Java Program to Find Hamiltonian Cycle in an UnWeighted Graph

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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.

  1.  
  2. package com.sanfoundry.hardgraph;
  3.  
  4. import java.util.Arrays;
  5. import java.util.Scanner;
  6.  
  7. public class HamiltonianCycle
  8. {
  9.     private int     V, pathCount;
  10.     private int[]   path;
  11.     private int[][] graph;
  12.  
  13.     /** Function to find cycle **/
  14.     public void findHamiltonianCycle(int[][] g)
  15.     {
  16.         V = g.length;
  17.         path = new int[V];
  18.         Arrays.fill(path, -1);
  19.         graph = g;
  20.         try
  21.         {
  22.             path[0] = 0;
  23.             pathCount = 1;
  24.             solve(0);
  25.             System.out.println("No solution");
  26.         }
  27.         catch (Exception e)
  28.         {
  29.             System.out.println(e.getMessage());
  30.             display();
  31.         }
  32.     }
  33.  
  34.     /** function to find paths recursively **/
  35.     public void solve(int vertex) throws Exception
  36.     {
  37.         /** solution **/
  38.         if (graph[vertex][0] == 1 && pathCount == V)
  39.             throw new Exception("Solution found");
  40.         /** all vertices selected but last vertex not linked to 0 **/
  41.         if (pathCount == V)
  42.             return;
  43.         for (int v = 0; v < V; v++)
  44.         {
  45.             /** if connected **/
  46.             if (graph[vertex][v] == 1)
  47.             {
  48.                 /** add to path **/
  49.                 path[pathCount++] = v;
  50.                 /** remove connection **/
  51.                 graph[vertex][v] = 0;
  52.                 graph[v][vertex] = 0;
  53.                 /** if vertex not already selected solve recursively **/
  54.                 if (!isPresent(v))
  55.                     solve(v);
  56.                 /** restore connection **/
  57.                 graph[vertex][v] = 1;
  58.                 graph[v][vertex] = 1;
  59.                 /** remove path **/
  60.                 path[--pathCount] = -1;
  61.             }
  62.         }
  63.     }
  64.  
  65.     /** function to check if path is already selected **/
  66.     public boolean isPresent(int v)
  67.     {
  68.         for (int i = 0; i < pathCount - 1; i++)
  69.             if (path[i] == v)
  70.                 return true;
  71.         return false;
  72.     }
  73.  
  74.     /** display solution **/
  75.     public void display()
  76.     {
  77.         System.out.print("\nPath : ");
  78.         for (int i = 0; i <= V; i++)
  79.             System.out.print(path[i % V] + " ");
  80.         System.out.println();
  81.     }
  82.  
  83.     /** Main function **/
  84.     public static void main(String[] args)
  85.     {
  86.         Scanner scan = new Scanner(System.in);
  87.         /** Make an object of HamiltonianCycle class **/
  88.         HamiltonianCycle hc = new HamiltonianCycle();
  89.         /** Accept number of vertices **/
  90.         System.out.println("Enter number of vertices");
  91.         int V = scan.nextInt();
  92.         /** get graph **/
  93.         System.out.println("Enter adjacency matrix");
  94.         int[][] graph = new int[V][V];
  95.         for (int i = 0; i < V; i++)
  96.             for (int j = 0; j < V; j++)
  97.                 graph[i][j] = scan.nextInt();
  98.         hc.findHamiltonianCycle(graph);
  99.         scan.close();
  100.     }
  101. }

Output:

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$ 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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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn