAAhE7UtKihK4gKAMByiZcWxXcFUQEACI9IaVF2VxAVAIBIiJEWBXcFUQEAiJzgaVFqVxAVAAChCJsWRXYFUQEAEJaAaRGlKx6PZ2RkRIxHJkQFAEAcQqVF4K54vd7m5uba2tru7u6KioqBgYHwH8vpjO3vX7AMUQEAEI/ftCy1Q/ZH4K7U19f/5S9/eeONN+rq6n7/+98/9NBDn3322bIf5ehR+tnPKCXl5qoq7gs6cIAQFQAA8S1Mi58dcgBCdsVqtZrN5j179nA309PT8/LyGhoalvcoJSX0wAPzljidtH+/M/dfCFEBABCfLy3O3H9ZcodMJSUBNheyK+3t7URUVFTkW5Kfn+9wOGw2W6gPceAAnTmz5D3Jf+mvaV1mogAAICxx+qjiN/8n+S9+Xvs6c2Zhb3iE7IrFYtHr9TExMb4lqampRNTX1xfS9mfO0P79QVbwUx0AABBSBDtkwboyMTExMzMTHx/PX6jX64nI6XSG9BBBV3M6yWIJazoAAFiOCHbIgnXF4XAQUUpKyrxH1+mIaGpqKqSHCKUZOF4BAJBABDvkKGEnCU9mZiYRvTE6WhBszcl168ZCPPoR2ujoqCzf1x/MEwBTwxBj8zA1DDE2D1PDkKzz3Dw0FBtsnRM225OZmYuXC9aVxMREIvJ6vfyFHo+HiGJjg4w3PDxMRHTgQJCX84hu3L79xuTk8KeMTLJ833pJmCcApoYhxuZhahhibB6mhiEZ59m6lYK9YeXX//M/v66poevHBj6CvQ6WkJAQFRU1ODjIXzg9PU3Xz94Ht3t38HUY+ycHAFCnCHbIgnVFp9MVFhZevnyZf8gyNDRE8688DiQ5Ocjxyv79VFwcwYwAABCaCHbIQl5nXFlZOTc31887dLLb7VlZWbm5uaE+xO7d/v5LJjYVmnc+EvGMAAAQEvPG7ef3/Hbp+4qLqanJ34ZCdqWkpKS4uNhkMnE3XS6X1Wpt8v+9l5CcTE1NCzPIZfOPfxTpTzEDAMACR89emPh5Qt5rL/jbIQfYVuDPB2tpaZmdnW1sbGxvb6+rq2ttbTUajct+lKYm+uMf6W9/++btt+nHH+lvf6OmJvH+FDMAAPDN+zDGpXbIgTcX+DrjVatWtbW1uVyu8fHx6upq7v0rYUpOnpm/gEvL+a8mzfaL92xYH9mkAACwhKU/4XfRDjkAUf7+SlJSksFgiCgqfuCoBQBAPIJ8bLzy/l4k0gIAIAah/haJ8rpCSAsAgNAE/ANXiuwKIS0AAMIR9q8mKrUrhLQAAAhB8D/Fq+CuENICABAZMf6+u7K7QkgLAEC4xIgKqaArhLQAACyfSFEhdXSFkBYAgOUQLyqkmq4Q0gIAEBpRo0Jq6gohLQAAwYgdFVJZVwhpAQDwT4KokPq6QkgLAMBSpIkKqbIrhLQAAMwnWVRIrV0hpAUA4Dopo0Iq7gohLQAAkkeF1N0VQloAQNukjwqpviuEtACAVskSFdJCVwhpAQDtkSsqpJGuENICAFoiY1RIO10hpAUAtEHeqJCmukJICwConexRIa11hZAWAFAvFqJCGuwKIS0AoEaMRIW02RVCWgBAXdiJCmm2K4S0AIBaMBUV0nJXCGkBAOVjLSqk8a4Q0gIASsZgVAhdIaQFAJSJzagQusJBWgBAWZiNCqErPkgLACgFy1EhdIUPaQEA9jEeFQq9Kx6PZ2RkZFkPPTk5OTU1tfyR5IS0AADL2I8KhdIVr9fb3NxcW1vb3d1dUVExMDAQdJOJiYmDBw9u3rzZ4XAIMaSkkBYAYJMiokJEUUHXqK+vdzqdHR0dRFReXr5z506TyZSdne1v/S+++KK3t7ezs9Ptdgs5qYS4tJz/atJsv3jPhvVyjwMAoJioUNDjFavVajab9+zZw91MT0/Py8traGgIsElqauru3bu3bNki2IxywFELALBDQVGhoF1pb28noqKiIt+S/Px8h8Nhs9kCbxgVFfxIiHFICwCwQFlRoaBdsVgser0+JibGtyQ1NZWI+vr6xJ2LDUgLAMhLcVGhwF2ZmJiYmZmJj4/nL9Tr9UTkdDpFHYsdvrSc+kKpp4sAQKHe+ewHUlpUKPB5e+5qrpSUFP5CnU5HRMJeQJyZmen7uqenx/f16OiogN8lEmvnvLOXL7320af/mnqD3LNcw86Tw2FqHqaGIcbmYWoYYmwepoZ557Mfvh//flf2akb+P37Bk1NWVuZvTSbOggwPD/u7Kzk5WcJBghhfsfb8pIedK8SYenKIsXmYGoYYm4epW4yiuwAAHsZJREFUYYixeRgZ5ujZC+vWxezKXs3IPBz+MPz9Nv/YgHxd8Xg8XV1d/DvuvvvuxMREIvJ6vfzlHo+HiGJjYwWel3lrYnS3/RwXHwOA6HznVBg5Ulmua11xu9379u3j31FaWpqQkBAVFTU4OMhfPj09TdfP3msN3tcCAGJT4on6Ba51JS4uzm638++Ijo4mosLCwt7eXq/Xy51WIaKhoSGaf+WxpiAtACAeFUSF+NeDRc/HLaysrJybm+vv7/etZrfbs7KycnNzpZ6UGbj4GADEoI6oUND3r5SUlBQXF5tMJu6my+WyWq1NTU3cTZvNZjQaDx06tHhD7qzMlStXBJ2WFUgLAAhLNVGhUD53sqWlZXZ2trGxsb29va6urrW11Wg0cncNDw+73e4Fn3N88eLFjo4Oi8VCRK+//vrJkyfFmFt2SAsACEVNUaFQrjNetWpVW1uby+UaHx+vrq72nWghoqqqqrS0tAWvia1fv/6+++677777hB+WMTjXAgCRU1lUKPS/v5KUlGQwGPhR4RQUFPA/5UVrcNQCAJFQX1QIfy8yckgLAIRHlVEhdEUQSAsALJdao0LoilCQFgAInYqjQuiKgJAWAAiFuqNC6IqwkBYACEz1USF0RXBICwD4o4WoELoiBqQFABbTSFQIXREJ0gIAfNqJCqEr4kFaAICjqagQuiIqpAUAtBYVQlfEhrQAaJkGo0LoigSQFgBt0mZUCF2RBtICoDWajQqhK5JBWgC0Q8tRIXRFSkgLgBZoPCqErkgMaQFQN0SF0BXpIS0AaoWocNAVGSAtAOqDqPigK/JAWgDUBFHhQ1dkg7QAqAOisgC6IiekBUDpEJXF0BWZIS0AyoWoLAldkR/SAqBEiIo/6AoTkBYAZUFUAkBXWIG0ACgFohIYusIQpAWAfYhKUOgKW5AWAJYhKqFAV5iDtACwCVEJEbrCIqQFgDWISujQFUYhLQDsQFSWJdSueDyekZGREFf2er0jIyNjY2PhTgVESAsAGxCV5QreFa/X29zcXFtb293dXVFRMTAwEHj9jo6OTZs2bd++/c4779yxY8e5c+cEGlWLkBYAeSEqYYgKukZ9fb3T6ezo6CCi8vLynTt3mkym7OzsJVc+efJkW1vbQw89dMstt5w8efLDDz+sqanp7OxMT08XeHDN4NJy/qtJs/3iPRvWyz0OgIYgKuEJcrxitVrNZvOePXu4m+np6Xl5eQ0NDf7W7+rq4tbfsWPHyy+/XFNTMzMzc/jwYSFH1h4ctQBID1EJW5CutLe3E1FRUZFvSX5+vsPhsNlsi1f2eDw1NTVr1qzxLXn00UeJ6NKlS8IMq2FIC4CUEJVIBOmKxWLR6/UxMTG+JampqUTU19e3eOXo6OhNmzbxl6xZs2blypWrV68WYlStQ1oApIGoRChQVyYmJmZmZuLj4/kL9Xo9ETmdzlAefWxs7MqVK+Xl5RFMCD9BWgDEhqhELlBXHA4HEaWkpMzbQKcjoqmpqVAevbu722AwbNmyJYIJYR5fWk594ZZ7FgC1eeezHwhRiVjw68HCNjU19fbbb7/22mtB18zMzPR93dPT4/t6dHRUlMnCwtQwa+e8s/+49NpHn/5r6g1yz3INU88PU8MQY/MwNQyxNM87n/3w/fj3u7JXh/h6jATYeXJo0TBlZWX+1rzWFY/H09XVxb/j7rvvTkxMJCKv18tf7vF4iCg2NjboEAcOHHj88ceTk5ODrjk8POzvrlA2lwxTwxDR+Iq15yc97Fx8zNTzw9QwxNg8TA1DbMxz9OyFdetidmWvZmEYPqbm4Q/D32/zjw3I1xW3271v3z7+HaWlpQkJCVFRUYODg/zl09PTdP3sfQDHjh3LyckpLS0NZ3YIwZoY3W0/x/taAATgO6fCzpGKol3rSlxcnN1u598RHR1NRIWFhb29vV6vlzutQkRDQ0M0/8rjxU6fPj0xMbF3715RRobr8JZJgMjhRL3gfjpvHz0ft7CysnJubq6/v9+3mt1uz8rKys3N9feIp0+f/uSTT/hRmZ2d/fjjj0UYHnCFGEBEEBUxBHn/SklJSXFxsclk4m66XC6r1drU1MTdtNlsRqPx0KFDvvVPnTpVX18/Ozv79HUNDQ3l5eU33XSTSP8BgLQAhAdREUnw68FaWlrq6uoaGxvT09PNZnNra6vRaOTuGh4edrvdvs85fv/99+vq6ojozTff5D9CRkaGv88TA0HgBTGA5UJUxBO8K6tWrWpra3O5XOPj49XV1b4TLURUVVWVlpbme01s27Zt27ZtE2tSCAhpAQgdoiKqUP/+SlJSksFg4EeFU1BQwP+UF5ARXhADCAWiIjb8vUhVQVoAAkNUJICuqA3SAuAPoiINdEWFkBaAxRAVyaAr6oS0APAhKlJCV1QLaQHgICoSQ1fUDGkBQFSkh66oHNICWoaoyAJdUT+kBbQJUZELuqIJSAtoDaIiI3RFK5AW0A5ERV7oioYgLaAFiIrs0BVtQVpA3RAVFqArmoO0gFohKoxAV7QIaQH1QVTYga5oFNICaoKoMAVd0S6kBdQBUWENuqJpSAsoHaLCIHRF65AWUC5EhU3oCiAtoEiICrPQFSBCWkBpEBWWoStwDdICSoGoMA5dgZ8gLcA+RIV96ArMg7QAyxAVRUBXYCGkBdiEqCgFugJLQFqANYiKgqArsDSkBdiBqCgLugJ+IS3AAkRFcdAVCARpAXkhKkqErkAQSAvIBVFRKHQFgkNaQHqIinKhKxASpAWkhKgoWqhd8Xg8IyMjIa7s9XpHRkbGxsbCnQpYhLSANBAVpQveFa/X29zcXFtb293dXVFRMTAwEHj906dP33HHHdu3b7/zzjsrKiq+/fZbgUYF+SEtIDZERQWigq5RX1/vdDo7OjqIqLy8fOfOnSaTKTs7e8mVbTbb8ePHn332WZ1Od/z48Q8//PC3v/3tsWPHBJ4a5MOl5fxXk2b7xXs2rJd7HFAVREUdghyvWK1Ws9m8Z88e7mZ6enpeXl5DQ4O/9R0OR1tbW0lJyZYtW15++eVf/OIXZ8+eFXJeYACOWkAMiIpqBOlKe3s7ERUVFfmW5OfnOxwOm8225PrV1dX8m9nZ2YmJiREPCcxBWkBYiIqaBOmKxWLR6/UxMTG+JampqUTU19cXyqNfuHDhySefjGQ+YBbSAkJBVFQmUFcmJiZmZmbi4+P5C/V6PRE5nc6gD33q1KmCgoLS0tLIJgR2IS0QuXc++4EQFXUJdN7e4XAQUUpKCn+hTqcjoqmpqQAbnjt3rrOz8/jx4ytXrrz11lt37doVeIjMzEzf1z09Pb6vR0dHA28oJaaGIZbmWTvn/WbiytuO76rknsSHnSeHw9Q8TA3zzmc/fD/+/a7s1aH8r6oEmHpyiLF5FgxTVlbmb83g14OFYcOGDUQ0Nzf37rvv7tu3Ly0tzWAwBFh/eHjY313JycmCjxc2poYhlua57barJ4nOT97AzhVi7Dw5HKbmYWSYo2cvrFsXsyt7NSPzcJgahhibhz8Mf7/NPzYgX1c8Hk9XVxf/jrvvvps75e71evnLPR4PEcXGxgb43tHR0QaDwWAwZGRkPPfcc2+99VbgroDSxemj/nn9yvEV0bj4GELkO6fCyJEKCOhaV9xu9759+/h3lJaWJiQkREVFDQ4O8pdPT0/T9bP3Qe3evfull15yu90CTQvsWhOju+3neF8LhAQn6tXtWlfi4uLsdjv/jujoaCIqLCzs7e31er3caRUiGhoaovlXHgeg0+ny8/Pj4uKEHBlYhbdMQigQFdX76Xqw6Pm4hZWVlXNzc/39/b7V7HZ7VlZWbm5uiN/A4XAEPW8PqoErxCAwREULgrx/paSkpLi42GQycTddLpfVam1qauJu2mw2o9F46NAh7qbX633hhRdOnDjh2/zgwYNlZWVGo1GEyYFRSAv4g6hoRPDrwVpaWurq6hobG9PT081mc2trq68Tw8PDbrfb9znHc3NzXV1d33333UsvvbRx48bJycnNmzc/9thjIo4PTMILYrAYoqIdwbuyatWqtrY2l8s1Pj5eXV3tO9FCRFVVVWlpab7XxKKjoy0Wy/nz52dmZlJSUm65BT9A2oW0AB+ioimhvn8lKSkpKSlp8fKCggL+TZ1Oh1e9gIO0AAdR0Rr8vUgQEc61AKKiQegKiAtp0TJERZvQFRAd0qJNiIpmoSsgBaRFaxAVLUNXQCJIi3YgKhqHroB0kBYtQFQAXQFJIS3qhqgAoSsgPaRFrRAV4KArIAOkRX0QFfBBV0AeSIuaICrAh66AbJAWdUBUYAF0BeSEtCgdogKLoSsgM6RFuRAVWBK6AvJDWpQIUQF/0BVgAtKiLIgKBICuACuQFqVAVCAwdAUYgrSwD1GBoNAVYAvSwjJEBUKBrgBzkBY2ISoQInQFWIS0sAZRgdChK8AopIUdiAosC7oC7EJaWICowHKhK8A0pEVeiAqEAV0B1iEtckFUIDzoCigA0iI9RAXChq6AMiAtUkJUIBLoCigG0iINRAUihK6AkiAtYkNUIHLoCigM0iIeRAUEga6A8iAtYkBUQCihdsXj8YyMjCz30ScnJ8+dO7fcrQCCQlqEhaiAgIJ3xev1Njc319bWdnd3V1RUDAwMhP7oDQ0NDz74YATjAfiFtAgFUQFhRQVdo76+3ul0dnR0EFF5efnOnTtNJlN2dnbQDU+cONHT03PDDTcIMCbAUri0nP9q0my/eM+G9XKPo0iICgguyPGK1Wo1m8179uzhbqanp+fl5TU0NAR93C+//LKzs3Pz5s0CzAjgH45aIoGogBiCdKW9vZ2IioqKfEvy8/MdDofNZgu84VNPPfXMM8/odLguAESHtIQHUQGRBNnvWywWvV4fExPjW5KamkpEfX19AbZqbW3dunVrcnKyEBMCBIe0LBeiAuIJ1JWJiYmZmZn4+Hj+Qr1eT0ROp9PfVp9++qndbq+qqhJoQoCQIC2hQ1RAVIG64nA4iCglJWXeBjodEU1NTS25yfT0dHNz8+9+9zvhJgQIlS8tp75wyz0Lu9757AdCVEBMwa8HW5bnn3/+kUceiYuLW9ZWmZmZvq97enp8X4+Ojgo2WcSYGoYwj39r57yz/7j02kef/msqK9cisvPkvPPZD9+Pf78re3WAlxwkxs6TQ4wNQ4zNs2CYsrIyf2te64rH4+nq6uLfcffddycmJhKR1+vlL/d4PEQUGxu7+LEsFsvVq1eNRqPvaObq1atENDU1tWLFCv5JmgWGh4f93cXUSRqmhiHME9D4irXnJz3sXHzMwpNz9OyFdetidmWvZmEYPqbmYWoYYmwe/jD8/Tb/2IB8XXG73fv27ePfUVpampCQEBUVNTg4yF8+PT1N18/eL9DV1fXee+9x73ThMxgMxcXFbW1tYfxnAIRhTYzutp/jfS3z+M6psHOkAmp1rStxcXF2u51/R3R0NBEVFhb29vZ6vV7fFcNDQ0M0/8pjnwceeGDbtm38Ja2trZ9//vmLL7540003iTE9gD94yyQfTtSDlH46v8KFZIHKysozZ8709/ffcccd3BK73Z6VlZWbm7t45ZycnJycHP6S48ePO53O0tJSQWcGCAnSwkFUQGJB3r9SUlJSXFxsMpm4my6Xy2q1NjU1cTdtNpvRaDx06JC4MwKECxcfIyogveDvh29paZmdnW1sbGxvb6+rq2ttbTUajdxdw8PDbrc7jM85BpCMltOCqIAsgl9nvGrVqra2NpfLNT4+Xl1dzf9olqqqqrS0tCVfE+PgXD2wQJsviCEqIJdQP78rKSnJYDAs/ryvgoKCABcQAzBCa0ctiArICJ8LCVqhnbQgKiAvdAU0RAtpQVRAdugKaIu604KoAAvQFdActaYFUQFGoCugRepLC6IC7EBXQKPUlBZEBZiCroB2qSMtiAqwBl0BTVN6WhAVYBC6Alqn3LQgKsAmdAVAkWlBVIBZ6AoAkdLSgqgAy9AVgGuUkhZEBRiHrgD8hP20ICrAPnQFYB6W04KogCKgKwALsZkWRAWUAl0BWAJraUFUQEHQFYClsZMWRAWUBV0B8IuFtCAqoDjoCkAg8qYFUQElQlcAgpArLYgKKBS6AhCc9GlBVEC50BWAkEiZFkQFFA1dAQiVNGlBVEDp0BWAZRA7LYgKqAC6ArA84qUFUQF1QFcAlk2MtCAqoBroCkA4hE0LogJqgq4AhEmotCAqoDLoCkD4Ik8LogLqg64ARCSStCAqoEqhdsXj8YyMjIg6CoBChZcWRAXUKiroGl6v99lnnx0aGjIajb29vU888cSmTZsCbzI2NvarX/1qbm6Ou3nzzTf/4Q9/0OlwbASqxaXl/FeTZvvFezasD7o+ogIqFrwr9fX1Tqezo6ODiMrLy3fu3GkymbKzswNscuTIkdjYWN/N+++/H1EB1VsiLU4n/e//ktO5bnKStm+n5GQqLiZEBdQuSFesVqvZbH7llVe4m+np6Xl5eQ0NDSdOnPC3yfj4+J///Ofe3l4hxwRQgnlp6Wyl/fu55TcS0TvvUHIy1dQc3fYQISqgakEOI9rb24moqKjItyQ/P9/hcNhsNn+bvPHGGxs3bvS9CAagKVxaiv+jwheVnzidtH//Pf/33xAVULcgXbFYLHq9PiYmxrckNTWViPr6+pZc//Lly0eOHHn11Vdvv/32hoaGL7/8UsBZARQhruNY3MDHfu8d+JiOHpVwHACpBerKxMTEzMxMfHw8f6Ferycip9O55CYul2vHjh133XUXEXV2dpaXl1ssFsGGBVCEAwciXQFAyQKdX3E4HESUkpLCX8idgZ+amlpyk5ycnJycHCKanJx85ZVXDh8+vHfv3q6uLu4oB0AT/Pxf1zJWAFCy4NeDhefGG2984oknEhMTDxw4cPjw4WeeeSbAypmZmb6ve3p6fF+Pjo6KNF4YmBqGME9AMg4T299/cwirfWMyzfzyl6JPsxSm/qWIsXmYGoYYm2fBMGVlZf7WvNYVj8fT1dXFv+Puu+9OTEwkIq/Xy1/u8XiIiH8ZcQD333//iRMn+vv7A682PDzs767k5ORQvpE0mBqGME9ATA2z2M2//CXJNyFrTw5T8zA1DDE2D38Y/n6bf2xAvq643e59+/bx7ygtLU1ISIiKihocHOQvn56eputn70OxdevWN998cxmDAyga9yaVM2eCrwagUte6EhcXZ7fb+XdER0cTUWFhYW9vr9fr9b2xcWhoiOZfeRzkG0RF5efnCzYvAPt27w7SlT/+UaJJAOTw0/Vg0fNxCysrK+fm5vgvZNnt9qysrNzc3BC/wQcffFBbWyvgxACsq6nh3le/tOLiQPcCKF+Q96+UlJQUFxebTCbupsvlslqtTU1N3E2bzWY0Gg8dOuRb/+GHH25sbBwfHycij8fz9NNP33vvvQteegtdgPNC0mNqGMI8Ack/zJEjS7wvkoj275f9YEX+J2c+puZhahhibJ7Qhwl+PVhLS0tdXV1jY2N6errZbG5tbTUajdxdw8PDbreb/znHK1as6Ojo6OzszMzMXLlyZV1dXdAPqQRQoeRkamq69oKYxXLi3Xd//f/+H+3ejdMqoAXBu7Jq1aq2tjaXyzU+Pl5dXc3/BMmqqqq0tDT+a2Ktra1Op/Prr7/Oyspau3atKCMDKEVyMtXUUE3Nk319v75+lA+geqG+fyUpKSkpKWnx8oKCggVLkpOTmbowDgAApISPrwcAACH97Mcff5R3grDP6gMAACP4b5OUvysAAKAmeB0MAACEhK4AAICQ0BUAABASugIAAEJCVwAAQEjoCgAACAldAQAAIaErAAAgJHQFAACEhK4AAICQ2OqKx+Ph/zUXeYU3zOTk5Llz5+Qdxuv1joyMjI2NCT4Gm/OE8S81OTk5NTUl0jwLyPVTvdzvK+pzEvowEvz0sjZPeD/AYuxnwhtmMVa64vV6m5uba2tru7u7KyoqBgYGgm4yNjaWn59vvG7btm1er1euYXwaGhoefPBBQcYIb5jTp0/fcccd27dvv/POOysqKr799lsBhwljno6Ojk2bNnHz7NixQ9hfhjD+pSYmJg4ePLh582aHwyHgJEKNJ8v3FfU5WdYwov60hDEPa79NPoLvZ8IYJtAe+Ec2PP744//2b//Gff3Xv/719ttvdzgcgTf5/e9/X8jzxhtvyDgM5913383IyDAYDEJNstxhPvnkk4ceeuijjz46c+bMo48+mpGR8Zvf/EbAYZY7zwcffFBSUvLaa691d3dz89x+++1//etfZRnmxx9//Pzzz48ePbp58+aMjIyzZ88KNYZQ48nyfcV+TkIfRuyfluXOw9pvk48Y+5kwhgmwB2aiK2fPns3IyPjwww99S/793//9nnvuCbDJpUuXBP83DnsYzt///vff/OY3//Ef/yHgv/dyh1kQ1+3bt2dkZAg1TBjz/Od//uc//vEP383f/e53GRkZ9fX1sgzj89///d8SdCXs8WT5viI9J8saRtSfljDmYe23iSPGfiaMYQLvgZl4Hay9vZ2IioqKfEvy8/MdDofNZvO3yRtvvLFx48a5uTkWhuE89dRTzzzzDP/vNEs/THV1Nf9mdnZ2YmKiXPN4PJ6ampo1a9b4ljz66KNEdOnSJemH4YuKCvXPpEYi7PFk+b4iPSehDyP2T8ty5yHGfpt8xNjPhDFM4D0wE12xWCx6vT4mJsa3JDU1lYj6+vqWXP/y5ctHjhx59dVXb7/99oaGhi+//FLGYTitra1bt24V/A8whzeMz4ULF5588km55omOjt60aRN/yZo1a1auXLl69Wrph5GeXOMx9bSEPozYPy3LnWcxeX+bOCLtZ5Y7TNA9sPxdmZiYmJmZiY+P5y/U6/VE5HQ6l9zE5XLt2LHjrrvuIqLOzs7y8nKLxSLXMET06aef2u32qqoqQWaIcBifU6dOFRQUlJaWMjIPEY2NjV25cqW8vJyFYUQl13hMPS0RDiPgT0vk87Dw2yTSfiaMYYLugaV4QSAw7hKUlJQU/kLuKM/fVY85OTk5OTlENDk5+corrxw+fHjv3r1dXV1cYCUeZnp6urm5ubW1NcJvLcgwnHPnznV2dh4/fnzlypW33nrrrl275J3Hp7u722AwbNmyhYVhRCXXeEw9LREOI+BPSyTzMPLbJN5+Joxhgu6B5T9eicSNN974xBNPNDU1Xbly5fDhw7LM8Pzzzz/yyCNxcXGyfPclbdiwYefOnRUVFVeuXNm3b59I17kv19TU1Ntvv/3cc8/JPQgoADs/LYz8NjG4nyH/e2Cpj1c8Hk9XVxd/Cdf/BW898Xg8RBQbGxvKY95///0nTpzo7++XfhiLxXL16lWj0eir+tWrV4loampqxYoV/BcrJRjGJzo62mAwGAyGjIyM55577q233jIYDKFPIvg8nAMHDjz++OPhvTQsxo+NqLgTvNKPJ9f3FXyYSH5ahJ1HkN+mCIcRcD8T+TCLLd4DS90Vt9u9b98+/pJdu3ZFRUUNDg7yF05PT9P1E0eh2Lp165tvvin9MF1dXe+9915HR8eC5QaDobi4uK2tTcphFtu9e/dLL73kdrtDH0OkeY4dO5aTkxP2y9Mi/diIJyEhQZbx5Pq+wg4T4U+L4PNwIvltinAYAfczkQ+zpAV7YKm7EhcXZ7fbFywsLCzs7e31er2+i+eGhoZo/kVvgUVFReXn50s/zAMPPLBt2zb+ktbW1s8///zFF1+86aabJB5mMZ1Ol5+fH96xs4DznD59emJiYu/evWGMIfgw0tDpdLKMJ9f3FXCYyH9ahJ2Hv3nYv00RDiPgfibyYZa0YA8sw/mV6PmIqLKycm5ujn8YZbfbs7KycnNzQ3zMDz74oLa2VvphuP+r4lu/fv2KFStKS0vDOFgW45lxOBxhn2kUZJ7Tp09/8skn/N3E7Ozsxx9/LMswUpJrPKaeluUOI9RPi1DzLBDJb1Mkwwi7n4lwmCUt2AMzcd6+pKSkuLjYZDJxN10ul9VqbWpq8q1gs9mMRuOhQ4e4mw8//HBjY+P4+DgReTyep59++t57783MzJRlGFEtaxiv1/vCCy+cOHHCd+/BgwfLysqMRqMs8xDRqVOn6uvrZ2dnn76uoaGhvLxckP/JCvtfinsd+cqVK5HPEMl4snxfiZ+TZQ0j6k/LcueR/bdJyv3McocJugeW/zpjTktLS11dXWNjY3p6utlsbm1t5f/7DQ8Pu91u36dsrlixoqOjo7OzMzMzc+XKlXV1dQveUSXlMGILfZi5ubmurq7vvvvupZde2rhx4+Tk5ObNmx977DG55nn//ffr6uqIaMGpr4yMjOzsbImH4Vy8ePGjjz7irrV//fXXL1++vHXrVkEmCWM8Wb6v9M9JiMNI8NOyrHlk/22SeD+zrGGC74EF/ISZyDmdTpvNNjc3t/iugYGBmZkZ382//e1vf/rTny5dusTCMBIIcZi5ublPPvnkT3/609dff83CPNJgapjFAowny/eV5TlhapgQ55H9t4nlf6nAe+Cf/fjjj5L1EAAAVI+J8ysAAKAa/x9/o6z9ZMUpJgAAAABJRU5ErkJggg==\",\"relationship\":null},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image4.