Question

Suppose that queue is a queueType object and the size of the array implementing queue is \(100 .\) Also, suppose that the value of queueFront is 50 and the value of queueRear is 99 a. What are the values of queueFront and queueRear after adding an element to queue? b. What are the values of queueFront and queueRear after removing an element from queue?

Short answer

After adding: queueFront = 50, queueRear = 0; after removing: queueFront = 51, queueRear = 99.

Step-by-step solution

Understanding Initial Conditions

The initial setup is a queue of size 100. The queueFront is at position 50, and queueRear is at position 99. This means elements are currently stored from index 50 to 99 in the array.

Adding an Element to a Circular Queue

When adding an element to a circular queue, the queueRear will move to the next position. Since the queue is circular, after the last index (99 in this case), it wraps around to the first index. So, the new queueRear will be \( (queueRear + 1) \mod 100 = (99 + 1) \mod 100 = 0 \).Hence, queueRear becomes 0. The queueFront remains unchanged at 50.

Removing an Element from the Queue

When an element is removed from the queue, the queueFront moves to the next position. Therefore, the new queueFront will be \( (queueFront + 1) \mod 100 = (50 + 1) \mod 100 = 51 \).Hence, queueFront becomes 51. The queueRear remains unchanged after this operation.

Key concepts

Queue Implementation

A queue is a linear data structure that follows the first-in-first-out (FIFO) principle, meaning the element that is added first to the queue will be the one to be removed first. Think about it like a line at a grocery store, where the person who joins first is the first to leave. In computer science, this data structure is crucial for managing jobs in scheduling systems, handling tasks in processor time management, and more.

To implement a queue in a programming environment, we use an array or a linked list. In our case, we are using an array-based approach, which involves maintaining two important indices: **queueFront** and **queueRear**. **queueFront** is the index in the array where the first element of the queue is stored, and **queueRear** is the index where the last element of the queue is stored. Efficient queue implementations often use modulo arithmetic to manage these indices, especially when dealing with circular queues, ensuring that they handle wrap-around efficiently without "overflow" when reaching the end of the array.

Array-Based Queue

An array-based queue is a straightforward way to implement a queue using a fixed-size array. It's essential for the queue size to be known in advance because the size of the array cannot change during execution.

In an array-based queue, elements are inserted from the rear end and removed from the front end. To efficiently utilize the array's space, especially when an element is added or removed, the queue can be implemented in a circular way by using modulo operations. This means when an element reaches the final index of the array, it can wrap around to the start if space is available. For instance, if the queue array size is 100, an element that needs to be added after index 99 will wrap around to index 0.

This prevents elements from shifting or the array becoming full prematurely when there is still available space at the beginning of the array. In circular queues, achieving this wrap-around is easy with the modulo operation, a crucial part of the implementation.

Queue Operations

Queue operations are fundamental to managing the flow of data within the queue. The primary operations include adding an element (enqueue), removing an element (dequeue), and sometimes peeking at the front element without removing it.

**Enqueue Operation:** This operation adds an element to the rear of the queue. In a circular queue, when adding an element by enqueue, the **queueRear** moves one position forward. If **queueRear** is at the last index of the array, it wraps around to index 0 using modulo arithmetic. This efficient handling ensures no wasted space in the array.

**Dequeue Operation:** This is used to remove an element from the front of the queue. Post-dequeue, **queueFront** is incremented by one. Similar to enqueue, if **queueFront** is at the last index of the array, it wraps around to index 0, ensuring the circular nature of the queue.

Both operations help maintain a dynamic system where elements can continuously flow through the queue, using space efficiently and without unnecessary shifts within the array. This design keeps the queue functional while managing memory usage effectively.