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.




class Solution {
    public int[] findRedundantConnection(int[][] edges) {
        int max = 0;
        for(int i = 0;i<edges.length;i++){
            for(int x: edges[i]){
                if(x>max)max = x;
        int[] index = new int[max+1];
        int[] result = new int[2];
        for(int i = 0;i<index.length;i++) index[i] = i;
        for(int i = 0;i<edges.length;i++){
            if(findRedundantConnectionHelper(index,edges[i])) result = edges[i];
        return result;
    public static boolean findRedundantConnectionHelper(int[] index,int[] pair){
        int a = pair[0];
        int b = pair[1];
        int ida = index[a];
        int idb = index[b];
        if(index[a] == index[b]) return true;
        for(int i = 0;i<index.length;i++){
            if(index[i]==ida) index[i] = idb;
        return false;