Java Program to Check if a Given Graph must 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.

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package com.sanfoundry.hardgraph;
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import java.util.Arrays;
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import java.util.Scanner;
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public class CheckHamiltonianCycle
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{
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    private int     V, pathCount;
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    private int[]   path;
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    private int[][] graph;
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    /** Function to find cycle **/
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    public void findHamiltonianCycle(int[][] g)

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    {
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        V = g.length;
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        path = new int[V];
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        Arrays.fill(path, -1);
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        graph = g;
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        try
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        {
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            path[0] = 0;
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            pathCount = 1;
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            solve(0);
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            System.out.println("No solution");

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        }
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        catch (Exception e)
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        {
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            System.out.println(e.getMessage());

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            display();
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        }
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    }
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    /** function to find paths recursively **/

    public void solve(int vertex) throws Exception

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    {
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        /** solution **/
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        if (graph[vertex][0] == 1 && pathCount == V)

            throw new Exception("Solution found");

        /** all vertices selected but last vertex not linked to 0 **/

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        if (pathCount == V)
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            return;
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        for (int v = 0; v < V; v++)
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        {
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            /** if connected **/
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            if (graph[vertex][v] == 1)
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            {
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                /** add to path **/
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                path[pathCount++] = v;
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                /** remove connection **/

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                graph[vertex][v] = 0;
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                graph[v][vertex] = 0;
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                /** if vertex not already selected solve recursively **/

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                if (!isPresent(v))
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                    solve(v);
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                /** restore connection **/

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                graph[vertex][v] = 1;
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                graph[v][vertex] = 1;
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                /** remove path **/
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                path[--pathCount] = -1;
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            }
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        }
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    }
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    /** function to check if path is already selected **/

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    public boolean isPresent(int v)
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    {
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        for (int i = 0; i < pathCount - 1; i++)

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            if (path[i] == v)
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                return true;
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        return false;
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    }
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    /** display solution **/
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    public void display()
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    {
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        System.out.print("\nPath : ");
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        for (int i = 0; i <= V; i++)
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            System.out.print(path[i % V] + " ");

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        System.out.println();
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    }
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    /** Main function **/
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    public static void main(String[] args)

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    {
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        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");

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        int V = scan.nextInt();
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        /** get graph **/
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        System.out.println("Enter adjacency matrix");

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        int[][] graph = new int[V][V];
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        for (int i = 0; i < V; i++)
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            for (int j = 0; j < V; j++)
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                graph[i][j] = scan.nextInt();

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        hc.findHamiltonianCycle(graph);
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        scan.close();
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    }
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}
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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

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