With the recent golf events lately, i've been diving back into some number theory. The one part that always most amazed me were partitions. Oddly enough, i scoured the web looking for a formula to produce a list of the partitions for a number, and came up emtpy handed. This post is in SOPW becuase this algorithm isn't correct yet, but when finished it should be a decent go.

Let's start with some code:

sub P {
# This is so that we don't go off the deep end with recursion : )
   return [1,1] if $_[0]==1&&$_[1]==1;
   return [1] if $_[0]==1;

# If there's only one argument, return a list of lists containing
# the argument and it's partitions.
   if (@_==1) {
      return [@_], P($_[0]-1,1)

# Otherwise return a list of lists containing the arguments and
# the partitions of the opposites.
   } else {
      return [@_],
         map({ [@$_, $_[1]] } P($_[0])),
         map({ [$_[0], @$_] } P($_[1]))
   }
}
[download]

So firstly, the problem i'm having with the algorithm is that it doesn't return the else lists correctly. In particular it doesn't return the original [@_] part of the list. This is made obvious by running it and finding that the code returns a list including (for 5):

5
4 1
3 1 1
2 1 1 1
1 1 1 1 1
And many duplicates (which i handle seperately)
[download]

Note how <bold>3 2</bold> did not show up. Although Part(2) gets called, it's not returning correctly, or so it seems. i've tried to loop trace on paper, stepping through each recruse, but i think i missed something, because it should work.

Any enlightenment would be most helpful with this, yet again, after days of work, i'm blinded...

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Golf: Create a subroutine (or set of subroutines) that returns a list of partitions of a number n.

My entry (which is rather long) is above if included with this snippet for removing duplicates (which could probably also be optimized). Currently i weigh in at a whopping 235 characters (without whitespace) if the following is included:

sub u{map{[split//,$_]}sort{$b cmp$a}keys%{{map{my$t=join'',@$_;$t=>1}
+@_}}}
[download]

nuf evah,
jynx