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Circular buffer was the move and I got there eventually, but I spent an embarrassing amount of time second-guessing whether I needed a deque instead.
Use a circular buffer (or deque) to store the last N integers and maintain a running sum. For each new integer, add it to the sum, remove the oldest if the buffer exceeds N, and output the average as sum divided by the current count. This gives O(1) time per update and O(N) space.
Pro tip: Mention that this is a classic sliding window average problem and that the same pattern extends to weighted averages or exponential moving averages, which are common in ML feature pipelines. Also, clarify edge cases like N=1 or N=0 upfront to show attention to detail.
Confirm N is a positive integer, discuss behavior for N=0 or N=1, and whether the stream can contain negative numbers or floats. This ensures the solution is robust.
Select a circular buffer (fixed-size array with head/tail pointers) or a deque to efficiently add new elements and evict old ones in O(1) time.
Keep a variable for the sum of elements currently in the buffer. On each new integer, add it to the sum and subtract the evicted element if the buffer is full.
After updating the sum and buffer, output sum divided by the current number of elements (which is min(count, N)). Handle division by zero if no elements have arrived.
State that each update is O(1) time and O(N) space. Mention potential optimizations like using a fixed-size array for cache efficiency or handling floating-point precision.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and the desired weighting scheme, then propose a concrete redesign using exponentially decaying weights or a custom weight vector. Discuss the algorithmic changes, data structures, and trade-offs (time/space complexity, numerical stability, and implementation complexity) compared to the original solution.
Pro tip: Mention that exponential decay can be implemented efficiently with a running weighted sum and a decay factor, but be cautious about numerical underflow and consider periodic renormalization. Also, relate the choice to the business context—Atlassian values practical, scalable solutions.
Ask whether the weighting should apply to a fixed window (last N elements) or all history, and whether the decay rate is fixed or tunable. Confirm if the weights need to be normalized.
Decide between exponential decay (e.g., weight = α^(N-i)) and a custom weight vector (e.g., linear, polynomial, or learned weights). Justify the choice based on the use case and data characteristics.
Modify the original algorithm to incorporate weights. For exponential decay, use a running sum with a decay factor to achieve O(1) update and O(1) query. For custom weights, precompute the weight vector and compute the weighted sum over the window.
Compare time and space complexity, numerical stability, and ease of implementation. Discuss how the new approach affects latency, memory, and accuracy, and whether it scales with data volume.
Propose testing with synthetic and real data to tune parameters (e.g., decay factor) and validate performance. Mention monitoring and potential need for renormalization to avoid underflow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.