### Divide and Conquer Strategy

Kurskal\'s algo to solve Minimum Cost Spanning Tree Towers of Hanoi Problem using Recursive Algorithm

### Cubic Time Algorithms

Prim\'s algo solve Minimum Spanning Tree - Graphic Bubble Sort Algorithm

### Logrithmic Time Algorithms

n_th term of fibonacci series - Toplogical Order Compute, display factorial using recursive algo Product of 2 matrices - Strassen\'s Algorithm

### Dynamic Programming Technique

Kurskal\'s algo - min cost spanning tree - graphics n_th term of fibonacci series - Divide and Conquer

### Exponential Time Algorithms

Prim\'s algo - min Spanning Tree - Mouse support Multiply two matrices

Prim\'s algo to solve Minimum Spanning Tree Problem Binary search algorithm

### Linear Time Algorithms

n_th term of fibonacci series

### Minimum Cost Spanning Tree Problem

Kurskal\'s - min cost spanning tree - mouse support Product of 2 matrices - Divide and Conquer

# Program to implement the Prims Algorithm to solve Minimum Spanning Tree Problem (MST) using Graphics

``` # include <iostream.h>
# include <graphics.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( );
};

//------------------------  Function Definitions  -----------------------//

//----------------------------  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);
}

//------------------------------  main( )  ------------------------------//

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 PRIMS Algorithm  ********************\";

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

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

int U[MAX_VERTICES];
int vertex_1[MAX_VERTICES];
int vertex_2[MAX_VERTICES];
int edge_weights[MAX_VERTICES];
int resultant_weights[MAX_VERTICES];

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) )
{
E[i].ShowEdge( );
resultant_weights[(u_count-2)]=E[i].weight;

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

getch( );

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

break;
}
}
}

else
break;
}
while(1);

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

gotoxy(1,1);
cout<<\"*******************  Result  ********************\"<<endl;
cout<<\" U = { \";

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

cout<<(U[count]+1)<<\" }\"<<endl<<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;

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

getch( );
closegraph( );
return 0;
}
```