- Data structures allow for efficient processing and organization of large volumes of data. They define logical relationships between related data elements and how operations like storage, retrieval, and access are carried out on the data. - Common data structures include arrays, lists, stacks, queues, trees, graphs, dictionaries, maps, hash tables, sets, and lattices. Linear data structures like arrays and lists store elements in a linear order, while non-linear structures like trees and graphs have more complex relationships between elements. - Linked lists are a data structure where each element contains a link to the next element, rather than using contiguous memory locations. This allows for more flexible insertion and deletion than arrays. Doubly linked lists add a link to

1. Data Structures
-- Data processing often involves in processing huge volumes of data. Many Companies handle million
records of data stored in database. Many ways are formulated to handle data efficiently.
-- An User-defined data type is a combination of different primary data types, which represents a
complex entity.
-- An Abstract Data Type ( A D T ) not only represents a set of complex data objects, but also includes a
set of operations to be performed on these objects, defines that how the data objects are organized.
-- The group of methods implements a set rules, which defines a logical way of handling data.
-- The complex entity along with its group of methods is called Abstract Data Type ( A D T ) .
-- Data structure is described as an instance of Abstract Data Type ( ADT ).
-- We can define that Data structure is a kind of representation of logical relationship between related
data elements. In data structure, decision on the operations such as storage, retrieval and access must be
carried out between the logically related data elements.
Data Structure Some Data structures
Arrays
Strings
Linear Non-Linear Lists
Stacks
Queues
Linear Lists Stacks Queues Trees Graphs Trees
Graphs
Some Common Operations on Data structures Dictionaries
Insertion : adding a new element to the collection. Maps
Deletion : removing an element from a collection. Hash Tables
Traversal : access and examine each element in collection. Sets
Search : find whether an element is present or not. Lattice
Sorting : rearranging elements in a particular order. Neural-Nets
Merging : combining two collections into one collection.

2. Arrays – Linked Lists
What is a Linked List
Limitations of Arrays The elements of a linked list are not constrained to
2) Fixed in size : be stored in adjacent locations. The individual
Once an array is created, the size of array elements are stored “somewhere” in memory, rather
cannot be increased or decreased. like a family dispersed, but still bound together. The
4) Wastage of space : order of the elements is maintained by explicit links
If no. of elements are less, leads to wastage of between them.
space.
6) Sequential Storage :
Array elements are stored in contiguous
memory locations. At the times it might so
happen that enough contiguous locations might
not be available. Even though the total space The Linked List is a collection of elements called
requirement of an array can be met through a nodes, each node of which stores two items of
combination of non-contiguous blocks of information, i.e., data part and link field.
memory, we would still not be allowed to create -- The data part of each node consists the data
the array. record of an entity.
8) Possibility of overflow : -- The link field is a pointer and contains the
If program ever needs to process more than address of next node.
the size of array, there is a possibility of -- The beginning of the linked list is stored in a
overflow and code breaks. pointer termed as head which points to the first
10) Difficulty in insertion and deletion : node.
In case of insertion of a new element, each -- The head pointer will be passed as a parameter
element after the specified location has to be to any method, to perform an operation.
shifted one position to the right. In case of -- First node contains a pointer to second node,
deletion of an element, each element after the second node contains a pointer to the third node and
specified location has to be shifted one position so on.
to the left. -- The last node in the list has its next field set to
NULL to mark the end of the list.

