# NAME `Regexp::N_Queens` - Solve the `N`-Queens problem by using a regular expression. # VERSION This is version `2023021701` of `Regexp::N_Queens`. # 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 about 3 seconds, size 20 in about 20 seconds, size 21 in just over 1 second, but it get pretty bad for size 22 and above. Some optimizations may be possible. # SEE ALSO # DEVELOPMENT The current sources of this module are found on [github](https://github.com/Abigail/Regexp-N_Queens). # AUTHOR [Abigail](mailto:cpan@abigail.freedom.nl). # COPYRIGHT and LICENSE Copyright © 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 ~~~~