Problem 45303. Combinatorics - 01

Created by Asif Newaz

Solve Later

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<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

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14 Solutions
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Last Solution submitted on Oct 22, 2022

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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.

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Problem 45303. Combinatorics - 01

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