## 261. Graph Valid Tree

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`.

## Rust Solution

``````struct Solution;

struct UnionFind {
parent: Vec<usize>,
n: usize,
}

impl UnionFind {
fn new(n: usize) -> Self {
let parent = (0..n).collect();
UnionFind { parent, n }
}
fn find(&mut self, i: usize) -> usize {
let j = self.parent[i];
if i == j {
i
} else {
let k = self.find(j);
self.parent[i] = k;
k
}
}

fn union(&mut self, i: usize, j: usize) -> bool {
let i = self.find(i);
let j = self.find(j);
if i != j {
self.parent[i] = j;
self.n -= 1;
true
} else {
false
}
}
}

impl Solution {
fn valid_tree(n: i32, edges: Vec<Vec<i32>>) -> bool {
let n = n as usize;
let mut uf = UnionFind::new(n);
for edge in edges {
let i = edge[0] as usize;
let j = edge[1] as usize;
if !uf.union(i, j) {
return false;
}
}
uf.n == 1
}
}

#[test]
fn test() {
let n = 5;
let edges = vec_vec_i32![[0, 1], [0, 2], [0, 3], [1, 4]];
let res = true;
assert_eq!(Solution::valid_tree(n, edges), res);
let n = 5;
let edges = vec_vec_i32![[0, 1], [1, 2], [2, 3], [1, 3], [1, 4]];
let res = false;
assert_eq!(Solution::valid_tree(n, edges), res);
}
``````

Having problems with this solution? Click here to submit an issue on github.