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

problem11_euler.py

a = [
    [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 product():
  maxProduct = 1
  for x in xrange(len(a)):
    for y in xrange(len(a)):
      verticalProduct = horizontalProduct = diagoalProduct1 = diagoalProduct2 = 0

      try :
        verticalProduct = a[x][y] * a[x+1][y] * a[x+2][y] * a[x+3][y]

        horizontalProduct = a[x][y] * a[x][y+1] * a[x][y+2] * a[x][y+3]

        diagonalProduct1 = a[x][y] * a[x+1][y+1] * a[x+2][y+2] * a[x+3][y+3]

        diagonalProduct2 = a[x][y] * a[x-1][y+1] * a[x-2][y+2] * a[x-3][y+3]
      except IndexError:
        pass;

      maxProduct = max(maxProduct, verticalProduct,horizontalProduct,
        diagonalProduct1, diagonalProduct2)

  return maxProduct


print product()