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| """Solve Problem 11 from Project Euler."""
import itertools
import operator
OFFSET = 3
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, 0],
[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, 0, 76, 44, 20, 45, 35, 14, 0, 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, 0, 17, 54, 24, 36, 29, 85, 57],
[86, 56, 0, 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]
]
INVALID_COORDS_PRODUCT = 0
def _calc_down(row_index, col_index):
"""Calculate the product of the sequence going straight down from ``row_index``."""
cols = itertools.repeat(col_index, OFFSET + 1)
last_row = min(row_index + OFFSET + 1, len(GRID))
coords = zip(xrange(row_index, last_row), cols)
values = (GRID[row][col] for row, col in coords)
return reduce(operator.mul, values)
def _calc_right(row_index, col_index):
"""Calculate the product of the sequence going straight right from ``col_index``."""
rows = itertools.repeat(row_index, OFFSET + 1)
last_col = min(col_index + OFFSET + 1, len(GRID[row_index]))
coords = zip(rows, xrange(col_index, last_col))
values = (GRID[row][col] for row, col in coords)
return reduce(operator.mul, values)
def _calc_up_right(row_index, col_index):
"""Calculate the product of the sequence going up and to the right from (``row_index``, ``col_index``)."""
last_row = max(row_index - OFFSET - 1, -1)
last_col = min(col_index + OFFSET + 1, len(GRID[row_index]))
coords = zip(xrange(row_index, last_row, -1), xrange(col_index, last_col))
values = (GRID[row][col] for row, col in coords)
return reduce(operator.mul, values)
def _calc_down_right(row_index, col_index):
"""Calculate the product of the sequence going down and to the right from (``row_index``, ``col_index``)."""
last_row = min(row_index + OFFSET + 1, len(GRID))
last_col = min(col_index + OFFSET + 1, len(GRID[row_index]))
coords = zip(xrange(row_index, last_row), xrange(col_index, last_col))
values = (GRID[row][col] for row, col in coords)
return reduce(operator.mul, values)
def _get_max_product_for_coordinate(row, col):
"""Find the maximum product achievable from (``row``, ``col``)."""
return max(_calc_up_right(row, col), _calc_right(row, col), _calc_down_right(row, col), _calc_down(row, col))
def problem_11():
"""Find the largest product of four adjacent elements."""
products = set()
for row in range(len(GRID)):
for col in range(len(GRID[row])):
products.add(_get_max_product_for_coordinate(row, col))
return max(products)
if __name__ == '__main__':
print problem_11()
|