View difference between Paste ID: y1Cdi1vB and 4WXR5VrS

 #!/bin/perl
 #
 # Enumerate all the partitions of {1, 3, 4, 5, 7, 15, 16, 17, 21, 23, 25, 31}
 # into 4 subsets.
 #
 # Samuel DEVULDER, fev 2014
 #
 
 # 1st: the set
 $set = 0;
 for my $x (1, 3, 4, 5, 7, 15, 16, 17, 21, 23, 25, 31) {$set |= 1<<$x;}
 
-for $part (&all_k_partition(4, $set, 0)) {
+# 2nd: the number of partitions
 $num = 4;
 
 # 3rd: enumerate all
 $n = 0;
 for $part (&all_k_partition($num, $set, 0)) {
 	print ++$n, " ";
 	for my $subset (split(',', $part)) {&print_set($subset);}
 	print "\n";
 }
 
 sub print_set {
 	my($set) = @_;
 
 	print "{";
 	my($first) = 1;
 	for(my $i=0; (1<<$i)<=$set; ++$i) {
 		if($set & (1<<$i)) {
 			print "," unless $first; $first = 0;
 			print $i;
 		}
 	}
 	print "} ";
 }
 
 sub next_in_set {
         my($x, $set) = @_;
         return ($x-$set) & $set;
 }
 
 sub all_k_partition {
         my($k, $set, $i) = @_;
         return () if $set==0 || $k==0 || $set<=$i;
         return ($set) if $k==1;
 
         my(@r);
         while($i = &next_in_set($i, $set)) {
                 my($m) = $i;
                 for (my $j = 1;$m>>$j;$j<<=1) {$m|=$m>>$j;}
                 for my $j (&all_k_partition($k-1, $set^$i, $m)) {
                         push(@r, "$i,$j");
                 }
         }
 
         return @r;
 }