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;
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import java.util.Arrays;
```
```
 
```
```
/** Class HamiltonianCycle **/
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```
public class HamiltonianCycle
```
```
{
```
```
    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;        
```
```
        try
```
```
        {            
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            path[0] = 0;
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            pathCount = 1;            
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            solve(0);
```

            System.out.println("No solution");

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

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            display();
```
```
        }
```
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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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                /** add to path **/

                path[pathCount++] = v;

                /** remove connection **/

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                graph[vertex][v] = 0;
```
```
                graph[v][vertex] = 0;
```
```
 
```

                /** 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;

```
            }
```
```
        }
```
```
    }    
```

    /** function to check if path is already selected **/

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

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

            System.out.print(path[i % V] +" ");

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        System.out.println();
```
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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);

        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");

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        int V = scan.nextInt();
```
```
 
```
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        /** get graph **/
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        System.out.println("\nEnter matrix\n");

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        int[][] graph = new int[V][V];
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        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

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