[LeetCode]Minimum Path Sum

原题链接：http://oj.leetcode.com/problems/minimum-path-sum/

题意描述：

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.

题解：

　　这是提到基本的动态规划题，转移方程为：dp[i][j] = min(dp[i-1][j],dp[i][j-1])+a[i][j]。

 1 class Solution {

 2 public:

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

 4         int m = grid.size();

 5         int n = grid[0].size();

 6         int ret;

 7         int** dp = new int*[m];   

 8         for(int i = 0; i < m; i++)   

 9         dp[i] = new int[n];   

10 

11         dp[0][0] = grid[0][0];

12          

13         for(int i = 1; i < m; i++)

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

15              

16         for(int i = 1; i <n; i++)

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

18         

19         for(int i=1; i<m; i++){

20             for(int j=1; j<n; j++){

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

22             }

23         }

24         ret = dp[m-1][n-1];

25          for(int i = 0; i < m; i++)   

26              delete []dp[i];   

27         

28          delete []dp;

29         

30         return ret;

31     }

32 };

View Code