[LeetCode] 684. Redundant Connection (Medium) (JAVA)
Subject address: https://leetcode.com/problems/redundant-connection/
Title description:
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.
General idea
In this problem, the tree refers to a connected and acyclic undirected graph.
Enter a graph, which consists of a tree with N nodes (the node values do not repeat 1, 2, …, N) and an additional edge. The two vertices of the additional edge are contained between 1 and N. This additional edge does not belong to an existing edge in the tree.
The resulting graph is a two-dimensional array of edges. The elements of each edge are a pair of [u, v], satisfying u <v, representing the edges of the undirected graph connecting vertices u and v.
Return an edge that can be deleted so that the resulting graph is a tree with N nodes. If there are multiple answers, the last edge in the two-dimensional array is returned. The answer side [u, v] should satisfy the same format u <v.
Problem-solving method
- Adopt and find
- If the parent nodes of the two nodes are the same, it means that the two are connected, and the result is returned directly; if the parent nodes of the two nodes are different, the two nodes are merged
class Solution {
public int[] findRedundantConnection(int[][] edges) {
int[] fa = new int[edges.length + 1];
for (int i = 0; i < fa.length; i++) {
fa[i] = i;
}
for (int i = 0; i < edges.length; i++) {
if (find(fa, edges[i][0]) == find(fa, edges[i][1])) return edges[i];
merge(fa, edges[i][0], edges[i][1]);
}
return new int[]{-1, -1};
}
private int find(int[] fa, int x) {
if (fa[x] != x) return fa[x] = find(fa, fa[x]);
return fa[x];
}
private void merge(int[] fa, int x, int y) {
fa[find(fa, x)] = find(fa, y);
}
}
Execution time: 1 ms, beating 87.99% of Java users
Memory consumption: 38.8 MB, beating 34.46% of Java users
