Problem 1771. Polygonal numbers

Created by Jan Orwat

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{"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>The task of</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.co.uk/matlabcentral/cody/problems/5\"><w:r><w:t>Problem 5</w:t></w:r></w:hyperlink><w:r><w:t> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ * * * *\n * * * * * * *\n * * * * * * * * *\n1: * 4: * * 9: * * * 16: * * * *]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>or hexagonal numbers:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ * * * *\n * *\n * * * * * * * *\n * * * * * *\n * * * * * * * * * * * \n * * * * * * * * *\n1: * 6: * * 15: * * * 28: * * * *]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>According to those rules we can create</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Polygonal_number\"><w:r><w:t>polygonal numbers</w:t></w:r></w:hyperlink><w:r><w:t> for all regular polygons.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Your task: given</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>S</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>calculate</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-th</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:r><w:rPr><w:b/><w:i/></w:rPr><w:t>S</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>-gonal numbers</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>P(S,N)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>&amp;nbsp</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Examples:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(4, 3)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[9]</w:t></w:r><w:r><w:t> because 3-rd square number is 9,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(3, 1:5)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[1, 3, 6, 10, 15]</w:t></w:r><w:r><w:t> first 5 triangular numbers,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P(3:6, 4)</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[10, 16, 22, 28]</w:t></w:r><w:r><w:t> 4-th triangular, square, pentagonal and hexagonal numbers,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:rPr><w:i/></w:rPr><w:t>P([3, 4], [1; 2])</w:t></w:r><w:r><w:t> returns</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>[1, 1; 3, 4]</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>see the test suite for more hints</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>"}]}

The task of <a href = "http://www.mathworks.co.uk/matlabcentral/cody/problems/5">Problem 5</a> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:<pre> * * * *
 * * * * * * *
 * * * * * * * * *
1: * 4: * * 9: * * * 16: * * * *</pre>or hexagonal numbers:<pre> * * * *
 * *
 * * * * * * * *
 * * * * * *
 * * * * * * * * * * * 
 * * * * * * * * *
1: * 6: * * 15: * * * 28: * * * *</pre>&nbspAccording to those rules we can create <a href = "http://en.wikipedia.org/wiki/Polygonal_number">polygonal numbers</a> for all regular polygons.&nbspYour task: given S and N calculate N-th S-gonal numbers P(S,N)&nbspExamples:<ol><li>P(4, 3) returns [9] because 3-rd square number is 9,</li><li>P(3, 1:5) returns [1, 3, 6, 10, 15] first 5 triangular numbers,</li><li>P(3:6, 4) returns [10, 16, 22, 28] 4-th triangular, square, pentagonal and hexagonal numbers,</li><li>P([3, 4], [1; 2]) returns [1, 1; 3, 4].</li></ol>see the test suite for more hints

The task of <http://www.mathworks.co.uk/matlabcentral/cody/problems/5 Problem 5> is to calculate triangular numbers. By playing with dots we can produce also square numbers like:

* * * *
                     * * *       * * * *
           * *       * * *       * * * *
1: *    4: * *    9: * * *   16: * * * *

or hexagonal numbers:

* * * *
                                         *       *
                         * * *          * * * *   *
                        *     *        * *     *   *
            * *        * * *   *        * * *   * * 
           *   *        *   * *          *   * * *
1: *    6:  * *    15:   * * *       28:  * * * *

&nbsp

According to those rules we can create <http://en.wikipedia.org/wiki/Polygonal_number polygonal numbers> for all regular polygons.

&nbsp

Your task: given _S_ and _N_ *calculate _N_-th _S_-gonal numbers* _P(S,N)_

&nbsp

Examples:

# _P(4, 3)_ returns _[9]_    because 3-rd square number is 9,
# _P(3, 1:5)_ returns _[1, 3, 6, 10, 15]_   first 5 triangular numbers,
# _P(3:6, 4)_ returns _[10, 16, 22, 28]_   4-th triangular, square, pentagonal and hexagonal numbers,
# _P([3, 4], [1; 2])_ returns _[1, 1; 3, 4]_.

see the test suite for more hints

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Last Solution submitted on Nov 11, 2021

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Matthew Eicholtz on 25 Aug 2015

I think the numbers in the description may be wrong. For hexagonal numbers, shouldn't the progression be [1,6,15,28]?

Daniel Pereira on 11 Feb 2016

I believe that test suite number 6 is a little bit unfair, since the difficulty of this problem relies on creating the function that gives the n-th s-gonal number, and not making use of meshgrid or bsxfun.

Massimo Zanetti on 14 Oct 2016

Remove test case 6 please.. it makes no sense

Jan Orwat on 15 Oct 2016

Explain why. It makes a lot of sense to me, and it's a lot easier (and makes even more educational sense) with 2016b. Just learn the difference between * and .* and ask yourself you need 1st or 2nd.

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