lc 684 Redundant Connection

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]

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.

Union Find Accepted

Union Find的關鍵思想是使各結點依次連結在一起，如果有從1到2的邊，則令uni[1] = 2，如果有從2到3的邊，則令uni[2] = 3，這樣如果此時新加一條從1到3的邊，那麽從1開始尋找，uni1為2，uni[2]為3，即1已經有了一條從1到3的邊，再加會導致形成環路，所以這就是我們要的答案。

class Solution {
public:
    vector<int> findRedundantConnection(vector<vector<int>>& edges) {
        vector<int> uni(2001, -1);
        for (auto edge : edges) {
            int head = edge[0], tail = edge[1];
            int x = find(uni, head), y = find(uni, tail);
            if (x == y) return edge;
            uni[x] = y;
        }
        return {};
    }
    int find(vector<int>& uni, int num) {
        while(uni[num] != -1) {
            num = uni[num];
        }
        return num;
    }
};

LN : leetcode 684 Redundant Connection