DS LAB

om sakthi

ADHIPARASAKTHI ENGINEERING COLLEGE

MELMARUVATHUR

DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING

LAB MANUALFOR

141352 Data Structures Lab

By, Balamurugan.R

Assistant Professor

Department of Computer Science and Engineering

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CONTENT

EX. NO EXPERIMENT NAME PAGE NO.

1A IMPLEMENT SINGLY LINKED LIST 3

1B IMPLEMENT DOUBLY LINKED LIST 9

2 POLYNOMIAL ADDITION 15

3 CONVERT INFIX TO POSTFIX EXPRESSION 19

4 DOUBLE-ENDED QUEUE (DEQUEUE) 22

5 EXPRESSION TREE 27

6 BINARY SEARCH TREE 31

7 AVL TREES 37

8 PRIORITY QUEUE USING BINARY HEAPS 43

9 HASHING WITH OPEN ADDRESSING 47

10 PRIM'S ALGORITHM 50

11 DIJKSTRA’S ALGORITHM 54

12 BUBBLE SORT 58

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1 a. SINGLY LINKED LIST

Aim:

To write a C program to perform a singly linked list

Algorithm:

1. Start the program

2. Declare all the functions and using the switch case select the operation to be

performed

3. Declare a structure with all the required variables and allocate the memory using the

malloc function

4. In the insert beginning function set y->link=head. For the insert middle check if c<pos

if so set z=x; and x=x->link;and increment c

5. In the delete beginning function check the above function but perform delete

operation

6. In the display function display the array elements

7. Stop the program

Program:

#include<stdio.h>#include<conio.h>#include<stdlib.h>struct node{int data;struct node *link;};struct node *head,*x,*y,*z;void main(){void create();void insbeg();void insmid();void insend();void delbeg();

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void delmid();void delend();void display();int ch;clrscr();while(1){printf("\n 1.Creation");printf("\n 2.Insertion at beginning");printf("\n 3.Insertion at middle");printf("\n 4.Insertion at end");printf("\n 5.Deletion at beginning");printf("\n 6.Deletion at middle");printf("\n 7.Deletion at end");printf("\n 8.Display");printf("\n 9.Exit");printf("\n Enter ur choice:");scanf("%d",&ch);switch(ch){case 1:create();break;case 2:insbeg();break;case 3:insmid();break;case 4:insend();break;case 5:delbeg();break;case 6:delmid();break;case 7:delend();break;case 8:display();break;default:exit(0);}}}void create()

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{int c;head=NULL;x=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data:");scanf("%d",&x->data);x->link=NULL;head=x;printf("\n Do u wish to continue press 1 otherwise 0:");scanf("%d",&c);while(c!=0){y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data:");scanf("%d",&y->data);y->link=NULL;x->link=y;x=y;printf("\n Do u wish to continue press 1 otherwise 0:");scanf("%d",&c);}}void insbeg(){y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data:");scanf("%d",&y->data);y->link=head;head=y;}void insmid(){int pos,c=1;y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data:");scanf("%d",&y->data);printf("\n Enter the position to be inserted:");scanf("%d",&pos);x=head;while(c<pos){z=x;x=x->link;c++;}y->link=x;z->link=y;}void insend(){

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y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data:");scanf("%d",&y->data);y->link=NULL;x=head;while(x->link!=NULL){x=x->link;}x->link=y;}void delbeg(){if(head==NULL)printf("\n List is empty");else{x=head;head=x->link;free(x);}}

void delmid(){int pos,c=1;if(head==NULL)printf("\n List is empty");else{printf("\n Enter the position to be deleted:");scanf("%d",&pos);x=head;while(c<pos){z=x;x=x->link;c++;}z->link=x->link;free(x);}}void delend(){if(head==NULL)printf("\n List is empty");else{x=head;

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while(x->link!=NULL){y=x;x=x->link;}y->link=NULL;free(x);}}void display(){if(head==NULL)printf("\n List is empty");else{x=head;printf("\n List elements are \n");while(x->link!=NULL){printf("%d->",x->data);x=x->link;}printf("%d",x->data);}}

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Output:

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Result:

Thus the lists operations are performed using singly linked list in C perform.

