The two-stack trick is one of those things where you either know it or you sit there staring at the screen for an uncomfortable amount of time.
Start by clarifying the problem and constraints, then explain the two-stack approach where one stack handles enqueue and the other handles dequeue. Walk through the amortized O(1) analysis and discuss trade-offs.
Pro tip: Emphasize that while individual operations can be O(n), the amortized cost is O(1) because each element is moved at most once between stacks. This demonstrates understanding of amortized analysis, which is highly valued at Apple.
Confirm the operations needed (push, pop, peek, empty) and discuss any constraints like thread safety or memory limits.
Use one stack (inbox) for enqueue and another (outbox) for dequeue. When outbox is empty, transfer all elements from inbox to outbox.
For push, add to inbox. For pop/peek, if outbox is empty, move all from inbox to outbox, then pop/peek from outbox. For empty, check both stacks.
Explain that each element is moved at most once from inbox to outbox, so amortized time per operation is O(1). Space is O(n).
Mention alternatives like using a linked list or circular buffer, and compare performance characteristics.
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