NAME

Algorithm::Metric::Chessboard - Calculate distances on a square grid with optional wormholes (the 'chessboard metric').

DESCRIPTION

Calculates the minimum number of moves between two points in a game played on a square grid, where one move is a jump from a point to a horizontal, vertical or diagonal neighbour.

With no other features, the number of moves taken to go from the point (x1, y1) to (x2, y2) would be quite simple:

  d( (x1, y1), (x2, y2) ) = max( abs( x1 - x2 ), abs( y1 - y2) )

However within the space are "wormholes" which allow you to travel between any two distant points, so the actual number of moves may be smaller than the above. Wormhole travel costs a fixed number of moves.

SYNOPSIS

  my @wormholes = (
    Algorithm::Metric::Chessboard::Wormhole->new( x => 5, y => 30 ),
    Algorithm::Metric::Chessboard::Wormhole->new( x => 98, y => 99 ),
  );

  my $grid = Algorithm::Metric::Chessboard->new(
                                   x_range       => [ 0, 99 ],
                                   y_range       => [ 0, 99 ],
                                   wormholes     => \@wormholes,
                                   wormhole_cost => 3,
                                               );

  my $wormhole = $grid->nearest_wormhole( x => 26, y => 53 );

  my $journey = $grid->shortest_journey(start => [1, 6], end => [80, 1]);

METHODS

new

  my @wormholes = (
    Algorithm::Metric::Chessboard::Wormhole->new(
                                                  x => 5,
                                                  y => 30,
                                                ),
    Algorithm::Metric::Chessboard::Wormhole->new(
                                                  x => 98,
                                                  y => 99,
                                                ),
  );

  my $grid = Algorithm::Metric::Chessboard->new(
                                   x_range       => [ 0, 99 ],
                                   y_range       => [ 0, 99 ],
                                   wormholes     => \@wormholes,
                                   wormhole_cost => 3,
                                               );

wormholes is optional. wormhole_cost defaults to 0.

nearest_wormhole

  my $wormhole = $grid->nearest_wormhole( x => 26, y => 53 );
  print "Nearest wormhole is " . $wormhole->id . " at ("
        . $wormhole->x . ", " . $wormhole->y . ")";

Returns a Algorithm::Metric::Chessboard::Wormhole object.

shortest_journey

  my $journey = $grid->shortest_journey(
                                         start => [1, 6],
                                         end   => [80, 1],
                                       );
  my $distance = $journey->distance;
  my @via = $journey->via;
  print "Shortest journey is $distance move"
        . ( $distance == 1 ? "" : "s" );
  if ( scalar @via ) {
      print " via " . $via[0]->id . " and " . $via[1]->id;
  }

Returns a Algorithm::Metric::Chessboard::Journey object.

AUTHOR

Kake Pugh (kake@earth.li).

COPYRIGHT

     Copyright (C) 2004 Kake Pugh.  All Rights Reserved.

This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

CREDITS

Jon Chin helped me figure out the name, Andy Armstrong and Mike Stevens helped me clarify the statement of the problem.

SEE ALSO

Why I wrote this:

• Gothador - Devilishly Good Fun!

• Vampires! The Dark Alleyway