3. struct node {
int rollno; struct node *next;
Creating a Singly Linked List
}; /* deleting n2 node */
int main() { n1->next = n4;
struct node *head,*n1,*n2,*n3,*n4; free(n2);
/* creating a new node */ }
n1=(struct node *) malloc(sizeof(struct node));
n1->rollno=101; 150 101 NULL
n1->next = NULL; head 150 n1-node
/* referencing the first node to head pointer
*/ 150 101 720 102 NULL
head = n1; 720
150
/* creating a new node */ n1-node n2-node
n2=(struct node *)malloc(sizeof(struct node));
n2->rollno=102; 150 101 720 102 910 104 NULL
n2->next = NULL; 150 720 910
n1-node n2-node n3-node
/* linking the second node after first node */
n1->next = n2;
/* creating a new node * / 150 101 400 102 720 104 NULL
n3=(struct node *)malloc(sizeof(struct node)); head 150 400 910
n3->rollno=104; n1-node n2-node 103 910 n3-node
n3->next=NULL; 720
n4-node
/* linking the third node after second node */
n2->next = n3;
/* creating a new node */ 150 101 720 103 910 104 NULL
n4=(struct node *)malloc (sizeof (struct node)); head 150
720 910
n4->rollno=103; n3-node
n1-node n4-node
n4->next=NULL; 102 720
/* inserting the new node between
400
second node and third node */ n2-node
n2->next = n4;

4. Implementing Singly Linked List
struct node { }
int data; }
struct node *next; void insert_after(struct node **h) {
}; struct node *new,*temp; int k;
struct node *createnode() { if(*h == NULL) return;
struct node *new; printf("nEnter data of node after which node : ");
new = (struct node *)malloc(sizeof(struct node)); scanf("%d",&k);
printf("nEnter the data : "); temp = *h;
scanf("%d",&new->data); while(temp!=NULL && temp->data!=k)
new->next = NULL; temp = temp->next;
return new; if(temp!=NULL) {
} new=createnode();
void append(struct node **h) { new->next = temp->next;
struct node *new,*temp; temp->next = new;
new = createnode(); }
if(*h == NULL) { }
*h = new; void insert_before(struct node **h) {
return; struct node *new,*temp,*prev ;
} int k;
temp = *h; if(*h==NULL) return;
while(temp->next!=NULL) temp = temp->next; printf("nEnter data of node before which node :
temp->next = new; ");
} scanf("%d",&k);
void display(struct node *p) { if((*h)->data == k) {
printf("nContents of the List : nn"); new = createnode();
while(p!=NULL) { new->next = *h;
printf("t%d",p->data); *h = new; return;
p = p->next; }
temp = (*h)->next; prev = *h;

5. Implementing Singly Linked List ( continued )
while(temp!=NULL && temp->data!=k) { if(temp!=NULL) {
prev=temp; prev->next = temp->next;
temp=temp->next; free(temp);
} }
if(temp!=NULL) { }
new = createnode(); void search(struct node *h) {
new->next = temp; struct node *temp;
prev->next = new; int k;
} if(h==NULL)return;
} printf("nEnter the data to be searched : ");
void delnode(struct node **h) { scanf("%d",&k);
struct node *temp,*prev; temp=h;
int k; while(temp!=NULL && temp->data!=k)
if(*h==NULL) return; temp=temp->next;
printf("nEnter the data of node to be removed : "); (temp==NULL)?
scanf("%d",&k); printf("nt=>Node does not exist") :
if((*h)->data==k) { printf("nt=>Node exists");
temp=*h; }
*h=(*h)->next; void destroy(struct node **h) {
free(temp); struct node *p;
return; if(*h==NULL) return;
} while(*h!=NULL) {
temp=(*h)->next; p = (*h)->next;
prev=*h; free(*h);
while(temp!=NULL && temp->data!=k) { *h=p;
prev=temp; }
temp=temp->next; printf("nn ******Linked List is destroyed******");
} }

