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 99 and the value of queueRear is 25 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, queueRear = 26 and queueFront = 99. After removing, queueRear = 25 and queueFront = 0.

Step-by-step solution

Understanding the Problem

We have a queue implemented as an array with a size of 100. The current positions of `queueFront` and `queueRear` are 99 and 25, respectively. The task is to determine their new positions after adding or removing elements from the queue.

Adding an Element

Currently, `queueRear` is at 25. To add an element, `queueRear` moves one position forward. Since the queue is linear but cyclic (due to being an array), `queueRear` will become 26. `queueFront` remains unchanged when adding an element, so it stays at 99.

Removing an Element

To remove an element, `queueFront` moves one position forward. Since `queueFront` is currently at 99 and the array is cyclic, it will wrap around to the beginning of the array. Therefore, `queueFront` becomes 0. `queueRear` stays at 25 since removing an element does not affect its position.

Key concepts

Cyclic Arrays

Cyclic arrays are a fascinating concept in data structures. Imagine an array that wraps around like a circle. This allows us to continue using the array as if it has no end. Usually, arrays are linear, meaning once you reach the last element, you have finished, but a cyclic array lets you go back to the beginning.
This can be especially useful when implementing queues. In a cyclic array, when one of the two pointers (representing positions in the array) reaches the end, it simply "wraps around" and starts from zero. For example, if you have a queue with positions represented by pointers starting at 99 in a 100 element array, the next position would not be 100 but 0. This makes cyclic arrays very efficient in ensuring no space is wasted.
Using a cyclic array helps queues avoid the issue of having unused space in a situation called the 'false fully occupied queue'. This property supports continuous data flows in queue operations, such as streaming data or regularly coming requests.

Queue Operations

Queue operations follow a first-in, first-out (FIFO) approach, just like people waiting in line. When using C++, we can implement queues using arrays and these operations involve both adding and removing elements.
- **Adding Elements (enqueue):** This involves placing a new element at the end of the queue. In cyclic arrays, when `queueRear` reaches the end of the array and you wish to "add" another element, `queueRear` simply rotates back to the start (position 0) of the array. - **Removing Elements (dequeue):** This operation removes an element from the front of the queue. Using cyclic arrays, if `queueFront` is at the last index, the removal process wraps it back to the beginning at index 0 post removal.
Through proper incrementing and cycling of `queueFront` and `queueRear`, operations can be handled efficiently, avoiding index overflows or underflows. This cyclic behaviour is what allows for constant addition and deletion without needing to shift elements or resize arrays constantly.

Data Structures

Data structures are integral in organizing and managing data efficiently. In the context of queue implementations using arrays, they provide the blueprint for how data is stored, accessed, and manipulated.
By using a data structure like a queue, tasks can be processed in the order they are received, which is beneficial in many real-world applications, such as managing print jobs, order processing, or handling asynchronous requests.
- **Arrays** within data structures are used to store queue elements. They provide structure and a place to manage data sequentially and effectively. - **Pointers** such as `queueFront` and `queueRear` in C++ implementations are crucial in navigating through the elements. They give the abstraction needed to implement cyclic behavior easily by adjusting their positions as needed.
Using such organized forms offers both simplicity and powerful handling of complex data manipulations, making algorithm execution more efficient and the codebase easier to manage.