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"""

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

"""

import os

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 range(nColumns):

for j in range(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

def solution():

"""Returns the sum of all the multiples of 3 or 5 below n.

>>> solution()

70600674

"""

grid = []

with open(os.path.dirname(__file__) + "/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 range(len(grid))]

return largest_product(grid)

if __name__ == "__main__":

print(solution())

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