Question

Describe the output for the following sequence of queue operations: enqueue(5), enqueue(3), dequeue(), enqueue(2), enqueue(8), dequeue(), dequeue(), enqueue(9), enqueue(1), dequeue(), enqueue(7), enqueue(6), dequeue(), dequeue(), enqueue(4), dequeue(), dequeue().

Short answer

Final queue state: [4]

Step-by-step solution

Initial Enqueue Operations

Start with an empty queue. First, enqueue 5, hence the queue is [5]. Next, enqueue 3, so the queue becomes [5, 3].

First Dequeue

Dequeue removes the front element (5) from the queue. Now the queue is [3].

Subsequent Enqueue Operations

Enqueue 2, which results in [3, 2]. Then, enqueue 8, leading to the queue [3, 2, 8].

Second and Third Dequeues

Dequeue removes the front element (3), making the queue [2, 8]. Another dequeue removes 2, thus the queue becomes [8].

More Enqueue Operations

Enqueue 9, resulting in [8, 9]. Then, enqueue 1, leading to [8, 9, 1].

Fourth Dequeue

Dequeue removes 8, leaving the queue as [9, 1].

Additional Enqueue Operations

Enqueue 7, making it [9, 1, 7]. Then, enqueue 6, resulting in [9, 1, 7, 6].

Fifth and Sixth Dequeues

Dequeue removes 9, resulting in [1, 7, 6]. Another dequeue removes 1, giving [7, 6].

Final Enqueue and Dequeue Operations

Enqueue 4, updating the queue to [7, 6, 4]. Dequeue removes 7, resulting in [6, 4]. Finally, dequeue removes 6, leaving [4] as the final state.

Key concepts

Enqueue

In queue operations, 'enqueue' is a fundamental action. It simply means to add an element to the end of the queue. Think of it as standing in line; the new person joins at the back.
For example, if the queue is currently [5, 3], and you enqueue 2, the queue becomes [5, 3, 2].

• The 'enqueue' operation is crucial for adding new elements as it maintains the order of insertion.
• It helps ensure that the queue follows its definition of First In First Out (FIFO).

Enqueue operations are generally simple and very efficient. They usually operate in constant time, meaning the time to add an element does not depend on the size of the queue itself.

Dequeue

The 'dequeue' operation is another core function of a queue, and it removes an element from the front. Similar to the front person exiting a line.
For instance, if the queue is [5, 3, 2], a 'dequeue' would remove the 5 and update the queue to [3, 2].

• The 'dequeue' operation maintains the FIFO property by removing the oldest element first.
• This operation is vital for processing tasks in the order they arrive, which is useful in real-world scenarios.

Just like 'enqueue', the 'dequeue' operation is generally performed in constant time, making it efficient for use cases where elements need to be processed in sequence.

Data Structures

A queue is a fundamental data structure used in computer science. Data structures are ways to store and organize data to make it efficient for access and modification.
Queues are essential for their FIFO property, ensuring orderly processing.

• They are commonly implemented using arrays or linked lists.
• Queues are useful in various applications like task scheduling, printer spooling, and managing requests in web servers.

Understanding data structures is crucial because they enable effective data operations and algorithms.

Algorithm

An algorithm is a step-by-step process for solving a problem or accomplishing a task. In the context of queue operations, algorithms determine how 'enqueue' and 'dequeue' are implemented and optimized.
Consider the provided sequence of queue operations and the steps to solve what the final state of the queue is. An effective algorithm ensures that each operation is performed efficiently, maintaining the integrity of the data structure.

• Algorithms are essential for optimizing how operations are performed on data structures like queues.
• They help improve performance, speed, and resource utilization.

Mastering algorithms is key to becoming proficient in programming and problem-solving in computer science.