#!/usr/bin/perl
use strict;
use warnings;

my $depth = 4;
my %results;

sub recurse
{
    if (@_ == $depth) {
        shift; #discard $num
        my @deck = (1 .. $depth);
        shuffle(\@deck, [@_]);
        $results{join('', @deck)}++;
    } else {
        my $num = shift || $depth - 1;
        # one less element each iteration
        recurse($num, @_, $_) for 0 .. $num--;
    }
}

sub shuffle
{
    my($deck, $rand) = @_;
    my $i = @$deck;
    # uncomment the following line
    # print "@$rand\n";
    # pre-decrement $i instead of post - the last would be a no-op in this case
    while (--$i) {
        my $j = shift @$rand;
        @$deck[$i,$j] = @$deck[$j,$i];
    }
}

recurse;
for (sort {$results{$b} <=> $results{$a}} keys %results) {
    printf "%10d %s\n", $results{$_}, $_;
}

##</code><code>##

   1 4321
   1 2143
   1 4123
   1 2413
   1 3421
   1 1324
   1 4312
   1 4231
   1 3412
   1 1432
   1 1423
   1 2431
   1 2314
   1 3214
   1 3142
   1 1342
   1 2134
   1 3241
   1 1243
   1 4213
   1 3124
   1 4132
   1 1234
   1 2341