Final ds record

Ex no –1(A) IMPLEMENTATION OF SINGLY
LINKED LIST
AIM:
To write a c program to implement singly linked list.

ALGORITHM:
Step1: Start the program.

Step2: Include the required header files at the top of the program.

Step3: Create a structure named node and declare variables to denote a node for

singly linked list.

Step4: In the create () method, check whether the head is NULL or not. If it is

NULL, then get the number of nodes from user and get data for each

node that are created.

Step5: In the insert () method, check whether the head is NULL or not. If it is

NOT NULL, then get the position from the user and then insert into list.

Step6: In the delete () method, check whether the head is NULL or not. If it is

NOT NULL, then get the position to be deleted from the user.

Step7: Insert and delete according to the position.

Step8: In display () method, print the elements of singly linked list.

Step9: In main () method, use switch case statement to invoke the methods

according to the user choice entered.

Step10: End of the program.

1

PROGRAM:
#include<conio.h>
#include<stdio.h>
void creation(int);
void display();
void insertion(int,int);
void deletion(int);
struct list
{
int num;
struct list *next;
}*head, *l;
void main()
{
int n1,ch,pos,val;
clrscr();
do
{
printf("n1.creationn2.insertionn3.deletionn4.displayn5.exitn");
printf("nenter ur choice : ");
scanf("%d",&ch);
switch(ch)
{
case 1:
creation(n1);
break;
case 2:
printf("nnenter the postion in which to be inserted : ");
scanf("%d",&pos);
printf("nnenter the value : ");
scanf("%d",&val);
insertion(pos,val);
break;
case 3:
printf("nnenter the position to be deleted : ");
scanf("%d",&pos);
deletion(pos);
break;
case 4:
display();
getch();
break;
case 5:
exit(0);
}
}while(ch!=5);

2

getch();
}
void creation(int n1)
{
int i,n;
head=((struct list *)malloc(sizeof(struct list)));
l=head;
printf("nEnter the no of nodes:");
scanf("%d",&n1);
for(i=0;i<n1;i++)
{
printf("enter the %d node : ",i+1);
scanf("%d",&n);
l->num=n;
l->next=((struct list *)malloc(sizeof(struct list)));
l=l->next;
}
l->next=0;
}
void display()
{
l=head;
printf("nthe nodes entered are : ");
while(l->next>0)
{
printf("%dt",l->num);
l=l->next;
}
printf("null");
}
void insertion(pos,val)
{
int i;
struct list *x,*y;
l=head;
i=2;
if(pos==1)
{
x=((struct list *)malloc(sizeof(struct list)));
x->num=val;
x->next=l;
head=x;
}
else
{
while(l->next>0)

3

{
if(pos==i-1)
{
x=((struct list *)malloc(sizeof(struct list)));
x->num=val;
x->next=l;
y->next=x;
}
y=l;
l=l->next;
i++;
}
}
}
void deletion(pos)
{
int i;
struct list *y;
l=head;
i=1;
if(pos==1)
{ head=l->next; }
else
{
while(l->next>0)
{
if(pos==i)
{ l=l->next;
y->next=l;
break;
}
y=l;
l=l->next;
i++;
}
}
}

4

INPUT & OUTPUT:

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 1
Enter the no of nodes:2
enter the 1 node : 1
enter the 2 node : 2

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 2
enter the postion in which to be inserted : 1
enter the value : 6

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 4
the nodes entered are : 6 1 2 null

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 2
enter the value : 4

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice :2


5

enter the value : 4

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 3
enter the position to be deleted : 2

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 4
the nodes entered are : 6 1 2 null

1.creation
2.insertion
3.deletion
4.display
5.exit
enter ur choice : 5<Exiting>

RESULT:

Thus the program for program for implementation of singly linked list has been
completed successfully and output verified.

Ex no –1(B) IMPLEMENTATION OF DOUBLY
6

LINKED LIST
AIM:
To write a c program to implement doubly linked list.

ALGORITHM:


Step3: Create a structure named node and declare variables to denote a node for

doubly linked list.

Step4: In the create () method, get the number of nodes and iterate the loop to

get data for each node that are created.

Step5: In the insert () method, get the position from the user. If it is valid

position, get the data for a node and give forward link and backward link.

Step6: In the delete () method, get the position to be deleted. If it is valid

position, by rearranging forward link and backward link to delete the

node from the list.

Step7: Insert and delete according to the valid position.

Step8: In display () method, print the elements of doubly linked list.

Step9: In main () method, use switch case statement to invoke the methods



PROGRAM:
#include<stdio.h>
7

#include<conio.h>
struct list
{
int data;
struct list *llink,*rlink;
};
typedef struct list node;
node *head=NULL, *tail=NULL;
void ins(node *head)
{
node *p,*q;
int d,t;
q=(node*)malloc( sizeof(node) );
printf("enter the element into the list :");
scanf("%d" ,&d);
q->data=d;
q->rlink=q-> llink=NULL;
p=head;
do
{
if(p->rlink->llink==NULL)
{ q->llink=head;
head->rlink= q;
q->rlink=tail;
tail->llink= q;
t=1;
}
else
if(p->rlink->data>d)
{
p->rlink->llink= q;
q->llink=p;
q->rlink=p-> rlink;
p->rlink=q;
t=1;
}
else
p=p->rlink;
}
while(t!=1);
while(p->llink!=NULL)
p=p->llink;
head=p;
}
void delete(node *head)
{

8

int d,t;
node *p, *fntptr;
printf("enter the deleted element :");
scanf("%d",& d);
p=head;
do
{
fntptr=p->rlink;
if(p->rlink->data==d)
{
fntptr=fntptr->rlink;
p->rlink=fntptr;
fntptr=p;
t=1;
}
else
if(d>p->rlink->data)
p=fntptr;
else
{
puts("n data not found n");
t=1;
}
}
while(t!=1);
p=p->llink;
head=p;
}
void dis(node *head)
{
node *p;
p=head->rlink;
while(p->rlink!=NULL)
{
printf("%d-> ",p->data) ;
p=p->rlink;
}
p=p->rlink;
head=p;
printf("NULLn");
}
void main()
{
int ch;

