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.

EasyTechnical

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Describe a realistic inference-service scenario where you would trade increased memory usage for lower latency (e.g., caching precomputed embeddings or features). Explain how you would quantify the trade-off, what metrics you'd collect (hit rate, QPS, latency reduction), and how you would decide whether the additional memory allocation is justified given a cost or budget constraint.

MediumTechnical

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Compare Amdahl's Law and Gustafson's Law for parallel scalability. If 70% of a training job is perfectly parallelizable, compute theoretical speedup on 8 GPUs using both laws. Explain which law is more realistic for strong scaling vs weak scaling in machine learning workloads and why.

MediumTechnical

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Estimate the approximate GPU memory footprint for training a transformer with 24 layers, hidden size 1024, sequence length 512, vocabulary embeddings 50,000 x 1024, and batch size 8. Include parameter storage, optimizer states for Adam (assume 2x extra for m and v), and activations (assume activations must be stored for backprop). State assumptions clearly and show intermediate calculations.

HardSystem Design

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In synchronized distributed training, straggler workers slow the overall step time. Describe detection and mitigation strategies such as backup workers, elastic training, gradient compression, and asynchronous updates. For each strategy, model the trade-offs in terms of throughput, convergence stability, implementation complexity, and cost.

EasyTechnical

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Explain the difference between Big O, Big Theta, and Big Omega notation. Provide concrete examples of each using simple algorithms (e.g., linear search, binary search, insertion sort). State which bound describes worst, average, and best case, and discuss how constant factors and lower-order terms affect practical performance when translating asymptotic notation into real-world expectations.

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