Minimum Path Sum <leetcode>

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.

思路：看到这道题想到两种方法，第一种是分支限界，不过时间复杂度比较高，估计会超时，另一种方法是动态规划，时间复杂度为O(m*n,代码如下：

 1 class Solution {
 2 public:
 3     vector<vector<int>>  mi;
 4     int minPathSum(vector<vector<int> > &grid) {
 5         mi=grid;
 6         for(int i=1;i<grid[0].size();i++)
 7         {
 8             mi[0][i]=mi[0][i-1]+mi[0][i];
 9         }
10         for(int i=1;i<grid.size();i++)
11         {
12             mi[i][0]=mi[i-1][0]+mi[i][0];
13             for(int j=1;j<grid[0].size();j++)
14             {
15                 mi[i][j]=min(mi[i-1][j],mi[i][j-1])+mi[i][j];
16             }
17         }
18         return mi[grid.size()-1][grid[0].size()-1];
19     }
20 };