9

clrscr();
printf(" Doubly linked list operationsn" );
printf("1.insert 2.delete 3.display 4.exit n");
head=(node*) malloc(sizeof( node));
tail=(node*) malloc(sizeof( node));
head->data=0;
head->llink= NULL;
tail->data=1000;
tail->rlink= NULL;
head->rlink= tail;
tail->llink= head;
do
{
printf("enter your choice :");
scanf("%d",& ch);
switch(ch)
{
case 1:
ins(head);
break;
case 2:
delete(head) ;
break;
case 3:
dis(head);
getch();
}
}
while(ch!=4) ;
free(head);
free(tail);
}

INPUT & OUTPUT:

10

Doubly linked list operations
1.insert 2.delete 3.display 4.exit

enter your choice :1
enter the element into the list :1

enter the element into the list :2

1-> 2-> NULL

enter the deleted element :4
data not found

enter the deleted element :1

2-> NULL

<Exiting>

RESULT:

Thus the program for program for implementation of doubly linked list has been

Ex no – 2 POLYNOMIAL ADDITION

11

AIM:
To write a c program represent a polynomial as a linked list and write functions
for polynomial addition
.
ALGORITHM:


Step3: Declare the needed variables and initialize them.

Step4: Get the value of co – efficient and exponent value of two polynomial

expressions

Step5: Compare the exponent of two polynomial expressions.

Step6: If the exponent values are same add the polynomial co – efficient.

Step7: If the exponent values are different add the biggest exponent’s co –

efficient value in to the result polynomial.

Step8: Print the result polynomial expression.


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

12

typedef struct poly
{
int coeff;
int expo;
}p;
p p1[10],p2[10],p3[10];
void main()
{
int t1,t2,t3;
int read(p p1[10]);
int add(p p1[10],p p2[10],int t1,int t2,p p3[10]);
void print(p p2[10],int t2);
void printo(p pp[10],int t2);
t1=read(p1);
print(p1,t1);
t2=read(p2);
print(p2,t2);
t3=add(p1,p2,t1,t2,p3);
printo(p3,t3);
getch();
}
int read(p p[10])
{
int t1,i;
printf("nEnter the total no of terms in polynomial:");
scanf("%d",&t1);
printf("Enter the coefficient and exponent in descending order");
for(i=0;i<t1;i++)
scanf("%d%d",&p[i].coeff,&p[i].expo);
return(t1);
}
int add(p p1[10],p p2[10],int t1,int t2,p p3[10])
{
int i=0,j=0,k=0,t3;
while(i<t1&&j<t2)
{
if(p1[i].expo==p2[j].expo)
{
p3[k].coeff=p1[i].coeff+p2[j].coeff;
p3[k].expo=p1[i].expo;
i++;j++;k++;
}
else if(p1[i].expo>p2[j].expo)
{
p3[k].coeff=p1[i].coeff;

13

i++;k++;
}
else
{
p3[k].coeff=p2[j].coeff;
p3[k].expo=p2[j].expo;
j++;k++;
}
}
while(i<t1)
{
p3[k].coeff=p1[i].coeff;
i++;k++;
}
while(j<t2)
{
p3[k].coeff=p2[j].coeff;
p3[k].expo=p2[j].expo;
j++;k++;
}
t3=k;
return(t3);
}
void print(p pp[10],int term)
{
int k;
printf("Printing the polynomial");
for(k=0;k<term-1;k++)
printf("%dx^%d+",pp[k].coeff,pp[k].expo);
printf("%dx^%d",pp[k].coeff,pp[k].expo);
}
void printo(p pp[10],int term)
{
int k;
printf("nAddition of polynomial");
for(k=0;k<term-1;k++)
printf("%dx^%d+",pp[k].coeff,pp[k].expo);
printf("%dx^%d",pp[k].coeff,pp[k].expo);
}

INPUT & OUTPUT:

14

Enter the total no of terms in polynomial:3
Enter the coefficient and exponent in descending order3
3
2
2
1
0
Printing the polynomial3x^3+2x^2+1x^0

Enter the total no of terms in polynomial:3
Enter the coefficient and exponent in descending order4
2
3
1
5
0
Printing the polynomial4x^2+3x^1+5x^0

Addition of polynomial3x^3+6x^2+3x^1+6x^0

RESULT:

Thus the program for program for polynomial addition has been

Ex no – 3 IMPLEMENTATION OF STACK

15

AIM:
To write a c program to implement stack operations using array.

ALGORITHM:



Step4: In push () operation, check whether the stack is full or not. If the stack is

not full, insert the element into the stack by incrementing top value.

Step5: In pop () operation, check whether the stack is empty or not. If the stack

is not empty, delete the element from the stack by decrementing top

value.

Step6: In display () method, print the stack elements using for loop.

Step7: In main () method, using switch case statement to invoke the methods



PROGRAM:
#include<stdio.h>

16

#include<conio.h>
#define size 10
int stack[size],top=-1;
void push();
void pop();
void display();
void main()
{
int c;
clrscr();
printf("nn1.pushn2.popn3.displayn4.Exit");
do
{
printf("nnEnter your choice::");
scanf("%d",&c);
switch(c)
{
case 1:
push();
break;
case 2:
pop();
break;
case 3:
printf("nnContents of stack ist");
display();
break;
default:
printf("nInvalid Choice");
exit(0);
}
}while(c<4);
getch();
}
void push()
{
int b;
if(top>size-1)
{
printf("nstack over flow");
return;
}
else
{
printf("nEnter the number to push into the stack:");
scanf("%d",&b);

17

top++;
stack[top]=b;
return;
}
}
void pop()
{
int res;
if(top==0)
{
printf("nStack Underflow");
}
else
{
res=stack[top];
top--;
printf("nDeleted element is %d",res);
return;
}
}
void display()
{
int i;
if(top==-1)
{
printf("nStack Under flow");
return;
}
else
{
for(i=top;i>=0;i--)
printf("%d",stack[i]);
}
}

INPUT & OUTPUT:
1.push

18

2.pop
3.display
4.Exit

Enter your choice::1
Enter the number to push into the stack:1



Contents of stack is 3 2 1

Deleted element is 3

Contents of stack is 2 1

Enter your choice:: 4
<Exiting>

RESULT:

Thus the program for program for implementation of stack using array has been
Ex.No:4 INFIX TO POSTFIX CONVERSION
19

AIM:
Write a C program to Implement stack and use it to convert infix to postfix
expression

ALGORITHM:

Step2: Initialize the stack.

