# # Solution to Project Euler problem 11 # Copyright (c) Project Nayuki. All rights reserved. # # https://www.nayuki.io/page/project-euler-solutions # https://github.com/nayuki/Project-Euler-solutions # # We visit each grid cell and compute the product in the 4 directions starting from that cell. def compute(): ans = -1 width = len(GRID[0]) height = len(GRID) for y in range(height): for x in range(width): if x + CONSECUTIVE <= width: ans = max(grid_product(x, y, 1, 0, CONSECUTIVE), ans) if y + CONSECUTIVE <= height: ans = max(grid_product(x, y, 0, 1, CONSECUTIVE), ans) if x + CONSECUTIVE <= width and y + CONSECUTIVE <= height: ans = max(grid_product(x, y, 1, 1, CONSECUTIVE), ans) if x - CONSECUTIVE >= -1 and y + CONSECUTIVE <= height: ans = max(grid_product(x, y, -1, 1, CONSECUTIVE), ans) return str(ans) def grid_product(ox, oy, dx, dy, n): result = 1 for i in range(n): result *= GRID[oy + i * dy][ox + i * dx] return result GRID = [ [ 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8], [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0], [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65], [52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91], [22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80], [24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50], [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70], [67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21], [24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72], [21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95], [78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92], [16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57], [86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58], [19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40], [ 4,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66], [88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69], [ 4,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36], [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16], [20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54], [ 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48], ] CONSECUTIVE = 4 if __name__ == "__main__": print(compute())