# problem-18.py ---
# Filename: problem-18.py
# Description: https://projecteuler.net/problem=18
# Author: Amritendu Mondal
# Email:  amritoit@gmail.com
# Organization:  IIT Madras
# Created: Mon Jul 22 16:38:40 2019 (+0530)
# Last-Updated:
#           By:
#     Update #: 49

# solution: I create a new blank triangle with the same dimensions as the original big triangle.
# For each cell of the big triangle, I consider the sub-triangle whose top is at this cell,
# calculate the maximum path sum when starting from this cell, and store the result
# in the corresponding cell of the blank triangle.
#
# If I start at a particular cell, what is the maximum path total? If the cell is at the
# bottom of the big triangle, then it is simply the cell's value. Otherwise the answer is
# the cell's value plus either {the maximum path total of the cell down and to the left}
# or {the maximum path total of the cell down and to the right}, whichever is greater.
# By computing the blank triangle's values from bottom up, the dependent values are always
# computed before they are utilized. This technique is known as dynamic programming.


# triangle = [
#     [3],
#     [7, 4],
#     [2, 4, 6],
#     [8, 5, 9, 3]
# ]


import time
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],
]


def max_weight_of_paths(triangle):
    for i in range(len(triangle)-2, -1, -1):
        for j in range(0, len(triangle[i])):
            triangle[i][j] += max(triangle[i+1][j], triangle[i+1][j+1])
    return triangle[0][0]


start_time = time.time()
print("compute result =", max_weight_of_paths(triangle),
      ", time taken - ", (time.time() - start_time), " seconds")