Step3: Read the given infix expression into string called infix.

Step4: If the character is an operand, place it on the output.

Step5: If the character is an operator, push it on to the stack. if the stack operator

has a higher or equal priority than input operator then pop that operator

from the stack and place it onto the output.

Step6: If the character is a left parenthesis, push it onto the stack.

Step7: If the character is a right parenthesis, pop all operators from the stack till it

encounters left parenthesis, discard both the parenthesis in the output.

Step8: Display the postfix expression for the given infix expression.

Step9: End the program.

PROGRAM:
#include<stdio.h>

20

#include<conio.h>
#include<stdlib.h>
char inf[40],post[40];
int top=0,st[20];
void postfix();
void push(int);
char pop();
void main()
{
clrscr():
printf(“Enter the infix expression:”);
scanf(“%s”,&inf);
postfix();
getch();
}
void postfix()
{
int i,j=0;
for(i=0;inf[i]!=’0’;i++) {
switch(inf[i]) {
case ‘+’:
while(st[top>=1)
post[j++]=pop();
push(1);
break;
case ‘-’:
while(st[top>=1)
post[j++]=pop();
push(2);
break;
case ‘*’:
while(st[top>=3)
post[j++]=pop();
push(3);
break;
case ‘/’:
while(st[top>=3)
post[j++]=pop();
push(4);
break;
case ‘^’:
while(st[top>=4)
post[j++]=pop();
push(5);
break;
case ‘(’:

21

push(0);
break;
case ‘)’:
while(st[top!=0)
post[j++]=pop();
top--;
break;
default: post[j++]=inf[i];
} }
while(top>0)
post[j++]=pop();
printf(“nPostfix expression is %s”,post);
}
void push(int ele) {
top++;
st[top]=ele;
}
char pop()
{
int e1;
char e;
e1=st[top];
top--;
switch(e1)
{
case 1:
e=’+’;
break;
case 2:
e=’-’;
break;
case 3:
e=’*’;
break;
case 4:
e=’/’;
break;
case 5:
e=’^’;
break;
}
return(e);
}

INPUT & OUTPUT:
Enter the infix expression: a+b

22

Postfix expression is ab+

RESULT:

Thus the program for program for infix to postfix expression conversion has been

Ex no – 5 IMPLEMENTATION OF QUEUE
23

AIM:
To write a c program to implement queue operations using array.

ALGORITHM:



Step4: In insert () operation, check whether the queue is full or not. If the queue

is not full, insert the element into the queue by incrementing rear value.

Step5: In delete () operation, check whether the queue is empty or not. If the

queue is not empty, delete the element from the queue by incrementing

front value.

Step6: In display () method, print the queue elements using for loop.




PROGRAM:
#include <stdio.h>

24

#include<conio.h>
#define MAXSIZE 2
int q[MAXSIZE];
int front=-1,rear=-1,ch;
void main()
{
void insert();
int del();
void display();
clrscr();
do
{
printf("nMAIN MENU:1.Insert 2.Delete 3.Display 4.ExitnEnter ur choice:");
scanf("%d",&ch);
switch(ch)
{
case 1:
insert();
break;
case 2: del();
break;
case 3:
display();
break;
case 4:
exit(0);
default: printf("Invalid Choice ... ");
}
} while(ch!=4);
}
void insert()
{
int num;
if(rear==(MAXSIZE-1))
{
printf("QUEUE FULL");
return;
}
else
{
printf("Enter the no:");
scanf("%d",&num);
rear=rear+1;
q[rear]=num;
if(front==-1)
front++;

25

}return;
}
int del()
{
int num;
if(front==-1)
{
printf("QUEUE EMPTY");
return 0;
}
else
{
num=q[front];
printf("nDeleted element is %d",q[front]);
front++;
}
return(num);
}
void display()
{
int i;
if(front==-1)
{
printf("Queue empty");
return;
}
else
{
printf("nQueue elements are:");
for(i=front;i<=rear;i++)
printf("%dt",q[i]);
}
}

INPUT & OUTPUT:

26

MAIN MENU:1.Insert 2.Delete 3.Display 4.Exit
Enter ur choice:3
Queue empty

Enter ur choice:1
Enter the no:1

Enter ur choice:1
Enter the no:2

Enter ur choice:1
QUEUE FULL

Enter ur choice:2

Enter ur choice:2

Enter ur choice:3
Queue elements are:

Enter ur choice:4
<Exiting>

RESULT:

Thus the program for program for implementation of queue using array has been

Ex no – 6 IMPLEMENTATION OF CIRCULAR

27

QUEUE

AIM:
To write a c program to implement circular queue using array.

ALGORITHM:



Step4: In insert () operation, check whether the queue is full or not. If the queue

is not full, check the front value if no element is there, insert the element

into the queue in front position.

Step5: In delete () operation, check whether the queue is empty or not. If the

queue is not empty, delete the element from the queue by incrementing

front value.

Step6: In display () method, print the queue elements using for loop.




