Connected Component in Undirected Graph

Posted 2020-11-23 flagyuri

Description

Find connected component in undirected graph.

Each node in the graph contains a label and a list of its neighbors.

(A connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph.)

You need return a list of label set.

Nodes in a connected component should sort by label in ascending order. Different connected components can be in any order.

Clarification

Learn more about representation of graphs

Example

Example 1:

Input: {1,2,4#2,1,4#3,5#4,1,2#5,3}
Output: [[1,2,4],[3,5]]
Explanation:

  1------2  3
        |  | 
        |  |
        |  |
        |  |
        4   5

Example 2:

Input: {1,2#2,1}
Output: [[1,2]]
Explanation:

  1--2
思路：无向图连通块, 可以使用BFS或者并查集union find求解 .

/**
 * Definition for Undirected graph.
 * class UndirectedGraphNode {
 *     int label;
 *     ArrayList<UndirectedGraphNode> neighbors;
 *     UndirectedGraphNode(int x) { label = x; neighbors = new ArrayList<UndirectedGraphNode>(); }
 * };
 */


public
class Solution {
    class UnionFind {
        HashMap<Integer, Integer> father = new HashMap<Integer, Integer>();
        UnionFind(HashSet<Integer> hashSet)
        {
            for (Integer now : hashSet) {
                father.put(now, now);
            }
        }
        int find(int x)
        {
            int parent = father.get(x);
            while (parent != father.get(parent)) {
                parent = father.get(parent);
            }
            return parent;
        }
        int compressed_find(int x)
        {
            int parent = father.get(x);
            while (parent != father.get(parent)) {
                parent = father.get(parent);
            }
            int next;
            while (x != father.get(x)) {
                next = father.get(x);
                father.put(x, parent);
                x = next;
            }
            return parent;
        }

        void union(int x, int y)
        {
            int fa_x = find(x);
            int fa_y = find(y);
            if (fa_x != fa_y)
                father.put(fa_x, fa_y);
        }
    }
    
    List<List<Integer> > print(HashSet<Integer> hashSet, UnionFind uf, int n) {
        List<List<Integer> > ans = new ArrayList<List<Integer> >();
        HashMap<Integer, List<Integer> > hashMap = new HashMap<Integer, List<Integer> >();
        for (int i : hashSet) {
            int fa = uf.find(i);
            if (!hashMap.containsKey(fa)) {
                hashMap.put(fa, new ArrayList<Integer>());
            }
            List<Integer> now = hashMap.get(fa);
            now.add(i);
            hashMap.put(fa, now);
        }
        for (List<Integer> now : hashMap.values()) {
            Collections.sort(now);
            ans.add(now);
        }
        return ans;
    }

public
    List<List<Integer> > connectedSet(List<UndirectedGraphNode> nodes)
    {
        // Write your code here

        HashSet<Integer> hashSet = new HashSet<Integer>();
        for (UndirectedGraphNode now : nodes) {
            hashSet.add(now.label);
            for (UndirectedGraphNode neighbour : now.neighbors) {
                hashSet.add(neighbour.label);
            }
        }
        UnionFind uf = new UnionFind(hashSet);

        for (UndirectedGraphNode now : nodes) {

            for (UndirectedGraphNode neighbour : now.neighbors) {
                int fnow = uf.find(now.label);
                int fneighbour = uf.find(neighbour.label);
                if (fnow != fneighbour) {
                    uf.union(now.label, neighbour.label);
                }
            }
        }

        return print(hashSet, uf, nodes.size());
    }
}