Queue

A queue is a useful data structure in programming. It is similar to the ticket queue outside a cinema hall, where the first person entering the queue is the first person who gets the ticket.

Queue follows the First In First Out (FIFO) rule - the item that goes in first is the item that comes out first.

Basic Operations of Queue

A queue is an object (an abstract data structure - ADT) that allows the following operations:

• Enqueue: Add an element to the end of the queue

• Dequeue: Remove an element from the front of the queue

• IsEmpty: Check if the queue is empty

• IsFull: Check if the queue is full

• Peek: Get the value of the front of the queue without removing it

Programs:

• Linear Queue

• Circular Queue

• Priority Queue

Working of Linear Queue

Queue operations work as follows:

• two pointers FRONT and REAR

• FRONT track the first element of the queue

• REAR track the last element of the queue

• initially, set value of FRONT and REAR to -1

Enqueue Operation

• check if the queue is full

• for the first element, set the value of FRONT to 0

• increase the REAR index by 1

• add the new element in the position pointed to by REAR

Dequeue Operation

• check if the queue is empty

• return the value pointed by FRONT

• increase the FRONT index by 1

• for the last element, reset the values of FRONT and REAR to -1

Circular Queue Data Structure

A circular queue is the extended version of a regular queue where the last element is connected to the first element. Thus forming a circle-like structure.

Circular increment in circular queue

The circular queue solves the major limitation of the normal queue. In a normal queue, after a bit of insertion and deletion, there will be non-usable empty space.

• Limitation of the regular Queue

  Here, indexes 0 and 1 can only be used after resetting the queue (deletion of all elements). This reduces the actual size of the queue.

How Circular Queue Works

Circular Queue works by the process of circular increment i.e. when we try to increment the pointer and we reach the end of the queue, we start from the beginning of the queue.

Here, the circular increment is performed by modulo division with the queue size. That is,

    if REAR + 1 == 5 (overflow), REAR = (REAR + 1)%5 = 0 (start of queue)

Circular Queue Operations

The circular queue work as follows:

• two pointers FRONT and REAR

• FRONT track the first element of the queue

• REAR track the last elements of the queue

• initially, set value of FRONT and REAR to -1

Enqueue Operation

• check if the queue is full

• for the first element, set value of FRONT to 0

• circularly increase the REAR index by 1 (i.e. if the rear reaches the end, next it would be at the start of the queue)

• add the new element in the position pointed to by REAR

Dequeue Operation

• check if the queue is empty

• return the value pointed by FRONT

• circularly increase the FRONT index by 1

• for the last element, reset the values of FRONT and REAR to -1

• However, the check for full queue has a new additional case:

Case 1: FRONT = 0 && REAR == SIZE - 1

Case 2: FRONT = REAR + 1

The second case happens when REAR starts from 0 due to circular increment and when its value is just 1 less than FRONT, the queue is full.