Consider the following operation along with Enqueue and Dequeue operations on queues, where $k$ is a global parameter.MultiDequeue (Q) { m = k while (Q is not empty) and (m > 0) { Dequeue(Q) m = m - 1 } }What is the worst case time complexity of a sequence of $n$ queue operations on an initially empty queue?

We use aggregate (amortized) analysis to find the worst-case total time for a sequence of $n$ operations:

1. In any sequence of $n$ operations starting from an empty queue, the operations can be Enqueue, Dequeue, or MultiDequeue.

2. An element can be dequeued (either in standard Dequeue or inside MultiDequeue) at most once for each time it was enqueued.

3. Since there are at most $n$ operations in total, at most $n$ elements can ever be enqueued into the queue.

4. Consequently, the total number of element deletions across the entire sequence cannot exceed $n$.

5. Each operation takes $O(1)$ time in overhead plus $O(1)$ time per element dequeued.

6. Therefore, the total time for all $n$ operations combined is bounded by $O(n)$. Since each of the $n$ operations takes at least $\Omega(1)$ time, the worst-case total time is $\Theta(n)$.

Hence, the correct option is (A).