problem-018.py

### Problem 18 - Maximum Path Sum I
###-----------------------------------------------------------------------------------------------------------------------------------------
### 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

### Solution
"""
Problem 18 - Maximum Path Sum I

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
"""

from typing import List


def max_path_sum(triangle: List[int]) -> int:
    """
    Parameters
        triangle (List[int]): 2D list of number triangle
    Returns
        sum (int): maximum path sum
    """

    for i in range(len(triangle) - 2, -1, -1):
        for j in range(len(triangle[i])):
            if triangle[i + 1][j] > triangle[i + 1][j + 1]:
                triangle[i][j] += triangle[i + 1][j]
            else:
                triangle[i][j] += triangle[i + 1][j + 1]
    return triangle[0][0]


if __name__ == "__main__":
    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],
    ]

    print("The maximum path sum is: " + str(max_path_sum(triangle)))