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?
Here's my implementation in Python and I had to implement the getting the matrix's diagonals thing and I was wondering whether there is some Python library that includes a similar function.
from functools import reduce
from operator import mul
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
"""
def get_matrix_rows(matrix):
"""Return a list of lists containing n * n matrix rows."""
return [[int(number) for number in row.split()] for row in matrix.rstrip().split('\n')]
def get_matrix_columns(matrix_rows):
"""Return a list of lists containing n * n matrix columns."""
return [[row[column_index] for row in matrix_rows] for column_index in range(len(matrix_rows))]
def get_non_diagonal_partitions(rows, columns, size):
"""Generate up, down, right & left partitions of length size for n * n matrix."""
for index in range(len(rows) - size + 1):
for row in rows:
yield row[index: index + size]
for column in columns:
yield column[index: index + size]
def get_modified_matrix_columns(modified_matrix_rows):
"""Return a list of lists containing columns of n * m matrix n != m is True."""
columns = []
for column_index in range(len(modified_matrix_rows[0])):
temp = []
for index in range(len(modified_matrix_rows)):
temp.append(modified_matrix_rows[index][column_index])
columns.append(temp)
return columns
def get_matrix_diagonals(matrix_rows):
"""Return matrix right & left diagonals by modifying the matrix to the right and to the left."""
matrix_modified_right = []
matrix_modified_left = []
right_start_count = len(matrix_rows) - 1
right_end_count = 0
left_start_count = 0
left_end_count = len(matrix_rows) - 1
for index in range(len(matrix_rows)):
matrix_modified_right.append(right_start_count * [0] + matrix_rows[index] + [0] * right_end_count)
right_start_count -= 1
right_end_count += 1
for index in range(len(matrix_rows)):
matrix_modified_left.append(left_start_count * [0] + matrix_rows[index] + [0] * left_end_count)
left_start_count += 1
left_end_count -= 1
right_diagonals = \
[[number for number in row if number != 0] for row in get_modified_matrix_columns(matrix_modified_right)]
left_diagonals = \
[[number for number in row if number != 0] for row in get_modified_matrix_columns(matrix_modified_left)]
return right_diagonals, left_diagonals
def get_diagonal_partitions(matrix_rows, size):
"""Return right and left partitions of length size for n * n matrix."""
right_diagonals, left_diagonals = get_matrix_diagonals(matrix_rows)
all_diagonals = [diagonal for diagonal in right_diagonals + left_diagonals if len(diagonal) >= size]
valid_diagonals = [diagonal for diagonal in all_diagonals if len(diagonal) == size]
for diagonal in all_diagonals:
if diagonal not in valid_diagonals:
length = len(diagonal)
for count in range(length - size + 1):
valid_diagonals.append(diagonal[count: count + size])
return valid_diagonals
def get_matrix_maximum_partition(partition_size, matrix_rows):
"""Return matrix partition of length partition_size with maximum number product."""
matrix_columns = get_matrix_columns(matrix_rows)
non_diagonal_partitions = get_non_diagonal_partitions(matrix_rows, matrix_columns, partition_size)
diagonal_partitions = get_diagonal_partitions(matrix_rows, partition_size)
all_partitions = list(non_diagonal_partitions) + diagonal_partitions
products = [reduce(mul, partition) for partition in all_partitions]
return max(products)
if __name__ == '__main__':
matrix = get_matrix_rows(grid)
print(get_matrix_maximum_partition(4, matrix))