6. Implementing Singly Linked List ( continued )
int main() { /* function to sort linked list */
struct node *head=NULL; void sort(struct node *h) {
int ch; struct node *p,*temp;
while(1) { int i, j, n, t, sorted=0;
printf("n1.Append"); temp=h;
printf("n2.Display All"); for(n=0 ; temp!=NULL ; temp=temp->next) n++;
printf("n3.Insert after a specified node"); for(i=0;i<n-1&&!sorted;i++) {
printf("n4.Insert before a specified node"); p=h; sorted=1;
printf("n5.Delete a node"); for(j=0;j<n-(i+1);j++) {
printf("n6.Search for a node"); if ( p->data > ( p->next )->data ) {
printf("n7.Distroy the list"); t=p->data;
printf("n8.Exit program"); p->data =(p->next)->data;
printf("nntEnter your choice : "); (p->next)->data = t;
scanf("%d",&ch); sorted=0;
switch(ch) { }
case 1:append(&head);break; p=p->next;
case 2:display(head);break; }
case 3:insert_after(&head);break; }
case 4:insert_before(&head);break; }
case 5:delnode(&head);break;
case 6:search(head);break; /* function to count number of node in the list */
case 7:destroy(&head);break; int count ( struct node *h)
case 8:exit(0);break; {
default : int i;
printf( "Wrong Choice, Enter correct one : "); for( i=0 ; h!=NULL ; h=h->next)
} i++;
} return i;
} }

7. Algorithm for adding two polynomials in linked lists
Add_Polynomial( list p, list q )
set p, q to point to the two first nodes (no headers)
initialize a linked list r for a zero polynomial
while p != null and q != null
if p.exp > q.exp
create a node storing p.coeff and p.exp
insert at the end of list r
advance p
else if q.exp > p.exp
create a node storing q.coeff and q.exp
insert at the end of list r
advance q
else if p.exp == q.exp
if p.coeff + q.coeff != 0
create a node storing p.coeff + q.coeff and p.exp
insert at the end of list r
advance p, q
end while
if p != null
copy the remaining terms of p to end of r
else if q != null
copy the remaining terms of q to end of r

8. Doubly Linked List
Pitfalls encountered while using singly linked list :
2) A singly linked list allows traversal of the list in forward direction, but not in backward direction.
3) Deleting a node from a list requires keeping track of the previous node,.
4) In the list any node gets corrupted, the remaining nodes of the list become unusable.
These problems of singly linked lists can be overcome by doubly linked list.
A Doubly Linked List is a data structure having an ordered list of nodes, in which each node
consists of two pointers. One pointer is to store the address of next node like in singly linked list. The
second pointer stores the address of previous node. It is also known as two-way list.
The specialty of DLL is that the list can be traversed in forward as well as backward directions.
The concept of DLL is also used to representing tree data structures.
head tail
A B C
/* a node in doubly linked list */
struct node
B
{
struct node *prev;
A D
int data ;
struct node *next; C
}
Tree structure using Doubly Linked List

9. Insertion of node in Doubly Linked List
q
A B D
C
p q
A B C D
Deletion of node in Doubly Linked List
A B C p
D
A B C

10. Implementing Doubly Linked List
struct node { void forward_display(struct node *p)
struct node *prev; {
int data; printf("nContents of the List : nn");
struct node *next; while(p!=NULL)
}; {
struct node *createnode() { printf("t%d",p->data);
struct node *new; p = p->next;
new = (struct node *)malloc(sizeof(struct node)); }
printf("nEnter the data : "); printf("n");
scanf("%d",&new->data); }
new->prev = NULL; void insert_after(struct node **h) {
new->next = NULL; struct node *new,*temp;
return new; int k;
} if(*h == NULL) return;
void append(struct node **h) { printf("nEnter data of node after which node : ");
struct node *new,*temp; scanf("%d",&k);
new = createnode(); temp = *h;
if(*h == NULL) while(temp!=NULL && temp->data!=k)
{ temp = temp->next;
*h = new; if(temp!=NULL) {
return; new=createnode();
} new->next = temp->next;
temp = *h; temp->next = new;
while(temp->next!=NULL) new->prev = temp;
temp = temp->next; if(new->next != NULL)
temp->next = new; new->next->prev = new;
new->prev = temp; }
} }

