Classic caching problem. Each cell is computed only once. 

#!/usr/bin/perl

use strict;
use warnings;
use List::Util qw( min );

local $_ = <<END;
            1
           2 4
          6 4 9
         5 1 7 2
END
my @d = map [ split ], split /\n/;

my %cache;

print path(0, 0), "\n";

sub path
  {
  my ($r, $c) = @_;
  $cache{"@_"} //= $r < $#d
    ? $d[$r][$c] + min(path($r+1, $c), path($r+1, $c+1))
    : $d[$r][$c]
  }

[download]

It wasn't clear from the problem whether just the sum was needed or the whole path. This just returns 8

In reply to Re: Brute force vs algorithm (PWC # 100) by tybalt89
in thread Brute force vs algorithm (PWC # 100) by 1nickt

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