28

PROGRAM:
#include<stdio.h>
#include<conio.h>
#define max 5
int q[max];
int front=-1;
int rear=-1;
void main()
{
int ch;
clrscr();
while(1)
{
printf("enter your choice");
scanf("%d",&ch);
switch(ch)
{
case 1:
insert();
break;
case 2:
del();
break;
case 3:
display();
break;
case 4:
exit(1);
default:
printf("in wrong choice");
}
}
}
insert()
{
int item;
if((front==0&&rear==max-1)||(front==rear+1))
{
printf("n queue overflow");
return;
}
if (front==-1)
{
front=0;
rear=0;
}

29

else
if(rear==max-1)
rear=0;
else
rear=rear+1;
printf("enter the element");
scanf("%d",&item);
q[rear]=item;
}
del()
{
if(front==-1)

{
printf("queue underflown");
return;
}
printf("element deleted from queue is %d:n",q[front]);
if(front==rear)
{
rear=-1;
front=-1;
}
else
if(front==max-1)
front=0;
else
front=front+1;
}
display()
{
int fpos=front,rpos=rear;
if(front==-1)
{
printf("queue is emptyn");
return;
}
printf("queue elements:n");
if(fpos<=rpos)
while(fpos<=rpos)
{
printf("%dn",q[fpos]);
fpos++;
}
else
{

30

while(fpos<=max-1)
{
printf("%dn",q[fpos]);
fpos++;
}
fpos=0;
while(fpos<=rpos)
{
printf("%d",q[fpos]);
fpos++;
}
}
printf("n");
}

31

INPUT & OUTPUT:

1.insert 2.delete 3.display 4.quit
enter your choice1
enter the element1

enter your choice1
enter the element2

enter your choice3
queue elements:
1
2

enter your choice2
element deleted from queue is 1:

enter your choice3
queue elements:
2

enter your choice4
<Exiting>

RESULT:
Thus the program for implementation of circular queue has been completed
successfully and output verified.

32

Ex no – 7 IMPLEMENTATION OF EXPRESSION
TREE

AIM:
To write a c program to implement an expression tree. Produce its pre-order, in-
order, and post order traversals.

ALGORITHM:


Step3: Declare the function inorder(), postorder(), preorder().

Step4: Read the input in the form of postfix expression.

Step5: In inorder () function, traversal will be from left child-->root-->right

child.

Step6: In preorder () function, traversal will be from root-->left child--> right

child.

Step7: In postorder () function, traversal will be from left child--> right

child-->root.




33

PROGRAM:
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#define size 20
typedef struct node
{
char data;
struct node *left;
struct node *right;
}btree;
btree *stack[size];
int top;
void main()
{
btree *root;
char exp[80];
btree *create(char exp[80]);
void inorder(btree *root);
void preorder(btree *root);
void postorder(btree *root);
clrscr();
printf(“nEnter the postfix expression:”);
scanf(“%s”,&exp);
top=-1;
root=create(exp);
printf(“nInorder traversal:”);
inorder(root);
printf(“nPreorder traversal:”);
preorder(root);
printf(“nPostorder traversal:”);
postorder(root);
getch();
}
btree *create(char exp[])
{
btree *temp;
int pos;
char ch;
void push(btree *);
btree *pop();
pos=0;
ch=exp[pos];
while(ch!=’0’)
{
temp=(btree *)malloc(sizeof(btree));

34

temp->left=temp->right=NULL;
temp->data=ch;
if(isalpha(ch))
push(temp);
else if(ch==’+’||ch==’-‘||ch==’*’||ch==’/’)
{
temp->right=pop();
temp->left=pop();
push(temp);
}
else
printf(“nInvalid character in expression”);
pos++;
ch=exp[pos];
}
temp=pop();
return(temp);
}
void push(btree *node)
{
if(top+1>=size)
printf(“Error:Stack is full”);
top++;
stack[top]=node;
}
btree *pop()
{
btree *node;
if(top==-1)
printf(“Error:Stack empty”);
node=stack[top];
top--;
return(node);
}
void inorder(btree *root)
{
btree *temp;
temp=root;
if(temp!=NULL)
{
inorder(temp->left);
printf(“%c”,temp->data);
inorder(temp->right);
}
}
void preorder(btree *root) {

35

btree *temp;
temp=root;
if(temp!=NULL)
{
preorder(temp->left);
preorder(temp->right);
}
}
void postorder(btree *root)
{
btree *temp;
temp=root;
if(temp!=NULL) {
postorder(temp->left);
postorder(temp->right);
}
}

36

INPUT & OUTPUT:

Enter the postfix expression:ab+cd-*

Inorder traversal:a+b*c-d
Preorder traversal:*+ab-cd
Postorder traversal:ab+cd-*

RESULT:
Thus the program for implementation of expression tree and its traversal order has
been completed successfully and output verified.

37

Ex no – 8 IMPLEMENTATION OF BINARY
SEARCH TREE

AIM:
To write a c program to implement binary search tree.
ALGORITHM:



Step3: Declare the function add(),search(), findmin(),findmax() and display().



Step5: In add () function, get the number from user and insert it into tree.

Step6: In search () function, the number given for search will be traversed and

result of the searching will be displayed.

Step7: In findmin () function, display the minimum element in the tree

Step8: In findmax () function, display the maximum element in the tree

Step8: In display() function, the binary search tree will be displayed.


38

PROGRAM:
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
typedef struct node
{
int data;
struct node *left, *right;
}*nptr;
nptr root,t,p,q;
void add();
void search();
void findmin();
void findmax();
void disp(nptr,int,int,int);
void main()
{
int ch;
root=NULL;
while(1)
{
printf(“1.Create 2.Search 3.Display 4.Findmin 5.Findmax 6.ExitnEnter ur choice:”);
scanf(“%d”,&ch);
switch(ch)
{
case 1:
add();
break;
case 2:
search();
break;
case 3:
clrscr();
disp(root,40,7,16);
break;
case 4:
findmin();
break;
case 5:
findmax();
break;
case 6:
exit(0);
}
}
}

