## 684. Redundant Connection

In this problem, a tree is an undirected graph that is connected and has no cycles.

The given input is a graph that started as a tree with N nodes (with distinct values 1, 2, ..., N), with one additional edge added. The added edge has two different vertices chosen from 1 to N, and was not an edge that already existed.

The resulting graph is given as a 2D-array of `edges`. Each element of `edges` is a pair `[u, v]` with `u < v`, that represents an undirected edge connecting nodes `u` and `v`.

Return an edge that can be removed so that the resulting graph is a tree of N nodes. If there are multiple answers, return the answer that occurs last in the given 2D-array. The answer edge `[u, v]` should be in the same format, with `u < v`.

Example 1:

```Input: [[1,2], [1,3], [2,3]]
Output: [2,3]
Explanation: The given undirected graph will be like this:
1
/ \
2 - 3
```

Example 2:

```Input: [[1,2], [2,3], [3,4], [1,4], [1,5]]
Output: [1,4]
Explanation: The given undirected graph will be like this:
5 - 1 - 2
|   |
4 - 3
```

Note:

• The size of the input 2D-array will be between 3 and 1000.
• Every integer represented in the 2D-array will be between 1 and N, where N is the size of the input array.

• Update (2017-09-26):
We have overhauled the problem description + test cases and specified clearly the graph is an undirected graph. For the directed graph follow up please see Redundant Connection II). We apologize for any inconvenience caused.

## 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 {
true
} else {
self.parent[i] = j;
false
}
}
}

impl Solution {
fn find_redundant_connection(edges: Vec<Vec<i32>>) -> Vec<i32> {
let n = edges.len();
let mut uf = UnionFind::new(n);
for edge in edges {
let u = (edge - 1) as usize;
let v = (edge - 1) as usize;
if uf.union(u, v) {
return edge;
}
}
vec![]
}
}

#[test]
fn test() {
let edges = vec_vec_i32![[1, 2], [1, 3], [2, 3]];
let res = vec![2, 3];
assert_eq!(Solution::find_redundant_connection(edges), res);
let edges = vec_vec_i32![[1, 2], [2, 3], [3, 4], [1, 4], [1, 5]];
let res = vec![1, 4];
assert_eq!(Solution::find_redundant_connection(edges), res);
}
``````

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