[LintCode] Connecting Graph

Given n nodes in a graph labeled from 1 to n. There is no edges in the graph at beginning.

You need to support the following method:

1. connect(a, b), add an edge to connect node a and node b. 2.query(a, b)`, check if two nodes are connected

Example

5 // n = 5
query(1, 2) return false
connect(1, 2)
query(1, 3) return false
connect(2, 4)
query(1, 4) return true

 

Solution 1. BFS, O(1) connect, O(V) query, O(V + E) space 

 

public class ConnectingGraph { 
    private ArrayList<HashSet<Integer>> lists = null;
    public ConnectingGraph(int n) {
        // initialize your data structure here.
        lists = new ArrayList<HashSet<Integer>>(n);
        for(int i = 0; i < n; i++){
            lists.add(new HashSet<Integer>());    
        }
    }

    public void connect(int a, int b) {
        // Write your code here
        lists.get(a - 1).add(b - 1);
        lists.get(b - 1).add(a - 1);
    }
        
    public boolean query(int a, int b) {
        // Write your code here
        return bfs(a - 1, b - 1);
    }
    
    private boolean bfs(int source, int target){
        Queue<Integer> queue = new LinkedList<Integer>();
        HashSet<Integer> visited = new HashSet<Integer>();
        queue.add(source);
        visited.add(source);
        
        while(!queue.isEmpty()){
            int curr = queue.poll();
            for(Integer i : lists.get(curr)){
                if(!visited.contains(i)){
                    if(i == target){
                        return true;
                    }
                    queue.add(i);
                    visited.add(i);
                }
            }
        }
        return false;
    }
}

 

 

Solution 2. Union Find, O(1) connect and query on average, O(V) space(not storing edge information)

 

class UnionFind {
    private int[] father = null;
    public UnionFind(int n){
        father = new int[n];
        for(int i = 0; i < n; i++){
            father[i] = i;
        }
    }
    public int find(int x){
        if(father[x] == x){
            return x;
        }
        return father[x] = find(father[x]);
    }
    public void connect(int a, int b){
        int root_a = find(a);
        int root_b = find(b);
        if(root_a != root_b){
            father[root_a] = root_b;
        }
    }
}
public class ConnectingGraph { 
    private UnionFind uf = null;
    public ConnectingGraph(int n) {
        // initialize your data structure here.
        uf = new UnionFind(n);
    }

    public void connect(int a, int b) {
        uf.connect(a - 1, b - 1);
    }
        
    public boolean query(int a, int b) {
        return uf.find(a - 1) == uf.find(b - 1);
    }
}

 

 

 

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