39

void add()
{
int x;
t=(nptr)malloc(sizeof(struct node));
printf(“nEnter data:”);
scanf(“%d”,&x);
t->data=x;
t->left=NULL;
t->right=NULL;
if (root==NULL)
root=t;
else
{
p=q=root;
while(q!=NULL&&x!=p->data)
{
p=q;
if(x<p->data)
q=p->left;
else
q=p->right;
}
if(x==p->data)
printf(“%d is duplicate no n”,x);
else if(x<p->data)
p->left=t;
else
p->right=t;
}
}
void search()
{
int x;
printf(“Enter the element to search:”);
scanf(“%d”,&x);
p=q=root;
while(q!=NULL&&x!=p->data)
{
p=q;
if(x<p->data)
q=p->left;
else
q=p->right;
}
if(x==p->data)
printf(“Element is present”);

40

else
printf(“Element not present”);
}
void disp(nptr root,int col,int row,int wid)
{
gotoxy(col,row);
if(root!=NULL)
{
printf(“%d”,root->data);
disp(root->left,col-wid,row+2,wid/2);
disp(root->right,col+wid,row+2,wid/2);
}
}
void findmax()
{
t=root;
while(t->right!=NULL)
t=t->right;
printf(Maximum value in BST is %d”,t->data);
}
void findmin()
{
t=root;
while(t->left!=NULL)
t=t->left;
printf(Minimum value in BST is %d”,t->data);
}

41

INPUT & OUTPUT:
1.Create 2.Search 3.Display 4.Findmin 5.Findmax 6.Exit
Enter ur choice:1
Enter data:10
Enter ur choice:1
Enter data:9
Enter ur choice:1
Enter data:8
Enter ur choice:1
Enter data:11
Enter ur choice:1
Enter data:12
Enter ur choice:3
10

9 11

8 12

Enter ur choice:2
Enter the element to search:8
Element is present
Enter ur choice:2
Enter the element to search:7
Element not present
Enter ur choice:4
Minimum value in BST is 8
Enter ur choice:5
Maximum value in BST is 12
Enter ur choice:6 <Exiting…..>

RESULT:
Thus the program for implementation of binary search tree has been completed

42

Ex no – 9 IMPLEMENTATION OF PRIORITY
QUEUE USING HEAPS

AIM:
To write a c program to implement priority queue using heap.

ALGORITHM:




Step4: By defining the priority queue, we can perform operations on heap.

Step5: Insert an item arbitrarily at anywhere in the priority queue.

Step6: Delete an item that has highest priority i.e. maximum value from the

priority queue. This is called max heap.

Step7: Delete an item that has lowest priority i.e. minimum value from the

priority queue. This is called min heap.

Step8: Print the contents of heap using for loop.


43

PROGRAM:
#include<stdio.h>
#include<conio.h>
#define size 5
void main(void)
{
int rear,front,que[size],choice;
int qfull(int rear),qempty(int rear,int front);
int insert(int que[size],int rear,int front);
int delet(int que[size],int front);
void display(int que[size],int rear,int front);
clrscr();
front=0;
rear=-1;
do
{
printf("nMainmenu1:insert 2:delete 3:display 4.Exitnenter ur choice: ");
scanf("%d",&choice);
switch(choice)
{
case 1:if(qfull(rear))
printf("nqueue is full");
else
rear=insert(que,rear,front);
break;
case 2:
if(qempty(rear,front))
printf("ncannot delete element");
else
front=delet(que,front);
break;
case 3:
if(qempty(rear,front))
printf("nqueue is empty");
else
display(que,rear,front);
break;
case 4:
exit(0);
default:
printf("nwrong choice");
break;
}
}while(choice!=4);
getch();
}

44

int insert(int que[size],int rear,int front)
{
int item,j;
printf("nenter the element : ");
scanf("%d",&item);
if(front==-1)
front++;
j=rear;
while(j>=0&&item<que[j])
{que[j+1]=que[j];
j--;
}
que[j+1]=item;
rear=rear+1;
return rear;
}
int qfull(int rear)
{
if(rear==size-1)
return 1;
else
return 0;
}
int delet(int que[size],int front)
{
int item;
item=que[front];
printf("nthe item deleted is %d",item);
front++;
return front;
}
qempty(int rear,int front)
{
if((front==-1)||(front>rear))
return 1;
else
return 0;
}
void display(int que[size],int rear,int front)
{
int i;
printf("nthe queue is :");
for(i=front;i<=rear;i++)
printf(" %d",que[i]);
}

45

INPUT & OUTPUT:

Mainmenu1:insert 2:delete 3:display 4.Exit
enter ur choice: 1
enter the element : 1

enter ur choice: 1

enter ur choice: 1

enter ur choice: 3
the queue is : 1 2 3

enter ur choice: 2
the item deleted is 1

enter ur choice: 2

enter ur choice: 2

enter ur choice: 2
cannot delete element

enter ur choice: 3
queue is empty

enter ur choice: 4<Exiting>

RESULT:

Thus the program for implementation of priority queue using heap has been

46

Ex no – 10 IMPLEMENTATION OF HASHING
TECHINQUE

AIM:
To write a c program to implement hashing by linear probing.

ALGORITHM:



Step3: Declare and initialize needed variables.

Step4: Get the size of the hash table from the user and makes the indices

sequentially based on size.

Step5: Then get the integer number from the user . And compute the hash

function for that number using the given formula.

Hash function= (int) e % size of the hash table

Step6: Finally, store the number in corresponding location in the hash table.

Step7: Check whether the hash table is empty or full during insertion and

deletion function.

Step8: Print the contents of hash table whenever the user needs to view.


