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Copy path11-largestProductInAGrid.py
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11-largestProductInAGrid.py
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grid = ((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 calculate_products(x,y):
''' Calculate the product of four numbers, starting from x,y, in all applicable directions '''
products = []
# Up
if y >= 3:
products.append(grid[x][y] * grid[x][y-1] * grid[x][y-2] * grid[x][y-3])
# Up and Right
if y >= 3 and x <= 16:
products.append(grid[x][y] * grid[x+1][y-1] * grid[x+2][y-2] * grid[x+3][y-3])
# Right
if x <= 16:
products.append(grid[x][y] * grid[x+1][y] * grid[x+2][y] * grid[x+3][y])
# Right and Down
if x <= 16 and y <= 16:
products.append(grid[x][y] * grid[x+1][y+1] * grid[x+2][y+2] * grid[x+3][y+3])
# Down
if y <= 16:
products.append(grid[x][y] * grid[x][y+1] * grid[x][y+2] * grid[x][y+3])
# Down and Left
if y <= 16 and x >= 3:
products.append(grid[x][y] * grid[x-1][y+1] * grid[x-2][y+2] * grid[x-3][y+3])
# Left
if x >= 3:
products.append(grid[x][y] * grid[x-1][y] * grid[x-2][y] * grid[x-3][y])
# Left and Up
if x >= 3 and y >= 3:
products.append(grid[x][y] * grid[x-1][y-1] * grid[x-2][y-2] * grid[x-3][y-3])
return products
max_product = 0
for i in range(0,20):
for j in range(0,20):
products = calculate_products(i,j)
max_p = max(products)
if max_p > max_product:
max_product = max_p
print max_product