However, the module Math::Combinatorics can still be used to iterate through the 2**N subsets as well as the nCr combinations and the N! permutations.

Thank you, for pointing me to the "factorial"
Note to self: Don't transfer mathematical/technical terms from German to English without consulting a dictionary first.

Also, would you be able to give example code for the subset iteration with Math::Combinatorics?

If there is an easy way to do so, it has escaped me.

The closest I saw in the docs was that example to generate:
"Morse signals: diferent signals of 3 positions using the two symbols - and .".

Now Morse signals of length 3 are surely one-to-one and onto the subsets of a 3 element set (set elements = pos in signal; element not/contained = dot/dash)

The given iteration using next_multiset and next_string is like computing 2**n as sum_k=0..n nCk

At least this is not trivial application of the modules methods.

I guess that's as good as it gets from Math::Combinatorics - doable, but not very natural.

There are plenty of other iterators out there that give all the subsets, though - List::PowerSet, Data::PowerSet, Algorithm::ChooseSubsets - We just have to convert them to give a bit mask instead - ie:


use List::PowerSet qw/powerset_lazy/;
my @set = (0) x $N;
my @C   = (1) x 2**$N;
my $M = 0;
my $ps_itr = powerset_lazy(0 .. $N-1);
while (my $ref_set = $ps_itr->()) {
    $_ = 1 for local @set[@$ref_set];
    $C[ $M ] *= $arr->[ $_ ][ $set[$_] ] for 0 .. $N-1;
    $M++;
}
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The 2**N doesn't need to be computed anyway. next_multiset() will just keep returning each possible set until all have been returned, at which point it returns undef().

Everything but the troll