Redundant Connection

Hard~20 min

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

You are given a graph that started as a tree with n nodes labeled from 1 to 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 graph is represented as an array edges of length n where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the graph.

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 input.

Examples

Example 1
Input: edges = [[1,2],[1,3],[2,3]]
Output: [2,3]
Explanation: The graph forms a triangle (1-2-3). Removing edge [2,3] (the last edge that completes the cycle) leaves a valid tree.
Example 2
Input: edges = [[1,2],[2,3],[3,4],[1,4],[1,5]]
Output: [1,4]
Explanation: The cycle is 1-2-3-4-1. Edge [1,4] is the last edge in the input that is part of this cycle, so removing it produces a tree.

Constraints

  • n == edges.length
  • 3 <= n <= 1000
  • edges[i].length == 2
  • 1 <= ai < bi <= n
  • ai != bi
  • There are no repeated edges
  • The given graph is connected
  • Expected time complexity: O(n)
Code
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Output

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