1 b. DOUBLY LINKED LIST

Aim:

To a write a C program to implement a doubly linked list

Algorithm:

1. Start the program

2. Declare all the required functions and select the operation to be performed

3. Declare a structure with all the required variables and allocate the memory using the

malloc function

4. Perform insertion, deletion and display operation to insert, delete and display the lists.

5. Stop the program

Program:

#include<stdio.h>#include<conio.h>#include<stdlib.h>struct node{int data;struct node *llink;struct node *rlink;};struct node *head,*x,*y,*z;void main(){void create();void insbeg();void insmid();void insend();void delbeg();void delmid();void delend();void display();int ch;clrscr();while(1){

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printf("\n 1.Creation");printf("\n 2.Insertion at beginning");printf("\n 3.Insertion at middle");printf("\n 4.Insertion at end");printf("\n 5.Deletion at beginning");printf("\n 6.Deletion at middle");printf("\n 7.Deletion at end");printf("\n 8.Display");printf("\n 9.Exit");printf("\n Enter your choice: ");scanf("%d",&ch);switch(ch){case 1:create();break;case 2:insbeg();break;case 3:insmid();break;case 4:insend();break;case 5:delbeg();break;case 6:delmid();break;case 7:delend();break;case 8:display();break;default:exit(0);}}}void create(){int c;head=NULL;x=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data: ");scanf("%d",&x->data);x->llink=NULL;

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x->rlink=NULL;head=x;printf("\n Do you wish to continue press 1 or 0:");scanf("%d",&c);while(c!=0){y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data: ");scanf("%d",&y->data);x->rlink=y;y->llink=x;y->rlink=NULL;x=y;printf("\n Do you wish to continue press 1 or 0:");scanf("%d",&c);}}void insbeg(){y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data: ");scanf("%d",&y->data);y->llink=NULL;y->rlink=head;head->llink=y;head=y;}void insmid(){int c=1,pos;y=(struct node*)malloc(sizeof(struct node));printf("\n Enter the data: ");scanf("%d",&y->data);printf("\n Enter the position to be inserted:");scanf("%d",&pos);x=head;while(c<pos){z=x;x=x->rlink;c++;}y->rlink=x;y->llink=z;x->llink=y;z->rlink=y;}void insend(){y=(struct node*)malloc(sizeof(struct node));

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printf("\n Enter the data: ");scanf("%d",&y->data);y->rlink=NULL;x=head;while(x->rlink!=NULL){x=x->rlink;}x->rlink=y;y->llink=x;}void delbeg(){if(head==NULL)printf("\n the list is empty");else{x=head;head=x->rlink;head->llink=NULL;free(x);}}void delmid(){int pos,c=1;if(head==NULL)printf("\n the list is empty");else{x=head;printf("\n Enter the position to be deleted:");scanf("%d",&pos);while(c<pos){z=x;x=x->rlink;c++;}z->rlink=x->rlink;x->rlink->llink=z;free(x);}}void delend(){if(head==NULL)printf("\n the list is empty");else{

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x=head;while(x->rlink!=NULL){y=x;x =x->rlink;}y->rlink=NULL;free(x);}}void display(){if(head==NULL)printf("\n the list is empty");else{x=head;printf("\nThe list elements are");while(x->rlink!=NULL){printf("%d->",x->data);x=x->rlink;}printf("%d",x->data);}}

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Output:

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Result:Thus the list operations are executed using doubly linked list in C program.

2. POLYNOMIAL ADDITION

Aim:

To write a C program to perform polynomial addition

Algorithm:

1. Start the program

2. Declare all the functions and using the switch case select the operation to be

performed

3. Declare a structure with all the required variables and allocate the memory using the

malloc function

4. Using the while loop check if node->next!=NULL if so print the values of

node->coeff,node->pow

5. Perform the addition according to the conditions of polynomial addition.

6. print the result

7. Stop the program

Program:

#include<stdio.h>#include<malloc.h>#include<conio.h>struct link{int coeff;int pow;struct link *next;};struct link *poly1=NULL,*poly2=NULL,*poly=NULL;void create(struct link *node){char ch;do{printf("\n enter coeff:");scanf("%d",&node->coeff);printf("\n enter power:");

