Problem 42692. Polynomial Evaluation

Created by Md Tariqul Islam

Solve Later

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Problem has been taken from</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"\"><w:r><w:t>Rosetta Code</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Use of polyval and regexp is prohibited</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.png","relationshipId":"rId1"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image2.png","relationshipId":"rId2"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image3.png","relationshipId":"rId3"}]},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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","relationship":null},{"partUri":"/media/image2.png","contentType":"image/png","content":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAOBAMAAABN+VgMAAAAMFBMVEX///8AAAC2trZ0dHRiYmJAQEDm5uYwMDDMzMwiIiIWFhZQUFCenp6KiooMDAwEBASQHDlWAAAApklEQVR42mNmwAJOPwg7gk2cyYAhnoEJiwTzMYaiC9gkOFYxMHxgwA5ARim7pphj6JnMwMLBe8T7bEMDA0NUAEjoWQGQ4LG7x8DAwsC1AdOi6QxMTAzfBf5hSLxyABIHMfyRwMD4gIWB4ScD2y8GZDvq+RkYBFiY/n1kiJ0LFFq2DKbjnT9DQgPT+Q5LhruoRk39wPDvA7P8mjuMahdQJP5dnft6KgABWy0b9cYVLwAAAABJRU5ErkJggg==","relationship":null},{"partUri":"/media/image3.png","contentType":"image/png","content":"data:image/png;base64,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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 292px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 146px; transform-origin: 407px 146px; vertical-align: baseline; "><div 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; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 382px 8px; transform-origin: 382px 8px; unicode-bidi: normal; "><span style="">Create a routine that takes a list of coefficients of a polynomial in order of increasing powers of x; together with a value of x to compute its value at, and return the value of the polynomial at that value using</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "/#null"><span style=""><span style="">Horner's Rule</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style="">.</span></span></div><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.5px 8px; transform-origin: 202.5px 8px; unicode-bidi: normal; "><span style="">For example: A fast scheme for evaluating a polynomial such as:</span></span></div><div style="block-size: 25.5px; 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: 384px 12.75px; text-align: center; transform-origin: 384px 12.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,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" data-image-state="image-loaded"></div><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; "><span style="">when</span></span></div><div 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: center; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAC8AAAAOBAMAAABN+VgMAAAAMFBMVEX///8AAAC2trZ0dHRiYmJAQEDm5uYwMDDMzMwiIiIWFhZQUFCenp6KiooMDAwEBASQHDlWAAAApklEQVR42mNmwAJOPwg7gk2cyYAhnoEJiwTzMYaiC9gkOFYxMHxgwA5ARim7pphj6JnMwMLBe8T7bEMDA0NUAEjoWQGQ4LG7x8DAwsC1AdOi6QxMTAzfBf5hSLxyABIHMfyRwMD4gIWB4ScD2y8GZDvq+RkYBFiY/n1kiJ0LFFq2DKbjnT9DQgPT+Q5LhruoRk39wPDvA7P8mjuMahdQJP5dnft6KgABWy0b9cYVLwAAAABJRU5ErkJggg==" data-image-state="image-loaded"></div><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; "><span style="">is to arrange the computation as follows:</span></span></div><div style="block-size: 26.5px; 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: 384px 13.25px; text-align: center; transform-origin: 384px 13.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/png;base64,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" data-image-state="image-loaded"></div><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 108px 8px; transform-origin: 108px 8px; unicode-bidi: normal; "><span style="">N.B. Problem has been taken from</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "><span style=""> </span></span><a target='_blank' href = "/#null"><span style=""><span style="">Rosetta Code</span></span></a></div><div 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: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122px 8px; transform-origin: 122px 8px; unicode-bidi: normal; "><span style="">Use of polyval and regexp is prohibited</span></span></div></div></div>

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Solution Stats

114 Solutions
53 Solvers

Last Solution submitted on Oct 23, 2022

Last 200 Solutions

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3 Comments

3 Comments

Jihye Sofia Seo on 9 Feb 2017

seems like a really fun and challenging problem!

Rafael S.T. Vieira on 17 Sep 2020

Maybe the author should prohibit the use of polyval, str2num and regexp for this problem.

Subhashini Neelamegam on 18 Oct 2021

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