A case with Combinations in Sets

[anirbid.banerjee]

Hi,

I have two Sets A and B with N DISTINCT elements each. Both A and B
are related to each other so that B contains complement of A. For eg.A
= {a, b, c} , B = {a*, b* c*}. I would need a perl script to generate
all possible combinations between A and B satisfying the following
conditions:

a) The number of elements in the Combined set n(C) = N.
b) None of the combination should contain both an element and its
complement : i.e. {a, a*, b}, {b,c, c*} are invalid combinations.
c) There should be exactly 2^N combinations.

Regards,
Anirbid

 

[xhoster]

Hi,

I have two Sets A and B with N DISTINCT elements each. Both A and B
are related to each other so that B contains complement of A. For eg.A
= {a, b, c} , B = {a*, b* c*}. I would need a perl script to generate
all possible combinations between A and B satisfying the following
conditions:

Since set B is completely and readily determined by set A, there is really
no point in actually having it. Just let it be implied by A.

a) The number of elements in the Combined set n(C) = N.
b) None of the combination should contain both an element and its
complement : i.e. {a, a*, b}, {b,c, c*} are invalid combinations.
c) There should be exactly 2^N combinations.

So take all numbers from 0 to 2^N and map each bit-position to one of the
elements in A. Call the ones the elements and the zeros the complements to
the elements.

$n=6;
foreach (0..2**$n-1) {
print sprintf "%0${n}b", $_ ;
};


Xho

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