Project Euler Problem 011

http://projecteuler.net/index.php?section=problems&id=11

In the 20x20 grid below, four numbers along a diagonal line have been marked in red.
What is the greatest product of four adjacent numbers
  in any direction (up, down, left, right, or diagonally) in the 20x20 grid?

問題文に上下左右斜めと書いてあるのがいやらしい。
実際は縦、横、右斜め、左斜めで走査しないといけない。

import operator

Q = """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 func(l, x, y, direction):
    if not (0 <= x + direction[-1][0] < len(l[y])): return []
    if not (0 <= y + direction[-1][1] < len(l   )): return []
    return [ L[y+i[1]][x+i[0]] for i in direction ]


def make_direction(length):
    result = [ [], [], [], [] ]
    
    for i in xrange(length):
        result[0].append(( i,0))
        result[1].append(( 0,i))
        result[2].append(( i,i))
        result[3].append((-i,i))
    
    return result


L = [ [ int(y) for y in x.split(' ') ] for x in Q.split('\n') ]

direction = make_direction(4)

result   = []
maxvalue =  0

for i in xrange(len(L)):
    for j in xrange(len(L[i])):
        for k in direction:
            l = func(L, i, j, k)
            if not l: continue
            
            x = reduce(operator.mul, l)
            
            if x > maxvalue:
                result = l
                maxvalue = x

print result, maxvalue

答え: 89 * 94 * 97 * 87 = 70600674
実行時間: 0.032876秒くらい