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image5.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image6.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFind the number of diagonals in a n sided polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = count_diagonals(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx =12;\r\ny_correct =54;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =4;\r\ny_correct =2;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n\r\nx =3;\r\ny_correct =0;\r\nassert(isequal(count_diagonals(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3469688,"edited_by":3469688,"edited_at":"2024-05-02T19:23:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":29,"test_suite_updated_at":"2024-05-02T19:23:51.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2024-05-02T18:52:26.000Z","updated_at":"2026-03-15T05:04:28.000Z","published_at":"2024-05-02T19:23:51.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the number of diagonals in a n sided polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52854,"title":"Poly2mask, drawpolygon or patch","description":"Recently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\r\nvertexes coordinates is given as follow:\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nTips: patch is the answer!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 183px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91.5px; transform-origin: 407px 91.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003evertexes coordinates is given as follow:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ex = [0 1 1 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003ey = [0 0 1 1];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTips: patch is the answer!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function Output = Plot_polygon(x,y)\r\nbw = poly2mask(x,y,256,256);\r\nimshow(bw)\r\n\r\nmy_vertices = [x;y];\r\nh = drawpolygon('Position',my_vertices,'LineWidth',1,'Color','cyan');\r\n\r\npatch(x,y,'cyan')\r\n\r\nOutput = 'poly2mask';\r\nend","test_suite":"%%\r\nx = [0 1 1 0];\r\ny = [0 0 1 1];\r\nassert(isequal(Plot_polygon(x,y),'patch'));\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1133393,"edited_by":427930,"edited_at":"2024-07-08T18:22:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":20,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-03T05:53:41.000Z","updated_at":"2026-03-02T13:59:55.000Z","published_at":"2021-10-03T05:53:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecently, I tried to plot a polygon in matlab, and I found there is a lot of embedded function that can be used. However, some functions will plot points at vertexes, it is really disgusting. Try to use different embedded functions given in the title and find their difference!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003evertexes coordinates is given as follow:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex = [0 1 1 0];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [0 0 1 1];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTips: patch is the answer!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":43034,"title":"angle in regular polygon","description":"Make a function which returns measure of interior angle in x-side regular polygon. x is as input.\r\nPlease pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\r\n\r\nif x=3 its triangle and angle is 60 degrees\r\nx=4 -\u003e angle = 90 degrees","description_html":"\u003cp\u003eMake a function which returns measure of interior angle in x-side regular polygon. x is as input.\r\nPlease pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\u003c/p\u003e\u003cp\u003eif x=3 its triangle and angle is 60 degrees\r\nx=4 -\u0026gt; angle = 90 degrees\u003c/p\u003e","function_template":"function y = pol_angle(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 60;\r\nassert(isequal(pol_angle(x),y_correct))\r\n%%\r\nx = 4;\r\ny_correct = 90;\r\nassert(isequal(pol_angle(x),y_correct))\r\n%%\r\nx = 5;\r\ny_correct = 108;\r\nassert(isequal(pol_angle(x),y_correct))\r\n\r\n%%\r\nx = 6;\r\ny_correct = 120;\r\nassert(isequal(pol_angle(x),y_correct))","published":true,"deleted":false,"likes_count":28,"comments_count":0,"created_by":90955,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":215,"test_suite_updated_at":"2016-10-07T08:18:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-05T08:26:32.000Z","updated_at":"2026-02-16T12:26:33.000Z","published_at":"2016-10-05T08:26:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMake a function which returns measure of interior angle in x-side regular polygon. x is as input. Please pay attention, that 1 and 2 side polygon don't exist, so if input is 1 or 2 return 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eif x=3 its triangle and angle is 60 degrees x=4 -\u0026gt; angle = 90 degrees\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45178,"title":"An n-sided regular polygon is drawn within a circle whose radius is 'r', what will be the area of the polygon?","description":"area of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 21px; transform-origin: 407px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.5px 8px; transform-origin: 376.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003earea of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y=poly(n,r)\r\ny=n\r\nend","test_suite":"\r\n%%\r\nn = 6;\r\nr = 6;\r\ny_correct = 93.5307;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 8;\r\nr = 6;\r\ny_correct = 101.8234;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 11;\r\nr = 7;\r\ny_correct = 145.7027;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n\r\n%%\r\nn = 13;\r\nr = 13;\r\ny_correct = 510.4984;\r\nassert(abs(poly(n,r) - y_correct) \u003c 1e-4);\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":39,"test_suite_updated_at":"2021-12-25T10:22:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-10-18T23:23:26.000Z","updated_at":"2026-02-18T09:44:32.000Z","published_at":"2019-10-18T23:55:49.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003earea of a polygon is p*a/2. where, p is the perimeter and a is the apothem i.e. the normal distance from center to any of the sides of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":45196,"title":"Determine whether a given point is inside or outside a polygon","description":"A closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\r\nIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\r\nHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 186px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 93px; transform-origin: 407px 93px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361px 8px; transform-origin: 361px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function InOut = inOrOut(p,r)\r\n% inOrOut() Determines whether point r is inside (InOut = 1) or \r\n% outside (InOut = 0) polygon p\r\n    InOut = 0;\r\nend\r\n","test_suite":"p = [0,0; 0,100; 5,10; 10,100; 15,20; 20,100; 25,30; 30,100; ...\r\n    35,40; 40,100; 45,50; 50,100; 50,0; 0,0];\r\n%%\r\nr = [44.28, 60.99];\r\np = [0,0; 0,100; 5,10; 10,100; 15,20; 20,100; 25,30; 30,100; ...\r\n    35,40; 40,100; 45,50; 50,100; 50,0; 0,0];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [38.33, 57.67];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [0.98, 23.99];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [27.07, 95.94];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [ -7.45, 7.14];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [43.19, 2.87];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [19.39, 16.79];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [48.72, 71.27];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [-6.42, 68.20];\r\ny_correct = 0;\r\nassert(inOrOut(p,r) == y_correct);\r\n%%\r\nr = [20.03, 47.11];\r\ny_correct = 1;\r\nassert(inOrOut(p,r) == y_correct);\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":2,"created_by":8580,"edited_by":223089,"edited_at":"2022-09-09T08:55:17.000Z","deleted_by":null,"deleted_at":null,"solvers_count":33,"test_suite_updated_at":"2022-09-09T08:55:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-11-06T23:11:51.000Z","updated_at":"2026-01-23T09:40:37.000Z","published_at":"2019-11-06T23:20:58.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA closed polygon may be described by an N x 2 array of nodes, where the last node and the first node are the same. Each row of the array is a 2-element vector giving the x and y coordinates of a node. The polygon is described by straight-line segments that go from node to node.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem, we provide you with a polygon p of this type, and with a number of points r, each having an x and y coordinate. You are to determine whether each point falls inside or outside the polygon. If the point is inside the polygon, return the value 1. If outside, return the value 0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINT: One way to solve this is to find a point 'p_test' that is outside of the polygon, and then to count the number of times that a line from 'r' to 'p_test' crosses the sides of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60982,"title":"Mesh the square with triangles","description":"Problem statement\r\n\r\nAn square is a regular polygon with 4 vertices and 4 edges.\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh, that is to say give one triangulation T of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 995.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 497.617px; transform-origin: 408px 497.617px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.608px 8px; transform-origin: 183.608px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.275px 8px; transform-origin: 192.