#!/usr/bin/perl

use strict;

my $transforms = {
  a => {
    '000' => '200',
    '100' => '210',
    '200' => '220',
    '210' => '120',
    '220' => '020',
    '120' => '010',
    '020' => '000',
    '010' => '100',
  },
  b => {
    '002' => '202',
    '102' => '212',
    '202' => '222',
    '212' => '122',
    '222' => '022',
    '122' => '012',
    '022' => '002',
    '012' => '102',
  },
  c => {
    '000' => '020',
    '010' => '021',
    '020' => '022',
    '021' => '012',
    '022' => '002',
    '012' => '001',
    '002' => '000',
    '001' => '010',
  },
  d => {
    '200' => '220',
    '210' => '221',
    '220' => '222',
    '221' => '212',
    '222' => '202',
    '212' => '201',
    '202' => '200',
    '201' => '210',
  },
  e => {
    '000' => '200',
    '100' => '201',
    '200' => '202',
    '201' => '102',
    '202' => '002',
    '102' => '001',
    '002' => '000',
    '001' => '100',
  },
  f => {
    '020' => '220',
    '120' => '221',
    '220' => '222',
    '221' => '122',
    '222' => '022',
    '122' => '021',
    '022' => '020',
    '021' => '120',
  }
};

foreach my $t (keys %$transforms) {
  my $t_inv = {};
  foreach my $from (keys %{$transforms->{$t}}) {
    my $to = $transforms->{$t}{$from};
    $t_inv->{$to} = $from;
  }
  $t = uc($t);
  $transforms->{$t} = $t_inv;
}

my $orig = [qw(
  000 001 002
  010     012
  020 021 022

  100     102
             
  120     122

  200 201 202
  210     112
  220 221 222
)];

sub print_cube {
  my ($cube) = @_;
  printf "
    %s %s %s
    %s     %s
    %s %s %s

    %s     %s

    %s     %s
    
    %s %s %s
    %s     %s
    %s %s %s
  ", @$cube;
}

sub is_equal {
  my ($c1, $c2) = @_;
  $c1 = [@$c1];
  $c2 = [@$c2];
  my ($e1, $e2);
  while ($e1 = shift @$c1) {
    $e2 = shift @$c2;
    return 0 if $e1 ne $e2;
  }
  return 1;
}


sub transform {
  my ($cube, @t) = @_;
  foreach my $t (@t) {
    $cube = [ map { $transforms->{$t}{$_} || $_ } @$cube ];
  }
  return $cube;
}


sub find_cycle {
  my ($cube, @t) = @_;
  my $new_cube = [@$cube];
  my $i = 0;
  while(1) {
    $i++;
    $new_cube = transform($new_cube, @t);
    #print "New Cube:";
    #print_cube($new_cube);
    #print "\n";
    return $i if is_equal($cube, $new_cube);
  }
}

sub T {
  my $t = shift;
  my @t = split //,$t;
  return @t;
}

sub rand_letter {
  my @choices = qw(a b c d e f A B C D E F);
  return $choices[rand $#choices];
}

sub rand_seq {
  my ($num) = @_;
  my $str;
  for(1..$num) {
    $str .= rand_letter();
  }
  return T($str);
}

my $grid;

my ($x, $y);
#my @choices = qw(A a B b C c D d E e F f);
my @choices = qw(a A b B c C d D e E f F);

foreach my $t1 (@choices) {
  $x++;
  $y = 0;
  print "$t1\t";
  foreach my $t2 (@choices) {
    $y++;
    my @seq = ($t1, $t2);
    my $c = find_cycle($orig, @seq);
    #print "'@seq' cycles in $c moves\n";
    $grid->[$x][$y] = $c;
  }
}
  print "\n";

for($x = 1; $x < scalar @{$grid}; $x++) {
  my $row = $grid->[$x];
  for($y = 1; $y < scalar @$row; $y++) {
    print "$grid->[$x][$y]\t";
  }
  print "\n";
}