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scanf("%d",&node->pow);node->next=(struct link*)malloc(sizeof(struct link));node=node->next;node->next=NULL;printf("\n continue(y/n):");ch=getch();}while(ch=='y' || ch=='Y');}void show(struct link *node){while(node->next!=NULL){printf("%dx^%d",node->coeff,node->pow);node=node->next;if(node->next!=NULL)printf("+");}}void polyadd(struct link *poly1,struct link *poly2,struct link *poly){while(poly1->next && poly2->next){if(poly1->pow>poly2->pow){poly->pow=poly1->pow;poly->coeff=poly1->coeff;poly1=poly1->next;}else if(poly1->pow<poly2->pow){poly->pow=poly2->pow;poly->coeff=poly2->coeff;poly2=poly2->next;}else{poly->pow=poly1->pow;poly->coeff=poly1->coeff+poly2->coeff;poly1=poly1->next;poly2=poly2->next;}poly->next=(struct link *)malloc(sizeof(struct link));poly=poly->next;poly->next=NULL;}while(poly1->next || poly2->next){if(poly1->next){

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poly->pow=poly1->pow;poly->coeff=poly1->coeff;poly1=poly1->next;}if(poly2->next){poly->pow=poly2->pow;poly->coeff=poly2->coeff;poly2=poly2->next;}poly->next=(struct link *)malloc(sizeof(struct link));poly=poly->next;poly->next=NULL;}}main(){char ch;clrscr();do{poly1=(struct link *)malloc(sizeof(struct link));poly2=(struct link *)malloc(sizeof(struct link));poly=(struct link *)malloc(sizeof(struct link));printf("\nenter 1st number:");create(poly1);printf("\nenter 2nd number:");create(poly2);printf("\n1st Number:");show(poly1);printf("\n2nd Number:");show(poly2);polyadd(poly1,poly2,poly);printf("\nAdded polynomial:");show(poly);printf("\n add two more numbers:");ch=getch();}while(ch=='y' || ch=='Y');return 0;}

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Output:

Result:

Thus the program for polynomial addition using linked list is executed and verified.

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3. INFIX TO POSTFIX CONVERSION

Aim:

To write a C program to convert infix to postfix expression

Algorithm:

1. Start the program

2. Using the strlen function determine the length of the string

3. Declare three arrays; the decremented value of one array is assigned to the

incremented value. This process is repeated until the parenthesis matches.

4. Until t==0 assign the values to sack1

5. Check if (top2==-1) if the condition is satisfied then assign stack2 [++top2]=str[i];

6. Print the result.

7. Stop the program

Program:

#include<stdio.h>#include<conio.h>#include<string.h>char str[50],stack1[50],stack2[50];int i=0,j,n,top1=-1,top2=-1;int prec(char);void main(){int t=0;clrscr();printf("\nEnter the infix expression:");scanf("%s",str);printf("%s",str);n=strlen(str);for(i=0;i<n;i++){t=0;if(str[i]==')'){stack1[++top1]=stack2[top2--];top2--;t=1;}if(str[i]=='('){stack2[++top2]='(';t=1;}

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if(t==0){if(((str[i]>='a')&&(str[i]<='z'))||(( str[i]>='A')&&(str[i]<='Z')))stack1[++top1]=str[i];else{if(top2==-1)stack2[++top2]=str[i];else{if(prec(str[i])>prec(stack2[top2])){stack2[++top2]=str[i];}else{while(prec(str[i])<=prec(stack2[top2]))stack1[++top1]=stack2[top2--];stack2[++top2]=str[i];}}}}}printf("\nANSWER\n");while(top2>=0)stack1[++top1]=stack2[top2--];for(i=0;i<=top1;i++)printf("%c",stack1[i]);getch();}int prec(char ch){int tt;if((ch=='+')||(ch=='-'))tt=2;if((ch=='*')||(ch=='/'))tt=3;if(ch=='(')tt=1;return tt;}

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Output:

Result:

Thus an infix expression is converted to postfix expression using stack.

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4. LINKED LIST IMPLEMENTATION OF DEQUEAim:

To perform the linked list implementation of Deque using C program

Algorithm:

1. Start the program

2. Declare all the required functions and select the operation to be performed

3. Allocate the memory location using malloc function and if the queue is empty then

the front and the rear element are the same

4. For deletion operation check if the queue has only one element if so perform deletion.

if the queue contains more elements then perform deletion accordingly.

5. For the display operation use the while loop and check if x->link!=NULL if so print

the elements.

