LeetCode:Minumus Path Sum(矩阵路线的元素最小值DP)

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：与求两个字符串的最长公共子序列的长度思路一致。

状态转移方程为：dp[i][j]=min(dp[i-1][j],dp[i][j-1])+grid[i-1][j-1];（Ps:i j 从1开始 防止越界问题）

 

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