'''
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
'''

'''
final answer: 1074
'''

import numpy as np

# init constant
t = np.array([
    [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],
])


# compute the maximum sum path
def compute():
    # all we need to do is start from the one to the last row and replace every number with the maximum of the current
    # number plus the bottom adjacent number and work our way up to the top
    # note: t.shape[0] = number of rows, since it starts from 0 and we want one to the last -> t.shape[0]-2
    for i in range(t.shape[0] - 2, -1, -1):
        max_num = 0
        for j in range(len(t[i])):
            t[i][j] = t[i][j] + max(t[i + 1][j], t[i + 1][j + 1])

    return t[0][0]  # this would be the max


if __name__ == '__main__':
    print("The maximum path sum is " + str(compute()))
