684. Redundant Connection #

Problem #

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.

Problem Summary #

In this problem, a tree refers to a connected and acyclic undirected graph. The input is a graph composed of a tree with N nodes (node values are distinct: 1, 2, …, N) and one additional edge. The two vertices of the additional edge are between 1 and N, and this additional edge is not an edge that already existed in the tree. The resulting graph is a 2D array composed of edges. Each edge element is a pair [u, v], satisfying u < v, representing an undirected edge 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, return the edge that appears last in the 2D array. The answer edge [u, v] should satisfy the same format u < v.

Note:

• The size of the input 2D array is between 3 and 1000.
• The integers in the 2D array are between 1 and N, where N is the size of the input array.

Solution Approach #

• Given a connected acyclic undirected graph and some connected edges, the requirement is to delete one edge among these edges so that the N nodes in the graph are still connected. If there are multiple such edges, output the last one.
• This problem can be solved directly with Union-Find. Scan all edges in order, and merge the two endpoints of each edge together with union(). If an edge is encountered whose two endpoints are already in the same set, it means this is a redundant edge and should be deleted. Finally, output these edges.

Code #

package leetcode

import (
	"github.com/halfrost/leetcode-go/template"
)

func findRedundantConnection(edges [][]int) []int {
	if len(edges) == 0 {
		return []int{}
	}
	uf, res := template.UnionFind{}, []int{}
	uf.Init(len(edges) + 1)
	for i := 0; i < len(edges); i++ {
		if uf.Find(edges[i][0]) != uf.Find(edges[i][1]) {
			uf.Union(edges[i][0], edges[i][1])
		} else {
			res = append(res, edges[i][0])
			res = append(res, edges[i][1])
		}
	}
	return res
}