6. For the display operation if rear== null then print that the queue is empty

7. Stop the program

Program:

#include<stdio.h>#include<conio.h>#include<stdlib.h>struct node{int data;struct node *link;};struct node *front=NULL,*rear=NULL,*x;void main(){int a;void enqfro();void deqrea();void enqrea();void deqfro();void display1();void display2();clrscr();while(1){printf("\n1.insertion at front");printf("\n2.insertion at rear ");printf("\nenter choice");

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scanf("%d",&a);while(a==1){int ch;printf("\n1.insertion at front");printf("\n2.deletion at rear ");printf("\n3.display1");printf("\n4.exit");printf("\nenter ur choice");scanf("%d",&ch);switch(ch){ case 1: enqfro(); break; case 2: deqrea(); break; case 3: display1(); break; default: exit(0);}}while(a==2){int ch;printf("\n1.insertion at rear");printf("\n2.deletion at front");printf("\n3.display2");printf("\n4.exit");printf("\nenter ur choice");scanf("%d",&ch);switch(ch){ case 1: enqrea(); break; case 2: deqfro(); break; case 3: display2(); break; default: exit(0); }}}

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}void enqfro(){if(front==NULL){x=(struct node*)malloc(sizeof(struct node));printf("\nenter the data");scanf("%d",&x->data);x->link=NULL;rear=x;front=x;}else{x=(struct node*)malloc(sizeof(struct node));printf("\nenter the data");scanf("%d",&x->data);x->link=NULL;front->link=x;front=x;}}void deqrea(){if(rear==NULL)printf("\nQueue is empty");else{x=rear;printf("\ndeleted elementis %d",x->data);rear=x->link;free(x);}}void enqrea(){if(rear==NULL){x=(struct node*)malloc(sizeof(struct node));printf("\nenter the data");scanf("%d",&x->data);x->link=NULL;rear=x;front=x;}else{x=(struct node*)malloc(sizeof(struct node));printf("\nenter the data");scanf("%d",&x->data);

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x->link=NULL;rear->link=x;rear=x;}}void deqfro(){if(front==NULL)printf("\nQueue is empty");else{x=front;printf("\ndeleted elementis %d",x->data);front=x->link;free(x);}}void display2(){if(front==NULL)printf("\nqueue is empty");else{x=front;printf("\nqueue elements are");while(x->link!=NULL){printf("%d\t",x->data);x=x->link;}printf("%d",x->data);}}void display1(){if(rear==NULL)printf("\nqueue is empty");else{x=rear;printf("\nqueue elements are");while(x->link!=NULL){printf("%d\t",x->data);x=x->link;}printf("%d",x->data);}}

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Output:

Result:

Thus the C program to implement the Deque is verified successfully.

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5. EXPRESSION TREE

Aim:

To construct an expression tree using C program

Algorithm:

1. Start the program

2. Declare all the required functions and select the operation to be performed

3. Allocate the memory location using malloc function

4. In the post function check if p!=NULL if call the recursive function post with

parameters p->rlink and p->llink

5. Using the switch case construct the expression tree

6. Using the push function insert the elements into the tree if topt==max then the tree is

full

7. Print the values

8. Stop the program

Program:

#include<stdio.h>#include<conio.h>#include<process.h>#include<string.h>#include<stdlib.h>struct node {char c;struct node *rlink;struct node *llink;}*stc[30];struct node *temp,*root;char prefix[20],ch;int topt=-1,max=50,len; //global declarationvoid pusht(struct node *p);struct node *popt();void tredis(struct node *ptr,int level);void exptree();void post(struct node *p);void main(){ clrscr(); printf("Enter a prefix expression:"); scanf("%s",prefix);

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exptree(); tredis(root,1); printf("\nThe postfix expression is:"); post(root); getch();}void post(struct node *p){ if(p!=NULL) { post(p->llink); post(p->rlink); printf("%c",p->c); }}void exptree(){ int i; len=strlen(prefix); i=len-1; while(i>=0) { switch(prefix[i]) { case '+': case '-': case '*': case '/': case '^':

temp=(struct node*)malloc(sizeof(struct node)); temp->c=prefix[i]; temp->llink=popt(); temp->rlink=popt(); pusht(temp); break;

default : temp=(struct node*)malloc(sizeof(struct node)); temp->c=prefix[i]; temp->rlink=NULL; temp->llink=NULL; pusht(temp);

