Find the Connected Component in the Undirected Graph

Question

Find the number connected component in the undirected graph. Each node in the graph contains a label and a list of its neighbors. (a connected component (or just 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.)

Notice

Each connected component should sort by label.

Clarification

Learn more about representation of graphs

Example

Given graph:

A------B  C
 \     |  |
  \    |  |
   \   |  |
    \  |  |
      D   E

Return {A,B,D}, {C,E}. Since there are two connected component which is {A,B,D}, {C,E}

Tags

Breadth First Search Union Find

Related Problems

  • Medium Graph Valid Tree
  • Medium Find the Weak Connected Component in the Directed Graph

Analysis

除了常规的BFS方法,还可以用Union Find。

  1. 两重循环遍历所有的node,并存入一个HashSet(为什么是HashSet,HashMap是否可以?)
  2. 用HashSet的元素初始化UnionFind(father HashMap的构建)
  3. 再度两重循环遍历所有node,将now node 和 neighbor node全部union起来
  4. 通过辅助函数print,对HashSet中的每一个节点进行父节点查找(find),把具有相同的父节点的子节点全部打包成ArrayList作为value,按照父节点的label为key,存入HashMap中,最后把这个HashMap的values打包成List,输出结果

Solution

/**
 * Definition for Undirected graph.
 * class UndirectedGraphNode {
 *     int label;
 *     ArrayList<UndirectedGraphNode> neighbors;
 *     UndirectedGraphNode(int x) { label = x; neighbors = new ArrayList<UndirectedGraphNode>(); }
 * };
 */
public class Solution {
    // Define UnionFind Class
    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 temp = -1;
            int fa = father.get(x);
            while(fa!=father.get(fa)) {
                temp = father.get(fa);
                father.put(fa, parent) ;
                fa = temp;
            }
            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;
    }

    /**
     * @param nodes a array of Undirected graph node
     * @return a connected set of a Undirected graph
     */
    public List<List<Integer>> connectedSet(ArrayList<UndirectedGraphNode> nodes) {
        HashSet<Integer> hashSet = new HashSet<Integer>();
        for (UndirectedGraphNode now : nodes) {
            hashSet.add(now.label);
            for (UndirectedGraphNode neighbor : now.neighbors) {
                hashSet.add(neighbor.label);
            }
        }

        UnionFind uf = new UnionFind(hashSet);

        for (UndirectedGraphNode now : nodes) {
            for (UndirectedGraphNode neighbor : now.neighbors) {
                int fnow = uf.find(now.label);
                int fneighbor = uf.find(neighbor.label);
                if (fnow != fneighbor) {
                    uf.union(now.label, neighbor.label);
                }
            }
        }
        return print(hashSet, uf, nodes.size());
    }
}

Reference

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