47

PROGRAM:
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#define MAX 10
void main()
{
int a[MAX],num,key,i;
char ans;
int create(int);
void linear_prob(int [],int,int),display(int []);
clrscr();
printf("nCollision handling by linear probing");
for(i=0;i<MAX;i++)
a[i]=-1;
do
{
printf("nEnter the number");
scanf("%d",&num);
key=create(num);
linear_prob(a,key,num);
printf("ndo you wish to continue? (y/n)");
ans=getche();
}while(ans=='y');
display(a);
getch();
}
int create(int num)
{
int key;
key=num%10;
return key;
}
void linear_prob(int a[MAX],int key,int num)
{
int flag,i,count=0;
void display(int a[]);
flag=0;
if(a[key]==-1)
a[key]=num;
else
{
i=0;
while(i<MAX)
{
if(a[i]!=-1)

48

count++;
i++;
}
if(count==MAX)
{
printf("nhash table is full");
display(a);
getch();
exit(1);
}
for(i=key+1;i<MAX;i++)
if(a[i]==-1)
{
a[i]=num;
flag=1;
break;
}
for(i=0;i<key&&flag==0;i++)
if(a[i]==-1)
{
a[i]=num;
flag=1;
break;
}}}
void display(int a[MAX])
{
int i;
printf("nthe hash table");
for(i=0;i<MAX;i++)
printf("n%dt%d",i,a[i]);
}

49

INPUT & OUTPUT:

Collision handling by linear probing
Enter the number33
do you wish to continue? (y/n)y
Enter the number83
Enter the number35
Enter the number42
Enter the number74
do you wish to continue? (y/n)n
the hash table
0 -1
1 -1
2 42
3 33
4 83
5 35
6 74
7 -1
8 -1
9 -1

RESULT:

Thus the program for implementation of hashing by linear probing has been

50

Ex no – 11 IMPLEMENTATION OF TOPOLOGICAL
SORTING

AIM:
To write a c program to implement topological sorting.

ALGORITHM:


Step3: Declare the function push(), pop(), ts().

Step4: In push () function, check whether the stack is full or not. If the stack is

not full, insert the vertex into the stack by incrementing top value.

Step5: In pop () operation, check whether the stack is empty or not. If the stack

is not empty, get the vertex from the stack by decrementing top

value.

Step6: In ts () function, traversal order for the given graph is found.

Step7: In main () method, get the adjacency matrix for given number of vertices

from user and call the required function.


51

PROGRAM:
#include<stdio.h>
#include<conio.h>
#define max 30
int stack[max],top=-1;
int push(int v);
int pop(int *v);
int ts(int mat[max][max],int n,int order[max]);
void main()
{
int i,j,n,mat[max][max],order[max],succ;
clrscr();
printf("nenter the no. of vertices : ");
scanf("%d",&n);
printf("nenter adjacency matrix :n");
for(i=0;i<n;i++)
for(j=0;j<n;j++)
scanf("%d",&mat[i][j]);
succ=ts(mat,n,order);
if(succ==1)
{printf("nnthe directed graph is acyclic");
printf("nnthe topological sorted order isn");
for(i=0;i<n;i++)
printf("%dt",order[i]+1);
}
else
printf("nthe directed graph is not acyclic");
getch();
}
int push(int v)
{
if(top==max-1)
return 0;
else
stack[++top]=v;
return -1;
}
int pop(int *v)
{
if(top==-1)
return 0;
else
*v=stack[top--];
return -1;
}
int ts(int mat[max][max],int n,int order[max])

52

{
int indegree[max],v,i,k,m;
for(i=0;i<n;i++)
{
indegree[i]=0;
for(k=0;k<n;k++)
if(mat[k][i]==1)
indegree[i]++;
if(indegree[i]==0)
push(i);
}
m=0;
while(pop(&v))
{
order[m++]=v;
for(k=0;k<n;k++)
if(mat[v][k]==1&&indegree[k]>0)
{indegree[k]--;
if(indegree[k]==0)
push(k);
}
}
return (i==n);
}

53

INPUT & OUTPUT:
Enter the no. of vertices : 7
Enter adjacency matrix:
0111000
0001100
0000010
0010011
0001001
0000000
0000010

The directed graph is acyclic

The topological sorted order is

1 2 5 4 7 3 6

RESULT:
Thus the program for implementation of topological sorting has been completed

54

Ex no – 12 IMPLEMENTATION OF DIJKSTRA’S
ALGORITHM
AIM:
To write a c program to implement dijkstra’s algorithm.

ALGORITHM:



Step3: Get the number of vertices from the user and get cost for each vertex.

Step4: The general algorithm for this process is as follows,

o select a starting node
o build the initial fringe from nodes connected to the starting node
o while we are not at the destination node do
• choose the fringe node with the shortest path to the starting node
• add that node and its edge to the tree
• update the fringe by:
 adding nodes to the fringe connected to the new node
 for each node in the fringe do
update its edge one connected to the tree on the
shortest path to the starting node
 end for
o end while

Step5: Print the shortest path.


55

PROGRAM:
#include<stdio.h>
#include<conio.h>
#define INFINITY 1000
int a[10][10],b[10][10];
int i,j,k,n;
void input();
void initialize();
void spath();
void display();
void input()
{
printf("nt *** DIJKSTRA’S ALGORITHM ***");
printf("n enter the no of vertices:");
scanf("%d",&n);
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
if(i!=j)
{
printf("cost between %d to %d",i,j);
scanf("%d",&a[i][j]);
}
}
}
void initialize()
{
for(i=1;i<=n;i++)
a[i][j]=0;
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
b[i][j]=a[i][j];
if(!a[i][j] && (i!=j))
{
b[i][j]=INFINITY;
}
}
}
void spath()
{
for(k=1;k<=n;k++)
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if((b[i][k] && b[k][j]) && (b[i][k]+b[k][j]<b[i][j]))
{

56

b[i][j]=b[i][k]+b[k][j];
}
}
void display()
{
i=1;
if(i<n)
{
for(j=2;j<=n;j++)
printf("Minimum cost FROM source vertex 1 TO %d is : %dn",j,b[i][j]);
}
}
void main()
{
clrscr();
input();
initialize();
spath();
display();
getch();
}

57

INPUT & OUTPUT:

*** DIJKSTRA’S ALGORITHM ***
enter the no of vertices: 5

cost between1—2: 2
minimum cost FROM 1 TO 2 is : 2

RESULT:

Thus the program for implementation of dijkstra’s algorithm has been completed

58

Ex no – 13(A) IMPLEMENTATION OF PRIM’S
ALGORITHM
AIM:
To write a c program to implement prim’s algorithm.

