in reply to Re: Faster alternative to Math::Combinatorics
in thread Faster alternative to Math::Combinatorics

I wrote my own Permutation module in this post .. but it looks like we may have different ideas about a permutation. Your example doesn't list all of the permutations of (0, 2, 3) in an array of four elements .. it just has arrays where the elements exist in ascending order. For example, (0, 0, 2, 0) isn't in your list, and I can't tell if that omission is intentional or not.

It's intentional — I'm only looking for unordered tuples. Think of it as simultaneously drawing w (e.g. 3) balls from an urn containing at least w balls each marked n for any element of the underlying list (e.g. (0, 2, 3)). Generating all possible permutations would be quite easy, otherwise.

I actually briefly entertained the thought of generating all possible tuples and then removing ones that are in the same equivalence class as previously-seen ones, but for larger w and longer lists, this would take a fair amount of time and memory. w won't go beyond 8, but the lists might be arbitrarily long, at least in theory.

(Without having checked I actually have a gut feeling that this is what Math::Combinatorics might be doing under the hood — it would explain why it's so slow, and why the first multisets I draw from it appear much faster than the later ones!)

In any case, I'd write code to do the deed myself, and perhaps benchmark it against the module you've chosen -- it could be that your code is faster because it has less overhead. If that quick test fails, you may have to put on your thinking cap and simplify the algorithm. Or allocate a couple of hours to generate the test cases.

Yeah, that's definitely an option. But I'm lazy (it's one of the chief virtues of a programmer!), and therefore prefer to, in order:

  1. Find CPAN modules that do what I want;
  2. Get the brothers and sister on Perlmonks to write code for me... oops, did I say that out loud? Of course, I actually mean:
  3. Get ideas, pointers to known standard algorithms etc. from Perlmonks;
  4. Solve the (mathematical) problem myself and then write my own code.

Thanks for taking the time to reply, BTW!