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 an element, queueFront = 99 and queueRear = 26. After removing an element, queueFront = 0 and queueRear = 25.

Step-by-step solution

Understanding the circular queue concept

In a circular queue, the last position is connected back to the first position to make a circle. This structure allows efficient usage of storage since we can enqueue elements to a previously occupied position that has been dequeued. The mod operation is used to simulate the circular behavior.

Determine initial indices for enqueue operation

Given that `queueFront = 99` and `queueRear = 25`, when enqueuing an element, the rear is incremented to insert the new element. The new rear index after enqueueing will be calculated as: \[ \text{queueRear} = (\text{queueRear} + 1) \mod 100 \] Substituting the given value: \[ \text{queueRear} = (25 + 1) \mod 100 = 26 \] Thus, the new value of `queueRear` is 26, while `queueFront` remains 99.

Determine indices for dequeue operation

For dequeueing an element, the front is incremented to remove the element from the front. The new front index after dequeueing will be: \[ \text{queueFront} = (\text{queueFront} + 1) \mod 100 \] Substituting the given values: \[ \text{queueFront} = (99 + 1) \mod 100 = 0 \] So, the new value of `queueFront` is 0, while `queueRear` remains 25.

Key concepts

Data Structures

Data structures are essential tools in programming that help organize, manage, and store data efficiently. One such structure is the queue, which follows the First In, First Out (FIFO) principle. This means the first element added is the first one to be removed. Picture a line of people waiting at a ticket counter; the person at the front is served first, resembling a queue.

Queues can be implemented in various ways, such as using arrays, linked lists, or even stacks. Each implementation has its own use cases and advantages. Circular queues, our focus here, are a type of queue where the last position wraps around to the first, forming a circle. This structure optimizes space, allowing elements to be enqueued or dequeued flexibly without being hindered by the physical end of the array.

• First In, First Out principle
• Implemented as arrays, linked lists, or stacks
• Circular queues wrap around to use space efficiently

Queue Operations

Queue operations primarily include enqueueing and dequeueing. Enqueueing is the operation of adding an element, while dequeueing is removing an element. These operations are designed with simplicity and efficiency in mind within the queue data structure.

When enqueueing in a circular queue, we need to ensure that we correctly adjust the rear index to insert the new element. Meanwhile, dequeueing requires adjusting the front index to ensure the queue remains consistent.

• Enqueue: Add elements at the rear
• Dequeue: Remove elements from the front
• Maintains FIFO order

Understanding these operations is crucial for implementing the queue effectively and ensuring elements are accessed in the correct order.

Modulo Operation

The modulo operation is a mathematical operation that finds the remainder of division of one number by another. In the context of circular queues, it is crucial for managing index wrapping in an array-based implementation.

For instance, when you want to move beyond the end of the queue, you use the modulo operation to "wrap around." If the size of your queue is 100 and the current rear index is at 25, adding a new item would normally increase this to 26. Using modulo, if you were at the end of the queue (index 99) and add one more, it wraps to index 0 instead. In formulas, this is expressed as \( ext{new ear} = ( ext{queueRear} + 1) ext{ mod } ext{queueSize} \).

• Helps manage circular wrapping in queues
• Maintains the continuity of indices

Array Implementation

In computer science, arrays are one of the simplest and most commonly used data structures. They store elements in contiguous memory locations, ensuring that each element can be efficiently accessed using an index.

When implementing circular queues, arrays offer a straightforward method. You begin with defining an array with a fixed size. In this context, imagine an array of size 100 for our queue. As new elements are enqueued, they are added at the rear index of the array; when elements are dequeued, they leave from the front index.

• Array provides linear index access
• Efficient traversal and management
• Fixed size, necessitating thoughtful implementation for circular behavior

For circular queues, careful management of front and rear pointers is crucial, often involving the use of the modulo operation to provide a natural wrap-around effect when inserting and removing elements.