As you can see in the above image, after a bit of enqueuing and dequeuing, the size of the queue has been reduced.

The indexes 0 and 1 can only be used after the queue is reset when all the elements have been dequeued.

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

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

2. 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.

Circular Queue Implementations in C

The most common queue implementation is using arrays, but it can also be implemented using lists.

// Circular Queue implementation in C

#include <stdio.h>

#define SIZE 5

int items[SIZE];
int front = -1, rear = -1;

// Check if the queue is full
int isFull(){
  if ((front == rear + 1) || (front == 0 && rear == SIZE - 1)) return 1;
  return 0;
}

// Check if the queue is empty
int isEmpty(){
  if (front == -1) return 1;
  return 0;
}

// Adding an element
void enQueue(int element){
  if (isFull())
    printf("n Queue is full!! n");
  else {
    if (front == -1) front = 0;
    rear = (rear + 1) % SIZE;
    items[rear] = element;
    printf("n Inserted -> %d", element);
  }
}

// Removing an element
int deQueue(){
  int element;
  if (isEmpty()) {
    printf("n Queue is empty !! n");
    return (-1);
  } else {
    element = items[front];
    if (front == rear) {
      front = -1;
      rear = -1;
    } 
    // Q has only one element, so we reset the 
    // queue after dequeing it. ?
    else {
      front = (front + 1) % SIZE;
    }
    printf("n Deleted element -> %d n", element);
    return (element);
  }
}

// Display the queue
void display(){
  int i;
  if (isEmpty())
    printf(" n Empty Queuen");
  else {
    printf("n Front -> %d ", front);
    printf("n Items -> ");
    for (i = front; i != rear; i = (i + 1) % SIZE) {
      printf("%d ", items[i]);
    }
    printf("%d ", items[i]);
    printf("n Rear -> %d n", rear);
  }
}

int main(){
  // Fails because front = -1
  deQueue();

  enQueue(1);
  enQueue(2);
  enQueue(3);
  enQueue(4);
  enQueue(5);

  // Fails to enqueue because front == 0 && rear == SIZE - 1
  enQueue(6);

  display();
  deQueue();

  display();

  enQueue(7);
  display();

  // Fails to enqueue because front == rear + 1
  enQueue(8);

  return 0;
}

Circular Queue Complexity Analysis

The complexity of the enqueue and dequeue operations of a circular queue is O(1) for (array implementations).

Applications of Circular Queue

• CPU scheduling
• Memory management
• Traffic Management