I started confidently with the two-heap setup and then kind of froze when they said 'now assume memory is the constraint.' My first instinct was to throw a quantile sketch at it and call it a day, but they pushed back immediately on accuracy guarantees.
Start by dissecting the memory bottlenecks of the two-heap approach: each element is stored, so memory grows linearly with stream size. Then propose a redesign that either bounds memory via approximation (e.g., sketches) or uses external storage with periodic compaction. Emphasize trade-offs between exactness, memory, and latency, and tailor the solution to the constraints.
Pro tip: Show awareness that Google often deals with massive data streams, so mention real-world systems like BigQuery or Dataflow and how they handle approximate quantiles. Also, discuss how you'd validate the solution with metrics like error bounds and throughput.
Explain that the two-heap approach stores all elements, leading to O(n) memory, and that rebalancing operations add overhead. Also note that for unbounded streams, memory will eventually exhaust.
Ask whether exact medians are required or if approximate is acceptable, and discuss memory constraints, latency, and accuracy trade-offs.
Suggest memory-efficient algorithms like t-digest, Greenwald-Khanna, or count-min sketch with a heap for approximate medians, highlighting their error guarantees.
If exact is needed, propose external sorting or storing data on disk with periodic merging, or using a distributed system with map-reduce to compute medians in batches.
Compare approaches on memory usage, accuracy, latency, and complexity, and recommend a solution based on the specific constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.