11. Implementing Doubly Linked List ( continued )
void insert_before(struct node **h) void delnode(struct node **h)
{ {
struct node *new,*temp; struct node *temp;
int k; int k;
if(*h==NULL) return; if(*h==NULL)
printf("nEnter data of node before which node : "); return;
scanf("%d",&k); printf("nEnter the data of node to be removed : ");
if((*h)->data == k) { scanf("%d",&k);
new = createnode(); if((*h)->data==k)
new->next = *h; {
new->next->prev=new; temp=*h;
*h = new; *h=(*h)->next;
return; (*h)->prev=NULL;
} free(temp);
temp = *h; return;
while(temp!=NULL && temp->data!=k) }
{ temp=*h;
temp=temp->next; while(temp!=NULL && temp->data!=k)
} {
if(temp!=NULL) temp=temp->next;
{ }
new = createnode(); if(temp!=NULL)
new->next = temp; {
new->prev = temp->prev; temp->next->prev = temp->prev;
new->prev->next = new; temp->prev->next = temp->next;
temp->prev = new; free(temp);
} }
} }

12. Implementing Doubly Linked List ( continued )
void search(struct node *h) int main() {
{ struct node *head=NULL;
struct node *temp; int ch;
int k; while(1) {
if(h==NULL) printf("n1.Append");
return; printf("n2.Display All");
printf("nEnter the data to be searched : "); printf("n3.Insert after a specified node");
scanf("%d",&k); printf("n4.Insert before a specified node");
temp=h; printf("n5.Delete a node");
while(temp!=NULL && temp->data!=k) printf("n6.Search for a node");
temp=temp->next; printf("n7.Distroy the list");
if (temp==NULL) printf("n8.Exit program");
printf("nt=>Node does not exist") printf("nntEnter your choice : ");
else scanf("%d",&ch);
printf("nt=>Node exists"); switch(ch) {
} case 1:append(&head);break;
void destroy(struct node **h) case 2:forward_display(head);break;
{ case 3:insert_after(&head);break;
struct node *p; case 4:insert_before(&head);break;
if(*h==NULL) return; case 5:delnode(&head);break;
while(*h!=NULL) case 6:search(head);break;
{ case 7:destroy(&head);break;
p = (*h)->next; case 8:exit(0);break;
free(*h); default :
*h=p; printf("Wrong Choice, Enter correct choice :
} ");
printf("nn ******Linked List is destroyed******"); }
} }
}

13. 910
101 400 102 720 103 910 104 150
Circular Singly tail
Linked List 150 400 720 910
n1-node n2-node n3-node n4-node
-- Singly Linked List has a major drawback. From a specified node, it is not possible to reach any of
the preceding nodes in the list. To overcome the drawback, a small change is made to the SLL so that
the next field of the last node is pointing to the first node rather than NULL. Such a linked list is called a
circular linked list.
-- Because it is a circular linked list, it is possible to reach any node in the list from a particular node.
-- There is no natural first node or last node because by virtue of the list is circular.
-- Therefore, one convention is to let the external pointer of the circular linked list, tail, point to the last
node and to allow the following node to be the first node.
-- If the tail pointer refers to NULL, means the circular linked list is empty.
Circular Doubly Linked List
prev data next prev data next prev data next prev data next
-- A Circular Doubly Linked List ( CDL ) is a doubly linked list with first node linked to last node and
vice-versa.
-- The ‘ prev ’ link of first node contains the address of last node and ‘ next ’ link of last node contains
the address of first node.
-- Traversal through Circular Singly Linked List is possible only in one direction.
-- The main advantage of Circular Doubly Linked List ( CDL ) is that, a node can be inserted into list
without searching the complete list for finding the address of previous node.
-- We can also traversed through CDL in both directions, from first node to last node and vice-versa.

