in reply to Re^3: Brute force vs algorithm (PWC # 100)
in thread Brute force vs algorithm (PWC # 100)

Here, my take on this,(a variation from that solution)

Our approaches are not that different, your dynamic "cache" is just my explicit "weight" triangle.

And you are needing more resources for recursion and hash.

But you could improve it by adding bound criteria (i.e. no need to calculate a subtree if it has no chance to be better than the current minimum).

edit

Though I'm not sure this will pay of, my algorithm is already O(m) with m #cells.

<Reveal this spoiler or all in this thread>

Cheers Rolf
(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery

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Re^5: Brute force vs algorithm (PWC # 100)
by tybalt89 (Monsignor) on Feb 16, 2021 at 04:39 UTC

    For people who don't like recursion and hashes :) 

    #!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11128406
use warnings;
use List::Util qw( reduce );

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

for my $r ( reverse 0 .. $#d - 1 )
  {
  for my $c ( 0 .. $r )
    {
    $d[$r][$c] .= ' + ' . reduce { eval $a <= eval $b ? $a : $b }
      $d[$r+1][$c], $d[$r+1][$c+1];
    }
  }

print "$d[0][0]\n";

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      Or for a big mess, compute the score and the path simultaneously :) 

      #!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11128406
use warnings;
use List::Util qw( reduce min );

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

$d[$#d][$_] = [ $d[$#d][$_], $d[$#d][$_] ] for 0 .. $#d;

for my $r ( reverse 0 .. $#d - 1 )
  {
  for my $c ( 0 .. $r )
    {
    $d[$r][$c] = [ $d[$r][$c] + min( $d[$r+1][$c][0], $d[$r+1][$c+1][0
+]),
      "$d[$r][$c] + " . (reduce { $a->[0] <= $b->[0] ? $a : $b }
      $d[$r+1][$c], $d[$r+1][$c+1])->[1] ];
    }
  }

print "value $d[0][0][0]  path $d[0][0][1]\n";

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      Outputs: 

      value 8  path 1 + 2 + 4 + 1

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In Section Meditations