Java Program to Implement Hamiltonian Cycle Algorithm

This is a Java Program to Implement Hamiltonian Cycle Algorithm. Hamiltonian cycle is a path in a graph that visits each vertex exactly once and back to starting vertex. This program is to determine if a given graph is a hamiltonian cycle or not. This program assumes every vertex of the graph to be a part of hamiltonian path.

Here is the source code of the Java Program to Implement Hamiltonian Cycle Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

/**
 **   Java Program to Implement Hamiltonian Cycle Algorithm
 **/
 
import java.util.Scanner;
import java.util.Arrays;
 
/** Class HamiltonianCycle **/
public class HamiltonianCycle
{
    private int V, pathCount;
    private int[] path;     
    private int[][] graph;
 
    /** Function to find cycle **/
    public void findHamiltonianCycle(int[][] g)
    {
        V = g.length;
        path = new int[V];
 
        Arrays.fill(path, -1);
        graph = g;        
        try
        {            
            path[0] = 0;
            pathCount = 1;            
            solve(0);
            System.out.println("No solution");
        }
        catch (Exception e)
        {
            System.out.println(e.getMessage());
            display();
        }
    }
    /** function to find paths recursively **/
    public void solve(int vertex) throws Exception
    {
        /** solution **/
        if (graph[vertex][0] == 1 && pathCount == V)
            throw new Exception("Solution found");
        /** all vertices selected but last vertex not linked to 0 **/
        if (pathCount == V)
            return;
 
        for (int v = 0; v < V; v++)
        {
            /** if connected **/
            if (graph[vertex][v] == 1 )
            {
                /** add to path **/            
                path[pathCount++] = v;    
                /** remove connection **/            
                graph[vertex][v] = 0;
                graph[v][vertex] = 0;
 
                /** if vertex not already selected  solve recursively **/
                if (!isPresent(v))
                    solve(v);
 
                /** restore connection **/
                graph[vertex][v] = 1;
                graph[v][vertex] = 1;
                /** remove path **/
                path[--pathCount] = -1;                    
            }
        }
    }    
    /** function to check if path is already selected **/
    public boolean isPresent(int v)
    {
        for (int i = 0; i < pathCount - 1; i++)
            if (path[i] == v)
                return true;
        return false;                
    }
    /** display solution **/
    public void display()
    {
        System.out.print("\nPath : ");
        for (int i = 0; i <= V; i++)
            System.out.print(path[i % V] +" ");
        System.out.println();
    }    
    /** Main function **/
    public static void main (String[] args) 
    {
        Scanner scan = new Scanner(System.in);
        System.out.println("HamiltonianCycle Algorithm Test\n");
        /** Make an object of HamiltonianCycle class **/
        HamiltonianCycle hc = new HamiltonianCycle();
 
        /** Accept number of vertices **/
        System.out.println("Enter number of vertices\n");
        int V = scan.nextInt();
 
        /** get graph **/
        System.out.println("\nEnter matrix\n");
        int[][] graph = new int[V][V];
        for (int i = 0; i < V; i++)
            for (int j = 0; j < V; j++)
                graph[i][j] = scan.nextInt();
 
        hc.findHamiltonianCycle(graph);        
    }    
}

HamiltonianCycle Algorithm Test
 
Enter number of vertices
 
8
 
Enter matrix
 
0 1 0 1 1 0 0 0
1 0 1 0 0 1 0 0
0 1 0 1 0 0 1 0
1 0 1 0 0 0 0 1
1 0 0 0 0 1 0 1
0 1 0 0 1 0 1 0
0 0 1 0 0 1 0 1
0 0 0 1 1 0 1 0
Solution found
 
Path : 0 1 2 3 7 6 5 4 0