Minimum path sum问题

Given a m x n grid
filled with non-negative numbers, find a path from top left to bottom right which minimizes the
sum of all numbers along its path.

Note: You can only move either down or right at any point in time.
面试时曾经遇到过这个题目，回来一查发现leetcode上也有https://leetcode.com/problems/minimum-path-sum/， 重新做一下
用动态规划的思路解题，当前位置(i,j)的sum值，等于当前位置权值，加上(i-1, j)和(i, j -1)sum值中较小的那个

动态方程为dp[i][j] = grid[i][j] + max {grid[i-1][j], grid[i][j-1]};

下面是我的答案，leetcode测试通过。

class Solution {

public:

    /**

     * @param grid: a list of lists of integers.

     * @return: An integer, minimizes the sum of all numbers along its path

     */

     

    int min(int a, int b)

    {

        return a < b ? a : b;

    }

    

    int minPathSum(vector<vector<int> > &grid) {

        // write your code here

        

        int row = grid.size();

        int col = grid[0].size();

        

        if(row == 0 || col == 0)

        {

            return 0;

        }

        

        int dp[row][col];

        dp[0][0] = grid[0][0];

        

        for(int i = 1; i < row ; i++)

        {

            dp[i][0] = grid[i][0] + dp[i-1][0];

        }

        

        for(int j = 1; j < col ; j++)

        {

            dp[0][j] = grid[0][j] + dp[0][j-1];

        }

        

        for(int i = 1; i < row ; i++)

         for(int j = 1; j < col ; j++)

         {

            dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1]);

         }

         

         return dp[row-1][col-1];

    }

};