# [LeetCode] 261. Graph Valid Tree 图验证树

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.

// DFS
class Solution {
public:
bool validTree(int n, vector<pair<int, int>>& edges) {
vector<vector<int>> g(n, vector<int>());
vector<bool> v(n, false);
for (auto a : edges) {
g[a.first].push_back(a.second);
g[a.second].push_back(a.first);
}
if (!dfs(g, v, 0, -1)) return false;
for (auto a : v) {
if (!a) return false;
}
return true;
}
bool dfs(vector<vector<int>> &g, vector<bool> &v, int cur, int pre) {
if (v[cur]) return false;
v[cur] = true;
for (auto a : g[cur]) {
if (a != pre) {
if (!dfs(g, v, a, cur)) return false;
}
}
return true;
}
};

// BFS
class Solution {
public:
bool validTree(int n, vector<pair<int, int>>& edges) {
vector<unordered_set<int>> g(n, unordered_set<int>());
unordered_set<int> s{{0}};
queue<int> q{{0}};
for (auto a : edges) {
g[a.first].insert(a.second);
g[a.second].insert(a.first);
}
while (!q.empty()) {
int t = q.front(); q.pop();
for (auto a : g[t]) {
if (s.count(a)) return false;
s.insert(a);
q.push(a);
g[a].erase(t);
}
}
return s.size() == n;
}
};

// Union Find
class Solution {
public:
bool validTree(int n, vector<pair<int, int>>& edges) {
vector<int> roots(n, -1);
for (auto a : edges) {
int x = find(roots, a.first), y = find(roots, a.second);
if (x == y) return false;
roots[x] = y;
}
return edges.size() == n - 1;
}
int find(vector<int> &roots, int i) {
while (roots[i] != -1) i = roots[i];
return i;
}
};

Github 同步地址：

https://github.com/grandyang/leetcode/issues/261

Number of Islands II

Number of Connected Components in an Undirected Graph

https://leetcode.com/problems/graph-valid-tree/

https://leetcode.com/problems/graph-valid-tree/discuss/69018/AC-Java-Union-Find-solution