Perl: the Markov chain saw  
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Re: Combinations of array?by jaredor (Curate) 
on Jun 17, 2012 at 06:30 UTC ( #976625=note: print w/ replies, xml )  Need Help?? 
Late to the party and, not only that, but wearing the same outfit as some (see ambrus's link above). I think the best answer for you is toolic's. My answer that follows just fills in a few conceptual details for you about the Power Set, illustrated by two functions that do the job two different ways. Earlier, I had copied this problem to my notepad and had misremembered your question as being about a string, "ABCD", rather than an array of elements. So both functions take in a string and return a list of strings. This makes my answer slightly different from the others in the recursive case and bulky in the enumeration case. Power SetGiven a set, A, the set of all subsets of elements of A is called the power set of A, here denoted P(A). A power set, P(A), of finite set A has size 2^{N}. So your example should have 16 results. (Note, one of those subsets is the empty set / empty string). Finding all combinations of elements of a set is an equivalent notion. Power sets get very big, very fast, so in general you don't see many applications for power sets unless you are writing advertisements for how many ways customers can put condiments on their hamburgers. If this question is motivated by a realworld problem (i.e., one that doesn't get a grade) it would be interesting to some of us if you could post some details about it. recursionThe first function, rpow, shows the recursive solution and its map block indicates that the results of the recursed function call are doubled, hence you can see how the 2^{N} subsets are built up.
enumerationThe second function, bpow, is a direct enumeration of the power set by using the on/off nature of a bit in the binary representation of a number as a representation for the in/out selection of an element of A for a given element of P(A). That is, it runs a bitmask of each nonnegative integer less than 2^{N} against your string. It produces the same results as rpow (in reverse order).
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