In an ideal implementations of a queue, all operations are ______________________ . A. O(1) B. O(n) C. O(n2) D. it depends on the operation E. O(n log n)

To answer the question about the ideal implementations of a queue, we need to evaluate the time complexity for the basic operations typically performed in a queue, which are enqueue (adding an item), dequeue (removing an item), and sometimes peek (returning the item at the front without removing it).

1. Understanding Queue Operations:

   • Enqueue: Adding an element to the end of the queue.
   • Dequeue: Removing an element from the front of the queue.
   • Peek: Viewing the first element in the queue without removing it.

2. Time Complexity of Operations:

   • In an ideal queue implementation, both enqueue and dequeue operations can be performed in constant time, $O(1)$. This is achieved by using a linked list or a circular array.

3. Final Answer:

   • Since all basic operations of an ideal queue implementation (enqueue, dequeue, and peek) can be performed in constant time, the correct answer is A. O(1).