The document describes different types of queues as data structures. A queue is a first-in, first-out (FIFO) data structure where elements are added to the rear and removed from the front. The document discusses linear (simple) queues, circular queues, double-ended queues, and priority queues. It provides algorithms and examples for insert and delete operations on each type of queue.

1. Queue
DATA STRUCTURE

2. Introduction
 A queue is a particular kind of abstract data type or collection in which the entities in the collection are kept in order and the
principal (or only) operations on the collection are the addition (insertion) of entities to the rear terminal position, known
as enqueue, and removal (deletion) of entities from the front terminal position, known as dequeue.
 This makes the queue a First-In-First-Out (FIFO) or a First-Come-First-Served (FCFS) data structure. In a FIFO data structure, the
first element added to the queue will be the first one to be removed.
Examples
 A checkout line at supermarket cash counter, cashier counter in a bank, ticket counter for fare, etc. The first person in the line is
(usually) the first to be checked out.
 Another example is of printing documents. The document given first for printing will be printed first & other documents will
follow the sequence.

3. Representation of Queue
 When queue is empty
FRONT = -1 and REAR = -1
 Adding an element in queue will increased value of REAR by 1
REAR = REAR + 1
 Removing an element from queue will increased value of FRONT by 1
FRONT = FRONT + 1
 The vector is assumed to consist of a large number of elements, enough to be sufficient to handle the variable length
property of queue.
 The vector representation of a queue requires pointers F & R which denote the positions of its front & rear elements
respectively.
Operations of Queue

4. Types of Queue
 Linear (Simple) Queue
 Circular Queue
 Double-ended Queue (Deque)
 Priority Queue
1. Linear (Simple) Queue

5.  Insert Operation
 Function: LQINSERT (Q,F,R,N,Y). Given F & R, pointers
to the front and rear elements of a queue, a vector Q
consisting of N elements and an element Y, this
procedure inserts Y at the rear of the queue.
 Set F=R=-1, when queue is empty.
Algorithm
Step-1: [Check overflow?]
if R>=N-1
then Write (‘Overflow’)
Return
Step-2: [Increment rear pointer R]
R  R + 1
Step-3: [Insert element]
Q[R]  Y
Step-4: [Set front pointer F]
if F=-1
then F  0
Return
 Delete Operation
 Function: LQDELETE (Q,F,R). Given F & R, pointers to the front and
rear elements of a queue, a queue Q consisting to which they
correspond, this function deletes and returns the last element of the
queue. Y is a temporary variable.
Algorithm
Step-1: [Check underflow?]
if F=-1
then Write (‘Underflow’)
Return
Step-2: [Delete element]
Y  Q[F]
Step-3: [Check for queue empty or has an element?]
if F=R
then F=R=-1
else
F  F + 1
Step-4: [Return element]
Return(Y)

6. Example

7. 2. Circular Queue
 In circular queue, all the elements are arranged in a circular form.
 Here, the left spaces can be reutilized to insert new variables which was not the case with linear queue.

8.  Insert Operation
 Function: CQINSERT (Q,F,R,N,Y). Given F & R, pointers
to the front and rear elements of a queue, a vector Q
consisting of N elements and an element Y, this
procedure inserts Y at the rear of the queue.
 Set F=R=-1, when queue is empty.
Algorithm
Step-1: [Reset rear pointer R]
if R>=N-1
then R  0
else R  R + 1
Step-2: [Check overflow?]
if F=R
then Write (‘Overflow’)
Return
Step-3: [Insert element]
Q[R]  Y
Step-4: [Set front pointer F]
if F=-1, then F  0
Return
 Delete Operation
 Function: CQDELETE (Q,F,R). Given F & R, pointers to the front and
rear elements of a queue, a queue Q consisting to which they
correspond, this function deletes and returns the last element of the
queue. Y is a temporary variable.
Algorithm
Step-1: [Check underflow?]
if F=-1
then Write (‘Underflow’)
Step-2: [Delete element]
Y  Q[F]
Step-3: [Check for queue empty or has an element?]
if F=R
then F=R=-1
Return(Y)
Step-4: [Increment front pointer F]
if F=N-1
then F  0,
else F  F + 1
Return(Y)

9. Example

10. 3. Double-ended Queue (Deque)
 A deque (double-ended queue) is a linear list in which insertions and deletions are made to or from either
end of the structure.
 It is clear that deque is more general than a stack or a queue.
 There are two variations of a deque, namely, the input-restricted deque and the output-restricted deque.
 The input-restricted deque allows insertions at only one end, while an output-restricted deque permits
deletions from only one end.

11.  Input-restricted Deque
 Output-restricted Deque

12. 4. Priority Queue
 A priority queue is collection of elements where elements are stored according to the their priority levels.
 Inserting and removing of elements from queue is decided by the priority of the elements.
 In a priority queue, an element with high priority is served before an element with low priority.
 If two elements have the same priority, they are served according to their order in the queue.
 The two fundamental methods of a priority queue P:
insertItem(k,e): Insert an element e with key k into P.
removeMin(): Return and remove from P an element with the smallest key.