Question

Why a circular queue is more benefiting than a single dimension array queue? How to do indexing in a circular queue? (In java)

Answer 1

Circular queue avoids the wastage of space in a regular queue implementation using arrays.

Limitation of the regular Queue

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 representation

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.

Enque and Deque Operations

// Circular Queue implementation in Java

public class CQueue {
  int SIZE = 5; // Size of Circular Queue
  int front, rear;
  int items[] = new int[SIZE];

  CQueue() {
    front = -1;
    rear = -1;
  }

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

  // Check if the queue is empty
  boolean isEmpty() {
    if (front == -1)
      return true;
    else
      return false;
  }

  // Adding an element
  void enQueue(int element) {
    if (isFull()) {
      System.out.println("Queue is full");
    } else {
      if (front == -1)
        front = 0;
      rear = (rear + 1) % SIZE;
      items[rear] = element;
      System.out.println("Inserted " + element);
    }
  }

  // Removing an element
  int deQueue() {
    int element;
    if (isEmpty()) {
      System.out.println("Queue is empty");
      return (-1);
    } else {
      element = items[front];
      if (front == rear) {
        front = -1;
        rear = -1;
      } /* Q has only one element, so we reset the queue after deleting it. */
      else {
        front = (front + 1) % SIZE;
      }
      return (element);
    }
  }

  void display() {
    /* Function to display status of Circular Queue */
    int i;
    if (isEmpty()) {
      System.out.println("Empty Queue");
    } else {
      System.out.println("Front -> " + front);
      System.out.println("Items -> ");
      for (i = front; i != rear; i = (i + 1) % SIZE)
        System.out.print(items[i] + " ");
      System.out.println(items[i]);
      System.out.println("Rear -> " + rear);
    }
  }

  public static void main(String[] args) {

    CQueue q = new CQueue();

    // Fails because front = -1
    q.deQueue();

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

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

    q.display();

    int elem = q.deQueue();

    if (elem != -1) {
      System.out.println("Deleted Element is " + elem);
    }
    q.display();

    q.enQueue(7);

    q.display();

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

}

Circular Queue Complexity Analysis

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