# Maximum path sum II

Author: Felix Herrmann

https://projecteuler.net/problem=67

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

```   Pod::FormattingCode<94304264470448>
Pod::FormattingCode<94304264470384> 4
2 Pod::FormattingCode<94304264470320> 6
8 5 Pod::FormattingCode<94304264470256> 3
```

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom in triangle.txt, a 15K text file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version of Problem 18. It is not possible to try every route to solve this problem, as there are 299 altogether! If you could check one trillion (1012) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)

Source code: prob067-felher.pl

```use v6;

my \$triangle = slurp(\$*SPEC.catdir(\$*PROGRAM-NAME.IO.dirname, '/triangle.txt'));
my @lines = string-to-array(\$triangle).reverse;

# reduce the triangle by adding up the lines until only one line with one
# element is left; then print it.

# this function assumes the shorter and longer array to be consecutive lines
# in an reversed triangle. It then adds each of the maxima of consecutive fields
# of the longer array to their shared diagonal neighbour in the shorter array.
sub add-maxima(@longer, @shorter is copy) {
for 0 .. @longer - 2 -> \$i {
@shorter[\$i] += max @longer[\$i], @longer[\$i + 1];
}
return @shorter;
}

sub string-to-array(\$string) {
my @lines = \$string.lines;
@lines .= map(-> \$line { \$line.comb(/\d+/).item });
}

```