[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]。

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        int m = grid.size();
        int n = grid[0].size();
        int ret;
        int** dp = new int*[m];   
        for(int i = 0; i < m; i++)   
        dp[i] = new int[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 i = 1; i <n; i++)
             dp[0][i] = dp[0][i-1] + grid[0][i];
        
        for(int i=1; i<m; i++){
            for(int j=1; j<n; j++){
                dp[i][j] = min(dp[i][j-1],dp[i-1][j])+grid[i][j];
            }
        }
        ret = dp[m-1][n-1];
         for(int i = 0; i < m; i++)   
             delete []dp[i];   
        
         delete []dp;
        
        return ret;
    }
};