Solution to Problem 11. Written in Python.
Problem: In the 20 x 20 grid below, four numbers along a diagonal line have been marked in red. The product of these numbers is 26 x 63 x 78 x 14 = 1788696. What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20 x 20 grid? You can find the 20 x 20 grid on Project Euler.
north = False
south = False
east = False
west = False
ne = False
se = False
sw = False
nw = False
maxProduct = 0
matrix = [[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8], #row 0
[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0], #row 1
[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65], #row 2
[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91], #row 3
[22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80], #row 4
[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50], #row 5
[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70], #row 6
[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21], #row 7
[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72], #row 8
[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95], #row 9
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92], #row 10
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57], #row 11
[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58], #row 12
[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40], #row 13
[4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66], #row 14
[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69], #row 15
[4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36], #row 16
[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16], #row 17
[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54], #row 18
[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]] #row 19
def product(north, south, east, west, ne, se, sw, nw, row, col):
tempProduct = 0
if(north == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row-1][col]*matrix[row-2][col]*matrix[row-3][col])
if(south == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row+1][col]*matrix[row+2][col]*matrix[row+3][col])
if(east == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row][col+1]*matrix[row][col+2]*matrix[row][col+3])
if(west == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row][col-1]*matrix[row][col-2]*matrix[row][col-3])
if(ne == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row-1][col+1]*matrix[row-2][col+2]*matrix[row-3][col+3])
if(se == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row+1][col+1]*matrix[row+2][col+2]*matrix[row+3][col+3])
if(sw == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row+1][col-1]*matrix[row+2][col-2]*matrix[row+3][col-3])
if(nw == True):
tempProduct = max(tempProduct, matrix[row][col]*matrix[row-1][col-1]*matrix[row-2][col-2]*matrix[row-3][col-3])
return tempProduct
for row in range(0, 20):
for col in range(0, 20):
if(row < 3 and col < 3): #if row < 3 and col < 3, can only go south, east, se
south = True
east = True
se = True
north = False
west = False
ne = False
sw = False
nw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row < 3 and col > 16): #if row < 3 and col > 16, can only go south, west, sw
south = True
west = True
sw = True
north = False
east = False
ne = False
se = False
nw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row > 16 and col > 16): #if row > 16 and col > 16, can only go north, west, northwest
north = True
west = True
nw = True
south = False
east = False
ne = False
se = False
sw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row > 16 and col < 3): #if row > 16 and col < 3, can only go north, east, northeast
north = True
east = True
ne = True
south = False
west = False
se = False
sw = False
nw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row < 3 and col > 2 and col < 17): #if row < 3 and col > 2 and col < 17, cannot go north, ne, or nw
north = False
south = True
east = True
west = True
ne = False
se = True
sw = True
nw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row > 16 and col > 2 and col < 17): #if row > 16 and col > 2 and col < 17, cannot go south, se, or sw
north = True
south = False
east = True
west = True
ne = True
se = False
sw = False
nw = True
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row > 2 and row < 17 and col > 16): #if row > 2 and row < 17 and col > 16, cannot go east, se, or ne
north = True
south = True
east = False
west = True
ne = False
se = False
nw = True
sw = True
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if(row > 2 and row < 17 and col < 3): #if row > 2 and row < 17 and col < 3, cannot go west, nw, or sw
north = True
south = True
east = True
west = False
ne = True
se = True
sw = False
nw = False
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
if (row > 2 and col > 2 and col < 17 and row < 17): #if row > 2 and col > 2 and col < 17 and row < 17, go all directions
north = True
south = True
east = True
west = True
ne = True
se = True
sw = True
nw = True
maxProduct = max(maxProduct, product(north, south, east, west, ne, se, sw, nw, row, col))
print( "maxProduct: " + str(maxProduct) )