} i--;} root=stc[topt];}

void pusht(struct node * p){ if(topt==max)

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{ printf("/**Beyond Capacity**/"); } else { stc[++topt]=p; }}struct node *popt(){ if(topt==-1) printf("/**No Expression**/"); else return(stc[topt--]);}void tredis(struct node *ptr,int level){ int i; if ( ptr!=NULL ) { tredis(ptr->rlink, level+1); printf(" "); for (i = 0; i < level; i++) printf(" "); printf("%c", ptr->c); tredis(ptr->llink, level+1); }}

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Output:

Result:

Thus the C program to construct an expression tree is execute

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6. BINARY SEARCH TREE

Aim:

To construct a binary search tree and perform various operation

Algorithm:

1. Start the program

2. Declare all the functions and using the switch case select the operation to be

performed

3. Declare a structure with all the required variables and allocate the memory using the

malloc function

4. In the insert function assign the memory and assign n->llink=NULL

n->rlink=NULL

5. In the deletion function perform deletion of node that has no child,having two

children

6. In the inorder function perform recursion by calling inorder(head->rlink).

7. In the display function display the values

8. Stop the program

Program:

#include<conio.h>#include<stdio.h>#include<malloc.h>#include<process.h>struct node{ struct node *llink; struct node *rlink; int data;};void main(){ struct node *head,*t; int s,d; struct node* finsert(); struct node* delenode(struct node*,int); void insert(struct node *); void inorder(struct node *); clrscr(); head=NULL; do {

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printf("\n1-Insertion"); printf("\n2-Deletion"); printf("\n3-Inorder"); printf("\n4-Exit"); printf("\nEnter Choice:"); scanf("%d",&s); switch(s) { case 1://insertion if(head==NULL) {

head=finsert(); } else

insert(head); break;

case 2://Deletion if(head==NULL) printf("\nBinary Tree Empty......."); else { printf("\nEnter Data to delete:"); scanf("%d",&d); if(head->llink==NULL && head->rlink==NULL && head->data==d)

{ t=head; head=NULL; free(t);}

else head = delenode(head,d);

} break; case 3://to display printf("\nIN-ORDER:"); if(head==NULL) printf("\nBinary Tree Empty...."); else inorder(head); break; case 4://exit exit(0); } }while(s<5 ||s>0); getch();}struct node* finsert(){ struct node * head;

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head=(struct node*)malloc(sizeof(struct node)); printf("\nEnter Data:"); scanf("%d",&head->data); head->llink=NULL; head->rlink=NULL; return head;}void insert(struct node *head){ struct node *t,*n; t=head; n=(struct node *)malloc(sizeof(struct node)); printf("\nEnter Data:"); scanf("%d",&n->data); n->llink=NULL; n->rlink=NULL; while(t->llink!=NULL || t->rlink!=NULL) { if(t->llink!=NULL) if(n->data < t->data) t=t->llink; if(t->rlink!=NULL) if(n->data>=t->data) t=t->rlink; if((t->llink==NULL) && (n->data < t->data) && (n->data <t->rlink->data)) break; if((t->rlink==NULL) && (n->data >= t->data) && (n->data >t->llink->data)) break; } if((n->data < t->data) && (t->llink==NULL)) t->llink=n; if((n->data > t->data) && (t->rlink==NULL)) t->rlink=n;}void inorder(struct node * head){ if(head!=NULL) { inorder(head->llink); printf("%d\t",head->data); inorder(head->rlink); }}struct node * delenode(struct node *head,int d){ int f=0,f1=0; struct node *p,*t,*t1,*x; t=head; //to search found or not while(t!=NULL)

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{ if(t->data==d) { f=1; x=t; break; } if(t->data > d) { p=t; t=t->llink; } else if(t->data <= d) { p=t; t=t->rlink; } } if(f==0) { printf("\nGiven element not found......."); return head; } //Deleted node has no child if(x->llink==NULL && x->rlink==NULL) { if(p->rlink==x) p->rlink=NULL; else p->llink=NULL; free(x); return head; } //deleted node has 2 children if(x->llink!=NULL && x->rlink!=NULL) { p=x; t1=x->rlink; while(t1->llink!=NULL) { p=t1; f1=1; t1=t1->llink; } if(t1->llink==NULL && t1->rlink==NULL) { x->data=t1->data; if(f1==1) p->llink=t1->llink; if(f1==0) x->rlink=t1->rlink;

