# 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

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

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;
}
```