class Solution {
  public:
    int maxValue(vector<vector<int> >& grid) {
        int m = grid.size();
        int n = grid[0].size();
        //第一列只能来自上方
        for (int i = 1; i < m; i++)
            grid[i][0] += grid[i - 1][0];
        //第一行只能来自左边
        for (int i = 1; i < n; i++)
            grid[0][i] += grid[0][i - 1];
        //遍历后续每一个位置
        for (int i = 1; i < m; i++)
            for (int j = 1; j < n; j++)
                //增加来自左边的与上边的之间的较大值
                grid[i][j] += max(grid[i - 1][j], grid[i][j - 1]);
        return grid[m - 1][n - 1];
    }
};