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free(t1); return head; } if(t1->rlink!=NULL) { x->data=t1->data; if(f1==1) p->llink=t1->rlink; if(f1==0) p->rlink=t1->rlink; free(t1); return head; } } //Deleted node has oniy right child if(x->llink==NULL && x->rlink!=NULL && x->data!=head->data) { if(p->llink==x) p->llink=x->rlink; else p->rlink=x->rlink; free(x); return head; } //Deleted node has oniy left child if(x->llink!=NULL && x->rlink==NULL && x->data!=head->data) { if(p->llink==x) p->llink=x->llink; else p->rlink=x->llink; free(x); return head; } if(x->llink!=NULL && x->rlink==NULL && x->data==head->data) { head=x->llink; free(p); return head; } if(x->llink==NULL && x->rlink!=NULL && x->data==head->data) { head=x->rlink; free(p); return head; }return 0;}

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Output:

Result:

Thus the binary search tree is constructed and various operations are performed using C program.

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7. AVL TREE

Aim:

To write a C program to perform insertion on an AVL tree

Algorithm:

1. Start the program

2. Declare all the functions and using the switch case select the operation to be

performed

3. Declare a structure with all the required variables and allocate the memory using the

malloc function

4. Check if (search (root, info) == NULL ), if so assign the value to the variable root

5. Insert an element into the tree.

6. After insertion check if the tree is balanced or not. If not balance the tree.

7. Stop the program.

Program:

#include<stdio.h>#include<conio.h>#include<stdlib.h>typedef enum { FALSE ,TRUE } bool;struct node{int info;int balance;struct node *lchild;struct node *rchild;};struct node *insert (int , struct node *, int *);struct node* search(struct node *,int);main(){bool ht_inc;int info ;int choice;struct node *root = (struct node *)malloc(sizeof(struct node));root = NULL;clrscr();while(1)

{printf("1.Insert\n");

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printf("2.Display\n");printf("3.Quit\n");printf("Enter your choice : ");scanf("%d",&choice);switch(choice){case 1:printf("Enter the value to be inserted : ");scanf("%d", &info);if( search(root,info) == NULL )root = insert(info, root, &ht_inc);elseprintf("Duplicate value ignored\n");break;case 2:if(root==NULL){printf("Tree is empty\n");continue;}printf("Tree is :\n");display(root, 1);printf("\n\n");printf("Inorder Traversal is: ");inorder(root);printf("\n");break;case 3:exit(1);default:printf("Wrong choice\n");}/*End of switch*/}/*End of while*/}/*End of main()*/struct node* search(struct node *ptr,int info){if(ptr!=NULL)if(info < ptr->info)ptr=search(ptr->lchild,info);else if( info > ptr->info)ptr=search(ptr->rchild,info);return(ptr);}/*End of search()*/struct node *insert (int info, struct node *pptr, int *ht_inc){struct node *aptr;struct node *bptr;if(pptr==NULL){pptr = (struct node *) malloc(sizeof(struct node));

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pptr->info = info;pptr->lchild = NULL;pptr->rchild = NULL;pptr->balance = 0;*ht_inc = TRUE;return (pptr);}if(info < pptr->info){pptr->lchild = insert(info, pptr->lchild, ht_inc);if(*ht_inc==TRUE){switch(pptr->balance){case -1: /* Right heavy */pptr->balance = 0;*ht_inc = FALSE;break;case 0: /* Balanced */pptr->balance = 1;break;case 1: /* Left heavy */aptr = pptr->lchild;if(aptr->balance == 1){printf("Left to Left Rotation\n");pptr->lchild= aptr->rchild;aptr->rchild = pptr;pptr->balance = 0;aptr->balance=0;pptr = aptr;}else{printf("Left to right rotation\n");bptr = aptr->rchild;aptr->rchild = bptr->lchild;bptr->lchild = aptr;pptr->lchild = bptr->rchild;bptr->rchild = pptr;if(bptr->balance == 1 )pptr->balance = -1;elsepptr->balance = 0;if(bptr->balance == -1)aptr->balance = 1;elseaptr->balance = 0;bptr->balance=0;pptr=bptr;

