Project Euler, Problem #11, Python

#! /usr/bin/env python3

# The task: find four adjacent numbers with the maximum product. The
# numbers should form a line: horizontal, vertical, or diagonal.
# Calculate the product.

m = (
    ( 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),
)

# global maximum product
mp = 1

# functions for calculating the product: horizontally, vertically,
# diagonally x 2
pfs = (
    lambda a, b: m[a][b] * m[a][b + 1] * m[a][b + 2] * m[a][b + 3],
    lambda a, b: m[a][b] * m[a + 1][b] * m[a + 2][b] * m[a + 3][b],
    lambda a, b: m[a][b] * m[a + 1][b + 1] * m[a + 2][b + 2] * m[a + 3][b + 3],
    lambda a, b: m[a][b + 3] * m[a + 1][b + 2] * m[a + 2][b + 1] * m[a + 3][b]
)

# mri — maximum row index, mci – maximum column index, pf – product
# function, lmp – local maximum product
def scan(mri, mci, pf, lmp):
    for a in range(mri):
        for b in range(mci):
            if pfs[pf](a, b) > lmp: lmp = pfs[pf](a, b)
    return lmp

mp = scan(19, 17, 0, mp)
mp = scan(17, 19, 1, mp)
mp = scan(17, 17, 2, mp)
mp = scan(17, 17, 3, mp)

print(mp)

# 70600674
# 1248 function calls in 0.002 seconds