2.最小路径和

题目：

给定一个只含非负整数的m*n网格，找到一条从左上角到右下角的可以使数字和最小的路径。

 

 注意事项

你在同一时间只能向下或者向右移动一步

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];
    }
};