I was asked by sporty to post this, so I am. It is not the fastest implementation of this algorithm, but it is the clearest one I could find. 
use strict;
use warnings;

use constant LEFT  => -1;
use constant RIGHT =>  1;

print "Enter N: ";
chomp( my $n = <> );

my (@dir, @p);
for (1 .. $n)
{
    $dir[$_ - 1] = LEFT;
    $p[$_ - 1] = $_;
}

my $count = 0;
while (1)
{
    printf "%03d: ", ++$count;
    print "$p[$_ - 1] " for 1 .. $n;
    print $/;

    # 1) Find the largest element that has a smaller element in the di
+rection
    #    of its arrow, aka the largest "mobile" element.
    my ($i, $val) = find_max_mobile(\@p, \@dir);

    # This means we couldn't find an element that's "mobile". That mea
+ns we've
    # run out of permutations.
    last if $i == -1;

    # 2) Swap it and the element it's pointing to. We also have to swa
+p the
    #    arrows to keep everything in sync.

    my @indices = ($i, $i + $dir[$i]);
    @p[ @indices ] = @p[ reverse @indices ];
    @dir[ @indices ] = @dir[ reverse @indices ];

    # 3) Reverse the direction of all arrows for elements bigger than 
+the
    #    currently largest "mobile" element.
    for (0 .. $#p)
    {
        $dir[$_] = -$dir[$_]
            if $p[$_] > $val;
    }
}

sub find_max_mobile
{
    my ($p, $dir) = @_;

    my ($i, $n) = (-1,0);

    # The first element is the max only if its arrow is pointing RIGHT
    ($i, $n) = (0, $p->[0])
        if $dir->[ 0 ] == RIGHT && $p->[0] > $p->[1];

    # A middle element is the max only if its arrow points to a smalle
+r value
    for ( 1 .. $#$p-1 )
    {
        if ( $p->[$_] > $p->[$_ + $dir->[$_]] )
        {
            ($i, $n) = ($_, $p->[$_])
                if $n < $p->[$_];
        }
    }

    # The last element is the max only if its arrow is pointing LEFT
    if ( $dir->[ $#$p ] == LEFT && $p->[$#$p] > $p->[$#$p - 1] )
    {
        ($i, $n) = ($#$p, $p->[-1])
            if $n < $p->[$#$p];
    }

    return ($i, $n);
}

[download]

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

In reply to Steinhaus - Johnson - Trotter Algorithm for Permutations by dragonchild

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