給定一個包含非負整數的 m x n 網格，請找出一條從左上角到右下角的路徑，使得路徑上的數字總和為最小。

說明：每次只能向下或者向右移動一步。

示例:

輸入:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
輸出: 7
解釋: 因為路徑 1→3→1→1→1 的總和最小。

思路：使用動態規劃
方法1：

class Solution:
    def minPathSum(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        m = len(grid)
        n = len(grid[0])
        dp=[[0]*n for _ in range(m)]
        for i in range(m):
            for j in range(n):
                if i == 0:
                    if j== 0:
                        dp[i][j]= grid[0][0]
                    else:
                        dp[i][j]=dp[i][j-1]+grid[i][j]
                elif j == 0:
                    dp[i][j]=dp[i-1][j]+grid[i][j]
                else:
                    dp[i][j] =  min(dp[i][j-1],dp[i-1][j]) + grid[i][j]
        return dp[m-1][n-1] 
                    
 

方法二：空間優化

	m = len(grid)
        n = len(grid[0])
        dp=[[0] for _ in range(n)]
        for i in range(m):
            for j in range(n):
                if i == 0:
                    if j== 0:
                        dp[j]= grid[0][0]
                    else:
                        dp[j]=dp[j-1]+grid[i][j]
                elif j == 0:
                    dp[j]=dp[j]+grid[i][j]
                else:
                    dp[j] =  min(dp[j-1],dp[j]) + grid[i][j]
        return dp[n-1]