NAME

Regexp::N_Queens - Abstract

SYNOPSIS

  use Regexp::N_Queens;

  my $N       = 8;
  my $solver  = Regexp::N_Queens:: -> new -> init (size => $N);
  my $subject = $solver -> subject;
  my $pattern = $solver -> pattern;
  if ($subject =~ $pattern) {
      foreach my $x (1 .. $N) {
          foreach my $y (1 .. $N) {
              print $+ {"Q_${x}_${y}"} ? "Q" : ".";
          }
          print "\n";
      }
  }
  else {
      say "No solution for an $N x $N board"
  }

DESCRIPTION

Solves the N-Queens problem using a regular expression. The N-Queens problem asks you to place N Queens on an N x N chess board such that no two Queens attack each other. There are solutions for each positive N, except for N == 2 and N == 3.

After creating the solver object with new, and initializing it with init (which takes a size parameter indicating the size of the board), the solver object can be queried by the methods subject and pattern. Matching the pattern returned by pattern against the string returned by subject solves the N-Queens problem: if there is a match, the Queens can be placed, if there is no match, no solution exists.

If there is a match, the content of the board can be found in the %+ hash: for each square (x, y) on the board, with 1 <= x, y <= N, we create a key $key = "Q_${x}_${y}". We can now determine whether the field contain a Queen: if $+ {$key} is true, there is a Queen on the square, else, there is no Queen.

Note that it doesn't matter in which corner of the board you place the square (1, 1), nor which direction you give to x and y, as each reflection and rotation of a solution to the N-Queens problem is also a solution.

BUGS

TODO

• Perhaps sometime, write some tests.

• This isn't fast for larger N. On the machine this module was written on, it does sizes up to 17, and size 19 in less than 1 second, size 18 in 3 seconds, size 20 in 20 seconds, size 21 in 1 second, and it gets pretty bad for larger sizes.

  Some optimizations may be possible.

SEE ALSO

DEVELOPMENT

The current sources of this module are found on github, git://github.com/Abigail/Regexp-N_Queens.git.

AUTHOR

Abigail, mailto:cpan@abigail.freedom.nl.

COPYRIGHT and LICENSE

Copyright (C) 2023 by Abigail.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

INSTALLATION

To install this module, run, after unpacking the tar-ball, the following commands:

   perl Makefile.PL
   make
   make test
   make install