Re: Re: Matrix Formation

[tall_man]

Here is a possible implementation of CheckSolution (for 3x3 only -- generalization is possible but it is left as an exercise for the reader):

sub CheckSolution
{
  my $pNum = shift;

  my @Sol=();

  # Do some easy pair checks first.
  my @digmap;
  foreach my $n (@$pNum) {
     my @digits = split //,$n;
     foreach (0..$#digits) {
        push @{$digmap[$_]->{$digits[$_]}},$n;
     }
  }
  # Two or more with same first digit.
  my $ref0 = $digmap[0];
  my @lst0 = grep { scalar(@{$ref0->{$_}}) > 1 } keys %$ref0;
  return @Sol if (! scalar(@lst0));

  # Two or more with same middle digit.
  my $ref1 = $digmap[1];
  my @lst1 = grep { scalar(@{$ref1->{$_}}) > 1 } keys %$ref1;
  return @Sol if (! scalar(@lst1));

  # Two or more with same last digit
  my $ref2 = $digmap[2];
  my @lst2 = grep { scalar(@{$ref2->{$_}}) > 1 } keys %$ref2;
  return @Sol if (! scalar(@lst2));

  #print "Passed pair test\n";

  # Use these lists for candidates for the three row positions.
  my @uppers = map { @{$ref0->{$_}} } @lst0;
  my @centers = map { @{$ref1->{$_}} } @lst1;
  my @bottoms = map { @{$ref2->{$_}} } @lst2;

  my ($upper, $center, $bottom);
  my ($a, $b, $c, $d, $e, $f, $g, $h, $i);
  my ($adg, $beh, $cfi);

  # hash to simplify checking for duplicates.
  my %wholeset = map { $_ => 1 } @$pNum;
  my (%t1, %t2, %t3);
  foreach $upper (@uppers) {
     %t1 = %wholeset;
     $t1{$upper} = 0;
     foreach $center (@centers) {
        next if (! $t1{$center});
        %t2 = %t1;
        $t2{$center} = 0;
        foreach $bottom (@bottoms) {
           next if (! $t2{$bottom});
           %t3 = %t2;
           $t3{$bottom} = 0;

           ($a, $b, $c) = split //,$upper;
           ($d, $e, $f) = split //,$center;
           ($g, $h, $i) = split //,$bottom;

           $adg = $a . $d . $g;
           next if (! $t3{$adg});
           $t3{$adg} = 0;

           $beh = $b . $e . $h;
           next if (! $t3{$beh});
           $t3{$beh} = 0;

           $cfi = $c . $f . $i;
           next if (! $t3{$cfi});

           # Solution found - return it.
           return ($upper, $center, $bottom);
        } # bottom
     } # center
  } #upper
  return @Sol;
}

I tried this and it found the 132-792-660 (divisor 44) case in about 4 seconds.