euler11.py

grid = [
"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"
]

# test grid = ["1 2 3 4", "1 2 3 4", "1 2 3 4", "1 2 3 4"]
"""
Put the grid into a matrix
"""
matrix = [] 
for line in grid:
	items = line.split(" ")
	matrix.append(map(int, items))
# matrix [y][x]

"""
Multiplies numbers left-right
"""
def mult_right(x, y, num_counter=0, result=1):
	if x < 0 or y < 0 or x > (len(matrix) - 1) or y > (len(matrix) - 1): # out of matrix
		return 0
	if num_counter == 3:	# bottom of recursion
		return result * matrix[x][y]
	else:
		result = matrix[x][y] * mult_right(x, y+1, num_counter + 1, result)  
		return result

"""
Multiplies numbers top-down
"""
def mult_down(x, y, num_counter=0, result=1):
	if x < 0 or y < 0 or x > (len(matrix) - 1) or y > (len(matrix) - 1): # out of matrix
		return 0
	if num_counter == 3:	# bottom of recursion
		return result * matrix[x][y]
	else:
		result = matrix[x][y] * mult_down(x+1, y, num_counter + 1, result)  
		return result

"""
Multiplies numbers diagonally left-top - right-down
"""
def mult_diag_leftop_rightdown(x, y, num_counter=0, result=1):
	if x < 0 or y < 0 or x > (len(matrix) - 1) or y > (len(matrix) - 1): # out of matrix
		return 0
	if num_counter == 3:	# bottom of recursion
		return result * matrix[x][y]
	else:
		result = matrix[x][y] * mult_diag_leftop_rightdown(x+1, y+1, num_counter + 1, result)  
		return result
	
"""
Multiplies numbers diagonally right-top - left-down
"""	
def mult_diag_rightop_leftdown(x, y, num_counter=0, result=1):
	if x < 0 or y < 0 or x > (len(matrix) - 1) or y > (len(matrix) - 1): # out of matrix
		return 0
	if num_counter == 3:	# bottom of recursion
		return result * matrix[x][y]
	else:
		result = matrix[x][y] * mult_diag_rightop_leftdown(x-1, y+1, num_counter + 1, result)  
		return result
"""
Now find the max num
"""
max_num = 0
for x in range (0, len(matrix)):
	for y in range (0, len(matrix)):
		mult_result = max([mult_down(x,y), mult_right(x,y), mult_diag_leftop_rightdown(x,y), mult_diag_rightop_leftdown(x,y)])
		if mult_result > max_num:
			max_num = mult_result

print max_num