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 > &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];
    }
};