GATE CS 2016 Set 1 Q10 — Arrays, Stacks and Queues

To implement a queue efficiently using an array, we use a circular array representation. This avoids the need to shift elements during insertion or deletion.

We maintain two pointers (or indices):

• front: Points to the element at the front of the queue.
• rear: Points to the element at the end of the queue.

Operations:

1. ENQUEUE: To insert an element, we advance the rear pointer circularly and place the element at that index:$$\text{rear} = (\text{rear} + 1) \pmod{\text{capacity}}$$This operation requires only a constant number of basic steps, taking $\mathcal{O}(1)$ time.
2. DEQUEUE: To remove an element, we retrieve the element at the front and advance the front pointer circularly:$$\text{front} = (\text{front} + 1) \pmod{\text{capacity}}$$This operation also requires only a constant number of basic steps, taking $\mathcal{O}(1)$ time.

Since both operations can be performed in constant time, Option A is the correct statement.