NAME
Games::Sudoku::Solver  Solve 9x9Sudokus recursively.
VERSION
This document describes Games::Sudoku::Solver version 1.0.0
SYNOPSIS
use Games::Sudoku::Solver qw(:Minimal set_solution_max count_occupied_cells);
# specify a Sudoku as flat array (this one has 10 solutions)
my @sudoku_raw = qw(
0 4 0 0 2 0 9 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 6 8 5 0
5 8 2 3 0 0 7 0 0
0 0 0 8 0 7 0 0 0
0 0 9 0 0 5 1 3 8
0 9 7 1 0 0 0 0 0
0 2 0 0 0 0 0 0 0
0 0 4 0 3 0 0 0 0
);
my @sudoku; # the Sudoku data structure
my @solution; # the solution data structure
sudoku_set( \@sudoku, \@sudoku_raw ); # convert raw to internal representation
print "\n===== Sudoku =====\n";
sudoku_print( \@sudoku ); # print the Sudoku
my $cells_occupied = count_occupied_cells( \@sudoku ); # some statistics
print "\n", $cells_occupied, " cells occupied, ",
81$cells_occupied, " cells free\n";
set_solution_max(4); # stop having 4 solutions found
my $solutions = sudoku_solve( \@sudoku, \@solution); # solve the Sudoku
foreach my $n ( 1..$solutions ) { # print the solutions
print "\n solution $n \n";
sudoku_print( $solution[$n1] );
}
DESCRIPTION
This module solves 9x9Sudoku puzzles by recursion. There is no restriction to the difficulty and the number of solutions.
The puzzle can be stored in a single dimension array or in a file, where unknown cells are presented by zeros or points.
Algorithm
Solving Sudokus is perfectly suited for the application of a recursive algorithm. The basic idea: Find the first free cell, insert an allowed value and get a new Sudoku with one free cell less or a solution if it is complete. In more details:
Build the list of free cells starting from the upper left corner. Set an index on the first free cell.
Build the set of allowed (and until now unused) values for the actual cell by inspecting the according row, column and submatrix.
If there exists an allowed values and the Sudoku is complete a solution is found. Discard this value for this cell from the set of allowed values. Go to step 2.
If there exists an allowed values and the Sudoku is not complete go ahead to the next free cell in the list of free cells. Go to step 2.
If there exists no allowed value free the actual cell and go back one position in the list of free cells. Go to step 2.
The algorithm walks through a tree of mostly incomplete Sudokus. The leaves which are complete are solutions (if any).
SUBROUTINES/METHODS
There are two export tags. Minimal
exports sudoku_set
, sudoku_solve
, and sudoku_print
. All
exports all subroutines described below.
count_occupied_cells
PURPOSE: count actually occupied cells
PARAMETERS: (1) reference to a Sudoku (array of arrays)
RETURNS: number of occupied cells
get_solution_max
PURPOSE: get maximal number of solutions to search for
PARAMETERS: 
RETURNS: maximal number of solutions to search for
set_solution_max
PURPOSE: set maximal number of solutions to search for
PARAMETERS: postive number (postive sign allowed)
RETURNS: 
sudoku_check
PURPOSE: Check Sudoku for correctness
DESCRIPTION:  check rows, columns
 check submatrices; numbering:
++++
 1  2  3 
++++
 4  5  6 
++++
 7  8  9 
++++
Die of error (croak) if Sudoku is not correct.
PARAMETERS: (1) reference to a Sudoku (array of arrays)
RETURNS: 
sudoku_print
PURPOSE: print Sudoku
DESCRIPTION: Simple text output
PARAMETERS: (1) reference to a Sudoku (array of arrays)
RETURNS: 
sudoku_read
PURPOSE: read a Sudoku from a file; check format
PARAMETERS: (1) reference to a Sudoku (array of arrays)
(2) name of the input file (scalar)
RETURNS: 
There a two file formats. Format 1 specifies empty cells with 0.
The cells are separated by whitespaces. Perl comments are allowed
on separate lines:
# 1 solution
0 3 0 2 6 7 0 4 0
1 0 0 0 0 0 0 0 5
7 4 0 5 0 1 0 9 2
9 0 5 0 0 0 1 0 3
6 0 0 0 5 0 0 0 8
8 0 4 0 0 0 7 0 9
2 9 0 7 0 4 0 8 6
3 0 0 0 0 0 0 0 4
0 5 0 6 1 2 0 3 0
The second format uses points for the empty cells. Separating whitespaces
are not allowed:
# 1 solution
3.4...6.2
9..627..4
6..1.4..7
249...731
16.....85
.83...46.
7..8.5..3
...263...
8.5...9.6
There is no restriction on the number of empty cells.
A completely empty Sudokus would generate all possible solutions:
# 6.670.903.752.021.072.936.960 solutions
#
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
sudoku_set
PURPOSE: store the 81 values of a Sudoku from a flat array into
the internal representation (array of arrays)
PARAMETERS: (1) reference to a Sudoku (array of arrays)
(2) reference to flat array of 81 values (digits)
RETURNS: 
COMMENTS: The Sudoku will be checked for correctness.
sudoku_solve
DESCRIPTION: solve a Sudoku by recursion
PARAMETERS: (1) reference to a Sudoku (array of arrays)
(2) reference to a solution array (array of arrays of arrays)
(3) restrictions (hash; optional)
RETURNS: number of solutions found
Possible restrictions are:
 Maximal number of solutions (0=unbound)

solution_max => 10
 Unique digits on the 1. diagonal (upperleft to lowerright)

diagonal_ul_lr => 0 # not unique diagonal_ul_lr => 1 # unique
 Unique digits on the 2. diagonal (lowerleft to upperright)

diagonal_ll_ur => 0 # not unique diagonal_ll_ur => 1 # unique
DIAGNOSTICS
 error
"$0 : failed to open input file $filename : $!\n"

Subroutine
sudoku_read
could not open the specified file.  error
"error in file '$filename', line ${.}.\n"

Subroutine
sudoku_read
found a format error when reading the specified file.  croak
"value repeated in line ${i} \n"

Subroutine
sudoku_check
found a format error when checking a Sudoku (may be after reading it withsudoku_read
).  croak
"value repeated in column ${i} \n"

Subroutine
sudoku_check
found a format error when checking a Sudoku (may be after reading it withsudoku_read
).  croak
"value repeated in submatrix ${i} \n"

Subroutine
sudoku_check
found a format error when checking a Sudoku (may be after reading it withsudoku_read
).  warning
"$0 : failed to close input file $filename : $!\n";

Subroutine
sudoku_read
could not close the specified file.
CONFIGURATION AND ENVIRONMENT
Games::Sudoku::Solver requires no configuration files or environment variables.
DEPENDENCIES
Carp  warn of errors
Clone  recursively copy Perl datatypes
INCOMPATIBILITIES
None reported.
BUGS AND LIMITATIONS
This module can only solve 9x9Sudokus. No bugs have been reported.
Please report any bugs or feature requests to buggamessudokusolver@rt.cpan.org
, or through the web interface at http://rt.cpan.org.
AUTHOR
Dr.Ing. Fritz Mehner <mehner@fhswf.de>
LICENSE AND COPYRIGHT
Copyright (c) 20062007, Dr.Ing. Fritz Mehner <mehner@fhswf.de>
. All rights reserved.
This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself. See perlartistic.
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