###
# Maximum path sum I
# 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.
# 37 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)
###


const 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],
]

function triangle_sum(triangle)
    if length(triangle) == 0
        return 0
    end
    low   = triangle[2:end]
    left  = map(row -> row[1:end - 1], low)
    right = map(row -> row[2:end], low)
    return triangle[1][1] + max(triangle_sum(left), triangle_sum(right))
end

result = triangle_sum(TRIANGLE)

println(result)