#
# MagicSquare.pm, version 2.04 13 Dec 2003
#
# Copyright (c) 2003 Fabrizio Pivari Italy
# fabrizio@pivari.com
#
# Free usage under the same Perl Licence condition.
#
package Math::MagicSquare;
use Carp;
use GD;
use strict;
use vars qw(@ISA @EXPORT @EXPORT_OK $VERSION);
use Exporter();
@ISA= qw(Exporter);
@EXPORT=qw();
@EXPORT_OK=qw(new check print printhtml rotation reflection);
$VERSION='2.04';
sub new {
my $type = shift;
my $self = [];
my $len = scalar(@{$_[0]});
my $numelem = 0;
for (@_) {
push(@{$self}, [@{$_}]);
$numelem += scalar(@{$_});
}
croak "Math::MagicSquare::new(): number of rows and columns must be equal"
if ($numelem != $len*$len);
bless $self, $type;
}
sub check {
my $self = shift;
my $i=0; my $j=0;
my $line1=0; my $line2=0; my $diag1=0; my $diag2=0; my $SUM=0;
my $sms=1;
my $len = scalar(@{$self});
# Magic Constant for a Magic Square 1,2,...,n
my $sum=$len*($len*$len+1)/2;
# Generic Magic Constant
for ($i=0;$i<$len;$i++) {
$SUM+=$self->[$i][0];
}
if ($SUM != $sum) {$sum=$SUM;}
# Check lines and columns
for ($i=0;$i<$len;$i++) {
$j=0; $line1=0; $line2=0;
for ($j=0;$j<$len;$j++) {
$line1+=$self->[$i][$j];
$line2+=$self->[$j][$i];
}
if ($line1 != $sum || $line2 != $sum) {
# This isn't a Magic
return(0);
}
}
# Check diagonals and broken diagonals
for ($j=0;$j<$len;$j++) {
$i=0; $diag1=0; $diag2=0;
for ($i=0;$i<$len;$i++) {
$diag1+=$self->[$i][($i+$j)%$len];
$diag2+=$self->[$len-1-$i][($i+$j)%$len];
}
if ($j == 0) {
if ($diag1 != $sum || $diag2 != $sum) {
# This is a Semimagic Square
return(1);
}
} else {
if ($diag1 != $sum || $diag2 != $sum) {
# This is a Magic Square
return(2);
}
}
}
# This is a Panmagic Square
return(3);
}
sub print {
my $self = shift;
my $initialtext = shift;
my $i=0; my $j=0;
my $len = scalar(@{$self});
print "$initialtext\n" if $initialtext;
print @_ if scalar(@_);
for ($j=0;$j<$len;$j++) {
for ($i=0;$i<$len;$i++) {
printf "%5d ", $self->[$j][$i];
}
print "\n";
}
}
sub printhtml {
my $self = shift;
my $i=0; my $j=0;
my $len = scalar(@{$self});
print qq!<TABLE border=3 width="2" height="2" cellpadding=1 cellspacing=1>\n!;
for ($j=0;$j<$len;$j++) {
print "<TR>\n";
for ($i=0;$i<$len;$i++) {
print "<TD align=right><FONT size=+2><B>$self->[$j][$i]</B></font></TD>\n";
}
print "</TR>\n";
}
print "</TABLE>\n";
}
sub printimage {
my $self = shift;
my $i=0; my $j=0;
my $len = scalar(@{$self});
my $CELLGRIDSIZE = 31;
my $GRIDSIZE = 8+($len -1)*2+$len*$CELLGRIDSIZE;
my $im=new GD::Image($GRIDSIZE,$GRIDSIZE);
my $bg=$im->colorAllocate(255,255,255);
my $fg=$im->colorAllocate(0,0,0);
# GRID
# $im->transparent($bg);
$im->filledRectangle(0,0,255,255,$bg);
$im->filledRectangle(0,0,4,$GRIDSIZE,$fg);
$im->filledRectangle(0,0,$GRIDSIZE,4,$fg);
my $tmp = $GRIDSIZE -5;
$im->filledRectangle($tmp,0,$GRIDSIZE,$GRIDSIZE,$fg);
$im->filledRectangle(0,$tmp,$GRIDSIZE,$GRIDSIZE,$fg);
my $xy = 4 + $CELLGRIDSIZE;
my $xy2 = $xy +2;
for (1..$len-1)
{
$im->filledRectangle($xy,0,$xy2,$GRIDSIZE,$fg);
$im->filledRectangle(0,$xy,$GRIDSIZE,$xy2,$fg);
$xy = $xy2 + $CELLGRIDSIZE;
$xy2 = $xy + 2;
}
# NUMBERS
my $x1 = 4 + 8;
my $y1 = 4 + 9;
$j=0;
for ($j=0;$j<$len;$j++)
{
$i=0;
for ($i=0;$i<$len;$i++)
{
# to hit the centre with numbers < -9
if ($self->[$j][$i] < -9) { $x1 = $x1 - 3; }
# to hit the centre with numbers between -9 and -1
if ($self->[$j][$i] < 0 && $self->[$j][$i] > -10) { $x1 = $x1 - 2; }
# to hit the centre with numbers between 0 and 9
if ($self->[$j][$i] < 10 && $self->[$j][$i] >= 0) { $x1 = $x1 + 4; }
# to hit the centre with numbers > 99
if ($self->[$j][$i] > 99) { $x1 = $x1 - 4; }
$im->string(gdLargeFont,$x1,$y1,"$self->[$j][$i]",$fg);
$x1 = $x1 + $CELLGRIDSIZE + 2;
if ($self->[$j][$i] < -9) { $x1 = $x1 + 3; }
if ($self->[$j][$i] < 0 && $self->[$j][$i] > -10) { $x1 = $x1 + 2; }
if ($self->[$j][$i] < 10 && $self->[$j][$i] >= 0) { $x1 = $x1 - 4; }
if ($self->[$j][$i] > 99) { $x1 = $x1 + 4; }
}
$x1 = 4 + 8;
$y1 = $y1 + $CELLGRIDSIZE + 2;
}
binmode STDOUT;
print $im -> png;