ALGORITHM:



Step3: Get the number of nodes from the user and get weight for each vertex.

Step4: The general algorithm for this process is as follows,

o select a starting node.

o build the initial fringe from nodes connected to the starting node

o while there are nodes left do

 choose the edge to the fringe of the smallest weight

 add the associated node to the tree

 update the fringe by:

• adding nodes to the fringe connected to the new node

• updating the edges to the fringe so that they are the smallest

o end while

Step5: Print the minimal spanning tree.


59

PROGRAM:
#include<stdio.h>
#include<conio.h>
void main()
{
int lowcost[20],min;
int n,noe,i,j,k,v,closest[20],u,cost[50][50];
clrscr();
printf("ENTER THE NO OF NODES:");
scanf("%d",&n);
printf("nENTER NO OF EDGES:");
scanf("%d",&noe);
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
cost[i][j]=1000;
}
}
for(i=1;i<=noe;i++)
{
printf("ENTER THE EDGE: ");
scanf("%d%d",&u,&v);
printf("ENTER COST OF EDGE:");
scanf("%d",&cost[u][v]);
cost[v][u]=cost[u][v];
}
printf("nThe output of minimum spanning tree will be...n");
for(i=2;i<=n;i++)
{
lowcost[i]=cost[1][i];
closest[i]=1;
}
for(i=2;i<=n;i++)
{
min=lowcost[2];
k=2;
for(j=3;j<=n;j++)
{
if(lowcost[j]<min)
{
min=lowcost[j];
k=j;
}

60

}
printf("%d ->%d:cost %dn",k,closest[k],lowcost[k]);
lowcost[k]=2000;
for(j=2;j<=n;j++)
if((cost[k][j]<lowcost[j]) && (lowcost[j]<2000))
{
lowcost[j]=cost[k][j];
closest[j]=k;
}
}
getch();
}

61

INPUT & OUTPUT:

ENTER THE NO OF NODES:4

ENTER NO OF EDGES:5
ENTER THE EDGE: 1
2
ENTER COST OF EDGE:9
ENTER THE EDGE: 1
3
ENTER THE EDGE: 1
4
ENTER THE EDGE: 2
4
ENTER THE EDGE: 3
4

The output of minimum spanning tree will be...
4 ->1:cost 2
2 ->4:cost 1
3 ->1:cost 3

RESULT:

Thus the program for implementation of prim’s algorithm has been completed

62

Ex no – 13(B) IMPLEMENTATION OF KRUSKAL’S
ALGORITHM
AIM:
To write a c program to implement kruskal’s algorithm.

ALGORITHM:



Step3: Get the number of nodes from the user and get weight for each node.

Step4: Sort the edges in nondecreasing order by weight and initialize partition

structure for finding the edges to be included in spanning tree.

Step5: Print the minimum spanning tree.

63

PROGRAM:
#include<stdio.h>
#include<conio.h>
typedef struct edge
{
int node1,node2,wt;
}edge;
void sortedge(edge a[],int n)
{
int i,j;
edge temp;
for(i=0;i<n;i++)
for(j=i+1;j<n;++j)
if(a[i].wt>a[j].wt)
{
temp=a[i];a[i]=a[j];a[j]=temp;
}
}
int check(int p[],int i,int j)
{
int v1,v2;
v1=i;
v2=j;
while(p[i]>-1)
i=p[i];
while(p[j]>-1)
j=p[j];
if(i!=j)
{
p[j]=i;
printf("%d->%dn",v1,v2);
return 1;
}
return 0;
}
void main()
{
edge e[100];
int r[100],n,i,j,k=1,m,cost=0;
clrscr();
printf("Kruskal algorithmn");
printf("Enter the no of nodes:");
scanf("%d",&n);
for(i=0;i<n;i++)

64

r[i]=-1;
i=0;
printf("nEnter no of edges:");
scanf("%d",&m);
for(i=0;i<m;i++)
{
printf("nENter the edge and cost of the edge:");
scanf("%d%d%d",&e[i].node1,&e[i].node2,&e[i].wt);
}
sortedge(e,m);
printf("nEdges of the MSTn");
i=0;
while(k<n)
{
if(check(r,e[i].node1,e[i].node2))
{
k++;
cost=cost+e[i].wt;
i++;
}
}
printf("Minimum cost:%d",cost);
getch();
}

65

INPUT & OUTPUT:

Kruskal algorithm
Enter the no of nodes:4

Enter no of edges:4

Enter the edge and cost of the edge:1
2
1

3
3

3
2

4
1

Edges of the MST
1->2
2->4
2->3
Minimum cost:4

RESULT:

66

Thus the program for implementation of kruskal’s algorithm has been completed

Ex no – 14 IMPLEMENTATION OF BACKTRACKING
ALGORITHM

AIM:
To write a c program to implement backtracking algorithm for Knapsack problem.

ALGORITHM:


Step3: Declare the function knap(), bound().

Step4: Get the input number of items and capacity of knapsack from user.

Step5: Get the weight and profit for each item from user.

Step6: In knap () function, the maximum capacity and profit are found

Step7: In bound () function, the maximum capacity for inserting the item is

checked.

Step8: In main () method, the values of knapsack are printed in descending

order.


