684. Redundant Connection

本文探讨了在一个原本为树形结构的图中,如何通过使用并查集(Disjoint Sets)算法找出额外添加的一条边,该边导致图中出现环。并查集是一种用于处理不相交集合的高效数据结构,适用于解决此类图论问题。

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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.

Problem URL


Solution

给一个图,有N个节点,labeled from 1 to N。本来是一棵树,但是现在多了一条边,找到多的这条边。

We could maintain a parent array to denote the parent of a connected component. An edge will connect two nodes into one connected component.

When we count an edge in, if the two nodes have already been in the same connected component, the edge will result in a cycle. That is, the edge is redundant.

We can make use of Disjoint Sets (Union Find).
If we regard a node as an element, a connected component is actually a disjoint set.

Code
class Solution {
    public int[] findRedundantConnection(int[][] edges) {
        int[] parents = new int[edges.length + 1];
        for (int[] edge: edges){
            if (find(parents, edge[0]) == find(parents, edge[1])){
                return edge;
            }
            else{
                parents[find(parents, edge[0])] = find(parents, edge[1]);
            }
        }
        return new int[2];
    }
    
    private int find (int[] parents, int n){
        if (parents[n] == 0){
            return n;
        }
        else{
            return find(parents, parents[n]);
        }
    }
}

Time Complexity: O()
Space Complexity: O()


Review
1. CLI - Command Line Interface 2. GUI - Graphical User Interface 3. SSH - Secure Shell 4. FTP - File Transfer Protocol 5. HTTP - Hypertext Transfer Protocol 6. TCP - Transmission Control Protocol 7. UDP - User Datagram Protocol 8. IP - Internet Protocol 9. DNS - Domain Name System 10. DHCP - Dynamic Host Configuration Protocol 11. NFS - Network File System 12. SMB - Server Message Block 13. RAID - Redundant Array of Independent Disks 14. LVM - Logical Volume Manager 15. RAID0 - Redundant Array of Independent Disks Level 0 16. RAID1 - Redundant Array of Independent Disks Level 1 17. RAID5 - Redundant Array of Independent Disks Level 5 18. RAID6 - Redundant Array of Independent Disks Level 6 19. RAID10 - Redundant Array of Independent Disks Level 10 20. ACL - Access Control List 21. SELinux - Security-Enhanced Linux 22. PAM - Pluggable Authentication Modules 23. SSHD - Secure Shell Daemon 24. SUDO - Superuser Do 25. CRON - Chronological Scheduler 26. IPTABLES - IP Tables 27. UFW - Uncomplicated Firewall 28. GRUB - Grand Unified Bootloader 29. LILO - Linux Loader 30. BIOS - Basic Input/Output System 31. UEFI - Unified Extensible Firmware Interface 32. GNOME - GNU Object Model Environment 33. KDE - K Desktop Environment 34. XFCE - XForms Common Environment 35. LXDE - Lightweight X11 Desktop Environment 36. ALSA - Advanced Linux Sound Architecture 37. PulseAudio - Pulse Audio 38. JACK - Jack Audio Connection Kit 39. GCC - GNU Compiler Collection 40. GDB - GNU Debugger 41. GNU - GNU's Not Unix 42. RPM - Red Hat Package Manager 43. DEB - Debian Package 44. YUM - Yellowdog Updater, Modified 45. APT - Advanced Packaging Tool 46. GIT - Global Information Tracker 47. SVN - Subversion 48. CVS - Concurrent Versions System 49. SSHFS - Secure Shell File System 50. NFS - Network File System.
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