It seemed wasteful to me to first create all partitions and then filter out the wanted ones. And I wanted to say that it should be simple to draw a partition algorithm that directly does what you want. But it took me longer than I thought... 

use strict;
use warnings;

sub partition {
  my( $n, $level, $max, @part ) = @_;
  $max //= $n;
  $level //= $n;
  my @solutions = $n <= $max ? [ @part, $n ]: ();
  $max = $n-1 if $max > $n-1;
  push @solutions, map { partition( $n-$_, $level-1, $_-1, @part, $_) 
+} reverse 1..$max if $level > 1 and $n > 2;
  return @solutions;
}

my( $number, $depth ) = @ARGV;
my @s = partition $number, $depth;
print "@$_\n" for @s;

[download]

Update: Changed 0..$max to 1..$max.

Update 2: You are not doing this to solve Kakuro puzzles?

In reply to Re: How to restrict partitions by hdb
in thread How to restrict partitions by crunch_this!

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