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Fun problem!

I call this "Smart Brute Force".
It fills in one column at a time with each remaining number in turn, then checks to see if the leading parts of each row are possible from left over numbers.

#!/usr/bin/perl -l # http://perlmonks.org/?node_id=1197354 use strict; use warnings; @ARGV or @ARGV = qw( 113443 143132 241131 321422 323132 331222 341114 412433 414422 431331 443112 444313 ); my $half = @ARGV / 2; my $steps = 0; my @stack = [ "\n" x $half, join '', map "$_\n", @ARGV ]; NEXT: while( @stack ) { my ($have, $rest) = @{ pop @stack }; $steps++; my %lefts; # validate legal so far $lefts{$_}++ for $have =~ /^(.+)\n/gm; for my $head (keys %lefts) { $lefts{$head} <= ( () = $rest =~ /^$head/gm ) or goto NEXT; } if( $rest =~ tr/\n// == $half ) # half left means completed { print "answer in $steps steps\n\n$have"; print "diagonal ", $have =~ /(\d)(?:..{$half})?/gs; exit; } while( $rest =~ /^(.+)\n/gm ) # try each number remaining { my ($before, $after, @digits) = ($`, $', split //, $1); push @stack, [ $have =~ s/(?=\n)/ shift @digits /ger, $before . $after ]; } } print "failed to find solution in $steps steps\n";

Output:

answer in 35 steps 412433 414422 431331 341114 143132 331222 diagonal 411132

Computes the answer in less than 0.1 seconds.


In reply to Re: Number Grid Fillin by tybalt89
in thread Number Grid Fillin by QM

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