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh, that is to say give one triangulation \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183.583px 8px; transform-origin: 183.583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 340.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 170.25px; text-align: left; transform-origin: 385px 170.25px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"447\" height=\"335\" style=\"vertical-align: baseline;width: 447px;height: 335px\" 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sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_square()\r\n  T = 1;\r\nend","test_suite":"%% Test every possible solutions\r\nT_correct1 = [1 2 3;\r\n              3 4 1];\r\n\r\nT_correct2 = [2 3 4;\r\n              1 2 4];\r\n\r\nassert(isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_square(),2)),sortrows(sort(T_correct2,2))))\r\n\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_square.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":149128,"edited_by":149128,"edited_at":"2025-07-26T07:45:03.000Z","deleted_by":null,"deleted_at":null,"solvers_count":34,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T16:29:27.000Z","updated_at":"2026-02-10T17:10:21.000Z","published_at":"2025-07-23T16:40:49.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn square is a regular polygon with 4 vertices and 4 edges.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh, that is to say give one triangulation \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of, this square.To do so, you will list the triangles/rows in a matrix of triangles, T.The row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"335\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"447\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh processing\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh generation 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the pentagon (with the minimum number of triangles)","description":"Problem statement\r\n\r\nAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set V, corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\r\n\r\nV = [1           0            0;\r\n     cos(2*pi/5) sin(2*pi/5)  0;\r\n     cos(4*pi/5) sin(4*pi/5)  0;\r\n     cos(4*pi/5) sin(-4*pi/5) 0;\r\n     cos(2*pi/5) sin(-2*pi/5) 0];\r\n\r\nA triangulated mesh T (stands for triangles here) -or a triangulation- is simply a N x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where N is the number of triangles. \r\n\r\nYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, F. The row order of the triangles in the list doesn't matter.\r\n\r\nExample\r\nThe first triangle here can be [1, 2, 3] if counterclockwise oriented.\r\n\r\n\r\n\r\n\r\nTip\r\nBeware to avoid self intersecting triangles.\r\n\r\nForbidden functions / expressions\r\nregexp\r\nassignin\r\nstr2num\r\necho\r\n\r\nSee also\r\nMesh processing\r\nMesh generation toolbox","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1278.4px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 639.2px; transform-origin: 408px 639.2px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63.0083px 8px; transform-origin: 63.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eProblem statement\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 327.525px 8px; transform-origin: 327.525px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 6.09167px 8px; transform-origin: 6.09167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eV,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.2417px 8px; transform-origin: 48.2417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 102.167px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 405px 51.0833px; transform-origin: 405px 51.0833px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eV = [1           0            0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(2*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(4*pi/5)  0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 123.2px 8.5px; tab-size: 4; transform-origin: 123.2px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(4*pi/5) sin(-4*pi/5) 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 405px 10.2167px; text-wrap-mode: nowrap; transform-origin: 405px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 127.05px 8.5px; tab-size: 4; transform-origin: 127.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e     cos(2*pi/5) sin(-2*pi/5) 0];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.1833px 8px; transform-origin: 64.1833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA triangulated mesh \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4.275px 8px; transform-origin: 4.275px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 176.983px 8px; transform-origin: 176.983px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 132.633px 8px; transform-origin: 132.633px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.05833px 8px; transform-origin: 5.05833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4px 8px; transform-origin: 84.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the number of triangles. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384.442px 8px; transform-origin: 384.442px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.25833px 8px; transform-origin: 7.25833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eF. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.575px 8px; transform-origin: 168.575px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe row order of the triangles in the list doesn't matter.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.7833px 8px; transform-origin: 28.7833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eExample\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92.9583px 8px; transform-origin: 92.9583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe first triangle here can be [\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.3833px 8px; transform-origin: 21.3833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1, 2, 3]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 89.8583px 8px; transform-origin: 89.8583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if counterclockwise oriented.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 339.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 169.75px; text-align: left; transform-origin: 385px 169.75px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"445\" height=\"334\" style=\"vertical-align: baseline;width: 445px;height: 334px\" 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.3667px 8px; transform-origin: 10.3667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eTip\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.092px 8px; transform-origin: 131.092px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBeware to avoid self intersecting triangles.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.308px 8px; transform-origin: 114.308px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eForbidden functions / expressions\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 392px 40.8667px; transform-origin: 392px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 21.4px 8px; transform-origin: 21.4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eregexp\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.6833px 8px; transform-origin: 25.6833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eassignin\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 25.2833px 8px; transform-origin: 25.2833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003estr2num\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 364px 10.2167px; text-align: left; transform-origin: 364px 10.2167px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 15.175px 8px; transform-origin: 15.175px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eecho\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.3917px 8px; transform-origin: 28.3917px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSee also\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/cody/groups/57483\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh processing\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://fr.mathworks.com/matlabcentral/fileexchange/85173-mesh-generation-toolbox?s_tid=prof_contriblnk\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMesh generation toolbox\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function T = mesh_the_pentagon()\r\n  T = 1;\r\nend","test_suite":"%%\r\nT_correct1 = [1 2 3;\r\n              1 3 4;\r\n              1 4 5];\r\n\r\nT_correct2 = [2 3 4;\r\n              2 4 5;\r\n              2 5 1];\r\n\r\nT_correct3 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct4 = [3 4 5;\r\n              3 5 1;\r\n              3 1 2];\r\n\r\nT_correct5 = [5 1 2;\r\n              5 2 3;\r\n              5 3 4];\r\n\r\n% Check every possible solutions\r\nassert(isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct1,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct2,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct3,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct4,2)))...\r\n     | isequal(sortrows(sort(mesh_the_pentagon(),2)),sortrows(sort(T_correct5,2))))\r\n\r\n%% Forbidden functions\r\nfiletext = fileread('mesh_the_pentagon.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'str2num') || contains(filetext, 'assignin') || contains(filetext, 'echo')\r\nassert(~illegal);","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":149128,"edited_by":149128,"edited_at":"2025-08-13T05:29:08.000Z","deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":"2025-08-13T05:29:08.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-07-23T12:59:46.000Z","updated_at":"2026-02-10T17:07:57.000Z","published_at":"2025-07-23T15:54:36.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eProblem statement\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn pentagon is a regular polygon with 5 vertices and 5 edges. Here below is an example of the vertex set \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eV,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e corresponding to the XYZ coordinates column vectors of a pentagon included in the unit circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[V = [1           0            0;\\n     cos(2*pi/5) sin(2*pi/5)  0;\\n     cos(4*pi/5) sin(4*pi/5)  0;\\n     cos(4*pi/5) sin(-4*pi/5) 0;\\n     cos(2*pi/5) sin(-2*pi/5) 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA triangulated mesh \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (stands for triangles here) -or a triangulation- is simply a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x 3 matrix of positive integers where each row contains the vertex indices of a triangle, and where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the number of triangles. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task here is to mesh this pentagon with the minimum possible number of triangles. To do so, you will list the pentagons/rows in a matrix of faces, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eF. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThe row order of the triangles in the list doesn't matter.