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DS LAB

}*ht_inc = FALSE;}/*End of switch */}/*End of if */}/*End of if*/if(info > pptr->info){pptr->rchild = insert(info, pptr->rchild, ht_inc);if(*ht_inc==TRUE){switch(pptr->balance){case 1: /* Left heavy */pptr->balance = 0;*ht_inc = FALSE;break;case 0: /* Balanced */pptr->balance = -1;break;case -1: /* Right heavy */aptr = pptr->rchild;if(aptr->balance == -1){printf("Right to Right Rotation\n");pptr->rchild= aptr->lchild;aptr->lchild = pptr;pptr->balance = 0;aptr->balance=0;pptr = aptr;}else{printf("Right to Left Rotation\n");bptr = aptr->lchild;aptr->lchild = bptr->rchild;bptr->rchild = aptr;pptr->rchild = bptr->lchild;bptr->lchild = pptr;if(bptr->balance == -1)pptr->balance = 1;elsepptr->balance = 0;if(bptr->balance == 1)aptr->balance = -1;elseaptr->balance = 0;bptr->balance=0;pptr = bptr;}/*End of else*/*ht_inc = FALSE;

40

DS LAB

}/*End of switch */}/*End of if*/}/*End of if*/return(pptr);}/*End of insert()*/display(struct node *ptr,int level){int i;if ( ptr!=NULL ){display(ptr->rchild, level+1);printf("\n");for (i = 0; i < level; i++)printf(" ");printf("%d", ptr->info);display(ptr->lchild, level+1);}/*End of if*/}/*End of display()*/inorder(struct node *ptr){if(ptr!=NULL){inorder(ptr->lchild);printf("%d ",ptr->info);inorder(ptr->rchild);}}/*End of inorder()*/

41

DS LAB

Output:

Result:

Thus the C program to perform insertion on an AVL tree is executed and verified

42

DS LAB

8. PRIORITY QUEUE USING BINARY HEAPS

Aim:

To write a C program to perform Priority queue using binary heaps.

Algorithm:

1. Start the program

2. Declare all the functions and the operation to be performed

3. Declare a structure with all the required variables and define the Max Size of packet

4. Exchange to maintain heap property

5. Find the correct place to insert the element

6. After insertion check if the tree is balanced or not

7. Stop the program.

Program:

#include <stdio.h>#define MAX_SIZE 10

typedef struct{

unsigned char priority;unsigned char packetType;unsigned int destinationAddress;unsigned int sourceAddress;char payload[26];

} Packet;

typedef struct{

Packet* packets[MAX_SIZE];unsigned int size;

} PacketHeap;

void heap_init(PacketHeap* h){

h->size=0;}

void heap_heapify(PacketHeap* h,int i){

int l,r,smallest;Packet* tmp;l=2*i; /*left child*/

43

DS LAB

r=2*i+1; /*right child*/

if ((l < h->size)&&(h->packets[l]->priority < h->packets[i]->priority))smallest=l;

elsesmallest=i;

if ((r < h->size)&&(h->packets[r]->priority < h->packets[smallest]->priority))smallest=r;

if (smallest!=i) {/*exchange to maintain heap property*/tmp=h->packets[smallest];h->packets[smallest]=h->packets[i];h->packets[i]=tmp;heap_heapify(h,smallest);

}}

void heap_addItem(PacketHeap* h,Packet* packet){

unsigned int i,parent;h->size=h->size+1;i=h->size-1;parent=i/2;/*find the correct place to insert*/while ((i > 0)&&(h->packets[parent]->priority > packet->priority)){

h->packets[i]=h->packets[parent];i=parent;parent=i/2;

}h->packets[i]=packet;

}

Packet* heap_extractMin(PacketHeap* h){

Packet* max;if (heap_isEmpty(h))

return 0;max=h->packets[0];h->packets[0]=h->packets[h->size-1];h->size=h->size-1;heap_heapify(h,0);return max;

}

int heap_isEmpty(PacketHeap *h){

return h->size==0;}

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DS LAB

int heap_isFull(PacketHeap *h){

return h->size>=MAX_SIZE;}

int main(){

PacketHeap heap;unsigned char i;Packet p[10];p[0].priority=123;p[1].priority=23;p[2].priority=0;p[3].priority=22;p[4].priority=255;p[5].priority=1;p[6].priority=10;p[7].priority=3;p[8].priority=101;p[9].priority=102;clrscr();

heap_init(&heap);for (i=0;i<10;i++){

printf("Add %i\n",p[i].priority);heap_addItem(&heap,&(p[i]));

