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:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

dp
class Solution(object):
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        if not grid or not grid[0]:
            return 0
        m=len(grid)
        n=len(grid[0])
        dp=[[0 for c in range(n)] for r in range(m) ]
        dp[0][0]=grid[0][0]
        for i in range(1,len(grid[0])):
            dp[0][i]=dp[0][i-1]+grid[0][i]
        for i in range(1,len(grid)):
            dp[i][0]=dp[i-1][0]+grid[i][0]
        for i in range(1,m):
            for j in range(1,n):
                dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i][j]
        return dp[m-1][n-1]