14. Implementing Circular Singly Linked List
struct node { void insert_after(struct node **t)
int data; struct node *next; {
}; struct node *new,*temp;
struct node *createnode() { int k, found=0;
struct node *new; if(*t == NULL) return;
new = (struct node *)malloc(sizeof(struct node)); printf("nEnter data of node after which node : ");
printf("nEnter the data : "); scanf("%d",&k);
scanf("%d",&new->data); if((*t)->data==k)
new->next = NULL; {
return new; new = createnode();
} new->next = (*t)->next;
void append(struct node **t) { (*t)->next = new;
struct node *new,*head; *t=new;
new = createnode(); return;
if(*t == NULL) { }
*t = new; new->next = *t; temp=(*t)->next;
return; while(temp!=*t)
} {
head = (*t)->next; (*t)->next = new; if(temp->data == k) {
new->next = head; *t = new; new = createnode();
} new->next = temp->next;
void display(struct node *t) { temp->next = new;
struct node *temp = t->next, *head=t->next; found=1;
printf("nContents of the List : nn"); break;
do { }
printf("t%d",temp->data);temp = temp->next; temp=temp->next;
}while(temp!=head); }
printf(“n”); if(found==0) printf("nNode does not exist..");
} }

15. Implementing Circular Singly Linked List ( continued )
void insert_before(struct node **t) { void delnode(struct node **t) {
struct node *new,*temp,*prev,*head; struct node *temp,*prev,*head;
int k,found=0; int k,found=0;
if(*t==NULL) return; if(*t==NULL) return;
printf("nEnter data of node before which node : printf("nEnter the data of node to be removed :
"); ");
scanf("%d",&k); scanf("%d",&k);
head=(*t)->next; head=(*t)->next;
if(head->data == k) { if(head->data==k) {
new = createnode(); temp=head;
new->next = head; if(temp->next!=head) (*t)->next=head->next;
(*t)->next = new; else *t = NULL;
return; free(temp);
} return;
temp = head->next; }
prev = head; temp=head->next; prev=head;
while(temp!=head) { while(temp!=head) {
if(temp->data==k) { if(temp->data == k) {
new = createnode(); prev->next = temp->next;
prev->next = new; if(temp==*t) *t = prev;
new->next = temp; free(temp);
found=1; found=1;
break; break;
} else { } else {
prev=temp; prev=temp;
temp=temp->next; temp=temp->next;
} }
} }
if(found==0) printf("nNode does not exist.."); if(found==0) printf("nNode does not exist..");

16. Implementing Circular Singly
Linked List ( continued )
int main() {
struct node *tail=NULL; Types of Data Structures
int ch;
while(1) {
printf("n1.Append"); Data structures are classified in several ways :
printf("n2.Display All"); Linear : Elements are arranged in sequential
printf("n3.Insert after a specified node"); fashion. Ex : Array, Linear list, stack, queue
printf("n4.Insert before a specified node"); Non-Linear : Elements are not arranged in
printf("n5.Delete a node"); sequence. Ex : trees, graphs
printf("n6.Exit program"); Homogenous : All Elements are belongs to same
printf("nntEnter your choice : "); data type. Ex : Arrays
scanf("%d",&ch); Non-Homogenous : Different types of Elements
switch(ch) are grouped and form a data structure. Ex:
{ classes
case 1:append(&tail);break; Dynamic : Memory allocation of each element in
case 2:display(tail);break; the data structure is done before their usage
case 3:insert_after(&tail);break; using D.M.A functions Ex : Linked Lists
case 4:insert_before(&tail);break; Static : All elements of a data structure are
case 5:delnode(&tail);break; created at the beginning of the program. They
case 6:exit(0);break; cannot be resized. Ex : Arrays
default :
printf(“ntWrong Choice… “);
}
}
}

