I knew the queue approach pretty quickly but fumbled explaining why a running sum matters.
Start by clarifying the problem requirements, such as handling the initial window when fewer than N elements are present, and whether the window size is fixed. Then, propose an efficient solution using a queue and a running sum to achieve O(1) time per insertion. Finally, discuss edge cases and potential optimizations.
Pro tip: Mention that you would use a circular buffer to avoid the overhead of deque operations and to maintain constant space, showing awareness of performance-critical systems.
Ask about the expected behavior when the number of elements is less than the window size, and whether the window size can change. Confirm the data type of the stream and the return type.
Select a queue (or circular buffer) to store the last N elements and maintain a running sum. This allows O(1) time per insertion and O(N) space.
On each insertion, add the new value to the sum and enqueue it. If the queue size exceeds N, dequeue the oldest value and subtract it from the sum. Then return sum divided by the current queue size (or N if full).
Consider cases like N=0 (invalid), empty stream, and integer overflow. Discuss how to handle them (e.g., throw exception, return 0, use long for sum).
State that each insertion is O(1) time and O(N) space. Mention that this is optimal for the problem.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.