Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Note: You can only move either down or right at any point in time.
Example 1:
[[1,3,1], [1,5,1], [4,2,1]]Given the above grid map, return
7. Because the path 1→3→1→1→1 minimizes the sum.走的方向决定了同一个位置不会走2次。
如果当前位置是（x,y）上一步来自哪呢？
上一步可能从左边【x-1,y】来，也可能从上边来[x,y-1] ,所以当前的最小路径就是 min(左边 + 当前值 ， 上边+当前值）
dp[0][0] = a[0][0]
dp[x][y] = min(dp[x-1][y]+a[x][y],+dp[x][y-1]+a[x][y])
1 class Solution: 2 def minPathSum(self, grid): 3 """ 4 :type grid: List[List[int]] 5 :rtype: int 6 """ 7 dp = [] 8 for i in grid: 9 dp.append(i) 10 11 for i in range(len(grid)): 12 for j in range(len(grid[0])): 13 if(i==0 and j ==0): 14 dp[i][j] = grid[i][j] 15 elif i==0 and j !=0 : 16 dp[i][j] = dp[i][j-1] + grid[i][j] 17 elif i!=0 and j==0: 18 dp[i][j] = dp[i-1][j] + grid[i][j] 19 else: 20 dp[i][j] = min(dp[i-1][j]+grid[i][j],dp[i][j-1]+grid[i][j]) 21 return dp[i][j] 22