Problem 45303. Combinatorics - 01

Created by Asif Newaz

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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=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Input=[x,n]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>where x is an array of numbers(or strings) and n is a +ve number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>for example, x=[1,2] and n=6.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The output will be a matrix containing all the possible permutations of the vector x having n elements(no of columns=n). besides that -</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>each row should contain equal number of occurance of the elements of x. (3 ones, 3 twos)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>no initial segment can have more 2's than 1's. e.g. [2 2 1 2 1 1] - is invalid.since there are more 2's in the 1st appearance than 1's.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>y=[</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[     1     1     1     2     2     2\n     1     1     2     1     2     2\n     1     1     2     2     1     2\n     1     2     1     1     2     2\n     1     2     1     2     1     2\n     1     2     1     2     2     1\n     2     1     1     1     2     2\n     2     1     1     2     1     2\n     2     1     1     2     2     1\n     2     1     2     1     1     2\n     2     1     2     1     2     1\n     2     1     2     2     1     1\n     2     2     1     1     1     2\n     2     2     1     1     2     1\n     2     2     2     1     1     1]]]></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>"}]}

<ul><li>Input=[x,n]</li><li>where x is an array of numbers(or strings) and n is a +ve number.</li></ul><p>for example, x=[1,2] and n=6.</p><p>The output will be a matrix containing all the possible permutations of the vector x having n elements(no of columns=n).
besides that -</p><ul><li>each row should contain equal number of occurance of the elements of x. (3 ones, 3 twos)</li><li>no initial segment can have more 2's than 1's. e.g. [2 2 1 2 1 1] - is invalid.since there are more 2's in the 1st appearance than 1's.</li></ul><ul><li>y=[</li></ul><pre>     1     1     1     2     2     2
     1     1     2     1     2     2
     1     1     2     2     1     2
     1     2     1     1     2     2
     1     2     1     2     1     2
     1     2     1     2     2     1
     2     1     1     1     2     2
     2     1     1     2     1     2
     2     1     1     2     2     1
     2     1     2     1     1     2
     2     1     2     1     2     1
     2     1     2     2     1     1
     2     2     1     1     1     2
     2     2     1     1     2     1
     2     2     2     1     1     1]</pre>

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Last Solution submitted on Apr 02, 2020

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3 Comments

Binbin Qi on 2 Apr 2020

I don't understand, can you explain the second rule?

Asif Newaz on 2 Apr 2020

all combinations of x & y of length n
1. they must appear n/2 times each
2. no initial segment of the string has more y's than x's
so, 'yyxyxx' -- the 2nd rule is broken here. since 1st appearance of x contains only one x while y [the second element] contains 2.

count (1stelement) >= count (2nd element) >= count (3rd element) ..
Hope this makes it clear

Binbin Qi on 2 Apr 2020

@Asif, thank you! I see.

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combinatorics logic

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Problem 45303. Combinatorics - 01

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