}while (!heap_isEmpty(&heap)){

i=heap_extractMin(&heap)->priority;printf("%i\n",i);

}getch();return 0;

}

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DS LAB

Output:

Result:

Thus the C program to perform Priority queue using binary heaps is executed and verified

46

DS LAB

9. HASHING WITH OPEN ADDRESSING

Aim:

To write a C program to perform Hashing with open addressing

Algorithm:

1. Start the program

2. Declare all the required variables

3. Get the size of the hash table

4. Get the hash value from user

5. Find the correct place to store the element

6. Stop the program.

Program:

#include<STDIO.H>#include<conio.h>void main(){int a[10]={0,0,0,0,0,0,0,0,0,0};int n,value,temp,hashvalue;clrscr();printf("\nEnter the value of n(table size):");scanf("%d",&n);do{printf("\nEnter the hash value");scanf("%d",&value);hashvalue=value%n;if(a[hashvalue]==0){a[hashvalue]=value;printf("\na[%d]the value %d is stored",hashvalue,value);}else{for(hashvalue++;hashvalue<n;hashvalue++){if(a[hashvalue]==0){printf("Space is allocated give other value");a[hashvalue]=value;printf("\n a[%d]the value %d is stored",hashvalue,value);goto menu;}

47

DS LAB

}hashvalue=0;for(hashvalue;hashvalue<n;hashvalue++){if(a[hashvalue]==0){printf("Space is allocated give other value");a[hashvalue]=value;printf("\n a[%d]the value %d is stored",hashvalue,value);goto menu;}}printf("ERROR");printf("\nEnter '0' and press 'Enter key' twice to exit");

}

menu:

printf("\n Do u want enter more ENTER 1 here:");

scanf("%d",&temp);

}

while(temp==1);

getch();

}

48

DS LAB

Output:

Result:

Thus the C program to perform Hashing with open addressing is executed and verified.

49

DS LAB

10. PRIM'S ALGORITHM

Aim:

To write a C program to find MST of an undirected graph using Prim’s algorithm.

Algorithm:

1. Start the program

2. Declare all the functions and the operation to be performed

3. Declare a structure with all the required variables

4. Get the number of nodes and edges of undirected graph

5. Find the minimum shortest path use the corresponding edge cost.

6. Check all the nodes are visited.

7. Stop the program.

Program:

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

int b[10][10],a[10][10],v,v1,v2,n,e,visited[10],edge,cost,i,j;

void initialize(){printf("\nEnter the number of nodes\n");scanf("%d",&n);printf("\Enter the number of edges\n");scanf("%d",&e);for(i=1;i<=n;i++)for(j=1;j<=n;j++)a[i][j]=0;for(i=1;i<=n;i++)visited[i]=0;for(i=1;i<=e;i++){printf("\nEnter the two vertices v1 & v2 \n");scanf("%d%d",&v1,&v2);printf("\nEnter the corresponding cost\n");scanf("%d",&edge);a[v1][v2]=edge;}}

int prim(){for(i=1;i<=n;i++)

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DS LAB

for(j=1;j<=n;j++)if(i==j)b[i][j]=0;elseb[i][j]=999;

for(i=1;i<=n-1;i++){findmin(&v1,&v2);edge=a[v1][v2];b[v1][v2]=b[v2][v1]=edge;visited[v1]=visited[v2]=1;cost=cost+edge;}return cost;}

int findmin(int *v1,int *v2){int edge=0,i;for(i=1;i<=n;i++){for(j=i+1;j<=n;j++){if((visited[i]==1&&visited[j]!=1)||(visited[i]!=1&&visited[j]==1)){if((edge>a[i][j]||edge==0)&&a[i][j]>0){edge=a[i][j];*v1=i;*v2=j;}}}}return;}

void main(){int val;clrscr();initialize();val=prim();

printf("\nThe cost is %d\n",val);printf("\nThe matrix is\n");

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

51

DS LAB

for(j=1;j<=n;j++){printf("%d\t",b[i][j]);}printf("\n");}getch();}

52

DS LAB

Output:

Result:

Thus the C program to find MST of an undirected graph using Prim’s algorithm is executed and verified

53