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10. IMPLEMENTATION OF TOPLOLOGICAL SORT ON A

DIRECTED GRAPH TO DECIDE IF IT IS CYCLIC

AIM

Write a C program to implement topological sort algorithm in a graph to decide if

it is cyclic.

ALGORITHM

1. Let L be the empty list that will contain the sorted elements2. Let S be the set of all nodes with no incoming edges

3. while S is non-empty do

a. remove a node n from S

b. insert n into L

4. for each node m with an edge e from n to m do

a. remove edge e from the graph

b. if m has no other incoming edges then

i. insert m into S

5. if graph has edges then

i. return error (graph has at least one cycle)

b. elsei. return L (a topologically sorted order)

SOURCE CODE

#include<stdio.h>

#include<conio.h>

void main(){

int i,j,k,a[10][10],indeg[10],flag[10],count=0,check=0,n;

clrscr();

printf("enter the maximum no. of elements:");scanf("%d",&n);printf("Enter the adjacency matrix:\n");for(i=0;i<n;i++)

for(j=0;j<n;j++){

printf("v%d->v%d:",i+1,j+1);scanf("%d",&a[i][j]);

}for(i=0;i<n;i++)



{

indeg[i]=0;flag[i]=0;

}

for(i=0;i<n;i++)

for(j=0;j<n;j++)

indeg[i]+=a[j][i];

printf("Topological sort is:\n");while(count<n)

{for(j=0;j<n;j++)

{if(indeg[j]==0&&flag[j]==0)

{ printf("%d->",j+1);

flag[j]=1;for(i=0;i<n;i++)

{

if(a[j][i]==1)indeg[i]--;

}check++;

}} count++;

}

if(check==n)

printf("\ngraph is acyclic");else

printf("\nNo topological sort\nGraph is cyclic");getch();

}

OUTPUT

enter the maximum no. of elements:4

Enter the adjacency matrix:

v1->v1:0

v1->v2:1

v1->v3:0v1->v4:1

v2->v1:0

v2->v2:0

v2->v3:1

v2->v4:1

v3->v1:0

v3->v2:0



v3->v3:0

v3->v4:0

v4->v1:0v4->v2:0

v4->v3:1

v4->v4:0

Topological sort is:

1->2->4->3->

graph is acyclic

enter the maximum no. of elements:4

Enter the adjacency matrix:

v1->v1:0

v1->v2:1v1->v3:0

v1->v4:1

v2->v1:0

v2->v2:0

v2->v3:1

v2->v4:0

v3->v1:0

v3->v2:0

v3->v3:0

v3->v4:1

v4->v1:0v4->v2:1

v4->v3:0

v4->v4:0

Topological sort is:

1->

No topological sort

Graph is cyclic

RESULT

Thus the C program to implement topological sort algorithm in a graph to decide if itis cyclic is written, executed and verified.



14. IMPLEMENTATION OF BRANCH AND BOUND ALGORITHM

FOR TRAVELING SALESMAN PROBLEM

AIM

Write a C program to implement branch and bound algorithm for travelling

sales man problem.

ALGORITHM

1. Get the number of cities

2. Get the cost of the edges

3. Let 0 be the starting city

4. Compute all possible paths from starting city and returning back to starting city

5. Find the shortest path(path with minimum cost) among the possible paths and

display

SOURCE CODE

#include<stdio.h>

int x[15],used[15];int adj[15][15]={0};

int path [15][15],wght[15];int c,min;

int path_ok(int k,int n)

{if(used[x[k]])

return 0;if(k<n-1)

return(adj[x[k-1]][x[k]]);else

return(adj[x[k-1]][x[k]])&& (adj[x[k]][x[0]]);}

void tsp(int k,int n){

int i,sum;

for(x[k]=1;x[k]<n;x[k]++){

if(path_ok(k,n)){

used[x[k]]=1;



if(k==n-1){

sum=0;printf("\n\n\t possible path %d: ",c+1);

for(i=0;i<n;i++){

printf("%d\t",x[i]);path[c][i]=x[i];sum+=adj[x[i]][x[i+1]];

}

printf(":%d",sum);wght[c]=sum;

if(c==0||sum<min)min=sum;

c++;used[x[k]]=0;

getch();}

else

tsp(k+1,n);used[x[k]]=0;}

}}

void findmin(int n)

{int i,j;

for(i=0;i<c;i++)if(wght[i]==min)

{

printf("\n\n\t minimum path :");for(j=0;j<n;j++)

printf("%d\t",path[i][j]);}

}

void main()

{int i,n,j;

int edg;clrscr();

printf("\n\n\t\t travelling salesman problem\n\n");printf("\n\t enter the no. of cities:");

scanf("%d",&n);printf("\n\n enter the cost if path exist between cities:{c1,c2}.else enter 0\n\n");

printf("\n\t cities\t\tcost\n\n");for(i=0;i<n;i++)

for(j=i+1;j<n;j++){

printf("\n\t %d------ %d \t:,i,j);scanf("%d",&edg);

if(edg)



adj[i][j]=adj[j][i]=edg;}

used[0]=1;tsp(1,n);

if(!c)printf("\n\n\t\t no path found to cover all the cities\n\n);

else{printf("\n\n\t\t minimum cost is %d and the paths are \n\n,min);

findmin(n);

}getch();

}

OUTPUT

travelling salesman problem

enter the no. of cities:4

enter the cost if path exist between cities:{c1,c2}.else enter 0

cities cost

0------ 1 2

0------ 2 4

0------ 3 2

1------ 2 3

1------ 3 5

2------ 3 1

possible path 1: 0 1 2 3 :8








minimum cost is 8 and the paths are

minimum path :0 1 2 3

minimum path :0 3 2 1

RESULT

Thus the C program to implement branch and bound algorithm for travelling sales manproblem is written, executed and verified.



15. IMPLEMENTATION OF RANDOMIZED ALOGORITHM-

RANDOM NUMBER GENERATOR

AIM

Write a C program to implement the randomized algorithm for random number

generator using c.

ALGORITHM

1. Initialize the random number generator using srand() with current time as seed.

2. Use the random function to get random numbers.

3. Display the random numbers.

SOURCE CODE

#include<stdio.h>

#include<stdlib.h>

#include<time.h>

int main(void)

{

int i;

time_t t;

srand((unsigned) time(&t));

printf(“ten random numbers from 0 to 99\n\n”);

for(i=0; i<10;i++)printf(“%d\n”,rand()%100);

getch();

}



OUTPUT

ten random numbers from 0 to 99

94

90

24

7

71

81

28

5

14

33

RESULT

Thus the C program to implement the randomized algorithm for random number

generator is written, executed and verified.



16. IMPLEMENTATION OF BINARY SEARCH ALGORITHM

AIM

Write a C program to implement binary search algorithm.

ALGORITHM

1. Get the element(search key) to be searched

2. Compare the search key with the element at the middle

2.1 If the value matches, return the value

2.2 If the search key < the middle element, search the elements between

the first element to the element before the middle element (MIDDLE

-1)

2.3 If the search key > the middle element, search the elements between

the MIDDLE+ 1 elements to the last element

3 Search is repeated until the searched key is found or the last element in the

subset is traversed

SOURCE CODE

#include<stdio.h>#include<conio.h>

void main()

{int n,i,search,f=0,low,high,mid,a[20];

clrscr();printf("Enter the n value:");

scanf("%d",&n);for(i=1;i<=n;i++)

{printf("Enter the number in ascending order a[%d]=",i);

scanf("%d",&a[i]);}

printf("Enter the search element:");scanf("%d",&search);

low=1;high=n;

while(low<=high){



if(search<a[mid]){high=mid-1;

}else if(search>a[mid])

low=mid+1;

}else

{

f=1;printf("obtainedin the position %d:",mid);getch();

exit();}

}if(f==0)

{printf("not present");

}getch();

}

OUTPUT

Enter the n value:5

Enter the number in ascending order a[1]=3Enter the number in ascending order a[2]=7

Enter the number in ascending order a[3]=11


Enter the search element:11obtainedin the position 3:

Enter the n value:5Enter the number in ascending order a[1]=2



Enter the search element:7not present



RESULT

Thus the C program to implement binary search algorithm is written, executed andverified.

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