LeetCode #261. Graph Valid Tree

题目描述：

Given n nodes labeled from 0 to n-1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree.

Example 1:

Input: 
n = 5, and edges = [[0,1], [0,2], [0,3], [1,4]]

Output: true

Example 2:

Input: n = 5, and edges = [[0,1], [1,2], [2,3], [1,3], [1,4]]

Output: false

Note: you can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0,1] is the same as [1,0] and thus will not appear together in edges.

class Solution {
public:
    bool validTree(int n, vector<vector<int>>& edges) {
        for(int i=0;i<n;i++) parent[i]=i;
        for(auto& edge:edges)
        {
            int u=edge[0], v=edge[1];
            int x=find(u), y=find(v);
            if(x==y) return false;
            else parent[x]=y;
        }
        return edges.size()==n-1; // 最后发现无环的时候，边数必须是点数减一，这样才能保证图连通
    }
    
    int find(int x)
    {
        while(parent[x]!=x) x=parent[x];
        return x;
    }
    
private:
    unordered_map<int,int> parent;
};