leetcode [64] Minimum Path Sum

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.

Example:

Input:

[

[1,3,1],

[1,5,1],

[4,2,1]

]

Output: 7

Explanation: Because the path 1→3→1→1→1 minimizes the sum.

题目大意：

找寻最小的路径和

 

解法：

在做了 https://www.cnblogs.com/xiaobaituyun/p/10619729.html和 https://www.cnblogs.com/xiaobaituyun/p/10627248.html之后，我发现这又是一个简单的动态规划问题。

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

        return dp[m-1][n-1];
    }
};