67

PROGRAM:
#include<stdio.h>
#include<conio.h>
int n,m,i,j,x[10],y[10];
float w[10],t,t1,t2,p[10],c1[10],b,c,fp=-1.0,fw;
void knap(int,float,float);
float bound(float,float,int);
void main()
{
clrscr();
printf("nenter the no. of items : ");
scanf("%d",&n);
printf("nenter the maximum capacity of knapsack : ");
scanf("%d",&m);
for(i=1;i<=n;i++)
{
printf("nnenter the weight & profit : n");
scanf("%f%f",&w[i],&p[i]);
}
for(i=1;i<=n;i++)
{
for(j=i+1;j<=n;j++)
{
if(c1[i]>=c1[j])
t1=w[i];
w[i]=w[j];
w[j]=t1;
t2=p[i];
p[i]=p[j];
p[j]=t2;
t=c1[i];
c1[i]=c1[j];
c1[j]=t;
} }
printf("nnweightttprofitn");
for(i=1;i<=n;i++)
{
printf("n%ft%fn",w[i],p[i]);
knap(1,0,0);
printf("nnthe selected objects: ");
for(i=1;i<=n;i++)
{
printf("%d",x[i]);

68

}
printf(“nFinal Weight=%0.2f”,fw);
printf(“nFinal Profit=%0.2f”,fp);
getch();
}
void knap(int k,float cp,float cw)
{
if(cw+w[k]<=m)
{
y[k]=1;
if(k<n)
knap(k+1,cp+p[k],cw+w[k]);
if((cp+p[k]>fp)&&(k==n))
{
fp=cp+p[k];
fw=cw+w[k];
for(j=1;j<=n;j++)
x[j]=y[j];
}
if(bound(cp,cw,k)>=fp)
{
y[k]=0;
if(k<n)
knap(k+1,cp,cw);
if((cp>fp)&&(k==n))
{
fp=cp;
fw=cw;
for(j=1;j<=n;j++)
x[j]=y[j];
}}}}
float bound(float cp,float cw,int k)
{
float b=cp,c=cw;
for(i=k+1;i<=n;i++)
{
c=c+w[i];
if(c<m)
b=b+p[i];
else
return(b+(1-(c-m))/w[i]*p[i]);
}
return b;
}

69

INPUT & OUTPUT:
Enter the no. of items : 5
Enter the maximum capacity of knapsack : 20
Enter the weight & profit ; 3 12

Weight profit
4.000000 12.000000
5.000000 10.000000
4.000000 8.0000000
2.000000 4.0000000
3.000000 12.000000

The selected objects are: 11111

Final Weight=18.00
Final Profit=46.00

RESULT:

70

Thus the program for implementation of backtracking algorithm for knapsack
problem has been completed successfully and output verified.

Ex no – 15 IMPLEMENTATION OF BRANCH AND
BOUND ALGORITHM

AIM:
To write a c program to implement branch and bound algorithm for travelling

salesman problem.

ALGORITHM:



Step3: Declare the function tsp(), display().

Step4: In main() method, get the number of cities and distance for each city

from user.

Step5: In tsp() function, finds the minimum distance from source.

Step6: In display() function, minimum cost and path is displayed.


71

PROGRAM:
#include<stdio.h>
#include<conio.h>
#define max 10
typedef struct
{
int nodes[max];
int vertex;int min;
}path;
path tsp(int src,path list,int ele[][max],int mcities)
{
int i,j;
path nlist,npath,nmin;
if(list.vertex==0)
{
nmin.min=ele[src][1];
nmin.nodes[mcities-1]=src;
nmin.vertex=mcities;
return nmin;
}
for(i=0;i<list.vertex;i++)
{
nlist.vertex=0;
for(j=0;j<list.vertex;j++)
if(i!=j)
nlist.nodes[nlist.vertex++]=list.nodes[j];
npath=tsp(list.nodes[i],nlist,ele,mcities);
npath.min=ele[src][list.nodes[i]]+npath.min;
npath.nodes[mcities-list.vertex-1]=src;
if(i==0)
nmin=npath;
else
if(npath.min<nmin.min)
nmin=npath;
}
return nmin;
}
void display(path path1)
{
int i;
printf("nnthe minimum cost is %dn",path1.min);
printf("nthe path is....n");

72

for(i=0;i<path1.vertex;i++)
printf("%d--",path1.nodes[i]);
printf("%d",path1.nodes[0]);
}
void main()
{
int i,j,ele[max][max],mcities;
path graph,path1;
clrscr();
printf("nenter number of cities : ");
scanf("%d",&mcities);
if(mcities==0)
{
printf("error : there is no city for proceeding the TSP");
}
else
{
for(i=1;i<=mcities;i++)
{
for(j=1;j<=mcities;j++)
if(i==j)
ele[i][i]=0;
else
{
printf("enter distance from city %d to %d [if no path put 999]: ",i,j);
scanf("%d",&ele[i][j]);
}
if(i>1)
graph.nodes[i-2]=i;
}
graph.vertex=mcities-1;
path1=tsp(1,graph,ele,mcities);
display(path1);
}
getch();
}

73

INPUT & OUTPUT:

Enter number of cities : 4
Enter distance from city 1 to 2 [if no path put 999]: 1

The minimum cost is 4

The path is…..
1---2---4---3---1

RESULT:

74

Thus the program for implementation of branch and bound algorithm for
travelling salesman problem has been completed successfully and output verified.

Ex no –16 IMPLEMENTATION OF RANDOMIZED
ALGORITHM

AIM:
To write a c program to implement randomized algorithm- to find repeated
elements in the array.

ALGORITHM:


Step3: Declare the function repetition().

Step4: In main () method, used to print the repeated elements in the given array.

Step5: Repetition () function, checks whether the declared array has repeated

elements.


75

PROGRAM:
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
#include<time.h>
int main(void)
{
int a[10]={10,20,30,40,11,12,13,10,30,30};
int n=10;
void repetition(int a[],int n);
clrscr();
printf("ntRANDOMIZED ALGORITHM - TO FIND REPEATED ELEMENTSn");
repetition(a,n);
getch();
return 0;
}
void repetition(int a[],int n)
{
int i,j,count;
time_t t;
srand((unsigned)time(&t));
count=1;
while(count<=100)
{
i=rand()%(n+1);
j=rand()%(n+1);
if((i!=j)&&(a[i]==a[j]))
printf("nthe repeated element is present at index %d",i);
count++;
}
}

76

INPUT & OUTPUT:

RANDOMIZED ALGORITHM – TO FIND REPEATED ELEMENTS
The repeated element is present at index 9

RESULT:
77

Thus the program for implementation of randomized algorithm to find repeated
elements in the array has been completed successfully and output verified.

78

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