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package Task089_2;
use strict;
use warnings;
=head1 NAME
Task089_2 - TASK 089 #2: Magical Matrix
=head1 SYNOPSIS
Display matrix as below with numbers 1 - 9. Make sure numbers are used once.
[ a b c ]
[ d e f ]
[ g h i ]
a + b + c = 15
d + e + f = 15
g + h + i = 15
a + d + g = 15
b + e + h = 15
c + f + i = 15
a + e + i = 15
c + e + g = 15
=cut
# Test the magic rules. A hash ref with a-i keys is required. Returns:
# 0: a rule failed
# 1: all rules are ok
sub _check_magic_rules_ {
my $matrix = shift;
return 0 if $matrix->{a} + $matrix->{b} + $matrix->{c} != 15;
return 0 if $matrix->{d} + $matrix->{e} + $matrix->{f} != 15;
return 0 if $matrix->{g} + $matrix->{h} + $matrix->{i} != 15;
return 0 if $matrix->{a} + $matrix->{d} + $matrix->{g} != 15;
return 0 if $matrix->{b} + $matrix->{e} + $matrix->{h} != 15;
return 0 if $matrix->{c} + $matrix->{f} + $matrix->{i} != 15;
return 0 if $matrix->{a} + $matrix->{e} + $matrix->{i} != 15;
return 0 if $matrix->{c} + $matrix->{e} + $matrix->{g} != 15;
return 1;
}
# Check if two array refs have at least one equal element (1) or not (0)
sub _match_arrays_ {
my $arr_1 = shift;
my $arr_2 = shift;
for my $i( $arr_1->@* ) {
for my $j( $arr_2->@* ) {
return 1 if $i == $j;
}
}
return 0;
}
sub _set_magic_matrix_values_ {
my $mag_mat = shift;
my $keys = shift;
my $values = shift;
for (my $i=0; $i<@$keys; $i++) {
$mag_mat->{$keys->[$i]} = $values->[$i];
}
}
=head2 magical_matrix
Return an array with valid solutions of magical matrix 3x3
=cut
sub magical_matrix {
my @solutions = ();
my $mag_mat = {};
# 1. fill @valid with 3-tuples that sum 15
my $valid = [];
my @digits = (1..9);
for my $i (@digits) {
for my $j (grep { !/$i/ } @digits ) {
for my $k (grep { !/$i|$j/ } @digits ) {
push $valid->@*, [$i, $j, $k] if $i+$j+$k == 15;
}
}
}
# Try valid 3-tuples for row 1
for my $current_1 ($valid->@*) {
_set_magic_matrix_values_ ( $mag_mat, [qw/a b c/], $current_1 );
# Filter the tuples candidates for 2nd row
my @valid_2 = grep { ! _match_arrays_ ($_, $current_1) } $valid->@*;
# Try valid 3-tuples for row 2
for my $current_2 (@valid_2) {
_set_magic_matrix_values_ ( $mag_mat, [qw/d e f/], $current_2 );
# Filter the tuples candidates for 3nd row
my @valid_3 = grep { ! _match_arrays_ ($_, $current_2) } @valid_2;
# Try valid 3-tuples for row 3
for my $current_3 ( @valid_3 ) {
_set_magic_matrix_values_( $mag_mat, [qw/g h i/], $current_3 );
# Check the magic rules, and if ok, add the current setup to
# the final solutions
_check_magic_rules_ ($mag_mat)
&& push @solutions, [$current_1, $current_2, $current_3];
}
}
}
return @solutions;
}
#----
1970;
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