project-euler/largest_product_in_a_grid.py

import re

''' In the 20×20 grid below, four numbers along a diagonal line have been
marked in red.

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

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


# To find the product of the four numbers diagonal numbers (from top-left
# to bottom-right) in the 20x20 grid
def get_diagonal_left_to_right_product(num_array, first_num_index):
    # To add 21 to the index, for each subsequent number
    second_num_index = first_num_index + 21
    third_num_index = second_num_index + 21
    fourth_num_index = third_num_index + 21

    # To make sure that none of the numbers have an index greater than the
    # length of the number array
    if second_num_index + 1 > len(num_array) \
    or third_num_index + 1 > len(num_array) \
    or fourth_num_index + 1 > len(num_array):
        raise Exception('There are not four numbers to multiply together.')
    else:
        return int(num_array[first_num_index]) * int(num_array[second_num_index]) \
        * int(num_array[third_num_index]) * int(num_array[fourth_num_index])


# To find the product of the four numbers diagonal numbers (from top-right
# to bottom-left) in the 20x20 grid
def get_diagonal_right_to_left_product(num_array, first_num_index):
    # To add 21 to the index, for each subsequent number
    second_num_index = first_num_index + 19
    third_num_index = second_num_index + 19
    fourth_num_index = third_num_index + 19

    # To make sure that none of the numbers have an index greater than the
    # length of the number array
    if second_num_index + 1 > len(num_array) \
    or third_num_index + 1 > len(num_array) \
    or fourth_num_index + 1 > len(num_array):
        raise Exception('There are not four numbers to multiply together.')
    else:
        return int(num_array[first_num_index]) * int(num_array[second_num_index]) \
        * int(num_array[third_num_index]) * int(num_array[fourth_num_index])


# To find the product of the four numbers vertical numbers (from top to bottom)
# in the 20x20 grid
def get_vertical_product(num_array, first_num_index):
    # To add 20 to the index, for each subsequent number
    second_num_index = first_num_index + 20
    third_num_index = second_num_index + 20
    fourth_num_index = third_num_index + 20

    # To make sure that none of the numbers have an index greater than the
    # length of the number array
    if second_num_index + 1 > len(num_array) \
    or third_num_index + 1 > len(num_array) \
    or fourth_num_index + 1 > len(num_array):
        raise Exception('There are not four numbers to multiply together.')
    else:
        return int(num_array[first_num_index]) * int(num_array[second_num_index]) \
        * int(num_array[third_num_index]) * int(num_array[fourth_num_index])


# To find the product of the four numbers horizonalt numbers (from left to right)
# in the 20x20 grid
def get_horizontal_product(num_array, first_num_index):
    # To add one index, for each subsequent number
    second_num_index = first_num_index + 1
    third_num_index = second_num_index + 1
    fourth_num_index = third_num_index + 1

    # To make sure that none of the numbers have an index greater than the
    # length of the number array
    if second_num_index + 1 > len(num_array) \
    or third_num_index + 1 > len(num_array) \
    or fourth_num_index + 1 > len(num_array):
        raise Exception('There are not four numbers to multiply together.')
    else:
        return int(num_array[first_num_index]) * int(num_array[second_num_index]) \
        * int(num_array[third_num_index]) * int(num_array[fourth_num_index])


number_string = '''
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
'''

# First and last elements in the list are empty strings
number_grid = re.split('\n|\s', number_string)[1:-1]

greatest_product = 0

for index, number in enumerate(number_grid):
    try:
        if get_diagonal_left_to_right_product(number_grid, index) > greatest_product:
            greatest_product = get_diagonal_left_to_right_product(number_grid, index)
    except:
        continue

    try:
        if get_diagonal_right_to_left_product(number_grid, index) > greatest_product:
            greatest_product = get_diagonal_right_to_left_product(number_grid, index)
    except:
        continue

    try:
        if get_vertical_product(number_grid, index) > greatest_product:
            greatest_product = get_vertical_product(number_grid, index)
    except:
        continue

    try:
        if get_horizontal_product(number_grid, index) > greatest_product:
            greatest_product = get_horizontal_product(number_grid, index)
    except:
        continue


print(greatest_product)