給定一個只含非負整數的m*n網格，找到一條從左上角到右下角的可以使數字和最小的路徑。

只能向下走或者向右走

class Solution:
    """
    @param grid: a list of lists of integers
    @return: An integer, minimizes the sum of all numbers along its path
    """
    def minPathSum(self, grid):
        # write your code here
        m = len(grid)
        n = len(grid[0])
        dp = [[0 for i in range(n)] for j in range(m)]
        if grid[0][0] is None:
            return None
        elif m==0:
            return None
        dp[0][0] = grid[0][0]
        """
        考慮邊界問題
        """
        for i in range(m):
            dp[i][0] = dp[i-1][0]+grid[i][0]
        for j in range(n):
            dp[0][j] = dp[0][j-1]+grid[0][j]

       """
        一般情況
        """

            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]