Re: Lights out puzzle (non-perl solution)

[ambrus]

Here's a non-perl solution, with explanation.

For larger boards, this one is much faster than my program above. (You could try (29, 30, 2) or (39, 40, 2) as large examples where there's a unique button combination this program finds very quickly but that would take ages to found with the previous program.)

<Reveal this spoiler or all in this thread>

[salva]

Now solving a linear equation over GF(2) is something apparently very few libraries can do

That's quite easy to implement, so easy that, well... see Algorithm::GaussianElimination::GF2.

Using that module, the Lights On problem gets reduced to:

use strict;
use warnings;

use Algorithm::GaussianElimination::GF2;

use 5.010;

(@ARGV >= 1 and @ARGV <= 2) or die "Usage:\n  $0 len [width]\n\n";

my ($len, $w) = @ARGV;

unless (defined $w) {
    $w = int sqrt($len);
    $w++ unless $w * $w == $len;
}

my $a = Algorithm::GaussianElimination::GF2->new;

for my $ix (0..$len-1) {
    my $eq = $a->new_equation;

    $eq->b(1);
    $eq->a($ix, 1);
    my $up = $ix - $w;
    $eq->a($up, 1) if $up >= 0;
    my $down = $ix + $w;
    $eq->a($down, 1) if $down < $len;
    my $left = $ix - 1;
    $eq->a($left, 1) if $left % $w + 1 != $w;
    my $right = $ix + 1;
    $eq->a($right, 1) if $right % $w and $right < $len;
}

my ($sol, @base0) = $a->solve;

if ($sol) {
    my @sol = @$sol;
    while (@sol) {
        my @row = splice @sol, 0, $w;
        say "@row";
    }

    for my $sol0 (@base0) {
        say "sol0:";
        my @sol0 = @$sol0;
        while (@sol0) {
            my @row = splice @sol0, 0, $w;
            say "@row";
        }
    }
}
else {
    say "no solution found"
}

On my computer the 14x14-7 problem gets solved in 0.06 seconds.