Program to implement the Kurskals Algorithm to solve Minimum Cost Spanning Tree Problem (MST)

 # include <iostream.h>
 # include   <stdlib.h>
 # include    <conio.h>

 # define MAX_VERTICES  10
 # define MAX_EDGES     15


 //-------------------------------  Vertex  ------------------------------//


 class Vertex
 {
    public:
       int label;

    public:
       Vertex( )   {  }
       ~Vertex( )  {  }

       void SetVertex(const int);
 };


 //-------------------------------  Edge  --------------------------------//


 class Edge
 {
    public:
       int weight;

       Vertex V1;
       Vertex V2;

    public:
       Edge( )   { }
       ~Edge( )  { }

       void SetEdge(const Vertex,const Vertex,const int);
 };



 //----------------------------  SetVertex( )  ---------------------------//


 void Vertex::SetVertex(const int _label)
 {
    label=_label;
 }


 //-----------------------------  SetEdge( )  ----------------------------//


 void Edge::SetEdge(const Vertex _V1,const Vertex _V2,const int _weight)
 {
    V1=_V1;
    V2=_V2;

    weight=_weight;
 }

 int main( )
 {
    clrscr( );
    textmode(BW80);

    /***************************************************************

            Sample Input
            ************

         Vertices  ,  Edges
            6  ,  10

           Vertex_1 , Vertex_2
            320 , 100
            170 , 200
            320 , 250
            470 , 200
            220 , 400
            420 , 400

          Vertxe_1 ---->  Vertex_2 ,  Weight
            1  ---->  2        ,  6
            1  ---->  4        ,  5
            1  ---->  3        ,  1
            2  ---->  3        ,  5
            2  ---->  5        ,  3
            3  ---->  5        ,  6
            3  ---->  6        ,  4
            3  ---->  4        ,  5
            4  ---->  5        ,  2
            5  ---->  5        ,  6

         Answer : 15

    ***************************************************************/

    int vertices=0;
    int edges=0;

    cout<<\"*******************  Input  ********************\"<<endl;
    cout<<\"Enter the Total Number of Vertices (1-10) = \";
    cin>>vertices;

    vertices=((vertices<1)?1:vertices);
    vertices=((vertices>10)?10:vertices);

    cout<<\"Enter the Total Number of Edges (1-15) = \";
    cin>>edges;

    edges=((edges<0)?0:edges);
    edges=((edges>15)?15:edges);

    Vertex  V[MAX_VERTICES];
    Edge    E[MAX_EDGES];

    for(int count=0;count<vertices;count++)
       V[count].SetVertex(count);

    int v1;
    int v2;
    int weight;

    cout<<\"\\n **********  Edges and their Weights  ********* \"<<endl;

    for(count=0;count<edges;count++)
    {
       cout<<\"    ----------       ---------->\";

       gotoxy(2,wherey( ));
       cin>>v1;

       gotoxy(35,(wherey( )-1));
       cin>>v2;

       gotoxy(17,(wherey( )-1));
       cin>>weight;

       v1=((v1<1)?1:v1);
       v1=((v1>vertices)?vertices:v1);

       v2=((v2<1)?1:v2);
       v2=((v2>vertices)?vertices:v2);

       weight=((weight<=0)?0:weight);

       E[count].SetEdge(V[(v1-1)],V[(v2-1)],weight);
    }

    cout<<endl<<\"Press any key to Apply Kruskal\'s Algorithm...\";

    getch( );
    clrscr( );

    cout<<\"*******************  Input  ********************\"<<endl;
    cout<<\" V = { \";

    for(count=1;count<vertices;count++)
       cout<<count<<\",\";

    cout<<count<<\" } \"<<endl;

    cout<<\" E = { \";

    for(count=0;count<edges;count++)
    {
       cout<<\"(\"<<(E[count].V1.label+1)<<\",\"<<(E[count].V2.label+1)<<\")\";

       if(count<(edges-1))
      cout<<\",\";
    }

    cout<<\" } \"<<endl<<endl;

    for(int i=0;i<edges;i++)
    {
       for(int j=0;j<(edges-1);j++)
       {
      if(E[j].weight>=E[(j+1)].weight)
      {
         Edge Temp;

         Temp=E[j];
         E[j]=E[(j+1)];
         E[(j+1)]=Temp;
      }
       }
    }

    int e_count=0;
    int cycle_flag=0;

    Edge _E[MAX_EDGES];

    int mst[MAX_VERTICES][MAX_VERTICES]={0};

    for(i=0;i<=vertices;i++)
    {
       mst[i][0]=i;

       for(int j=1;j<vertices;j++)
      mst[i][j]=-1;
    }

    for(count=0;count<edges;count++)
    {
       cycle_flag=0;

       for(i=1;i<vertices;i++)
       {
      if(mst[E[count].V1.label][i]==E[count].V2.label ||
                   mst[E[count].V2.label][i]==E[count].V1.label)
         cycle_flag=1;
       }

       if(!cycle_flag)
       {
      _E[e_count]=E[count];

      e_count++;

      for(i=1;i<vertices;i++)
      {
         if(mst[E[count].V1.label][i]==E[count].V2.label)
        break;

         if(mst[E[count].V1.label][i]==-1)
         {
        mst[E[count].V1.label][i]=E[count].V2.label;

        break;
         }
      }

      for(i=1;i<vertices;i++)
      {
         if(mst[E[count].V2.label][i]==E[count].V1.label)
        break;

         if(mst[E[count].V2.label][i]==-1)
         {
        mst[E[count].V2.label][i]=E[count].V1.label;

        break;
         }
      }

      for(i=0;i<vertices;i++)
      {
         for(int j=0;j<vertices;j++)
         {
        for(int k=1;k<vertices;k++)
        {
           if(mst[j][k]!=-1)
           {
              for(int l=1;l<vertices;l++)
              {
             if(mst[mst[j][k]][l]!=-1)
             {
                for(int m=0;m<vertices;m++)
                {
                   if(mst[mst[j][k]][l]==mst[j][m])
                  break;

                   if(mst[j][m]==-1)
                   {
                  mst[j][m]=mst[mst[j][k]][l];

                  break;
                   }
                }
             }
              }
           }
        }
         }
      }
       }
    }

    cout<<\"*******************  Result  ********************\"<<endl;
    cout<<\" V = { \";

    for(count=1;count<vertices;count++)
       cout<<count<<\",\";

    cout<<count<<\" }\"<<endl<<\" E = { \";

    for(count=0;count<(e_count-1);count++)
       cout<<\"(\"<<(_E[count].V1.label+1)<<\",\"<<(_E[count].V2.label+1)<<\"),\";

       cout<<\"(\"<<(_E[count].V1.label+1)<<\",\"<<(_E[count].V2.label+1)<<\") }\"<<endl;

    cout<<\" Total Cost = \";

    int cost=0;

    for(count=0;count<e_count;count++)
    {
       cost+=_E[count].weight;

       if(count<(e_count-1))
      cout<<_E[count].weight<<\"+\";
    }

    cout<<_E[count-1].weight<<\" =  \"<<cost<<endl<<endl;
    cout<<endl<<\" Press any Key to Exit...\";

    getch( );
    return 0;
 }