Python/Project Euler/Problem 11/sol1.py

from __future__ import print_function
'''
What is the greatest product of four adjacent numbers (horizontally, vertically, or diagonally) in this 20x20 array?

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
'''

try:
	xrange			#Python 2
except NameError:
	xrange = range	#Python 2

def largest_product(grid):
	nColumns = len(grid[0])
	nRows = len(grid)

	largest = 0
	lrDiagProduct = 0
	rlDiagProduct = 0

	#Check vertically, horizontally, diagonally at the same time (only works for nxn grid)
	for i in xrange(nColumns):
		for j in xrange(nRows-3):
			vertProduct = grid[j][i]*grid[j+1][i]*grid[j+2][i]*grid[j+3][i]
			horzProduct = grid[i][j]*grid[i][j+1]*grid[i][j+2]*grid[i][j+3]

			#Left-to-right diagonal (\) product
			if (i < nColumns-3):
				lrDiagProduct = grid[i][j]*grid[i+1][j+1]*grid[i+2][j+2]*grid[i+3][j+3]

			#Right-to-left diagonal(/) product
			if (i > 2):
				rlDiagProduct = grid[i][j]*grid[i-1][j+1]*grid[i-2][j+2]*grid[i-3][j+3]

			maxProduct = max(vertProduct, horzProduct, lrDiagProduct, rlDiagProduct)
			if maxProduct > largest:
				largest = maxProduct

	return largest

if __name__ == '__main__':
	grid = []
	with open('grid.txt') as file:
		for line in file:
			grid.append(line.strip('\n').split(' '))

	grid = [[int(i) for i in grid[j]] for j in xrange(len(grid))]

	print(largest_product(grid))