Loading problem…
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] = [a_i, b_i] indicates that there is an edge between nodes a_i and b_i 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.
Example 1
Input: edges = [[1,2],[1,3],[2,3]]
Output: [2,3]
Explanation: Edges [1,2] and [1,3] already connect all three nodes. Adding [2,3] closes the loop 1-2-3, so it is the redundant edge.
Example 2
Input: edges = [[1,2],[2,3],[3,4],[1,4],[1,5]]
Output: [1,4]
Explanation: The edges [1,2], [2,3] and [3,4] form a chain, so [1,4] closes the loop 1-2-3-4. Removing it leaves a tree, and [1,5] is still needed to reach node 5.
Example 3
Input: edges = [[1,2],[2,3],[1,3]]
Output: [1,3]
Explanation: [1,2] and [2,3] connect all three nodes, so the last edge [1,3] closes the loop and is the one to remove.
Add edges one by one with union-find. The graph is a tree plus one extra edge, so the first (and only) edge whose endpoints already share a root is the redundant one. Scanning in order returns the last such edge automatically.
Run checks all cases above. Submit evaluates all test cases.