<gh_stars>0
"""
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  
"""
# load as 2d array
# check if maximum of row+1 is reachable
# if yes: row = row+1
# if no: check if max row+1 is reachable by runner up from row and if max(row)+runnerUp(row+1) > runnerup(row)+max(row+1)

pyramid = [[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]]

def main():
    i = len(pyramid)-2
    while (i >= 0):
        for j in range(0,len(pyramid[i])):
            pyramid[i][j]+=max(pyramid[i+1][j],pyramid[i+1][j+1])
        i -= 1
    print("Problem 18: {0}".format(pyramid[0][0]))
