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：

class Solution {
public:
    vector<vector<int>>  mi;
    int minPathSum(vector<vector<int> > &grid) {
        mi=grid;
        for(int i=1;i<grid[0].size();i++)
        {
            mi[0][i]=mi[0][i-1]+mi[0][i];
        }
        for(int i=1;i<grid.size();i++)
        {
            mi[i][0]=mi[i-1][0]+mi[i][0];
            for(int j=1;j<grid[0].size();j++)
            {
                mi[i][j]=min(mi[i-1][j],mi[i][j-1])+mi[i][j];
            }
        }
        return mi[grid.size()-1][grid[0].size()-1];
    }
};