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I knew the circular buffer approach but blanked on articulating why it was O(1) for a second.
Start by clarifying the requirements: the class should maintain a rolling average of the last k values from a stream, with O(1) time per insertion. Use a circular buffer (or queue) to store the last k values and maintain a running sum to compute the average in constant time. Discuss edge cases such as when fewer than k values have been seen and how to handle k=0.
Pro tip: Mention that you would use a fixed-size array for the circular buffer to avoid the overhead of dynamic resizing, and emphasize that this design is thread-safe if needed by using locks or atomic operations, which is crucial in ML pipelines where data streams may be concurrent.
Ask about the expected input types, whether k is fixed, and how to handle the initial phase when fewer than k values are available. Confirm that O(1) time per insertion is required and that space complexity should be O(k).
Choose a circular buffer (array of size k) to store the last k values and a variable to maintain the running sum. Explain that this allows O(1) updates by replacing the oldest value with the new one and adjusting the sum accordingly.
Describe the algorithm: if the buffer is full, subtract the oldest value from the sum, overwrite it with the new value, and add the new value to the sum. If not full, simply add the new value and increment the count. Then compute the average as sum divided by the current count (or k if full).
Discuss handling k=0 (return 0 or throw exception), negative k, and non-numeric inputs. Also mention how to handle the initial period when the buffer isn't full, ensuring the average is computed over the available values.
State that time complexity per insertion is O(1) and space is O(k). Compare with alternative approaches like using a queue with O(1) amortized time or a linked list, and explain why the circular buffer is optimal for fixed k.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.