Question

Suppose that queue is implemented as an array with the special reserved slot, as described in this chapter. Suppose that the size of the array implementing queue is \(100 .\) Also, suppose that the value of queueFront is 74 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? Also, what is the position of the removed queue element?

Short answer

a. queueFront = 74, queueRear = 0; b. queueFront = 75, queueRear = 99, removed element at position 74.

Step-by-step solution

Initial Setup

We start with an array of size 100, and the position indicators are queueFront = 74 and queueRear = 99. This setup means the queue is approaching its capacity since queueRear is at the last index allowed, and queueFront is not far behind.

Adding an Element

When adding an element to the queue using a circular array, the queueRear position wraps around to the beginning of the array if it reaches the end. Thus, adding an element when queueRear = 99 results in queueRear being updated to (99 + 1) % 100 = 0.

Values After Adding

Since queueFront remains unchanged when adding an element, the values become queueFront = 74 and queueRear = 0 after the addition of an element.

Removing an Element

Removing an element changes the queueFront position. The element at the current queueFront (position 74) is removed. The new position of queueFront is calculated as (74 + 1) % 100 = 75.

Element Position After Removal

The removed element was at position 74. After the removal, queueFront is updated to 75, and the values are queueFront = 75 and queueRear = 99.

Key concepts

Queue Implementation

A queue is a linear data structure that follows the First In First Out (FIFO) principle. This means the first element added to the queue will be the first one to be removed. Queues are used in many scenarios such as handling requests in a server, printer queue management, and more.
Queue implementation can often be achieved using arrays or linked lists. The focus here is on array implementation, where a specific size must be declared when the queue is created.
The primary operations associated with queue implementation are:

• Enqueue: Adding an element to the end of the queue.
• Dequeue: Removing an element from the front of the queue.
• Peek: Viewing the element at the front of the queue without removing it.
• IsFull: Checking if the queue is at maximum capacity.
• IsEmpty: Checking if the queue is empty.

When implemented using arrays, special considerations like wrapping elements to use the array's space efficiently might be needed, especially to avoid memory wastage.

Circular Array

In a circular array, the end of the array is connected back to the beginning. This method enhances the queue implementation by efficiently using space.
The circular array concept is particularly useful in the queue scenario, where index recycling ensures that indices previously used for elements that have been removed are reused rather than left idle.
Consider an array of size 100. Typically, when an element is added at the last position and another needs to be added, a non-circular array would have to move all elements. But in a circular array, we simply wrap around to index 0.
This technique prevents a full queue for elements when memory is still available in the early parts of the array. For example, when queueRear is 99 and a new element is added, it doesn't increase to 100 to go out of bounds but wraps to 0: \[(99 + 1) \% 100 = 0\]This prevents data overflow and underflow, which optimizes memory usage and maintains the integrity of operations.

Queue Operations

The operations of a queue are fundamental to its functioning. Each operation in a queue manipulates one or more of its properties and ensures data movement and management. Here's how the key operations of a queue typically work:
- **Enqueue**: Adds an element at the next available position at the rear of the queue. In a circular array, if the rear is at the end, it wraps around to the front. For instance, if our queueRear is at 99, adding a new element wraps it to 0.
- **Dequeue**: Removes an element from the front of the queue. The queueFront pointer is adjusted to the next element. This operation moves in a similar wrap-around manner if using a circular array, moving from end to start when necessary.
- **Peek**: Allows access to the element at the queueFront without removing it, useful for checking the first element.
These operations help in managing the queue for efficient utilization of space and sequential data scattering, preventing memory leakage and unintentional overwrites.

QueueFront and QueueRear

QueueFront and QueueRear are the two essential pointers used to navigate the queue. These pointers facilitate the management of queue entries so that elements can be added or removed correctly.
- **QueueFront**: It points to the first element in the queue. Every time a dequeue operation occurs, the queueFront is updated to point to the next element. For example, if an element at position 74 is removed, the queueFront moves to 75: \[(74 + 1) \% 100 = 75\]
- **QueueRear**: It points to the position where the next element will be added. After each enqueue operation, this pointer is updated. In circular arrays, this updating facilitates continuous use of the array slots. For instance, moving from position 99 to 0 after an enqueue: \[(99 + 1) \% 100 = 0\]
These pointers work together for the seamless functioning of the queue, ensuring that elements appear in correct FIFO order and memory usage is optimized.