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# Program to implement the Prim's Algorithm to solve Minimum Spanning Tree Problem (MST)

Posted By: Easy Tutor     Category: C++ Programming     Views: 17033

## Code for Program to implement the Prim's Algorithm to solve Minimum Spanning Tree Problem (MST) in C++ Programming

``` # 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(constint);
};

/*************************************************************************///-------------------------------  Edge  --------------------------------///*************************************************************************/class Edge
{
public:
int weight;

Vertex V1;
Vertex V2;

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

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

/*************************************************************************///----------------------------  SetVertex( )  ---------------------------///*************************************************************************/void Vertex::SetVertex(constint _label)
{
label=_label;
}

/*************************************************************************///-----------------------------  SetEdge( )  ----------------------------///*************************************************************************/void Edge::SetEdge(const Vertex _V1,const Vertex _V2,constint _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);

cout<<endl;

int v1;
int v2;
int weight;

cout<<" **********  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 PRIMS Algorithm...";

getch( );
clrscr( );

int U[MAX_VERTICES]={0};
int vertex_1[MAX_VERTICES]={0};
int vertex_2[MAX_VERTICES]={0};
int edge_weights[MAX_VERTICES]={0};
int resultant_weights[MAX_VERTICES]={0};

int flag_1=0;
int flag_2=0;
int u_count=1;
int temp_vertex=0;
int temp_vertex_1=0;
int temp_vertex_2=0;
int lowest_edge_weight=0;

U[0]=0;

do
{
count=0;

for(int i=0;i<vertices;i++)
{
vertex_1[i]=0;
vertex_2[i]=0;
edge_weights[i]=0;
}

for(i=0;i<u_count;i++)
{
flag_1=0;

for(int j=0;j<edges;j++)
{
if(E[j].V1.label==U[i] || E[j].V2.label==U[i])
{
flag_2=0;

if(E[j].V1.label!=U[i])
{
temp_vertex=E[j].V1.label;
temp_vertex_1=E[j].V2.label;
}

else
{
temp_vertex=E[j].V2.label;
temp_vertex_1=E[j].V1.label;
}

for(int k=0;k<u_count;k++)
{
if(temp_vertex==U[k])
{
flag_2=-1;

break;
}
}

if(flag_2!=-1)
{
if(flag_1==0 || lowest_edge_weight>E[j].weight)
{
lowest_edge_weight=E[j].weight;
temp_vertex_2=temp_vertex;
flag_1=1;
}
}
}
}

if(flag_1==1)
{
vertex_2[count]=temp_vertex_2;
vertex_1[count]=temp_vertex_1;
edge_weights[count]=lowest_edge_weight;

count++;
}
}

flag_1=0;

for(i=0;i<count;i++)
{
if(flag_1==0 || lowest_edge_weight>edge_weights[i])
{
lowest_edge_weight=edge_weights[i];
temp_vertex_1=vertex_1[i];
temp_vertex_2=vertex_2[i];
flag_1=1;
}
}

if(flag_1==1)
{
U[u_count]=temp_vertex_2;
u_count++;

for(i=0;i<edges;i++)
{
if((E[i].V1.label==temp_vertex_1 && E[i].V2.label==temp_vertex_2) ||
(E[i].V1.label==temp_vertex_2 && E[i].V2.label==temp_vertex_1) )
{
resultant_weights[(u_count-2)]=E[i].weight;

break;
}
}
}

elsebreak;
}
while(1);

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;

cout<<"*******************  Result  ********************"<<endl;
cout<<" U = { ";

for(count=0;count<(u_count-1);count++)
cout<<(U[count]+1)<<",";

cout<<(U[count]+1)<<" }"<<endl;
cout<<" Total Cost = ";

int cost=0;

for(count=0;count<(u_count-1);count++)
{
cost+=resultant_weights[count];

if(count<(u_count-2))
cout<<resultant_weights[count]<<"+";
}

cout<<resultant_weights[(count-1)]<<" =  "<<cost<<endl<<endl;

cout<<endl<<" Press any Key to Exit...";

getch( );
return 0;
}

```
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