Connecting Graph

Medium Union Find

LintCode: https://www.lintcode.com/en/problem/connecting-graph/

Question

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

Thinking

Add an edge to connect node a and node b DOES NOT mean the edge from node a to node b. The edge maybe between some nodes which are A parent and B parent.

Review

Since n is known, we can use an array to store roots.

Solution

In this solution, we use root of each nodes to connect two nodes.

Java (Review)

public class ConnectingGraph { 
    
    private int[] roots = null;

    public ConnectingGraph(int n) {
        // initialize your data structure here.
        roots = new int[n + 1]; // we don't use index 0
        for (int i = 1; i <= n; i++) {
            roots[i] = i;
        }
    }

    public void connect(int a, int b) {
        // Write your code here
        int rootA = getRoot(a);
        int rootB = getRoot(b);
        if (rootA != rootB) {
            roots[rootA] = rootB; // connect a and b by root
        }
    }
        
    public boolean  query(int a, int b) {
        // Write your code here
        return getRoot(a) == getRoot(b);
    }
    
    private int getRoot(int node) {
        if (roots[node] == node) {
            return node;
        }
        int root = getRoot(roots[node]);
        roots[node] = root;
        return root;
    }
}

Java

public class ConnectingGraph { 
    
    private Map<Integer, Integer> rootMap = new HashMap<Integer, Integer>();

    public ConnectingGraph(int n) {
        // initialize your data structure here.
        for (int i = 1; i <= n; i++) {
            rootMap.put(i, i);
        }
    }

    public void connect(int a, int b) {
        // Write your code here
        int rootA = getRoot(a);
        int rootB = getRoot(b);
        if (rootA != rootB) {
            rootMap.put(rootA, rootB);
        }
    }
        
    public boolean  query(int a, int b) {
        // Write your code here
        return getRoot(a) == getRoot(b);
    }
    
    private int getRoot(int node) {
        Integer root = rootMap.get(node);
        if (root == null) {
            rootMap.put(node, node);
            return node;
        }
        if (root == node) {
            return node;
        }
        root = getRoot(root);
        rootMap.put(node, root);
        return root;
    }
    
}