http://qs321.pair.com?node_id=371228

Semantic nitpicking:
  • A permutation of a set is a rearrangement of its items, using all the items, where order is important.
  • The power set of a set is all of its possible subsets (order is not important within subsets).
  • A combination "N choose K" is the number of ways to choose K things from N things (where the order of the K things doesn't matter). Often, math textbooks extend this notation to "S choose K", where S is a set instead of a number, to mean the set of all K-sized-subsets of S. In short, combinations are when we specify the size of the subsets taken.
(tye)Re: Finding all Combinations is a canonical way to iterate over a set's power set. It won't get you combinations in the above sense (a better name would be (tye)Re: Finding all Subsets). Permuting with duplicates and no memory is a canonical way to iterate over permutations.

Here are some ways to iterate over @S choose $K, all the $K-sized subsets of @S.

## Filtering tye's "combinations" (power set) iterator: my $iter = combinations(@S); while ( my @c = $iter->() ) { next unless @c == $K; ... }
## Using tye's Algorithm::Loops: NestedLoops( [ 0 .. $#S ], ( sub { [$_+1 .. $#S] } ) x ($K - 1), sub { my @c = @S[@_]; ... } }
Finally, the code below which uses a similar principle as (tye)Re: Finding all Combinations, keeping track of a list of indices. The subsets are returned in the same order as a nested for-loop.

Update: see Re^8: Perl6 Contest: Test your Skills for a verbose explanation of what this code does.

sub combinations { my ($num, $arr) = @_; return sub { return } if $num == 0 or $num > @$arr; my @pick; return sub { return @$arr[ @pick = ( 0 .. $num - 1 ) ] unless @pick; my $i = $#pick; $i-- until $i < 0 or $pick[$i]++ < @$arr - $num + $i; return if $i < 0; @pick[$i .. $#pick] = $pick[$i] .. $#$arr; return @$arr[@pick]; }; }
You use it like this:
my $iter = combinations( 3 => ['a' .. 'f'] ); while ( my @c = $iter->() ) { print "@c\n"; }