If a queue is implemented using two stacks, what is the worst-case time complexity for a single enqueue operation?O(1)O(n)O(log n)O(n log n)

1. Break Down the Problem

To determine the worst-case time complexity of a single enqueue operation when using two stacks to implement a queue, we need to analyze how enqueue operations are handled in this structure.

2. Relevant Concepts

When a queue is implemented using two stacks (let's call them Stack A and Stack B), the enqueue operation typically involves pushing elements onto Stack A. If Stack B is used to reverse elements when performing a dequeue operation, the enqueue time complexity should be observed.

3. Analysis and Detail

1. When performing an enqueue operation, you simply push the element onto Stack A. This operation has a time complexity of $O(1)$.
2. In the worst case, when you need to perform a dequeue operation, if Stack B is empty, you have to pop all elements from Stack A and push them onto Stack B (this reverses the order, behaving like a queue). This transfer operation has a time complexity of $O(n)$.
3. However, since the question specifically asks about the complexity of only the enqueue operation, we focus solely on that.
4. The worst-case time complexity must consider worst case scenarios over many operations rather than any single operation.

4. Verify and Summarize

• The enqueue operation itself is $O(1)$ because you're merely adding to Stack A.
• The context of performing a dequeue operation could exacerbate time complexity but does not affect that of the enqueue.

Final Answer

The worst-case time complexity for a single enqueue operation is O(1).