Question

Suppose the entries in a queue require one memory cell each, the head pointer contains the value 11 , and the tail pointer contains the value 17 . What are the values of these pointers after one entry is inserted and two are removed?

Short answer

Head pointer: 13, Tail pointer: 18.

Step-by-step solution

Understand the Initial State

Before any operations are performed, the head pointer is at position 11, and the tail pointer is at position 17. This means there are pointers indicating where entries are being removed (head) and added (tail) in the queue.

Inserting One Entry

When we insert an entry into the queue, the tail pointer is incremented by one, indicating that a new entry is added at the next available position. Therefore, the tail pointer moves from 17 to 18.

Removing Two Entries

Removing entries in a queue affects the head pointer. For each removal, the head pointer moves one position forward to indicate the next item to be processed is one memory cell further along. Since two items are removed, the head pointer moves from position 11 to 13.

Determine the Final Pointer Positions

After performing the insertion and removal operations, the head pointer ends at position 13, and the tail pointer ends at position 18.

Key concepts

Head Pointer

In a queue data structure, the head pointer plays a critical role. It indicates the position of the first element in the queue. The queue follows a First-In-First-Out (FIFO) order, meaning that the first element added will be the first one removed. Hence, the head pointer points to this element.
When an element is removed from the queue, the head pointer advances to the next position. Each movement of the head pointer corresponds to one removal operation. For example, if the head pointer is currently at 11 and two elements are removed, it shifts to 13. This change occurs as management of the queue respects the order the elements were inserted, ensuring seamless dequeue operations.
Understanding the role of the head pointer is vital to grasping the dynamic nature of queues. By progressing with each deletion, it ensures that elements in the queue are precisely managed for processing.

Tail Pointer

The tail pointer is another essential component in a queue data structure. It indicates the position where the next new element will be inserted. Contrary to the head pointer, which deals with removal, the tail pointer manages additions to the queue.
Every time a new element is added, the tail pointer advances by one position. For instance, assuming the tail pointer starts at 17 and one entry is added to the queue, it will move to position 18. This increment reflects the queue's growth by allocating memory for the new addition.
By tracking the tail position, one can decipher the queue's current status. It ensures the systematic addition of items, maintaining the integrity of the queue operations.

Queue Operations

Queue operations are fundamental tasks that dictate how data is handled in this data structure. The two primary operations are enqueue, which adds an element, and dequeue, which removes one.

• Enqueue: This operation enables you to insert a new item at the end of the queue. When performing enqueue, the tail pointer moves to the next available position. This orderly process ensures that the first elements added will be the first to be processed, maintaining the FIFO structure.


• Dequeue: This action removes the frontmost element from the queue. Consequently, the head pointer advances, indicating where the next removal will occur. In sequential operations, this method guarantees that the queue works smoothly, as elements are taken in order.

Both enqueue and dequeue are vital for the performance of any queue-based system, ensuring efficient management of operations in varied computational tasks.