Question

Suppose the following operations are performed on an empty queue:\ enqueue (5): enqueue (7): dequeue (): enqueue (9): enqueue (12): dequeue (): enqueue (10): Insert numbers in the following diagram to show what will be stored in the static queue after the operations have executed.

Short answer

**Answer:** The final state of the static queue is Q = [9, 12, 10].

Step-by-step solution

Start with an empty queue

Initially, the queue is empty: Q = []

Enqueue 5

Execute the first operation (enqueue 5) by adding the number 5 to the end of the queue: Q = [5]

Enqueue 7

Execute the second operation (enqueue 7) by adding the number 7 to the end of the queue: Q = [5, 7]

Dequeue

Execute the third operation (dequeue) by removing the first element (5) from the queue: Q = [7]

Enqueue 9

Execute the fourth operation (enqueue 9) by adding the number 9 to the end of the queue: Q = [7, 9]

Enqueue 12

Execute the fifth operation (enqueue 12) by adding the number 12 to the end of the queue: Q = [7, 9, 12]

Dequeue

Execute the sixth operation (dequeue) by removing the first element (7) from the queue: Q = [9, 12]

Enqueue 10

Execute the seventh operation (enqueue 10) by adding the number 10 to the end of the queue: Q = [9, 12, 10]

Final State of the Queue

The final state of the static queue after performing all the given operations is Q = [9, 12, 10].

Key concepts

Enqueue

Adding an element to a queue is known as 'Enqueue'. It is an operation that places the new item at the rear end of the queue. Think of it like lining up for the movies; each new person adds to the end of the line.

When you perform an enqueue operation, the item is inserted at the back, adhering to the First In, First Out (FIFO) principle. This means that the first element added will be the first one to leave the queue. During our example, when you enqueue 5, then 7, 9, and finally 12, each number is added consecutively to the rear end of the queue.

An important note here is that enqueueing does not affect or move the items currently in the queue; it simply appends the new element to the end. This operation is incredibly efficient in terms of time complexity since you don't have to traverse the entire queue to add a new element at the end.

Dequeue

The operation of removing an element from the queue is called 'Dequeue'. Just like letting the first person in line buy their movie ticket, the first element is removed from the front.

In the FIFO system, the dequeue operation ensures that the element which has been in the queue the longest gets removed first. From our example, after enqueue operations, when we perform a dequeue, the number 5 is the first to be removed. Later, after further operations, when you dequeue again, the number 7 gets removed because it was the front element at that point.

This operation is also efficient as it generally requires updating only a few elements' positions—whatever is necessary to adjust the front pointer to the next element in line. It ensures the end number of elements left in the queue remains unchanged after dequeuing.

Static Queue

A 'Static Queue' is a type of queue with a fixed size. This limit on the queue size means only a certain amount of elements can be stored at any given time. Static queues are often implemented using arrays which makes them space-efficient but inflexible in resizing.

In the context of our example, the operations all occur within a static queue. With operations like enqueue and dequeue, the array retains its maximum assigned size even though the number of elements in the queue may vary as elements are added and removed.

While static queues are straightforward and useful in many situations, their fixed size can be a limitation. If the queue becomes full, no additional elements can be added without removing one first. Thus, careful planning of the queue's maximum capacity is essential.