}
sub rotation {
my $self = shift;
my $i=0; my $j=0;
my @TMP;
my $len = scalar(@{$self});
for ($j=0;$j<$len;$j++) {
for ($i=0;$i<$len;$i++) {
$TMP[$j][$i]=$self->[$j][$i];
}
}
for ($j=0;$j<$len;$j++) {
for ($i=0;$i<$len;$i++) {
$self->[$j][$i]=$TMP[$len-1-$i][$j];
}
}
}
sub reflection {
my $self = shift;
my $i=0; my $j=0;
my @TMP;
my $len = scalar(@{$self});
for ($j=0;$j<$len;$j++) {
for ($i=0;$i<$len;$i++) {
$TMP[$j][$i]=$self->[$j][$i];
}
}
for ($j=0;$j<$len;$j++) {
for ($i=0;$i<$len;$i++) {
$self->[$i][$j]=$TMP[$i][$len-1-$j];
}
}
}
1;
__END__
=pod
=head1 NAME
Math::MagicSquare - Magic Square Checker and Designer
=head1 SYNOPSIS
use Math::MagicSquare;
$a= Math::MagicSquare -> new ([num,...,num],
...,
[num,...,num]);
$a->print("string");
$a->printhtml();
$a->printimage();
$a->check();
$a->rotation();
$a->reflection();
=head1 DESCRIPTION
The following methods are available:
=head2 new
Constructor arguments are a list of references to arrays of the same
length.
$a = Math::MagicSquare -> new ([num,...,num],
...,
[num,...,num]);
=head2 check
This function can return 4 value
=over
=item *
B<0:> the Square is not Magic
=item *
B<1:> the Square is a B<Semimagic Square> (the sum of the rows and the columns
is equal)
=item *
B<2:> the Square is a B<Magic Square> (the sum of the rows, the columns and the
diagonals is equal)
=item *
B<3:> the Square ia B<Panmagic Square> (the sum of the rows, the columns, the
diagonals and the broken diagonals is equal)
=back
=head2 print
Prints the Square on STDOUT. If the method has additional parameters,
these are printed before the Magic Square is printed.
=head2 printhtml
Prints the Square on STDOUT in an HTML format (exactly a inside a TABLE)
=head2 printimage
Prints the Square on STDOUT in png format.
=head2 rotation
Rotates the Magic Square of 90 degree clockwise
=head2 reflection
Reflect the Magic Square
=head1 REQUIRED
GD perl module.
=head1 EXAMPLE
use Math::MagicSquare;
$A = Math::MagicSquare -> new ([8,1,6],
[3,5,7],
[4,9,2]);
$A->print("Magic Square A:\n");
$A->printhtml();
$i=$A->check();
if($i == 2) {print "This is a Magic Square.\n";}
$A->rotation();
$A->print("Rotation:\n");
$A->reflection();
$A->print("Reflection:\n");
$A->printimage();
This is the output:
Magic Square A:
8 1 6
3 5 7
4 9 2
<TABLE border=3 width="2" height="2" cellpadding=1 cellspacing=1>
<TR>
<TD align=right><FONT size=+2><B>8</B></font></TD>
<TD align=right><FONT size=+2><B>1</B></font></TD>
<TD align=right><FONT size=+2><B>6</B></font></TD>
</TR>
<TR>
<TD align=right><FONT size=+2><B>3</B></font></TD>
<TD align=right><FONT size=+2><B>5</B></font></TD>
<TD align=right><FONT size=+2><B>7</B></font></TD>
</TR>
<TR>
<TD align=right><FONT size=+2><B>4</B></font></TD>
<TD align=right><FONT size=+2><B>9</B></font></TD>
<TD align=right><FONT size=+2><B>2</B></font></TD>
</TR>
</TABLE>
This is a Magic Square.
Rotation:
4 3 8
9 5 1
2 7 6
Reflection:
8 3 4
1 5 9
6 7 2
=head1 AUTHOR
Fabrizio Pivari fabrizio@pivari.com
http://www.pivari.com/
=head1 Copyright
Copyright 2003, Fabrizio Pivari fabrizio@pivari.com
This library is free software; you can redistribute it and/or modify it under
the same terms as Perl itself.
Are you interested in a Windows cgi distribution?
Test http://www.pivari.com/squaremaker.html and contact me.
=head1 Availability
The latest version of this library is likely to be available from:
http://www.pivari.com/magicsquare.html
and at any CPAN mirror
=head1 Information about Magic Square
Do you like Magic Square?
Do you want to know more information about Magic Square?
Try to visit
=over
=item A very good introduction on Magic Square
http://mathworld.wolfram.com/MagicSquare.html
=item Whole collections of links and documents in Internet
http://mathforum.org/alejandre/magic.square.html
http://mathforum.org/te/exchange/hosted/suzuki/MagicSquare.html
=item A good collection of strange Magic Square
http://www.geocities.com/pivari/examples.html
=back
=cut