← Akuna Capital Interview Insights
I started with the obvious stuff: running sum and count for mean, a max-heap for maximum.
Start by clarifying requirements: streaming integers, need max, mean, and mode at any time. Propose a composite data structure: a max-heap for max, running sum and count for mean, and a hash map plus a frequency-ordered structure (e.g., bucket list or heap) for mode. Analyze each operation's time and space complexity, and discuss trade-offs between update and query efficiency.
Pro tip: Emphasize that mode is the trickiest: using a hash map alone gives O(1) update but O(distinct) query; a heap or bucket approach can give O(1) query at the cost of update complexity. Discuss the trade-off explicitly to show depth.
Ask about data volume, whether deletions are needed, and if queries are frequent. This determines whether to optimize for update or query.
Use a max-heap for O(log n) update and O(1) query for max; maintain running sum and count for O(1) update and query for mean.
Use a hash map to track frequencies. For efficient mode query, maintain a bucket list (array of sets) where index is frequency, or a max-heap of (frequency, value) pairs.
For each operation, state the complexity: e.g., update O(log n) for heap, O(1) for mean, O(1) for mode with bucket list; query O(1) for all. Space O(n).
Compare approaches: e.g., using a balanced BST for mode gives O(log n) update and query; bucket list gives O(1) but may need resizing. Mention potential concurrency issues if streaming.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Since the integer values are bounded within [1, 1001], use a fixed-size array of 1001 counters to tally frequencies, then scan the array to find the maximum frequency and the corresponding value(s). This approach runs in O(n) time and uses O(1) memory (1001 integers, independent of input size).
Pro tip: Mention that the memory is constant because the range is fixed, but if the range were huge or sparse, a hash map would be more memory-efficient. Also, clarify whether the mode should be the smallest value in case of ties, as that affects the final scan.
Confirm that the input is a stream or array of integers, and that values are guaranteed to be in [1, 1001]. Ask if the mode should be unique (e.g., smallest value in case of ties).
Select a fixed-size array (or list) of length 1002 (to accommodate indices 1 to 1001) to count occurrences. This avoids hash map overhead and ensures O(1) access.
Iterate through the input, incrementing the counter at the index equal to the value. This takes O(n) time.
Scan the frequency array from index 1 to 1001, tracking the maximum frequency and the corresponding value. If ties are allowed, collect all values with the maximum frequency.
State that the array uses 1001 integers, which is O(1) memory (constant, independent of n). In practice, this is about 4 KB if using 32-bit integers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I mentioned count-min sketch and heavy hitters algorithms.
Start by framing the problem: exact mode is impossible in one pass with limited memory, so we need an approximation algorithm. Discuss specific algorithms like Misra-Gries or Count-Min Sketch, explaining how they work and their guarantees. Then analyze the trade-offs between accuracy, memory, and update speed, and suggest how to choose parameters based on application needs.
Pro tip: Mention that for heavy hitters, Misra-Gries gives deterministic error bounds, while Count-Min Sketch is probabilistic but often more memory-efficient; showing awareness of both and when to use each demonstrates depth.
Ask about the data stream characteristics (e.g., frequency distribution, update rate) and the acceptable error tolerance. This determines whether a deterministic or probabilistic approach is better.
Select an algorithm like Misra-Gries (for frequent items) or Count-Min Sketch (for frequency estimation). Explain the core idea: maintaining a summary structure that uses sublinear memory.
For Misra-Gries, describe how counters are incremented and decremented, and how the final counters give candidates for heavy hitters. For Count-Min Sketch, explain how hashing and minimum over counters estimates frequencies, and how to find the max.
Discuss error bounds: Misra-Gries guarantees that any item with frequency > N/k is found, with error up to N/k. Count-Min Sketch provides probabilistic error bounds with parameters ε and δ. Trade-offs: more memory reduces error but increases cost; deterministic vs. probabilistic guarantees.
Suggest which algorithm to use given typical data science scenarios (e.g., real-time monitoring vs. offline analysis) and how to tune parameters (e.g., number of counters, hash functions) to balance accuracy and resources.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I started to feel the pressure.
Start by clarifying the data types and update pattern (streaming vs batch), then propose data structures tailored to each statistic: a monotonic deque for max, a running sum for mean, and a frequency map with a max-heap or bucket structure for mode. Explain how each updates in O(1) amortized time as the window slides, and discuss tie-breaking and empty window handling.
Pro tip: Emphasize that mode is the hardest to maintain efficiently; discuss the trade-off between exact O(1) updates with a heap and approximate or lazy deletion strategies. Also, mention that in practice, you might use a combination of data structures and that the choice depends on the query frequency and update rate.
Ask about data types (integers, floats, strings?), whether the window size k is fixed, and if updates are streaming or batch. Confirm that we need to support queries at any time, not just after each update.
Maintain a deque of indices with decreasing values. When a new element arrives, pop from the back while it's smaller, then push. When the window slides, remove indices that fall out. This gives O(1) amortized per update and O(1) query for max.
Keep a running sum of the window. On each update, add the new element and subtract the element leaving the window. Mean is sum/k (or sum/window_size if window not full). O(1) per update and query.
Maintain a frequency map of elements in the window. To get mode, use a max-heap keyed by frequency (with lazy deletion) or a bucket structure mapping frequency to set of elements. Update frequencies on add/remove. Discuss tie-breaking (e.g., smallest value, most recent, etc.) and empty window (return None or raise exception).
Summarize: max O(1) amortized, mean O(1), mode O(log n) with heap or O(1) with buckets if frequencies bounded. Discuss memory O(k). Mention that mode with ties may require additional logic and that exact mode maintenance can be costly; consider approximate algorithms if scale is large.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.