17. Stacks
-- Stack is an ordered collection of data elements into which new elements may be inserted and from
which elements may be deleted at one end called the “TOP” of stack.
-- A stack is a last-in-first-out ( LIFO ) structure.
-- Insertion operation is referred as “PUSH” and deletion operation is referred as “POP”.
-- The most accessible element in the stack is the element at the position “TOP”.
-- Stack must be created as empty.
-- Whenever an element is pushed into stack, it must be checked whether the stack is full or not.
-- Whenever an element is popped form stack, it must be checked whether the stack is empty or not.
-- We can implement the stack ADT either with array or linked list.
Stack ADT
Applications of stack struct stackNode {
int data; struct stackNode *next;
 Reversing Data series };
 Conversion decimal to binary  init_stack( )
 Parsing into tokens  push ( )
 Backtracking the operations  pop ( )
 Undo operations in Text Editor  isEmpty ( )
 Page visited History in web browser  display ( )
 Tracking of Function calls  peek ( )
 Maintaining scope and lifetime of local
variables in functions
 Infix to postfix conversion
 Evaluating postfix expression

18. Push(a) Push(b) Push(c) Pop( ) Push(d) Push(e) Pop( ) Pop( ) Pop( ) Pop( )
e
c d d d
b b b b b b b
a a a a a a a a a
Operations on Stack
Operation Stack’s contents TOP value Output
1. Init_stack( ) <empty> -1
2. Push( ‘a’ ) a 0
3. Push( ‘b’ ) ab 1
4. Push( ‘c’ ) abc 2
5. Pop( ) ab 1 c
6. Push( ‘d’ ) abd 2 c
7. Push( ‘e’ ) abde 3 c
8. Pop( ) abd 2 ce
9. Pop( ) ab 1 ced
10. Pop( ) a 0 cedb
11. Pop( ) <empty> -1 cedba

19. Implementing Stack ADT using Array
#define SIZE 50 int main() {
int stack[SIZE]; int top; int choice,item;
void init_stack() { init_stack();
top=-1; do
} {
void push( int n ) { printf("ntttMenunt1.Push.nt2.Pop.");
if( top==SIZE-1) printf("nStack is full"); printf("nt3.Peek.nt4.Display.nt5.Exit.n");
else stack[++top]= n; printf("nYour Choice: ");
} scanf("%d",&choice);
int pop( ) { switch(choice)
if(top== -1) { {
printf("nStack is empty"); case 1:printf("nEnter the element to push :
return -1; ");
} else return stack[top--]; scanf("%d",&item);
} push(item); break;
void display( ) { case 2:item = pop();
int i; printf("nElement poped : %d",item);
if(top== -1) printf("nStack is empty."); printf("nPress a key to continue...");
else { getche(); break;
printf("nElements are : n"); case 3:item = peek();
for(i=0;i<=top;i++) printf("nElement at top : %d",item);
printf("%5d ",stack[i]); printf("nPress a key to continue...");
}
} getche(); break;
int isEmpty( ) { case 4:display();
if ( top== -1 ) return 1; printf("nPress a key to continue...");
else return 0; getche(); break;
} case 5:exit(0);
int peek( ){ return stack[top]; } }

20. Implementing Stack ADT using Linked List
struct s_node { while(temp!=NULL) {
int data; printf("%dt",temp->data);
struct s_node *link; temp=temp->link;
} *stack; }
void push(int j) { }
struct s_node *m; void main() {
m=(struct s_node*)malloc(sizeof(struct s_node)); int choice,num,i;
m->data= j ; m->link=stack; while(1) {
stack=m; return; printf("ntt MENUn1. Pushn2. Popn3. Peek");
} printf("n4. Elements in Stackn5. Exitn");
int pop( ) { printf("ntEnter your choice: ");
struct s_node *temp=NULL; scanf("%d",&choice);
if(stack==NULL) { switch(choice) {
printf("nSTACK is Empty."); getch(); case 1: printf("nElement to be pushed:");
} else { scanf("%d",&num);
int i=stack->data; push(num); break;
temp = stack ; stack=stack->link; case 2: num=pop();
free(temp); return (i); printf("nElement popped: %d ",num);
} getch(); break;
} case 3: num=peek();
int peek( ) { printf("nElement peeked : %d ",num);
if(stack==NULL) { getch(); break;
printf("nSTACK is Empty."); getch(); case 4: printf("nElements present in stack : “ ):
} else display();getch(); break;
return (stack->data); case 5: exit(1);
} default: printf("nInvalid Choicen"); break;
void display() { }
struct s_node *temp=stack; }
}

