Python/project_euler/problem_11/sol2.py

"""
What is the greatest product of four adjacent numbers (horizontally,
vertically, or diagonally) in this 20x20 array?

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
"""

from __future__ import print_function
import os

try:
    xrange  # Python 2
except NameError:
    xrange = range  # Python 2


def solution():
    """Returns the sum of all the multiples of 3 or 5 below n.
    
    >>> solution()
    70600674
    """
    with open(os.path.dirname(__file__) + "/grid.txt") as f:
        l = []
        for i in xrange(20):
            l.append([int(x) for x in f.readline().split()])

        maximum = 0

        # right
        for i in xrange(20):
            for j in xrange(17):
                temp = l[i][j] * l[i][j + 1] * l[i][j + 2] * l[i][j + 3]
                if temp > maximum:
                    maximum = temp

        # down
        for i in xrange(17):
            for j in xrange(20):
                temp = l[i][j] * l[i + 1][j] * l[i + 2][j] * l[i + 3][j]
                if temp > maximum:
                    maximum = temp

        # diagonal 1
        for i in xrange(17):
            for j in xrange(17):
                temp = (
                    l[i][j]
                    * l[i + 1][j + 1]
                    * l[i + 2][j + 2]
                    * l[i + 3][j + 3]
                )
                if temp > maximum:
                    maximum = temp

        # diagonal 2
        for i in xrange(17):
            for j in xrange(3, 20):
                temp = (
                    l[i][j]
                    * l[i + 1][j - 1]
                    * l[i + 2][j - 2]
                    * l[i + 3][j - 3]
                )
                if temp > maximum:
                    maximum = temp
        return maximum


if __name__ == "__main__":
    print(solution())