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 25 and the value of queueRear is 75 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 enqueue: queueRear = 76, queueFront = 25; After dequeue: queueRear = 75, queueFront = 26.

Step-by-step solution

Understanding the Queue Structure

A queue implemented with an array behaves like a circular buffer. This means that the `queueRear` wraps around to the start once it reaches the end of the array. The same logic applies to the `queueFront`. The current capacity is 100, meaning the array indices go from 0 to 99.

Determine the New Rear for Enqueue

When adding an element to the queue (enqueue operation), `queueRear` is increased by 1. Given that `queueRear` is currently 75, after adding an element: :new_queueRear = (75 + 1) % 100 = 76. The `queueFront` remains unchanged during enqueue operations, so it will still be 25.

Determine the New Front for Dequeue

When removing an element from the queue (dequeue operation), `queueFront` is increased by 1. Given that `queueFront` is currently 25, after removing an element: :new_queueFront = (25 + 1) % 100 = 26. The `queueRear` remains unchanged during dequeue operations, so it will still be 75.

Key concepts

Queue

A queue is a fundamental data structure in computer science, specifically defined by its unique ordering principle known as FIFO (First In, First Out). This means that elements are processed in the exact order in which they arrive. Imagine a queue as a line at the grocery store - the first person to get in line will be the first one to be served.

Queues are versatile and can be applied in various scenarios such as managing tasks in operating systems, handling requests in a web server, or designing simulation models.

• Operations: The primary operations for a queue include enqueue (adding an element) and dequeue (removing an element).
• Characteristics: Unlike stacks which operate on a LIFO (Last In, First Out) principle, queues ensure that processing order is preserved.

Understanding these basic principles sets the foundation for comprehending more complex structures like circular buffers.

Circular Buffer

Circular buffers, also referred to as circular queues or ring buffers, are an efficient way to implement a queue using a fixed-size buffer. They allow for continuous operation by wrapping around the buffer's indices, meaning the end of the buffer is connected back to the beginning. This makes them ideal for situations where the buffer has a fixed size but the data stream is continuous.

Circular buffers provide the following benefits:

• Space Efficiency: Utilizes all available slots in the buffer, without needing to reset or move data.
• Performance: No need for shifting elements on enqueue and dequeue operations, reducing computational overhead.
• Applications: Commonly used in controlling hardware devices, digital signal processing, and streaming data management.

The circular nature helps to smoothly manage buffer overflow and maximize storage, effectively allowing the queue to function like a treadmill, where elements wrap around rather than stopping at the end.

Enqueue and Dequeue Operations

Enqueue and dequeue operations are the core functionalities of a queue, responsible for adding and removing elements, respectively.

Enqueue Operation: This is the process of adding an element to the rear of the queue. In the case of a circular buffer, if the rear reaches the end of the buffer, it wraps around to the front.

• Increment the rear position: ``` new_queueRear = (queueRear + 1) % size ```
• Check for overflow: Ensure the buffer doesn’t exceed its capacity by comparing the rear and front positions.

Dequeue Operation: This involves removing an element from the front of the queue. Like enqueue, the front position is incremented and can wrap around if it reaches the end.

• Increment the front position: ``` new_queueFront = (queueFront + 1) % size ```
• Check for underflow: Confirm the queue isn’t empty before removing elements.

By managing these operations effectively, queues ensure data integrity and efficiency.

Queue Implementation in C++

Implementing a queue in C++ typically involves the use of arrays or linked list structures. An array implementation using a circular buffer is efficient and commonly used. Here’s a simple breakdown:

1. Initialize the Queue: - Define an array with a fixed size. - Set initial values for queueFront and queueRear, often starting both at 0.
2. Implement Enqueue: - Add an element at the position indicated by queueRear. - Update queueRear using the formula: ```cpp queueRear = (queueRear + 1) % maxSize; ```
3. Implement Dequeue: - Remove an element from the position indicated by queueFront. - Update queueFront using the formula: ```cpp queueFront = (queueFront + 1) % maxSize; ```
4. Check Queue Conditions: - Before enqueueing, check for a full queue: ```cpp if ((queueRear + 1) % maxSize == queueFront) ``` - Before dequeueing, ensure the queue isn’t empty: ```cpp if (queueFront == queueRear) ```
Utilizing these principles ensures that the queue operates smoothly and efficiently within the constraints of its defined size.