"""
Copyright 2016 Peter Beard
Distributed under the GNU GPL v2. For full terms, see the LICENSE file.

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.

3
7 4
2 4 6
8 5 9 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)
"""

def solution():
    values = [
        [75],
        [95, 64],
        [17, 47, 82],
        [18, 35, 87, 10],
        [20, 4, 82, 47, 65],
        [19, 1, 23, 75, 3, 34],
        [88, 2, 77, 73, 7, 63, 67],
        [99, 65, 4, 28, 6, 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, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
        [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]
    ]
    # The maximum path can be found by moving through the graph from bottom to
    # top, replacing each value with itself plus its largest neighbor. By doing
    # this, the sum of the largest path will end up at the top of the triangle
    for y in reversed(range(0, len(values)-1)):
        for x in reversed(range(0, len(values[y]))):
            v = values[y][x]
            down = values[y+1][x]
            right = values[y+1][x+1]
            if down > right:
                values[y][x] = v + down
            else:
                values[y][x] = v + right

    # The sum of the largest path is now at the top of the triangle
    return values[0][0]

print("The maximum total route sums to {}".format(solution()))
