In [49]:

    

"""
   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
"""

# Idea: starting from the bottom, compute maximum sum for each row. Well, the first row is actually useless, but 
# from the second row on, get the maximum for each triangle of three numbers, and then use that. 

def findTriangleMaxPath(x):
    "Returns maximum from one path in triangle from file x."
    intLsts = []
    with open(x) as f:
        for line in f:
            int_list = [int(i) for i in line.split()]
            intLsts.append(int_list)
    # print(intLsts)
    # print(len(intLsts))
    for i in range(len(intLsts)-1,-1,-1):
        # print(i," ",intLsts[i])
        for j in range(len(intLsts[i]) - 1): # the last comparison happens at the second-to-last element
                                             # with the last one, so like 1:2, 2:3,..., n-1:n
            # print(intLsts[i][j],intLsts[i][j+1]) 
            # print(intLsts[i-1][j])
            if intLsts[i][j] + intLsts[i-1][j] > intLsts[i][j+1] + intLsts[i-1][j]:
                intLsts[i-1][j] = intLsts[i][j] + intLsts[i-1][j]
            else:
                intLsts[i-1][j] = intLsts[i][j+1] + intLsts[i-1][j]
    return intLsts[0][0]


    

In [50]:

    

findTriangleMaxPath("P18_triangle.txt")


    

    
Out[50]:





1074