solve18.py

# https://projecteuler.net/problem=18
# Run with: 'python solve18.py'
# using Python 3.6.9
# by Zack Sargent

# Prompt:

# 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:
# 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)

# formatted with a vim macro
triangle = [
                               [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],
]

# from the bottom to the top
for i in reversed(range(0, len(triangle)-1)):
    # find the maximum sum of the numbers to the left and right
    for j in range(0, i + 1):
        triangle[i][j] += max(triangle[i+1][j], triangle[i+1][j+1])

# This collapses the tree with the solution at (0,0)

print(triangle[0][0])
# -> 1074