# 261. Graph Valid Tree

## Description

You have a graph of n nodes labeled from 0 to n - 1. You are given an integer n and a list of edges where edges[i] = [ai, bi] indicates that there is an undirected edge between nodes ai and bi in the graph.

Return true if the edges of the given graph make up a valid tree, and false otherwise.

Example 1:

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


Example 2:

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


Constraints:

• 1 <= n <= 2000
• 0 <= edges.length <= 5000
• edges[i].length == 2
• 0 <= ai, bi < n
• ai != bi
• There are no self-loops or repeated edges.

## Solutions

Union find.

• class Solution {
private int[] p;

public boolean validTree(int n, int[][] edges) {
p = new int[n];
for (int i = 0; i < n; ++i) {
p[i] = i;
}
for (int[] e : edges) {
int a = e[0], b = e[1];
if (find(a) == find(b)) {
return false;
}
p[find(a)] = find(b);
--n;
}
return n == 1;
}

private int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}
}

• class Solution {
public:
vector<int> p;

bool validTree(int n, vector<vector<int>>& edges) {
p.resize(n);
for (int i = 0; i < n; ++i) p[i] = i;
for (auto& e : edges) {
int a = e[0], b = e[1];
if (find(a) == find(b)) return 0;
p[find(a)] = find(b);
--n;
}
return n == 1;
}

int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}
};

• class Solution:
def validTree(self, n: int, edges: List[List[int]]) -> bool:
def find(x):
if p[x] != x:
p[x] = find(p[x])
return p[x]

p = list(range(n))
for a, b in edges:
if find(a) == find(b):
return False
p[find(a)] = find(b)
n -= 1
return n == 1


• func validTree(n int, edges [][]int) bool {
p := make([]int, n)
for i := range p {
p[i] = i
}
var find func(x int) int
find = func(x int) int {
if p[x] != x {
p[x] = find(p[x])
}
return p[x]
}
for _, e := range edges {
a, b := e[0], e[1]
if find(a) == find(b) {
return false
}
p[find(a)] = find(b)
n--
}
return n == 1
}

• /**
* @param {number} n
* @param {number[][]} edges
* @return {boolean}
*/
var validTree = function (n, edges) {
let p = new Array(n);
for (let i = 0; i < n; ++i) {
p[i] = i;
}
function find(x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}
for (const [a, b] of edges) {
if (find(a) == find(b)) {
return false;
}
p[find(a)] = find(b);
--n;
}
return n == 1;
};