21. Queues
-- Queue is a linear data structure that permits insertion of new element at one end and deletion of an
element at the other end.
-- The end at which insertion of a new element can take place is called ‘ rear ‘ and the end at which
deletion of an element take place is called ‘ front ‘.
-- The first element that gets added into queue is the first one to get removed from the list, Hence
Queue is also referred to as First-In-First-Out ( FIFO ) list.
-- Queue must be created as empty.
-- Whenever an element is inserted into queue, it must be checked whether the queue is full or not.
-- Whenever an element is deleted form queue, it must be checked whether the queue is empty or
not.
-- We can implement the queue ADT either with array or linked list.
Queue ADT
4 rear front struct queueNode {
int data; struct queueNode *next;
3 6 8 2 5 };
 init_queue( )
addq (4) delq ( )  addq ( )
7  delq ( )
 isEmpty ( )
 printQueue ( )
Applications of Queues
Types of Queues
 Execution of Threads
 Job Scheduling
 circular queues
 Event queuing
 priority queues
 Message Queueing
 double-ended queues

22. Implementing Queue ADT using Array
int queue[10] ,front, rear ; printf("nElements are : n");
void init_queue() { for (i=front;i<=rear;i++)
front = rear = -1 ; printf("%5d",queue[i]);
} }
void addq ( int item ){ }
if ( rear == 9 ) { int main() {
printf("nQueue is full"); int ch,num;
return ; init_queue();
} do
rear++ ; {
queue [ rear ] = item ; printf("ntMENUnn1. Add to Queue”);
if ( front == -1 )front = 0 ; printf(“n2. Delete form Queue");
} printf("n3. Display Queuen4. Exit.");
int delq( ){ printf("nntYour Choice: ");
int data ; scanf("%d",&ch);
if ( front == -1 ) { switch(ch)
printf("nQueue is Empty"); {
return 0; case 1: printf("nEnter an element : ");
} scanf("%d",&num);
data = queue[front] ; addq(num);break;
queue[front] = 0 ; case 2: num=delq();
if ( front == rear ) front = rear = -1 ; printf("nElement deleted : %d",num);
else front++ ; break;
return data ; case 3: display(); break;
} case 4: exit(0);
void display() { default: printf("nInvalid option..");
int i; }
if(front==-1) printf("nQueue is empty."); }while(1);
else { }

23. Implementing Queue ADT using Liked List
struct q_node { else {
int data; struct q_node *next; printf("nElements in Queue :n");
}*rear,*front; while(temp!=NULL) {
void init_queue() { printf("%5d",temp->data);
rear=NULL; front=NULL; temp=temp->next;
} }
void addq(int item) { }
struct q_node *t; }
t=(struct q_node*)malloc(sizeof(struct q_node)); int main() {
t->data=item; t->next=NULL; int ch,num;
if(front==NULL) rear=front=t; init_queue();
else { do {
rear->next=t; rear=rear->next; printf("ntMENUnn1. Addn2. Delete");
} printf("n3. Display Queuen4. Exit.");
} printf("nntYour Choice: ");
int delq() { scanf("%d",&ch);
struct q_node *temp; switch(ch) {
if(front==NULL) { case 1: printf("nEnter an element : ");
printf("nQueue is empty."); return 0; scanf("%d",&num);
} else { addq(num);break;
int num = front->data; case 2: num=delq();
temp = front; front=front->next; printf("nElement deleted : %d",num); break;
free(temp); return num; case 3: display(); break;
} case 4: exit(0);
} default:printf("nInvalid option..");
void display() { }
struct q_node *temp=front; }while(1);
if(front==NULL) printf("nQueue is empty."); }

