该题类似AcWing上的 1015.摘花生，都是动态规划，且每次只能向下或者向右移动。

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        if (grid.empty()) return 0;
        int n = grid.size(), m = grid[0].size();

        vector<vector<int>> dp(n, vector<int>(m));

        dp[0][0] = grid[0][0];
        for (int i = 1; i < n; i ++ )                   //每次只能向下移动，初始化第一列
            dp[i][0] = dp[i - 1][0] + grid[i][0];

        for (int i = 1; i < m; i ++ )
            dp[0][i] = dp[0][i - 1] + grid[0][i];       //每次只能向右移动，初始化第一行

        for (int i = 1; i < n; i ++ )
            for (int j = 1; j < m; j ++ )               //当前状态只能从左边或上边转移过来
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];

        return dp[n - 1][m - 1];
    }
};