This is a java program to find hamilton cycle in graph. 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 Find Hamiltonian Cycle in an UnWeighted Graph. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.sanfoundry.hardgraph;

import java.util.Arrays;

import java.util.Scanner;

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);

`/** Make an object of HamiltonianCycle class **/`

HamiltonianCycle hc = new HamiltonianCycle();

`/** 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 HamiltonianCycle.java $ java HamiltonianCycle 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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