sub naive_shuffle {
  my $n = my @p = @_;
  for my $i ( 0..$n-1 ) {
    my $j = int rand $n;
    @p[ $i, $j ] = @p[ $j, $i ]; # swap
  }
  return @p;
}

##</code><code>##

# untested
sub naive_shuffle_rec {
  my $i = shift;
  my $n = my @p = @_;
  my $j = int rand $n;
  @p[ $i, $j ] = @p[ $j, $i ]; # swap
  return ++$i < $n ? naive_shuffle_rec( $i, @p ) : @p;
}

##</code><code>##

sub naive_shuffle_traverse {
  my $i = shift;
  my $j = shift;
  my $n = my @p = @_;
  @p[ $i, $j ] = @p[ $j, $i ] if defined $j; # swap
  if ( ++$i < $n ) {
    for my $j (0..$n-1) {
      naive_shuffle_traverse( $i, $j, $tally, @p );
    }
  }
  else {
    return;
  }
}

##</code><code>##

naive_shuffle_traverse(-1, undef, 1..3);

##</code><code>##

sub naive_shuffle_count {
  my $i = shift;
  my $j = shift;
  my $tally = shift;
  my $n = my @p = @_;
  @p[ $i, $j ] = @p[ $j, $i ] if $j > -1;
  if ( ++$i < $n ) {
    for my $j (0..$n-1) {
      naive_shuffle_count( $i, $j, $tally, @p );
    }
  }
  else {
    $tally->{ "@p" }++;
    return;
  }
}

##</code><code>##

my %tally = ();
naive_shuffle_count( -1, undef, \%tally, 1..3 );

##</code><code>##

  DB<2> x \%tally
0  HASH(0x82d7f94)
   '1 2 3' => 4
   '1 3 2' => 5
   '2 1 3' => 5
   '2 3 1' => 5
   '3 1 2' => 4
   '3 2 1' => 4

##</code><code>##

sub random_perm {
  my $n = my @p = @_;
  for ( my $i = $#p; $i > 0; --$i ) {
    my $j = int rand( $i + 1 );
    @p[ $i, $j ] = @p[ $j, $i ];
  }
  return @p;
}