# # Solution to Project Euler problem 18 # Copyright (c) Project Nayuki. All rights reserved. # # https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # # We create a new blank triangle with the same dimensions as the original big triangle. # For each cell of the big triangle, we 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 we 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. def compute(): for i in reversed(range(len(triangle) - 1)): for j in range(len(triangle[i])): triangle[i][j] += max(triangle[i + 1][j], triangle[i + 1][j + 1]) return str(triangle[0][0]) triangle = [ # Mutable [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], ] if __name__ == "__main__": print(compute())