← Goldman Sachs Interview Insights
I knew this one from practice but still fumbled the amortized complexity explanation.
Explain that a queue can be implemented using two stacks: an input stack for enqueue operations and an output stack for dequeue operations. When dequeuing, if the output stack is empty, transfer all elements from the input stack to the output stack, reversing their order, then pop from the output stack. This ensures FIFO order with amortized O(1) time per operation.
Pro tip: Emphasize the amortized O(1) time complexity and discuss edge cases like empty queue operations and handling multiple enqueues/dequeues. Mention that this approach is efficient and commonly used in practice, showing you understand trade-offs.
Ask if the queue should support standard operations (enqueue, dequeue, peek, isEmpty) and if there are any constraints on time or space complexity.
Explain that you'll use two stacks: one for enqueue (input) and one for dequeue (output). Enqueue pushes onto the input stack; dequeue pops from the output stack, transferring elements from input to output when output is empty.
Trace through a sequence of operations (e.g., enqueue 1,2,3; dequeue; enqueue 4; dequeue) to demonstrate how elements are transferred and order is maintained.
State that each element is moved at most twice (once to input, once to output), so enqueue is O(1) and dequeue is amortized O(1). Space complexity is O(n).
Mention handling empty queue operations (throw exception or return null), and note that if the queue is used in a multi-threaded environment, synchronization is needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.