24. --Arithmetic Expressions are represented using three notations infix, prefix and postfix. The prefixes
‘pre’, ‘post’, and ‘in’ refer to position of operators with respect to two operands.
-- In infix notation, the operator is placed between the two operands.
Ex: A + B A*B+C (A * B) + (C * D)
-- In Prefix notation, the operator is placed before the two operands.
Ex: +AB *A+BC +*AB*CD
-- In Postfix notation, the operator is placed after the two operands.
Ex: AB+ ABC+* AB*CD*+
Algorithm to Infix to Postfix Conversion
In-To-Post ( infix-expression )
Scan the Infix expression left to right
If the character x is an operand
Output the character into the Postfix Expression
If the character x is a left or right parenthesis
If the character is “(
Push it into the stack
If the character is “)”
Repeatedly pop and output all the operators/characters until “(“ is popped from the stack.
If the character x is a is a regular operator
Check the character y currently at the top of the stack.
If Stack is empty or y is ‘(‘ or y is an operator of lower precedence than x, then
Push x into stack.
If y is an operator of higher or equal precedence than x,
Pop and output y and push x into the stack.
When all characters in infix expression are processed
repeatedly pop the character(s) from the stack and output them until the stack is empty.

25. In-Fix To Post-Fix convertion
#define STACKSIZE 20 y=pop(&s) ;
typedef struct { while(y != '(') {
int top; char items[STACKSIZE]; printf("%c",y);
}STACK; y=pop(&s) ;
/*pushes ps into stack*/ }
void push(STACK *sptr, char ps) { } else {
if(sptr->top == STACKSIZE-1) { if(s.top ==-1 || s.items[s.top] == '(')
printf("Stack is fulln"); exit(1); push(&s ,x);
} else else {
sptr->items[++sptr->top]= ps; /* y is the top operator in the stack*/
} y = s.items[s.top];
char pop(STACK *sptr) { /* precedence of y is higher/equal to x*/
if(sptr->top == -1) { if( y=='*' || y=='/'){
printf("Stack is emptyn"); exit(1); printf("%c", pop(&s));
} else push(&s ,x);
return sptr->items[sptr->top--]; } else if ( y=='+' || y=='-')
} /* precedence of y is equal to x*/
int main() { if( x=='+' || x=='-') {
int i; STACK s; char x, y, E[20] ; printf("%c", pop(&s));
s.top = -1; /* Initialize the stack is */ push(&s ,x);
printf("Enter the Infix Expression:"); }
scanf("%s",E); /* precedence of y is less than x*/
for(i=0;E[i] != '0';i++) { else
x= E[i]; push(&s ,x);
/* Consider all lowercase letter }
from a to z are operands */ }
if(x<='z' && x>='a') printf("%c",x); }
else if(x == '(') push(&s ,x); while(s.top != -1) printf("%c",pop(&s));
else if( x == ')‘ ){ }

26. Evaluation of Post-Fix Expression
#include<stdio.h> case '*':push(op1*op2);break;
#include<ctype.h> case '/':push(op1/op2);break;
#include<math.h> case '^':push(pow(op1,op2));
float stack[10]; break;
int top=-1; }
void push(char c) }
{ j++;
stack[++top]=c; }
} return pop();
float pop() { }
float n; int main() {
n=stack[top--]; int j=0;
return (n); char expr[20];
} float number[20],result;
float evaluate(char expr[], float data[]) printf("nEnter a post fix expression : ");
{ gets(expr);
int j=0; while(expr[j]!='0')
float op1=0,op2=0; {
char ch; if(isalpha(expr[j]))
while(expr[j]!='0') { {
ch = expr[j]; fflush(stdin);
if(isalpha(expr[j])) { printf("nEnter number for %c : ",expr[j]);
push(data[j]); scanf("%f",&number[j]);
} else { }
op2=pop(); j++;
op1=pop(); }
switch(ch) { result = evaluate(expr,number);
case '+':push(op1+op2);break; printf("nThe result of %s is %f",expr,result);
case '-':push(op1-op2);break; }