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first triangle here can be [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1, 2, 3]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if counterclockwise oriented.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"334\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"445\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTip\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBeware to avoid self intersecting triangles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eForbidden functions / expressions\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eregexp\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eassignin\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003estr2num\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eecho\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://fr.mathworks.com/matlabcentral/cody/groups/57483\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMesh 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many ways?","description":"Create a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?","description_html":"\u003cp\u003eCreate a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?\u003c/p\u003e","function_template":"function y = how_many(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 3;\r\ny_correct = 1;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 4;\r\ny_correct = 2;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 6;\r\ny_correct = 14;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 8;\r\ny_correct = 132;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 9;\r\ny_correct = 429;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 12;\r\ny_correct = 16796;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 15;\r\ny_correct = 742900;\r\nassert(isequal( how_many(n),y_correct))\r\n%%\r\nn = 20;\r\ny_correct =  477638700;\r\nassert(isequal( how_many(n),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":363598,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":21,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-01-30T20:37:23.000Z","updated_at":"2026-03-14T18:50:24.000Z","published_at":"2020-01-30T20:38:45.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a program to determine in how many ways can a regular n-gon be divided into n-2 triangles?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":56413,"title":"how to determine is a point is inside, on or outside a polygon?","description":"design function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(232, 230, 227); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(232, 230, 227); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 84px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 42px; transform-origin: 407px 42px; vertical-align: baseline; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003edesign function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function dist = pointPolygonTest(contour,point,meatureDist)\r\n% Brief: how to determine is a point is inside, on or outside a polygon?\r\n% Details:\r\n%    The function determines whether the point is inside a contour, outside, or\r\n% lies on an edge (or coincides with a vertex). It returns positive (inside),\r\n% negative (outside), or zero (on an edge) value, correspondingly. When\r\n% measureDist=false , the return value is +1, -1, and 0, respectively.\r\n% Otherwise, the return value is a signed distance between the point and\r\n% the nearest contour edge.\r\n% \r\n% Syntax:  \r\n%     dist = pointPolygonTest(contour,point,meatureDist)\r\n% \r\n% Inputs:\r\n%    contour - [n,2] size,[double] type,Polygonal order vertices.\r\n%    points - [1,2] size,[double] type,Coordinate points of the query.\r\n%    meatureDist - [1,1] size,[logical] type,Whether meature distances.\r\n%\r\n% Outputs:\r\n%    dist - [m,1] size,[double] type,Description\r\n% \r\n% Example: \r\n%    None\r\n% \r\n% See also: None\r\n\r\narguments\r\n    contour (:,2) {mustBeNumeric}\r\n    point (1,2) {mustBeNumeric}\r\n   meatureDist (1,1) logical = false\r\nend\r\n\r\nassert(size(contour,1)\u003e=3,\"contour at least 3 vertices\");\r\n\r\nend\r\n\r\n","test_suite":"%% test\r\nL = linspace(0,2*pi,6);\r\nxv = cos(L)';\r\nyv = sin(L)';\r\nrng default\r\nxq = randn(250,1);\r\nyq = randn(250,1);\r\npoints = [xq,yq];\r\ndists = inf(size(points,1),1);\r\nfor i = 1:size(points,1)\r\n    dists(i) = pointPolygonTest([xv,yv],points(i,:));% use pointPolygonTest function determine points whether inside polygon \r\n    assert(dists(i)==1||dists(i)==-1||dists(i)==0)\r\nend\r\nassert(sum(dists==1)==80)\r\nassert(sum(dists==0)==0)\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":199546,"edited_by":199546,"edited_at":"2022-10-23T11:55:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":"2022-10-23T11:55:11.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-23T10:27:43.000Z","updated_at":"2025-10-18T10:21:59.000Z","published_at":"2022-10-23T10:27:43.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edesign function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside),negative (outside), or zero (on an edge) value, correspondingly. When measureDist=false , the return value is +1, -1, and 0, respectively. Otherwise, the return value is a signed distance between the point and the nearest contour edge.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":42821,"title":"Polygon division","description":"Given the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\r\n\r\n1. The division is done by drawing straight lines between existing vertices.\r\n\r\n2. The triangles are made of existing vertices.\r\n\r\n3. Different orientations of a similar solution are counted as different solutions.\r\n\r\nAssume that n is a positive integer greater than 2.\r\n\r\nExample 1:\r\n\r\nn = 4 (square)\r\n\r\nw = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\r\n\r\nExample 2:\r\n\r\nn = 5 (pentagon)\r\n\r\nw = 5","description_html":"\u003cp\u003eGiven the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\u003c/p\u003e\u003cp\u003e1. The division is done by drawing straight lines between existing vertices.\u003c/p\u003e\u003cp\u003e2. The triangles are made of existing vertices.\u003c/p\u003e\u003cp\u003e3. Different orientations of a similar solution are counted as different solutions.\u003c/p\u003e\u003cp\u003eAssume that n is a positive integer greater than 2.\u003c/p\u003e\u003cp\u003eExample 1:\u003c/p\u003e\u003cp\u003en = 4 (square)\u003c/p\u003e\u003cp\u003ew = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\u003c/p\u003e\u003cp\u003eExample 2:\u003c/p\u003e\u003cp\u003en = 5 (pentagon)\u003c/p\u003e\u003cp\u003ew = 5\u003c/p\u003e","function_template":"function w = polydiv(n)\r\n  w = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('polydiv.m');\r\nassert(isempty(strfind(filetext,'str')))\r\n\r\n%%\r\nn = 3;\r\nw_correct = 1;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 4;\r\nw_correct = 2;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 5;\r\nw_correct = 5;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 8;\r\nw_correct = 132;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 11;\r\nw_correct = 4862;\r\nassert(isequal(polydiv(n),w_correct))\r\n\r\n%%\r\nn = 15;\r\nw_correct = 742900;\r\nassert(isequal(polydiv(n),w_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2016-04-30T20:32:42.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2016-04-24T15:28:47.000Z","updated_at":"2026-01-19T17:32:36.000Z","published_at":"2016-04-24T15:28:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the number of vertices (or sides), n, of a planar convex polygon, return the number of ways, w, in which you can divide the polygon into triangles, such that:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1. The division is done by drawing straight lines between existing vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2. The triangles are made of existing vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3. Different orientations of a similar solution are counted as different solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that n is a positive integer greater than 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 4 (square)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = 2 (you can draw a line between vertices 1 and 3, as well as a line between vertices 2 and 4)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 5 (pentagon)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ew = 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":60999,"title":"Total Area Covered by Overlapping Polygons","description":"Given a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\r\np1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\r\np2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\r\n\r\nThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 617.571px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.997px 308.778px; transform-origin: 407.997px 308.785px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 425.554px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 212.77px; text-align: left; transform-origin: 385px 212.777px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"560\" height=\"420\" style=\"vertical-align: baseline;width: 560px;height: 420px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42.017px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21.0085px; text-align: left; transform-origin: 385px 21.0085px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. This comes out to 0.24 units.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.0085px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.4972px; text-align: left; transform-origin: 385px 10.5043px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = lapgon(P)\r\n    A=[];\r\nend","test_suite":"%% Test Case 1\r\nP{1}=[0.2,0.2;0.5,0.2;0.5,0.5;0.2,0.5];\r\nP{2}=[0.4,0.4;0.8,0.4;0.8,0.8;0.4,0.8];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.240000;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 2\r\nP{1}=[0.1783,0.2985;0.3849,0.6214;0.8407,0.8054];\r\nP{2}=[0.1112,0.8761;0.8927,0.4062;0.6089,0.0228];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.244813;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 3\r\nP{1}=[0.5967,0.2763;0.3286,0.2200;0.7586,0.4690];\r\nP{2}=[0.4809,0.5456;0.5589,0.2875;0.5021,0.3001;0.2000,0.7725];\r\nP{3}=[0.4260,0.0843;0.0140,0.4489;0.5535,0.8630;0.4133,0.3718;0.8033,0.0733];\r\nP{4}=[0.0169,0.7757;0.1636,0.9072;0.7480,0.9785;0.2718,0.4179;0.8687,0.2735;0.0599,0.1064];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.459378;\r\n\r\nassert(isequal(A,A_correct))\r\n\r\n%% Test Case 4\r\ntheta=0:0.01:2*pi;\r\nP{1}(:,1)=0.35*cos(theta)+0.6;\r\nP{1}(:,2)=0.22*sin(theta)+0.5;\r\nP{2}=[0.1083,0.3508;0.7413,0.9426;0.2748,0.0933];\r\n\r\nA=round(lapgon(P),6);\r\nA_correct=0.307282;\r\n\r\nassert(isequal(A,A_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":4910069,"edited_by":4910069,"edited_at":"2025-09-12T18:34:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2025-09-12T18:34:35.