"""
Problem 18: Find sum of max path from the top of pyramid to bottom if with every move, you can only move to adjacent
numbers on the next row.

Algorithm: Dynamic Programming
"""


def solve():
    string = '''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'''

    grid = [[int(i) for i in j.split(" ")] for j in string.split("\n")]

    # update the grid, grid[i][j] will represent max value path from i,j to bottom of pyramid, bottom up approach
    for i in range(13, -1, -1):
        for j in range(i, -1, -1):
            grid[i][j] += max(grid[i + 1][j], grid[i + 1][j + 1])

    return grid[0][0]
