# 684 Redundant Connection

## 684 [Redundant Connection](https://leetcode.com/problems/redundant-connection/description/)

## 1. 题目：

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.

## 2. 思路

利用Union-Find， 一旦发现有已经相连的Component, 则该边是redundant

## 3. Implementation

```java
class Solution {
    public int[] findRedundantConnection(int[][] edges) {
        int n = edges.length;
        UnionFind uf = new UnionFind(n);

        for (int[] edge : edges) {
            if (!uf.union(edge[0], edge[1])) {
                return new int[] {edge[0], edge[1]};
            }
        }

        return new int[0];
    }

    class UnionFind {
        int[] sets;
        int[] size;
        int count;

        public UnionFind(int n) {
            sets = new int[n + 1];
            size = new int[n + 1];
            count = n;

            for (int i = 0; i <= n; i++) {
                sets[i] = i;
                size[i] = 1;
            }
        }

        public int find(int node) {
            while (node != sets[node]) {
                node = sets[node];
            }
            return node;
        }

        public boolean union(int i, int j) {
            int node1 = find(i);
            int node2 = find(j);

            if (node1 == node2) {
                return false;
            }

            if (size[node1] < size[node2]) {
                sets[node1] = node2;
                size[node2] += size[node1];
            }
            else {
                sets[node2] = node1;
                size[node1] += size[node2];
            }

            --count;
            return true;
        }
    }
}
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://protegejj.gitbook.io/my-algorithm-summary/chapter1/union-find/684-redundant-connection.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.