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2025-09-12T17:15:15.000Z","updated_at":"2026-03-19T16:19:38.000Z","published_at":"2025-09-12T18:28:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a variable length set of polygon vertex coordinates, compute the total area covered. For example, take two polygons with the following vertex coordinates:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep1=[0.2,0.2; 0.5,0.2; 0.5,0.5; 0.2,0.5];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ep2=[0.4,0.4; 0.8,0.4; 0.8,0.8; 0.4,0.8];\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"420\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"560\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe total area covered is the area of the first polygon plus the area of the second polygon minus the overlap. 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61081,"title":"Slicing the area of a regular polygon","description":"Given the area, A, of a regular polygon with n sides, each of length s, consider its decomposition in congruent isosceles triangles of base s and heigth h. Find the rectangle, with dimensions L×h, which covers all n triangles in their adjacent positions (n\u003e3, cf. figure below). Complete the problem by determining the area, A_r, of the rectangle.\r\nHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\r\ninput: (A, n)\r\noutput: y = [L h A_r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 575.8px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 287.9px; transform-origin: 408px 287.9px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 31.5px; text-align: left; transform-origin: 385px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a regular polygon with \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e sides, each of length \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and heigth \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Find the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which covers all \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e triangles in their adjacent positions (\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u0026gt;3,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e cf. figure below). Complete the problem by determining the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, n)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey = [L h A_r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 413.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 206.9px; text-align: left; transform-origin: 385px 206.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"501\" height=\"408\" style=\"vertical-align: baseline;width: 501px;height: 408px\" 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\" alt=\"Slicing square (n=4)\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = slicing(A,n)\r\n  y = [L h A_r];\r\nend","test_suite":"%%\r\nA = 16;\r\nn = 4;\r\ny_correct = [10 2 20];\r\nassert(isequal(slicing(A,n),y_correct))\r\n\r\n%%\r\nA = 20;\r\nn = 5; \r\ny_correct = [10.22849568767431 2.34638608968871 24];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nfiletext = fileread('slicing.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 20;\r\nn = 6; \r\ny_correct = [7*sqrt(10*3^(-3/2)) sqrt(10*3^(-1/2)) 70/3];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n\r\n%%\r\nA = 32;\r\nn = 8; \r\ny_correct = [18*sqrt(sqrt(2)-1) 2/sqrt(sqrt(2)-1) 36];\r\ntolerance = 1e-13;\r\nassert(all(abs(slicing(A,n)-y_correct)\u003ctolerance))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-11-19T14:59:52.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-11-18T11:18:12.000Z","updated_at":"2026-03-20T13:59:51.000Z","published_at":"2025-11-19T14:59:52.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a regular polygon with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e sides, each of length \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, consider its decomposition in congruent isosceles triangles of base \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and heigth \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Find the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which covers all \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e triangles in their adjacent positions (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u0026gt;3,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e cf. figure below). Complete the problem by determining the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: Consider that we are slicing the polygon into triangular slices and put them into the rectangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey = [L h A_r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"408\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"501\\\"/\u003e\u003cw:attr 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PCkpKR+/fpNnTr1+PHjxoxksb5/8sknGRkZe/fuHTVq1M9//vPCwsInn3zyrbfeUi/xPp/vrbfemjhx4jfffDNq1Kjx48fX1dWtXr36ySef9Hq9sqfTkc/nW7Nmzc6dO2UPoq/9+/dPnDhxw4YNSUlJEyZM6Natm8J/uevWrZs0aZL2TP7FL37h9XpnzJgxd+7c6upq2aP5TUlJycKFC0+fPt1kvaam5re//e3MmTNramrGjx8/ePDgnJycCRMm7N2714ixfNZRXFw8bty4IUOG7NmzR1txu92jR48eOnTooUOH5M7md4cOHRo6dOjo0aPz8/O1lYqKijlz5iQmJr722mtyZ9PVZ5991rdv38TExJtuuumHH36QPY4uKioqHn300b59+27atKmurs7n850/f/65555LTEx87733ZE/nZwUFBSNHjmz8si0uLr7vvvsGDhy4e/duubP5y/fffz9u3LjExMTExMRt27Y1vsvlcg0cOPDBBx8sLS3VVv75z3/27dv30Ucfraio0HswK+3fv/7664MHD44dO3bQoEHaSkJCwvTp04uKij799FO5s/ndjh07Tp069eCDDyYmJmorYWFhv/zlL2NjY3fu3FlWViZ3PJ2cOnXq1Vdf7d+//09/+lPZs+joyy+/zMnJyczMvOOOOwICAoQQwcHBEydOjIyM3Ldvn2IHLoqKioqLi2+88cb6l21UVNTIkSPLysoM2sPqSTv2Mm7cuKNHjw4YMKDJvT6fb8uWLefOnXvkkUciIyO1xVtvvfX222/Py8s7evSo3uNZqe+7du2qrq5OTU3VXhKafv36xcTE7N69+9y5cxJn87vCwsLY2Nj+/fs3XgwPD+/SpYuskfRWU1OzfPnyU6dOPffcc/UvBiXt3bs3KCho7NixjZ/JAwcO3Ldv36JFi4KCgiTO5ndBQUEOh6O4uLiqqqp+UdugxMTEyJvLPw4ePDh37tygoKDVq1ffcccdTe4tLS3dt29fjx49+vTpU7/ocDiGDh3q9Xq//vprvcezUt8LCwsjIyO1n2tcr3v37mFhYadPn2787FHACy+8sHPnzpSUlMaLX375ZUFBQUJCQnh4uKzB9LNt27aNGzf+6le/ungfpBKfz5efnx8TE3P55Ze/88472ttuCr+/2qdPn9tvv33Hjh2rVq0qKyurra3dunXru+++e8011wwdOlT2dJ0VFBT00EMPbdu2bdiwYRffe+7cueLi4iuuuKJbt26N1y+//HIhxIkTJ/Qezw+/v8kY5eXlzZ5N0bVr1169ep04cUKx/fvFPB7P66+/Hh4efs899zTe96nB4/EsW7Zs+PDhDzzwgGIHKJooLy8vLCysrq5+6aWXXC5XSkpKWlpabm7u6tWrDxw4sHLlSsW+dwkODp47d25MTMzq1atXrlypLd52221z586Nj4+XO1vnDRgwoJXtSFFRUbOHUuPi4iIiIgoLC/UcTQgL9d3n89XU1DR7V2Cglb4L6ZhTp049/fTT+fn5s2fPVmDX00R1dfXKlStLS0ufeeaZsLAwVd9daOzkyZO1tbUffPBBcnKyLXeRrQAABHFJREFUEKKysvKVV15Zt27dn/70pxkzZsiezp9qa2vXr1//17/+NTQ0dMSIEV26dMnNzd22bVtkZOS8efMiIiJkD6ij2traZqsVGBhozBbNMmUMCAhwOJr/16iurs7gYQx2/PjxyZMn79q1a9q0aQ8//LB6m/etW7du3Lhx+vTp11xzjexZjDNt2jQt7kKIsLCwxx57rFevXjk5OWfPnpU7mH99/PHHv//975OTk3NyclasWLFkyZLt27dPmDAhOzt79erVPuXObG5Me+/h4nXtpCkDBrBM38PDw3v06HHxekVFxYkTJ6Kjo1V94/Hzzz/PzMzMz8+fN29eVlZWcHCw7In87Pjx4wsXLrz11lsnTJggexYjaDuV4ODgpKSkxuvR0dFXXXVVcXGxSkcaa2pqNm/eHBQUNH369KioKG0xLCzsqaeeuuaaa/7973+XlJTInVBXsbGxzX6DcurUqbKysp49e+o9gGWOzwghfvKTn3i93h9++GHgwIH1i2fPnq2srIyJiQkNDZU4mx58Pl92dvaLL77YpUuXP/7xj7fccot6O3chxLFjxwoKCgoKCjZv3tzkrrS0tCuuuGLDhg3N/tNuUeHh4QkJCTU1NRdf3aPed6JVVVXFxcXBwcFNXp5hYWHR0dEej6elg65q0N4d9Hg8FRUVjUP/ww8/CCF69eql9wBW6ntycnJwcHBubm7j0h04cKCoqGjIkCHq7d+3bt364osv9ujRY9WqVddee63scfTSs2fPzMzMxivV1dWfffZZZWXl6NGjL7/8cvX+5U5NTV23bl1OTs7IkSPrn8kej+fYsWN9+vTp2rWr3PH8KDQ0NDo6Wqt84/XKysri4mKHw6HklqVeRERE//799+zZ8+2339bvUWpqar744ovIyMjrrrtO9wn0voDKj06ePJmenj5kyJD6y94Uvn51z549Q4YMaXz9qn14vd6JEycqfP2q2+2+5ZZbhgwZsmPHDm1Fuzg5KSlJvetXN23alJSU9MADDxQXF2sr58+ff+2115KSkubPn68diVbDG2+8cfH1q9r12I2/fCOvX7XS/j0uLm7atGkzZ86cNGnSTTfd1KVLl5ycnPLy8tmzZze+fEABNTU1f/nLX7ST+idPntzk3uTk5FdffVXJU+BtIiEh4fnnn585c+bDDz+ckpISHx+fm5t78uTJUaNG3X333bKn87MxY8ZMnDhx7dq1N91007BhwyIjI10uV0FBwaBBg6ZOnar2/l0IkZaWNn78+A8++CA9PX348OEFBQW7du267LLLHn/88bCwML0/u5X6LoRIT0+PjY1dtGjR9u3b6+rqevfuPXPmzDFjxij2LCkuLtYu3S4vLy8vL29yr9Pp9Cl91oEd3HzzzRs2bFi8eLHL5XK5XPHx8fPmzZswYYIBr3mDBQcHz58//4Ybbli5cuWnn35aW1sbHx//3HPPTZw4Ue2TIzXal9+vX781a9Zs3LgxJCRkxIgRL7zwQv3PHdFVAKUAACVZ5vxIAEC7/H9xqHu+j/zRZwAAAABJRU5ErkJggg==\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61091,"title":"Slicing a 4-pointed star polygon","description":"Given the area, A, of a 4-pointed star polygon formed by the rectangle, with dimensions L×2L, and four triangles, with height h from their bases to the vertices, consider the area, A_r, of the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \r\nGiven (A,h), find the 9×2 matrix, M = [A1 a1; A2 a2; ...; A8 a8; A_r/π n], where\r\nin the first row (i=1), A1 stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and a1 stands for the logical 1 if A1 does not exceed the circle's area, A_r, or a1 stands for the logical 0 otherwise;\r\nin the second row (i=2), A2 stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and a2 has the same previous false-true meaning relative to the areas A2 and A_r;\r\nand so on, until last slice of the 4-pointed star polygon;\r\nin the last row (i=9), A_r is the area of the circle, and n stands for the maximum number of slices that their cumulative area does not exceed the circle area.\r\nHint: The slices of the 4-pointed star polygon are not congruent among each other.\r\ninput: (A, h)\r\noutput: M = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 840.862px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 420.425px; transform-origin: 408px 420.431px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eL\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2L\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and four triangles, with height \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eh\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from their bases to the vertices, consider the area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A,h)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e9\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e matrix, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, where\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 143.062px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 71.525px; transform-origin: 391px 71.5312px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the first row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=1)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e does not exceed the circle's area, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e or \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the logical \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e0\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e otherwise;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the second row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=2)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ea2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e has the same previous false-true meaning relative to the areas \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ein the last row \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(i=9)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eA_r\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the area of the circle, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(A, h)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi n]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 484.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 242.4px; text-align: left; transform-origin: 384px 242.4px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"601\" height=\"479\" style=\"vertical-align: baseline;width: 601px;height: 479px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function M = slicing_star(A,h)\r\n  M = x;\r\nend","test_suite":"%%\r\nA = 27;\r\nh = 1;\r\nM_correct = [3 1; 6.75 1; 10.5 1; 13.5 1; 16.5 1; 20.25 0; 24 0; 27 0; 6.25 5];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nA = 36;\r\nh = 2;\r\nM_correct = [3.75 1; 9 1; 14.25 1; 18 1; 21.75 1; 27 1; 32.25 1; 36 1; 12.25 8];\r\nassert(isequal(slicing_star(A,h),M_correct))\r\n\r\n%%\r\nfiletext = fileread('slicing_star.