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largest_product_in_a_grid.py
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# https://projecteuler.net/problem=11
class FindLargestProduct(object):
def __init__(self, input_matrix):
self.input_matrix = input_matrix
def left_diagonally_multiply(self, x_idx: int, y_idx: int) -> int:
if (0 <= x_idx-3) and (y_idx+3 < len(self.input_matrix[0])):
return self.input_matrix[y_idx][x_idx] \
* self.input_matrix[y_idx+1][x_idx-1] \
* self.input_matrix[y_idx+2][x_idx-2] \
* self.input_matrix[y_idx+3][x_idx-3]
return 0
def right_diagonally_multiply(self, x_idx: int, y_idx: int) -> int:
if (x_idx+3 < len(self.input_matrix)) and (y_idx+3 < len(self.input_matrix[0])):
return self.input_matrix[y_idx][x_idx] \
* self.input_matrix[y_idx+1][x_idx+1] \
* self.input_matrix[y_idx+2][x_idx+2] \
* self.input_matrix[y_idx+3][x_idx+3]
return 0
def across_multiply(self, x_idx: int, y_idx: int) -> int:
if x_idx+3 < len(self.input_matrix):
return self.input_matrix[y_idx][x_idx] \
* self.input_matrix[y_idx][x_idx+1] \
* self.input_matrix[y_idx][x_idx+2] \
* self.input_matrix[y_idx][x_idx+3]
return 0
def down_multiply(self, x_idx: int, y_idx: int) -> int:
if y_idx+3 < len(self.input_matrix):
return self.input_matrix[y_idx][x_idx] \
* self.input_matrix[y_idx+1][x_idx] \
* self.input_matrix[y_idx+2][x_idx] \
* self.input_matrix[y_idx+3][x_idx]
return 0
def largest_product_in_a_grid(self) -> int:
largest_product = float('-inf')
for y_idx in range(len(self.input_matrix)):
for x_idx in range(len(self.input_matrix[0])):
print(self.down_multiply(x_idx, y_idx), self.input_matrix[y_idx][x_idx])
largest_product = max(largest_product,
self.down_multiply(x_idx, y_idx),
self.across_multiply(x_idx, y_idx),
self.right_diagonally_multiply(x_idx, y_idx),
self.left_diagonally_multiply(x_idx, y_idx))
return largest_product
input_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, 00],
[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, 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, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57],
[86 ,56, 00, 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]]
if __name__ == "__main__":
find_largest_product = FindLargestProduct(input_grid)
print(find_largest_product.largest_product_in_a_grid())