Complexity Analysis and Performance Modeling Questions

Analyze algorithmic and system complexity including time and space complexity in asymptotic terms and real world performance modeling. Candidates should be fluent with Big O, Big Theta, and Big Omega notation and common complexity classes, and able to reason about average case versus worst case and trade offs between different algorithmic approaches. Extend algorithmic analysis into system performance considerations: estimate execution time, memory usage, I O and network costs, cache behavior, instruction and cycle counts, and power or latency budgets. Include methods for profiling, benchmarking, modeling throughput and latency, and translating asymptotic complexity into practical performance expectations for real systems.

MediumTechnical

69 practiced

Implement a memory-efficient Bloom filter in Python that supports add() and contains() with a target false-positive rate of 1% for 1,000,000 items. Show how to compute the optimal bit-array size m and number of hash functions k, provide working Python code using hashlib or mmh3, and analyze time/space complexity. Finally, discuss limitations of a Python implementation in production (GIL, memory overhead for bit arrays) and alternatives.

HardTechnical

69 practiced

Provide a formal amortized analysis (use either the accounting method or potential method) to show that appending to a dynamic array that doubles its capacity has O(1) amortized cost per append. Then analyze growth factors of 1.5 and 3: compute amortized cost and steady-state memory overhead, and discuss which growth factor you'd choose for a memory-constrained production system vs a performance-sensitive service.

HardTechnical

62 practiced

You have a custom convolution operator implemented in Python that takes ~500ms for a 3x3 conv on a 224×224 image. Outline the end-to-end steps to reimplement this operator in C++ with SIMD optimizations, integrate it into PyTorch as an ATen extension, and deploy it. For each step estimate expected types of speedups and how you would validate correctness and performance (unit tests, microbenchmarks, integration tests).

MediumTechnical

71 practiced

Compare exact k-NN (linear scan) to approximate nearest neighbor methods (HNSW, product quantization) for a low-latency recommendation system. For each approach analyze: time per query, index construction time, memory usage, update cost (dynamic inserts/deletes), expected recall, and operational trade-offs. Give situations where exact k-NN may still be preferable.

MediumTechnical

66 practiced

You are asked to lead a cross-functional effort to reduce end-to-end model inference latency by 50% over 6 months. Describe your plan: key metrics and KPIs, stakeholders and team composition, discovery and measurement phase, quick wins vs long-term technical investments (model compression, infra changes), resourcing, risk management, and how you will present progress and impact to executives.

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