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nA = 68;\r\nh = 1.2;\r\nM_correct = [7.75 1; 17 1; 26.25 1; 34 1; 41.75 1; 51 0; 60.25 0; 68 0; 13.69 5];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n\r\n%%\r\nA = 89;\r\nh = 2.6;\r\nM_correct = [9.5 1; 22.25 1; 35 1; 44.5 1; 54 1; 66.75 1; 79.5 1; 89 0; 26.01 7];\r\nassert(all(isapprox(slicing_star(A,h),M_correct), 'all'))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2025-12-08T13:42:41.000Z","deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-12-03T13:58:16.000Z","updated_at":"2025-12-19T15:03:36.000Z","published_at":"2025-12-08T13:42:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, of a 4-pointed star polygon formed by the rectangle, with dimensions \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eL\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2L\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and four triangles, with height \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eh\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e from their bases to the vertices, consider the area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof the circle that covers the shorter of the two distances between opposite vertices (cf. left figure below) and slice the star polygon by 8 slices (cf. right figure below). \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A,h)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/π n]\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the first row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of one 'blue' slice of the 4-pointed star polygon (cf. right figure), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e does not exceed the circle's area, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e or \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the logical \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e0\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e otherwise;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the second row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=2)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the area of two slices (cumulative sum of 'blue' and 'green' slices by consecutive vertices), and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e has the same previous false-true meaning relative to the areas \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand so on, until last slice of the 4-pointed star polygon;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ein the last row \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(i=9)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA_r\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is the area of the circle, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e stands for the maximum number of slices that their cumulative area does not exceed the circle area.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: The slices of the 4-pointed star polygon are not congruent among each other.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(A, h)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM = [A1 a1; A2 a2; ...; A8 a8; A_r/pi 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/r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you in or are you out?","description":"Given vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \"true\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\r\n\r\nExample:\r\n\r\n % The specified point is the center of the unit square:\r\n xv = [0 1 1 0];\r\n yv = [0 0 1 1];\r\n X = 0.5;\r\n Y = 0.5;\r\n\r\n inside(xv,yv,X,Y) -----\u003e true\r\n","description_html":"\u003cp\u003eGiven vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \"true\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e % The specified point is the center of the unit square:\r\n xv = [0 1 1 0];\r\n yv = [0 0 1 1];\r\n X = 0.5;\r\n Y = 0.5;\u003c/pre\u003e\u003cpre\u003e inside(xv,yv,X,Y) -----\u003e true\u003c/pre\u003e","function_template":"function tf = inside(xv,yv,X,Y)\r\n  tf = maybe;\r\nend","test_suite":"%%\r\nxv = [0 1 0];\r\nyv = [0 0 1];\r\nX = 0.8;\r\nY = 0.8;\r\ntf_correct = false;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n%%\r\nxv = [0 1 1 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 1 1 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 0.25 0.25 0];\r\nyv = [0 0 1 1];\r\nX = 0.5;\r\nY = 0.5;\r\ntf_correct = false;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n\r\n%%\r\nxv = [0 0.25 0.25 0] + 1000;\r\nyv = [0 0 1 1] + 1000;\r\nX = 1000.1;\r\nY = 1000.1;\r\ntf_correct = true;\r\nassert(isequal(inside(xv,yv,X,Y),tf_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":39,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":384,"test_suite_updated_at":"2012-01-31T14:13:38.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-31T14:13:38.000Z","updated_at":"2026-03-29T20:42:27.000Z","published_at":"2012-01-31T15:52:31.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return \\\"true\\\" if the point lies inside (or on the boundary) of the polygon defined by the vertices.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % The specified point is the center of the unit square:\\n xv = [0 1 1 0];\\n yv = [0 0 1 1];\\n X = 0.5;\\n Y = 0.5;\\n\\n inside(xv,yv,X,Y) -----\u003e true]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":194,"title":"Clockwise or Counterclockwise","description":"Given a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\r\n\r\nThe inputs to this function are two vectors *x* and *y* (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\r\n\r\nThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\r\n\r\nExample:\r\n\r\n  x = [-1,-1,1,1];\r\n  y = [-1,1,1,-1];\r\n\r\ndefines a square, the vertices are listed clockwise\r\n\r\n  d_correct = true;\r\n\r\n","description_html":"\u003cp\u003eGiven a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\u003c/p\u003e\u003cp\u003eThe inputs to this function are two vectors \u003cb\u003ex\u003c/b\u003e and \u003cb\u003ey\u003c/b\u003e (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\u003c/p\u003e\u003cp\u003eThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ex = [-1,-1,1,1];\r\ny = [-1,1,1,-1];\r\n\u003c/pre\u003e\u003cp\u003edefines a square, the vertices are listed clockwise\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ed_correct = true;\r\n\u003c/pre\u003e","function_template":"function tf = isSortedClockwise(x,y)\r\n  tf = false;\r\nend","test_suite":"%%\r\nx = [-1,-1,1,1];\r\ny = [-1,1,1,-1];\r\nd_correct = true;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-1,-1,-2,-2];\r\ny = [-1,1,1,-1];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-1,-1,-2,-2];\r\ny = [-1,1,1,-1];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-6,-7,-2,1,1,-2];\r\ny = [4,-7,-13,-11,0,5];\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [-59,-59,-55,-51,-50,-46,-45,-45,-39,-40,-40,-41,-46,-50,-50];\r\ny = [-68,-33, -5,-13,-28,-30,-20,-10, -8,-23,-34,-45,-48,-51,-51];\r\nd_correct = true;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = flip([-59,-59,-55,-51,-50,-46,-45,-45,-39,-40,-40,-41,-46,-50,-50]);\r\ny = flip([-68,-33, -5,-13,-28,-30,-20,-10, -8,-23,-34,-45,-48,-51,-51]);\r\nd_correct = false;\r\nassert(isequal(isSortedClockwise(x,y),d_correct))\r\n\r\n%%\r\nx = [1,1,2,2];\r\ny = [2,1,1,2];\r\nassert(isequal(isSortedClockwise(x,y),false));\r\n\r\n%%\r\nx = flip([1,1,2,2]);\r\ny = flip([2,1,1,2]);\r\nassert(isequal(isSortedClockwise(x,y),true));\r\n\r\n%%\r\nx = [-2,-2,-4,-4];\r\ny = [1,3,1,-1];\r\nassert(isequal(isSortedClockwise(x,y),false));\r\n\r\n%%\r\nx = flip([-2,-2,-4,-4]);\r\ny = flip([1,3,1,-1]);\r\nassert(isequal(isSortedClockwise(x,y),true));\r\n\r\n%%\r\nr=rand(100,15);\r\na=2*pi*rand(100,1);\r\nd=2*(rand(100,1)\u003e.5)-1;\r\nx=r.*cos(a*ones(1,15)+d*2*pi*(0:14)/15)+randn(100,1);\r\ny=r.*sin(a*ones(1,15)+d*2*pi*(0:14)/15)+randn(100,1);\r\nassert(all(arrayfun(@(i)isequal(isSortedClockwise(x(i,:),y(i,:)),d(i)\u003c0),1:100)))\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":3,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":216,"test_suite_updated_at":"2017-12-04T00:52:18.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-01-31T06:39:48.000Z","updated_at":"2026-03-31T15:28:48.000Z","published_at":"2012-02-02T02:42:52.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a list of 2-d points defining the vertices of a polygon, determine whether these points are sorted clockwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe inputs to this function are two vectors\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (with equal size) containing the x- and y- coordinates of the polygon vertices, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function should return true when sorted clockwise, and false when sorted counterclockwise (the polygon vertices will always be sorted either way).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[x = [-1,-1,1,1];\\ny = [-1,1,1,-1];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003edefines a square, the vertices are listed clockwise\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[d_correct = true;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44694,"title":"Monte Carlo integration:  area of a polygon","description":"The area of a polygon (or any plane shape) can be evaluated by \u003chttps://www.mathworks.com/matlabcentral/cody/problems/179 Monte Carlo integration\u003e.  The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape.  That is illustrated schematically below for a circle.  \r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\u003e\u003e\r\n\r\n^\r\n\r\n*Steps:*\r\n\r\n# Define a 2D region within which to sample points.  In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.  \r\n# By a 'random' process generate coordinates of a point within the bounding box.  In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed.  _Other schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon)._\r\n# Determine \u003chttps://www.mathworks.com/matlabcentral/cody/problems/198 whether the sampled point is inside or outside the polygon\u003e.  _Due to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null._  \r\n# Repeat steps 2–3 |N| times.  \r\n# Based upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.  \r\n\r\nInputs to your function will be |N|, the number of points to sample, and |polygonX| \u0026 |polygonY|, which together constitute \u003chttps://www.mathworks.com/matlabcentral/cody/problems/194 an ordered list of polygon vertices\u003e.  |N| will always be a positive integer.  |polygonX| \u0026 |polygonY| will always describe a single, continuous outline;  however, the polygon may be self-intersecting.  \r\n\r\nFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant.  A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\u003e\u003e\r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\u003e\u003e\r\n\r\n^\r\n\r\nEXAMPLE\r\n\r\n % Input\r\n N = 1000\r\n polygonX = [1 0 -1  0]\r\n polygonY = [0 1  0 -1]\r\n % Output\r\n A = 2.036\r\n\r\nExplanation:  the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°.  