Java Program to Check if a Given Graph Contain Hamiltonian Cycle or Not

This is a java program to check if the graph contains any Hamiltonian cycle. In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian path that is a cycle. Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete.

Here is the source code of the Java Program to Check if a Given Graph Contain Hamiltonian Cycle or Not. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.maixuanviet.hardgraph;
 
import java.util.Arrays;
import java.util.Scanner;
 
public class CheckHamiltonianCycle
{
    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);
        /** Make an object of HamiltonianCycle class **/
        CheckHamiltonianCycle hc = new CheckHamiltonianCycle();
        /** Accept number of vertices **/
        System.out.println("Enter number of vertices");
        int V = scan.nextInt();
        /** get graph **/
        System.out.println("Enter adjacency matrix");
        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);
        scan.close();
    }
}

Output:

$ javac CheckHamiltonianCycle.java
$ java CheckHamiltonianCycle
 
Enter number of vertices
6
Enter adjacency matrix
0 1 0 0 0 0
1 0 1 1 0 0
0 1 0 0 0 1 
0 1 0 0 1 1
0 0 0 1 0 1
0 0 1 1 1 0
No solution