Problem 577. Repopulate the City

Created by Ned Gulley

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For any population p of positive integers between pmin and pmax, we can calculate histogram count n for a list of evenly dividing divisors d. Here's how it works.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Consider the population p = [10, 12, 15, 11, 20, 11]. For the list of divisors d = [2, 3, 5] we get a histogram count n of [3, 2, 3]. That is, three of the numbers in the population are evenly divisible by 2, two are evenly divisible by 3, and three are evenly divisible by 5.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You will face the inverse problem. Given a histogram count corresponding to a list of divisors, produce a population of positive integers that fits the distribution. Your answer will not be unique and can be provided in any order. It just has to match the distribution. The elements of p can be no less than pmin and no greater than pmax.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ pmin = 5\n pmax = 10\n d = [1 2 3 4 5]\n n = [8 3 4 2 2]\n\n One answer (of many possible): p = [5 5 6 8 8 9 9 9]]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

69 Solutions
20 Solvers

Last Solution submitted on Jul 18, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

@bmtran (Bryant Tran) on 13 Apr 2012

It looks like there's an error in the test suite; test cases 3 and 4 have different length d and n vectors.

Ned Gulley on 13 Apr 2012

Oof! I hate it when that happens. Fixed it. Thanks for the note.

Problem Recent Solvers20

Problem Tags

factors

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 577. Repopulate the City

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Problem 577. Repopulate the City

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers20

Suggested Problems

More from this Author50

Problem Tags

Community Treasure Hunt

Players