我在这里做错什么了？Euler项目问题11

Question

这是我第一次在StackOverflow上发问，所以请原谅我的错误，但请告诉我。我试图在python中的euler项目中做问题11。我觉得我的方法是正确的，但我没有得到正确的答案。我得到的答案是51267216。请你能指出我的代码哪里出错了吗？

def main():
   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]]

   greatest_product_four_adjacent_numbers_same_direction = -1
   product = 0

   for i in range(20):
       for j in range(20):
           # Right
           if(i < 20 and j + 1 < 20 and j + 2 < 20 and j + 3 < 20):
               product = grid[i][j] * grid[i][j + 1] * grid[i][j + 2] * grid[i][j + 3]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product
           
           # Left
           if(i < 20 and j - 1 >= 0 and j - 2 >= 0 and j - 3 >= 0):
               product = grid[i][j] * grid[i][j - 1] * grid[i][j - 2] * grid[i][j - 3]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product
           
           # Down
           if(j < 20 and i + 1 < 20 and i + 2 < 20 and i + 3 < 20):
               product = grid[i][j] * grid[i + 1][j] * grid[i + 2][j] * grid[i + 3][j]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product
               
           # Up 
           if(i < 20 and j - 1 >= 0 and j - 2 >= 0 and j - 3 >= 0):
               product = grid[i][j] * grid[i - 1][j] * grid[i - 2][j] * grid[i - 3][j]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product

           # Diagonal right
           if(i + 1 < 20 and j + 1 < 20 and i + 2 < 20 and j + 2 < 20 and i + 3 < 20 and j + 3 < 20):
               product = grid[i][j] * grid[i + 1][j + 1] * grid[i + 2][j + 2] * grid[i + 3][j + 3]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product
           
           # Diagonal left
           if(i - 1 >= 0 and j - 1 >= 0 and i - 2 >= 0 and j - 2 >= 0 and i - 3 >= 0 and j - 3 >= 0):
               product = grid[i][j] * grid[i - 1][j - 1] * grid[i - 2][j - 2] * grid[i - 3][j - 3]
               if(product > greatest_product_four_adjacent_numbers_same_direction):
                   greatest_product_four_adjacent_numbers_same_direction = product
   print(greatest_product_four_adjacent_numbers_same_direction)

if __name__ == '__main__':
   main()

Answer 1

你们的对角线都在检查同一条线。

如果你要检查每条可能的线两次:你把右边的数字序列乘以左边的序列，再反过来检查相同的数字。

最后，检查相同的对角线两次(两个轴都在增加，然后两个轴都在减小)，但不检查在一个轴中增加而在另一个轴中减少的对角线。