#11: Largest product in a grid | Ben Cunningham

# #11: Largest product in a grid

Problem by Project Euler · on February 22, 2002

In the $20 \times 20$ grid below, four numbers along a diagonal line have been marked in red.

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


The product of these numbers is $26 \times 63 \times 78 \times 14 = 1788696$.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the $20 \times 20$ grid?

# Python

import functools
import operator

def v_prod(x):
if len(x) < 1:
return 0
return functools.reduce(operator.mul, x)

f = open('0011.txt', 'r')

mat = []
for line in f:
mat.append([int(x) for x in line.split(" ")])

f.close()

ans = 0

# Horizontal
for r in range(0, len(mat)):
for c in range(0, len(mat[0]) - 3):
prod = v_prod(mat[r][c:c + 4])
if prod > ans:
ans = prod

# Vertical
for r in range(0, len(mat) - 3):
for c in range(0, len(mat[0])):
prod = v_prod([x[c] for x in mat[r:r + 4]])
if prod > ans:
ans = prod

# Diagonal Down
for r in range(0, len(mat) - 3):
for c in range(0, len(mat[0]) - 3):
prod = v_prod([mat[r + x][c + x] for x in range(0, 4)])
if prod > ans:
ans = prod

# Diagonal Up
for r in range(3, len(mat)):
for c in range(0, len(mat[0]) - 3):
prod = v_prod([mat[r - x][c + x] for x in range(0, 4)])
if prod > ans:
ans = prod

print(ans)

## 70600674