class Solution {
public:
    /*
     * @param grid: a list of lists of integers
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    int minPathSum(vector<vector<int>> &grid) {
        // write your code here
        int m = grid.size();  
        int n = grid[0].size();  
        int dp[m][n];  
        dp[0][0] = grid[0][0];  
        for (int i = 1; i < m; i++)  
            dp[i][0] = dp[i-1][0] + grid[i][0];  
        for (int j = 1; j < n; j++)  
            dp[0][j] = dp[0][j-1] + grid[0][j];  
        for (int i = 1; i < m; i++)  
            for (int j = 1; j < n; j++)  
                dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];  
        return dp[m-1][n-1];  
    }
};