The exact area is hence 2.  As the value of |N| is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon).  \r\nOf course, if the code were run again then a slightly different value of |A| would probably be returned, such as |A|=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.  ","description_html":"\u003cp\u003eThe area of a polygon (or any plane shape) can be evaluated by \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/179\"\u003eMonte Carlo integration\u003c/a\u003e.  The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape.  That is illustrated schematically below for a circle.\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/2/20/MonteCarloIntegrationCircle.svg/247px-MonteCarloIntegrationCircle.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003e\u003cb\u003eSteps:\u003c/b\u003e\u003c/p\u003e\u003col\u003e\u003cli\u003eDefine a 2D region within which to sample points.  In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/li\u003e\u003cli\u003eBy a 'random' process generate coordinates of a point within the bounding box.  In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed.  \u003ci\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/i\u003e\u003c/li\u003e\u003cli\u003eDetermine \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/198\"\u003ewhether the sampled point is inside or outside the polygon\u003c/a\u003e.  \u003ci\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/i\u003e\u003c/li\u003e\u003cli\u003eRepeat steps 2–3 \u003ctt\u003eN\u003c/tt\u003e times.\u003c/li\u003e\u003cli\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eInputs to your function will be \u003ctt\u003eN\u003c/tt\u003e, the number of points to sample, and \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e, which together constitute \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/194\"\u003ean ordered list of polygon vertices\u003c/a\u003e.  \u003ctt\u003eN\u003c/tt\u003e will always be a positive integer.  \u003ctt\u003epolygonX\u003c/tt\u003e \u0026 \u003ctt\u003epolygonY\u003c/tt\u003e will always describe a single, continuous outline;  however, the polygon may be self-intersecting.\u003c/p\u003e\u003cp\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant.  A self-intersecting pentagram (left \u0026 middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Complex_polygon.svg/288px-Complex_polygon.svg.png\"\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Pentagram_interpretations.svg/320px-Pentagram_interpretations.svg.png\"\u003e\u003cp\u003e^\u003c/p\u003e\u003cp\u003eEXAMPLE\u003c/p\u003e\u003cpre\u003e % Input\r\n N = 1000\r\n polygonX = [1 0 -1  0]\r\n polygonY = [0 1  0 -1]\r\n % Output\r\n A = 2.036\u003c/pre\u003e\u003cp\u003eExplanation:  the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°.  The exact area is hence 2.  As the value of \u003ctt\u003eN\u003c/tt\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon).  \r\nOf course, if the code were run again then a slightly different value of \u003ctt\u003eA\u003c/tt\u003e would probably be returned, such as \u003ctt\u003eA\u003c/tt\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/p\u003e","function_template":"function A = monteCarloArea(N, polygonX, polygonY)\r\n    % Fun starts here\r\nend\r\n\r\n\r\n% Note:  the Test Suite has been designed to account for variability in outputs. \r\n%        Nevertheless, it is possible that on rare occasions a valid submission \r\n%        might fail the Test Suite in one instance.  \r\n%        If your submission has narrowly failed only one of the test cases, \r\n%        then please try resubmitting it, in case it was just due to 'bad luck'.  ","test_suite":"%% No silly stuff\r\n% This Test Suite can be updated if inappropriate 'hacks' are discovered \r\n% in any submitted solutions, so your submission's status may therefore change over time.  \r\n\r\n% BEGIN EDIT (2019-06-29).  \r\n% Ensure only builtin functions will be called.  \r\n! rm -v fileread.m\r\n! rm -v assert.m\r\n% END OF EDIT (2019-06-29).  \r\n\r\nassessFunctionAbsence({'regexp', 'regexpi', 'str2num'}, 'FileName','monteCarloArea.m')\r\n\r\nRE = regexp(fileread('monteCarloArea.m'), '\\w+', 'match');\r\ntabooWords = {'ans', 'area', 'polyarea'};\r\ntestResult = cellfun( @(z) ismember(z, tabooWords), RE );\r\nmsg = ['Please do not do that in your code!' char([10 13]) ...\r\n    'Found: ' strjoin(RE(testResult)) '.' char([10 13]) ...\r\n    'Banned word.' char([10 13])];\r\nassert(~any( testResult ), msg)\r\n\r\n\r\n%% Unit square, in first quadrant\r\nNvec = 1 : 7 : 200;\r\npolygonX = [0 1 1 0];\r\npolygonY = [0 0 1 1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 1;\r\nassert( all(areaVec==area_correct) )\r\n\r\n%% 3×3 square, offset from origin, in all four quadrants\r\nNvec = 1 : 19 : 500;\r\npolygonX = [ 1 1 -2 -2];\r\npolygonY = [-1 2  2 -1];\r\nareaVec = arrayfun(@(N) monteCarloArea(N, polygonX, polygonY), Nvec);\r\narea_correct = 9;\r\nassert( all(areaVec==area_correct) )\r\n\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (1)\r\nN = 1;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (2)\r\nN = 2;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0 2 4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  small N (3)\r\nN = 4;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_valid = [0:4];\r\nareaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:1000);\r\nassert( all( ismember(areaVec, area_valid) ) , 'Invalid areas reported' )\r\nassert( all( ismember(area_valid, areaVec) ) , 'Not all valid areas accessible in your sampling scheme')\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (1)\r\nN = 100;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (2)\r\nN = 1000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  moderate N (3)\r\nN = 10000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Diamond, centred on origin, in all four quadrants:  large N\r\nN = 100000;\r\npolygonX = [1 0 -1  0];\r\npolygonY = [0 1  0 -1];\r\narea_exact = 2;\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 7 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.0016 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.016 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants:  moderate N (1)\r\nN = 100;\r\npolygonX = [ 1 -1  1 -1];\r\npolygonY = [-1  1  1 -1];\r\narea_exact = 2;\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 4 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.05 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.40 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% Cross-quadrilateral, centred on origin, in all four quadrants:  moderate N (2)\r\nN = 10000;\r\nfor j = 1 : 10,\r\n    rVec = 100 * rand(2);\r\n    polygonX = [ 1 -1  1 -1] * rVec(1,1) + rVec(1,2);\r\n    polygonY = [-1  1  1 -1] * rVec(2,1) + rVec(2,2);\r\n    area_exact = 2 * rVec(1,1) * rVec(2,1);\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 6 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    assert( worstErrorFraction \u003e 0.004 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.049 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 12-cornered polygon of unit 'circumradius' centred on origin:  moderate N\r\nN = 1000;\r\npoints = 12;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\npolygonX = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\npolygonY = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\narea_exact = polyarea(polygonX, polygonY);\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% P-cornered polygon of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\nfor j = 1 : 10,\r\n    points = randi([5 100]);\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 100]);\r\n    r = rand();\r\n    polygonX = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    polygonY = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    area_exact = polyarea(polygonX, polygonY);\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.08 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% 5-pointed star of unit 'circumradius' centred on origin:  moderate N\r\nN = 1000;\r\npoints = 5;\r\ncentre = [0 0];\r\ncircumradius = 1;\r\nx = circumradius * cos(2 * pi * [0:points-1]/points) + centre(1);\r\ny = circumradius * sin(2 * pi * [0:points-1]/points) + centre(2);\r\npolygonX = x([1:2:end, 2:2:end]);\r\npolygonY = y([1:2:end, 2:2:end]);\r\narea_exact = sqrt(650 - 290* sqrt(5))/4  * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n% http://mathworld.wolfram.com/Pentagram.html\r\n\r\nfor j = 1 : 3,\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n%% 5-pointed star of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\npoints = 5;\r\nfor j = 1 : 10,\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 100]);\r\n    r = rand();\r\n    x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    polygonX = x([1:2:end, 2:2:end]);\r\n    polygonY = y([1:2:end, 2:2:end]);\r\n    area_exact = sqrt(650 - 290* sqrt(5))/4  * ( circumradius / sqrt((5 - sqrt(5))/10) )^2;\r\n    % http://mathworld.wolfram.com/Pentagram.html\r\n\r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.03 , 'Implausibly accurate' )\r\n    %assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\n    assert( worstErrorFraction \u003c 0.25 , 'Implausibly inaccurate' )\r\nend;\r\n\r\n\r\n%% P-pointed star of arbitrary 'circumradius', with centre offset from  the origin:  moderate N\r\nN = 1000;\r\nfor j = 1 : 20,\r\n    points = 3 * randi([3 10]) - 1;\r\n    centre = randi([2 100], [1 2]);\r\n    circumradius = randi([2 30]);\r\n    r = rand();\r\n    x = circumradius * cos(2 * pi * (r+[0:points-1])/points) + centre(1);\r\n    y = circumradius * sin(2 * pi * (r+[0:points-1])/points) + centre(2);\r\n    polygonX = x([1:3:end, 2:3:end, 3:3:end]);\r\n    polygonY = y([1:3:end, 2:3:end, 3:3:end]);\r\n    \r\n    area_polyarea = polyarea(polygonX, polygonY);                % Incorrect value\r\n    warning('off', 'MATLAB:polyshape:repairedBySimplify')\r\n    area_polyshapeArea1 = area( polyshape(polygonX, polygonY) ); % Incorrect value\r\n    area_polyshapeArea2 = area( polyshape(polygonX, polygonY, 'Simplify',false) );  % Incorrect value\r\n    \r\n    % REFERENCE:  http://web.sonoma.edu/users/w/wilsonst/papers/stars/a-p/default.html\r\n    % Here: a {points/3} star\r\n    k = 3;\r\n    sideLength = circumradius * sind(180/points) * secd(180*(k-1)/points);\r\n    apothem = circumradius * cosd(180*k/points);\r\n    area_exact = points * sideLength * apothem;                  % Correct value\r\n    fprintf('Area estimates from different methods:  \\r\\npolyarea = %4.1f;  polyshape.area = %4.1f or %4.1f;  geometrical analysis = %4.1f\\r\\n', ...\r\n        area_polyarea, area_polyshapeArea1, area_polyshapeArea2, area_exact);\r\n    \r\n    areaVec = arrayfun(@(dummy) monteCarloArea(N, polygonX, polygonY), 1:10);\r\n    assert( length(unique(areaVec)) \u003e 5 , 'Cannot have so many identical outputs')\r\n    worstErrorFraction = max( abs(area_exact - areaVec) ) / area_exact\r\n    %assert( worstErrorFraction \u003e 0.02 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003e 0.01 , 'Implausibly accurate' )\r\n    assert( worstErrorFraction \u003c 0.15 , 'Implausibly inaccurate' )\r\nend;\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":3,"created_by":64439,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":7,"test_suite_updated_at":"2019-06-29T13:06:05.