Question

Are short-answer questions. Write an algorithm that sets last equal to the last element in a queue, leaving the queue empty.

Short answer

Dequeue elements until the queue is empty, setting each to 'last'; the last set is the final element.

Step-by-step solution

Understand the Problem

The task is to create an algorithm that removes all elements from a queue while storing the last element in a variable called 'last'.

Initialize Variables

Initialize a variable 'last' to store the last element and ensure your queue is set up in the environment.

Iterate Over the Queue

Create a loop that continues as long as the queue is not empty. In each iteration, dequeue the front element of the queue.

Update Last Element

In each iteration of the loop, set the variable 'last' to the dequeued element. This ensures that by the end of the loop, 'last' stores the last element of the queue.

End the Loop and Return Result

Once the loop ends (when the queue is empty), the variable 'last' will contain the value of the last element that was in the queue. Return or print the value of 'last'.

Key concepts

Queue Operations

A queue is a special type of data structure that works based on the First-In-First-Out (FIFO) principle. This means the first element added to the queue is the first one to be removed. Queue operations are fundamental in algorithm design, where queues help to manage data in a sequential order. You can imagine a queue like a line of people waiting to get a ticket; the first person in line is the first one to get served.

There are several key operations you can perform on a queue:

• Enqueue: Add an element to the back of the queue.
• Dequeue: Remove the element from the front of the queue.
• Peek: View the front element of the queue without removing it.
• IsEmpty: Check whether the queue is empty.
• Size: Get the number of elements in the queue.

Using these operations in combination, you can manipulate the queue efficiently and use it as part of larger, more complex algorithms.

Dequeue

The dequeue operation is crucial because it allows us to remove elements from the front of the queue. This operation is unique because it respects the FIFO order, ensuring elements are removed in the same order as they were added. Think of it like a conveyor belt where items are dequeued from one end.

To perform a dequeue operation, you need to:

• Check if the queue is empty. If it is, you cannot dequeue an element.
• Remove the front element of the queue.
• Adjust the pointer (or reference) to the next available element in the queue.

This operation is efficient as it generally has a time complexity of O(1), making it a fast operation in the context of queue management. It plays a key role when you need to process elements sequentially, like in the algorithm we discussed, where each front element is removed until only the last one remains.

Variable Initialization

Initializing variables is a crucial step in programming, especially in algorithms, to ensure that the computations proceed correctly. In the context of the problem, initializing the variable 'last' is necessary to store the final value. This step sets up a placeholder that helps track specific values during the execution of an algorithm.

Consider these aspects of variable initialization:

• Purpose: Provides default values or sets up space to store critical data during the operation.
• Early Initialization: Helps to avoid errors and ensures all operations have a valid state to work with.
• Data Types: Ensure the variable is initialized with a type that corresponds to the data it will hold, e.g., integers, strings, or objects.

In the exercise, 'last' is initialized to store the last value from the queue. Without this initialization, we wouldn't have a dedicated place to save this crucial piece of information.

Loop Control

Loop control allows us to repeatedly carry out certain operations until a specific condition is met. This is particularly useful in processing data structures like queues. In the given exercise, loop control is used to keep operating on the queue until it becomes empty, ensuring all elements are properly handled.

Loops can be controlled through various structures, such as:

• For Loops: Execute a block a defined number of times.
• While Loops: Continue execution as long as a specified condition remains true. This is typically used when the number of iterations is not known beforehand.
• Do-While Loops: Similar to the while loop, but guarantees at least one execution of the loop block.

In our algorithm, a while loop checks if the queue is non-empty. Within each iteration, it dequeues an element and assigns it to 'last'. The loop ends once the queue has no more elements, ensuring the last processed element is the one stored in 'last'. Loop control structures are vital to controlling the flow of data processing and ensuring that algorithms run efficiently and correctly.