Task_11_Largest_Product_in_a-Grid.py

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

from functools import reduce, cache

grid = """
    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
"""

# text to matrix
grid = [list(map(int, i.strip().split(" "))) for i in grid.split("\n") if i]

width = len(grid[0])
height = len(grid)
product_length = 4
max_product = 0


@cache
def multiply(x: int, y: int) -> int:
    return x * y


def transpose(matrix):
    return list(zip(*matrix))


def find_max_product_horizontal(matrix):
    max_product = 0
    for row in range(height):
        for col in range(width - (product_length - 1)):
            new_max_product: int = reduce(
                multiply, matrix[row][col:col + product_length]
            )
            max_product = max(max_product, new_max_product)

    return max_product


def find_max_product_diagonal(matrix, reverse_row=False):
    max_product = 0
    for row in range(height - (product_length - 1)):
        for col in range(width - (product_length - 1)):
            product_adders = list(range(product_length))
            to_multiply = []
            for p_adder in product_adders:
                row_values = matrix[row + p_adder]
                if reverse_row:
                    row_values = row_values[::-1]

                to_multiply.append(row_values[col + p_adder])

            new_max_product: int = reduce(multiply, to_multiply)
            max_product = max(max_product, new_max_product)

    return max_product


if __name__ == "__main__":
    max_product = max(max_product, find_max_product_horizontal(grid))
    max_product = max(max_product, find_max_product_horizontal(transpose(grid)))
    max_product = max(max_product, find_max_product_diagonal(grid))
    max_product = max(
        max_product, find_max_product_diagonal(grid, reverse_row=True)
    )

    print(max_product)

    # the result is: 70600674
    assert max_product == 70600674