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2018-07-02T02:19:05.000Z","updated_at":"2025-09-14T14:22:43.000Z","published_at":"2018-07-02T08:55:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.png\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.png\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe area of a polygon (or any plane shape) can be evaluated by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/179\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMonte Carlo integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The process involves 'random' sampling of (x,y) points in the xy plane, and testing whether they fall inside or outside the shape. That is illustrated schematically below for a circle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSteps:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDefine a 2D region within which to sample points. In the present problem you must choose the rectangular box (aligned to the axes) that bounds the specified polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy a 'random' process generate coordinates of a point within the bounding box. In the present problem a basic scheme using the uniform pseudorandom distribution available in MATLAB must be employed. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOther schemes in use include quasi-random sampling (for greater uniformity of coverage) and stratified sampling (with more attention near the edges of the polygon).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/198\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ewhether the sampled point is inside or outside the polygon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDue to working in double precision, it is extremely unlikely to sample a point falling exactly on the edge of the polygon, and consequently if it does happen it doesn't really matter whether it's counted as inside or outside or null.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRepeat steps 2–3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e times.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBased upon the proportion of sampled points falling within the polygon, report the approximate area of the polygon.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs to your function will be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the number of points to sample, and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which together constitute\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/194\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ean ordered list of polygon vertices\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always be a positive integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonX\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u0026amp;\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003epolygonY\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will always describe a single, continuous outline; however, the polygon may be self-intersecting.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor polygons that are self-intersecting, you must find the area of the enclosed point set. In the case of the cross-quadrilateral, it is treated as two simple triangles (cf. three triangles in the first figure below), and the clockwise/counterclockwise ordering of points is irrelevant. A self-intersecting pentagram (left \u0026amp; middle of the second figure below) will therefore have the same area as a concave decagon (right).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEXAMPLE\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ % Input\\n N = 1000\\n polygonX = [1 0 -1  0]\\n polygonY = [0 1  0 -1]\\n % Output\\n A = 2.036]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExplanation: the above polygon is a square of side-length √2 centred on the origin, but rotated by 45°. The exact area is hence 2. As the value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e is moderate, the estimate by Monte Carlo integration is moderately accurate (an error of 0.036 in this example, corresponding to 509 of the 1000 sampled points falling within the polygon). Of course, if the code were run again then a slightly different value of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e would probably be returned, such as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e=1.992 (corresponding to 498 of the 1000 sampled points falling within the polygon), due to the random qualities of the technique.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" 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\"},{\"partUri\":\"/media/image2.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\"}]}"},{"id":60924,"title":"Largest Small n-Polygons or Biggest Little Polygon","description":"Largest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has diameter one and that has the largest area among all diameter-one n-gons. (from Wikipedia, MathWorld)\r\nIn the case n = 6, the polygon is called Graham's Biggest Little Hexagon.\r\nFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\r\nImage\r\nThe results for cases where n is 3 to 8 are as follows.\r\n\r\n\r\n\r\nReference program\r\n* https://github.com/tomtkg/Largest-Small-Polygon","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 1068px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 408px 534px; transform-origin: 408px 534px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 21px; text-align: left; transform-origin: 385px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLargest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e diameter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone and that has the largest\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eamong all diameter-one\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-gons. (from \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Biggest_little_polygon\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eWikipedia\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/BiggestLittlePolygon.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMathWorld\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIn the case n = 6, the polygon is called \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGraham's Biggest Little Hexagon\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 385px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 385px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eImage\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe results for cases where n is 3 to 8 are as follows.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 269px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 134.5px; text-align: left; transform-origin: 385px 134.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cimg class=\"imageNode\" width=\"271\" height=\"263\" style=\"vertical-align: baseline;width: 271px;height: 263px\" 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\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 20px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; font-size: 20px; font-weight: 700; line-height: 20px; margin-block-end: 5px; margin-block-start: 20px; margin-bottom: 5px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 20px; outline-color: rgb(60, 60, 60); perspective-origin: 385px 10px; text-align: left; text-decoration: none; text-decoration-color: rgb(60, 60, 60); text-emphasis-color: rgb(60, 60, 60); transform-origin: 385px 10px; white-space-collapse: preserve; margin-left: 4px; margin-top: 20px; margin-bottom: 5px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReference program\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 385px 10.5px; text-align: left; transform-origin: 385px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e* \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://github.com/tomtkg/Largest-Small-Polygon\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttps://github.com/tomtkg/Largest-Small-Polygon\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = LSP(n) % Largest Small Polygon (LSP)\r\n    X = [0 0.5; 0.5 0; 0 -0.5; -0.5 0]; % Case n = 4 passed\r\nend","test_suite":"%%\r\nn = 3;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.43301270 - 0.01);\r\n%%\r\nn = 4;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.50000000 - 0.01);\r\n%%\r\nn = 5;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.65716389 - 0.01);\r\n%%\r\nn = 6;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.67498144 - 0.01);\r\n%%\r\nn = 7;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.71974093 - 0.01);\r\n%%\r\nn = 8;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.72686848 - 0.01);\r\n%%\r\nn = 9;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.74561923 - 0.01);\r\n%%\r\nn = 10;\r\nX = LSP(n);\r\n\r\nassert(height(X) == n);\r\nassert(width(X) == 2);\r\nfor i = 1:n\r\n    for j = i+1:n\r\n        assert(norm(X(i,:) - X(j,:)) \u003c= 1.00);\r\n    end\r\nend\r\nassert(polyarea(X(:,1), X(:,2)) \u003e 0.74913735 - 0.01);","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":2217275,"edited_by":2217275,"edited_at":"2025-05-18T15:08:35.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2025-05-18T08:26:55.000Z","updated_at":"2026-03-13T22:08:20.000Z","published_at":"2025-05-18T08:40:48.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLargest Small n-Polygons or Biggest Little Polygon for a number n is the polygon that has\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e diameter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eone and that has the largest\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eamong all diameter-one\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-gons. (from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Biggest_little_polygon\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/BiggestLittlePolygon.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMathWorld\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn the case n = 6, the polygon is called \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://mathworld.wolfram.com/GrahamsBiggestLittleHexagon.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGraham's Biggest Little Hexagon\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given input n, output the set X of vertex coordinates of the Largest Small n-Polygons.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eImage\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe results for cases where n is 3 to 8 are as follows.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"263\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"271\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr 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\",\"relationship\":null},{\"partUri\":\"/media/image3.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image4.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image5.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null},{\"partUri\":\"/media/image6.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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