#11: Largest product in a grid | Ben Cunningham

#11: Largest product in a grid

Problem by Project Euler · on February 22, 2002

In the 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 .

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 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