# Program Shortest Path using Kruskal algorithm in cpp

### The following program illustrates Kruskal algorithm in cpp to find Shortest Path.

``` #include <iostream.h>
#include <graphics.h>
#include   <string.h>
#include   <stdlib.h>
#include    <conio.h>

#define MAX_VERTICES  10
#define MAX_EDGES     15

/*************************************************************************/
//-------------------------------  Vertex  ------------------------------//
/*************************************************************************/

class Vertex
{
public:
int x;
int y;
int label;

private:
char Label[5];

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

void SetVertex(const int,const int,const int);
void ShowVertex( );
};

/*************************************************************************/
//-------------------------------  Edge  --------------------------------//
/*************************************************************************/

class Edge
{
public:
int weight;

Vertex V1;
Vertex V2;

private:
char Weight[5];

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

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

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

void Vertex::SetVertex(const int _x,const int _y,const int _label)
{
x=_x;
y=_y;
label=_label;

itoa((label+1),Label,10);
}

/*************************************************************************/
//----------------------------  ShowVertex( )  --------------------------//
/*************************************************************************/

void Vertex::ShowVertex( )
{
setcolor(1);
setfillstyle(1,1);
pieslice(x,y,0,360,10);

setcolor(9);
circle(x,y,10);

setcolor(15);
settextstyle(2,0,4);

if(label<9)
outtextxy((x-2),(y-6),Label);

else if(label>=9)
outtextxy((x-5),(y-6),Label);
}

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

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

weight=_weight;

itoa(weight,Weight,10);
}

/*************************************************************************/
//----------------------------  ShowEdge( )  ----------------------------//
/*************************************************************************/

void Edge::ShowEdge( )
{
setlinestyle(0,0,3);

setcolor(11);
line(V1.x,V1.y,V2.x,V2.y);

setlinestyle(0,0,0);

V1.ShowVertex( );
V2.ShowVertex( );

int x=(((V1.x+V2.x)/2)-6);
int y=(((V1.y+V2.y)/2)-8);

setcolor(12);
settextstyle(2,0,7);
outtextxy(x,y,Weight);
outtextxy((x+1),y,Weight);
outtextxy((x+1),(y+1),Weight);
}

int main( )
{
textmode(C4350);

int driver=VGA;
int mode=VGAHI;
int error_code;

initgraph(&driver,&mode,"..Bgi");

error_code=graphresult( );

if(error_code!=grOk)
{
restorecrtmode( );
textmode(BW80);
clrscr( );

cout<<" n Fatal Error  : Graphic Driver not initialized"<<endl;
cout<<" Error Reason : "<<grapherrormsg(error_code)<<endl;
cout<<" n Press any key to exit...";

getch( );
exit(1);
}

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

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];

cleardevice( );

setcolor(15);
rectangle(45,85,595,415);

int x;
int y;

for(int count=0;count<vertices;count++)
{
gotoxy(1,1);
cout<<"*******  XY-Coordinates of Vertex-"<<(count+1)<<"  *******";

gotoxy(1,2);
cout<<"Enter value of x-coordinate (060-580) = ";
cin>>x;

x=((x<60)?60:x);
x=((x>580)?580:x);

gotoxy(1,3);
cout<<"Enter value of y-coordinate (100-400) = ";
cin>>y;

y=((y<100)?100:y);
y=((y>400)?400:y);

V[count].SetVertex(x,y,count);
V[count].ShowVertex( );

gotoxy(1,1);
cout<<"                                                       ";
gotoxy(1,2);
cout<<"                                                       ";
gotoxy(1,3);
cout<<"                                                       ";
}

gotoxy(1,28);
cout<<" V = { ";

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

cout<<count<<" } ";

gotoxy(1,30);
cout<<" E = { ";

x=wherex( );

int v1;
int v2;
int weight;

for(count=0;count<edges;count++)
{
gotoxy(1,1);
cout<<"******  Vertex Numbers for Edge-"<<(count+1)<<"  ******";

gotoxy(1,2);
cout<<"Enter the Vertice-1 (1-"<<vertices<<")  = ";
cin>>v1;

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

gotoxy(1,3);
cout<<"Enter the Vertice-2 (1-"<<vertices<<")  = ";
cin>>v2;

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

gotoxy(1,4);
cout<<"Enter the Edge Weight = ";
cin>>weight;

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

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

gotoxy(x,30);
cout<<"("<<v1<<","<<v2<<")";

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

x=wherex( );

gotoxy(1,1);
cout<<"                                                     ";
gotoxy(1,2);
cout<<"                                                     ";
gotoxy(1,3);
cout<<"                                                      ";
gotoxy(1,4);
cout<<"                                                      ";
}

gotoxy(x,30);
cout<<" } ";

getch( );
cleardevice( );

gotoxy(5,3);
cout<<" ******************  Applying Kruskal's Algorithm  *******************"<<endl;

setcolor(15);
rectangle(45,85,595,415);

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

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[e_count].ShowEdge( );

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;
}
}
}
}
}
}
}
}

gotoxy(48,28);
cout<<"Press any Key to Continue...";

getch( );

gotoxy(48,28);
cout<<"                            ";
}
}

gotoxy(1,1);
cout<<"                                                                           "<<endl;
cout<<"                                                                           "<<endl;
cout<<"                                                                           "<<endl;
cout<<"                                                                           "<<endl;
cout<<"                                                                           "<<endl;

gotoxy(1,1);
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;

gotoxy(54,28);
cout<<"Press any Key to Exit.";

getch( );
return 0;
}```