C++ Program to Find Hamiltonian Cycle

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This C++ Program demonstrates the implementation of Hamiltonian Cycle.

Here is source code of the C++ Program to Find Hamiltonian Cycle in a Graph. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

  1. /*
  2.  * C++ Program to Find Hamiltonian Cycle
  3.  */
  4. #include <iostream>
  5. #include <cstdio>
  6. #include <cstdlib>
  7. #define V 5
  8. using namespace std;
  9.  
  10. void printSolution(int path[]);
  11.  
  12. /* 
  13.  * check if the vertex v can be added at index 'pos' in the Hamiltonian Cycle 
  14.  */
  15. bool isSafe(int v, bool graph[V][V], int path[], int pos)
  16. {
  17.     if (graph [path[pos-1]][v] == 0)
  18.         return false;
  19.    for (int i = 0; i < pos; i++)
  20.         if (path[i] == v)
  21.             return false;
  22.     return true;
  23. }
  24.  
  25. /* solve hamiltonian cycle problem */
  26. bool hamCycleUtil(bool graph[V][V], int path[], int pos)
  27. {
  28.     if (pos == V)
  29.     {
  30.         if (graph[ path[pos-1] ][ path[0] ] == 1)
  31.             return true;
  32.         else
  33.             return false;
  34.     }
  35.  
  36.     for (int v = 1; v < V; v++)
  37.     {
  38.         if (isSafe(v, graph, path, pos))
  39.         {
  40.             path[pos] = v;
  41.             if (hamCycleUtil (graph, path, pos+1) == true)
  42.                 return true;
  43.             path[pos] = -1;
  44.         }
  45.     }
  46.     return false;
  47. }
  48.  
  49. /* solves the Hamiltonian Cycle problem using Backtracking.*/
  50. bool hamCycle(bool graph[V][V])
  51. {
  52.     int *path = new int[V];
  53.     for (int i = 0; i < V; i++)
  54.         path[i] = -1;
  55.     path[0] = 0;
  56.     if (hamCycleUtil(graph, path, 1) == false)
  57.     {
  58.         cout<<"\nSolution does not exist"<<endl;
  59.         return false;
  60.     }
  61.     printSolution(path);
  62.     return true;
  63. }
  64.  
  65. /* Main */
  66. void printSolution(int path[])
  67. {
  68.     cout<<"Solution Exists:";
  69.     cout<<" Following is one Hamiltonian Cycle \n"<<endl;
  70.     for (int i = 0; i < V; i++)
  71.         cout<<path[i]<<"  ";
  72.     cout<< path[0]<<endl;
  73. }
  74.  
  75. int main()
  76. {
  77.    /* Let us create the following graph
  78.       (0)--(1)--(2)
  79.        |   / \   |
  80.        |  /   \  |
  81.        | /     \ |
  82.       (3)-------(4)    */
  83.    bool graph1[V][V] = {{0, 1, 0, 1, 0},
  84.                       {1, 0, 1, 1, 1},
  85.                       {0, 1, 0, 0, 1},
  86.                       {1, 1, 0, 0, 1},
  87.                       {0, 1, 1, 1, 0},
  88.                      };
  89.    hamCycle(graph1);
  90.  
  91.    /* Let us create the following graph
  92.       (0)--(1)--(2)
  93.        |   / \   |
  94.        |  /   \  |
  95.        | /     \ |
  96.       (3)       (4)    */
  97.     bool graph2[V][V] = {{0, 1, 0, 1, 0},
  98.                       {1, 0, 1, 1, 1},
  99.                       {0, 1, 0, 0, 1},
  100.                       {1, 1, 0, 0, 0},
  101.                       {0, 1, 1, 0, 0},
  102.                      };
  103.     hamCycle(graph2);
  104.     return 0;
  105. }

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$ g++ hamiltonian.cpp
$ a.out
 
Solution Exists: Following is one Hamiltonian Cycle
 
0  1  2  4  3  0
 
Solution does not exist
 
------------------
(program exited with code: 1)
Press return to continue

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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