programming-examples/java/Graph_Problems_Algorithms/Java Program to Implement Hopcroft Algorithm.java

/*This is a Java Program to Implement Hopcroft Karp Algorithm. The Hopcroft–Karp algorithm is an algorithm that takes as input a bipartite graph and produces as output a maximum cardinality matching – a set of as many edges as possible with the property that no two edges share an endpoint.*/

/**
 ** Java Program to Implement Hopcroft Algorithm
 **/

import java.util.*;

/** Class Hopcroft **/
public class Hopcroft
{
    private final int NIL = 0;
    private final int INF = Integer.MAX_VALUE;
    private ArrayList<Integer>[] Adj;
    private int[] Pair;
    private int[] Dist;
    private int cx, cy;

    /** Function BFS **/
    public boolean BFS()
    {
        Queue<Integer> queue = new LinkedList<Integer>();
        for (int v = 1; v <= cx; ++v)
            if (Pair[v] == NIL)
                {
                    Dist[v] = 0;
                    queue.add(v);
                }
            else
                Dist[v] = INF;
        Dist[NIL] = INF;
        while (!queue.isEmpty())
            {
                int v = queue.poll();
                if (Dist[v] < Dist[NIL])
                    for (int u : Adj[v])
                        if (Dist[Pair[u]] == INF)
                            {
                                Dist[Pair[u]] = Dist[v] + 1;
                                queue.add(Pair[u]);
                            }
            }
        return Dist[NIL] != INF;
    }
    /** Function DFS **/
    public boolean DFS(int v)
    {
        if (v != NIL)
            {
                for (int u : Adj[v])
                    if (Dist[Pair[u]] == Dist[v] + 1)
                        if (DFS(Pair[u]))
                            {
                                Pair[u] = v;
                                Pair[v] = u;
                                return true;
                            }
                Dist[v] = INF;
                return false;
            }
        return true;
    }
    /** Function to get maximum matching **/
    public int HopcroftKarp()
    {
        Pair = new int[cx + cy + 1];
        Dist = new int[cx + cy + 1];
        int matching = 0;
        while (BFS())
            for (int v = 1; v <= cx; ++v)
                if (Pair[v] == NIL)
                    if (DFS(v))
                        matching = matching + 1;
        return matching;
    }
    /** Function to make graph with vertices x , y **/
    public void makeGraph(int[] x, int[] y, int E)
    {
        Adj = new ArrayList[cx + cy + 1];
        for (int i = 0; i < Adj.length; ++i)
            Adj[i] = new ArrayList<Integer>();
        /** adding edges **/
        for (int i = 0; i < E; ++i)
            addEdge(x[i] + 1, y[i] + 1);
    }
    /** Function to add a edge **/
    public void addEdge(int u, int v)
    {
        Adj[u].add(cx + v);
        Adj[cx + v].add(u);
    }
    /** Main Method **/
    public static void main (String[] args)
    {
        Scanner scan = new Scanner(System.in);
        System.out.println("Hopcroft Algorithm Test\n");
        /** Make an object of Hopcroft class **/
        Hopcroft hc = new Hopcroft();
        /** Accept number of edges **/
        System.out.println("Enter number of edges\n");
        int E = scan.nextInt();
        int[] x = new int[E];
        int[] y = new int[E];
        hc.cx = 0;
        hc.cy = 0;
        System.out.println("Enter "+ E +" x, y coordinates ");
        for (int i = 0; i < E; i++)
            {
                x[i] = scan.nextInt();
                y[i] = scan.nextInt();
                hc.cx = Math.max(hc.cx, x[i]);
                hc.cy = Math.max(hc.cy, y[i]);
            }
        hc.cx += 1;
        hc.cy += 1;
        /** make graph with vertices **/
        hc.makeGraph(x, y, E);
        System.out.println("\nMatches : "+ hc.HopcroftKarp());
    }
}

/*
Enter number of edges

11
Enter 11 x, y coordinates
0 0
0 3
1 0
1 2
1 4
2 1
3 0
3 2
3 3
3 4
4 2

Matches : 5