p011.py

'''
In the 20*20 grid below, four numbers along a diagonal line have been marked.

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?
'''

import common

DATA = [[ 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]]


def line_product(data, startx, starty, dx, dy, length=4):
  try:
    product = 1
    for k in range(length):
      product *= DATA[startx + dx*k][starty + dy*k]
    return product
  except IndexError:
    return 0

common.assertEquals(1788696, line_product(DATA, 6, 8, 1, 1))

result = max(line_product(DATA, i, j, di, dj)
             for i in range(len(DATA))
             for j in range(len(DATA[i]))
             for di,dj in [(1,1), (1,0), (0,1), (1,-1)])

common.submit(result, expected=70600674)