Problem 45303. Combinatorics - 01

Created by Asif Newaz

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=\"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>

* Input=[x,n]
* where x is an array of numbers(or strings) and n is a +ve number.

for example, x=[1,2] and n=6.

The output will be a matrix containing all the possible permutations of the vector x having n elements(no of columns=n).
besides that -

* each row should contain equal number of occurance of the elements of x. (3 ones, 3 twos)
* 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.

* y=[

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]

Solve

Solution Stats

32 Solutions
4 Solvers

Last Solution submitted on May 12, 2023

Last 200 Solutions

Problem Comments

4 Comments

4 Comments

Show 1 older comment

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.

Christian Schröder on 5 Oct 2022

Two suggestions:

1. Please clarify the second requirement, and in particular, avoid the term "initial segment", which is confusing. What I think you mean is that in each row, the number of elements in the first block of x(2)'s must not exceed the number of elements in the first block of x(1)'s.

2. Since you are not asking for the rows of y to be returned in any specific order, please change your test suite to use sortrows(), or indicate in which order they should be returned.

Solution Comments

Show comments

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 45303. Combinatorics - 01

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author165

Problem Tags

Community Treasure Hunt

Problem 45303. Combinatorics - 01

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author165

Problem Tags

Community Treasure Hunt

Players