package Math::MagicSquare::Generator;
use strict;
use Carp;
use vars qw($VERSION);
$VERSION = '0.01';
sub _sum {
my $sum = 0;
$sum += $_ for @_;
return $sum
}
sub new {
my ($class, %opt) = @_;
$opt{size} ||= 5;
$opt{start} ||= 1;
$opt{step} ||= 1;
croak "Size needs to be a positive, odd integer"
unless $opt{size} > 0 and
$opt{size} % 2 and
$opt{size} == int($opt{size});
my $self = [
map {
[ (undef) x $opt{size} ]
} 1..$opt{size}
];
my $value = $opt{start};
my $halv = int(@$self / 2);
for my $start_x (-$halv..$halv) {
my $x = $start_x - 1;
my $y = $x + @$self + 1;
for (1 .. @$self) {
$x = $x - @$self if ++$x > $#$self;
$y = $y - @$self if --$y > $#$self;
$self->[$y][$x] = $value;
$value += $opt{step};
}
}
return bless $self, $class;
}
sub hflip {
my ($self) = @_;
my $clone;
push @$clone, [ reverse @$_ ] for @$self;
return bless $clone, ref $self;
}
sub vflip {
my ($self) = @_;
my $clone;
push @$clone, [ @$_ ] for reverse @$self;
return bless $clone, ref $self;
}
sub sum {
my ($self) = @_;
return _sum( @{ $self->[0] } );
}
sub check {
my ($self) = @_;
my $sum = $self->sum;
# Horizontals
for (@$self[1..$#$self]) {
return undef if @$_ > @$self; # undef if not square
return undef if _sum(@$_) != $sum;
}
# Verticals
for my $x (0..$#$self) {
return undef if _sum(map $self->[$_][$x], 0..$#$self) != $sum;
}
# Diagonals
return undef if _sum(map $self->[$_][$_], 0..$#$self) != $sum;
return undef if _sum(map $self->[$#$self - $_][$_], 0..$#$self) != $sum;
# Duplicates
my %seen;
$seen{$_}++ for map @$_, @$self;
return undef if _sum(values %seen) != keys %seen;
# Passed all tests!
return $sum;
}
sub as_string {
my ($self) = @_;
my $max = 0;
length > $max and $max = length for map @$_, @$self;
return map { join(' ', map {' 'x($max - length) . $_} @$_) . "\n" } @$self;
}
sub as_html {
my ($self) = @_;
return "\n" . join("\n",
map { '| ' . join(' | ', @$_) . ' |
' } @$self) .
"\n
\n";
}
sub as_csv {
my ($self) = @_;
return join("\n", map { join ',', @$_ } @$self) . "\n";
}
1;
__END__
=head1 NAME
Math::MagicSquare::Generator - Magic Square Generator
=head1 SYNOPSIS
use Math::MagicSquare::Generator
my $square = Math::MagicSquare::Generator->new(size => 5,
step => 3,
start=> 6);
for ($square, $square->vflip, $square->hflip) {
print $_->as_string;
print "-----\n";
}
$square->[0][0] = -15; # Break magic :)
print $square->check ? "Magic square\n" : "Just a square\n";
print '';
print Math::MagicSquare::Generator->new->hflip->vflip->as_html;
print '';
=head1 DESCRIPTION
This module creates magic squares. A magic square is a square in which
all numbers are different and the sums of all rows, all columns and
the two diagonals are equal.
Math::MagicSquare::Generator cannot create panmagic squares, or squares
that have an even size. (A panmagic square is magic square where the
"wrapped" diagonals are also equal.)
=head1 EXAMPLE
3 16 9 22 15 This square is the output of
20 8 21 14 2 print Math::MagicSquare::Generator->new->as_string;
7 25 13 1 19
24 12 5 18 6
11 4 17 10 23
The sums of the rows are 65.
The sums of the columns are 65.
The sums of the diagonals are 65.
=head1 METHODS
=over 10
=item new
The constructor that generates the square immediately. It
creates an object using the given named arguments. Valid arguments are
C, C and C. C has to be positive, odd and
integer.
=item check
A checker - returns the common sum if the square is magic, or undef if
it's not. Because the sum can never be 0, you can use this as a boolean
value. (Well, the sum in a 1x1 square can be 0, if the single number is
0.) You can use this method to check if the square has been tampered with.
=item sum
Returns the common sum of the rows, columns and diagonals.
=item vflip, hflip
These methods return a vertically or horizontally flipped clone of the
square. The clone is a Math::MagicSquare::Generator, so stacking these
methods is possible.
=item as_string, as_html, as_csv
DWYM - return the square as a formatted string, piece of html or in
CSV format.
=back
=head1 THIS MODULE AND Math::MagicSquare
Math::MagicSquare is a module that checks if a square is magical. It
takes a list in its C method, so you'll have to dereference the
generated square:
use Math::MagicSquare;
use Math::MagicSquare::Generator;
my $square = Math::MagicSquare::Generator->new;
print Math::MagicSquare->new( @$square )->check, "\n"; # 2
Its C will always return 2 for squares generated using this
module (or 3 if it's a 1x1 square.
=head1 KNOWN BUGS
None yet.
=head1 AUTHOR
Juerd
=cut