# Path sum: two ways

Author: Moritz Lenz

https://projecteuler.net/problem=81

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold and is equal to 2427.

131 673 234 103 18⎞ ⎜201 96 342 965 150⎟ ⎜630 803 746 422 111⎟ ⎜537 699 497 121 956⎟ ⎝805 732 524 37 331

Find the minimal path sum, in matrix.txt, a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.

Source code: prob081-moritz.pl

```use v6;

my @m;

my \$matrix-file = \$*SPEC.catdir(\$*PROGRAM-NAME.IO.dirname, 'matrix.txt');
my \$f = open \$matrix-file or die "Can't open file for reading: \$!";
for \$f.lines -> \$line {
@m.push: \$line.comb(/\d+/).Array.item;
}
\$f.close;

my (\$max-x, \$max-y) = +@m[0], +@m;

@m[0][\$_] += @m[0][\$_-1] for 1..\$max-x-1;
@m[\$_][0] += @m[\$_-1][0] for 1..\$max-y-1;

for 1..\$max-y-1 -> \$y {
for 1..\$max-x-1 -> \$x {
@m[\$y][\$x] += @m[\$y-1][\$x] min @m[\$y][\$x-1];
}
}

say @m[*-1][*-1];

```