# Maximum path sum I

Author: Felix Herrmann

https://projecteuler.net/problem=18

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<94304264456112>
Pod::FormattingCode<94304264456048> 4
2 Pod::FormattingCode<94304264455984> 6
8 5 Pod::FormattingCode<94304264455920> 3
```

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

Find the maximum total from top to bottom of the triangle below:

```75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23```

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

Source code: prob018-felher.pl

```use v6;

my \$triangle =
'75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23';

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 });
}

```