Data-Centric Algorithmic Problem Solving Questions
Foundational algorithm design and data-structure concepts with an emphasis on data-centric problem solving. Covers algorithmic paradigms (e.g., greedy, dynamic programming, divide-and-conquer, graph algorithms), data structures, complexity analysis, and practical approaches to solving computational problems using data.
MediumTechnical
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Implement an efficient Python function to compute pairwise cosine similarity between sparse high-dimensional vectors represented as dictionaries (index->value). Input: List[Dict[int, float]] of vectors. Output: list of pairs with similarity > threshold. Aim for efficiency using inverted index ideas.
MediumTechnical
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Explain Bloom filters: how they are constructed, how false positive probability depends on parameters (m bits, k hash functions, n inserted items), and example data-science use-cases where a Bloom filter is the right tool.
HardTechnical
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Compare optimization algorithms used for training models: SGD, mini-batch SGD, Momentum, RMSProp, Adam. Explain convergence behavior, sensitivity to learning rate, and why adaptive methods sometimes generalize worse than SGD. Suggest tuning heuristics for non-convex problems.
MediumTechnical
0 practiced
Implement reservoir sampling in Python to sample k items uniformly at random from a streaming source of unknown length. Signature: def reservoir_sample(stream: Iterable[Any], k: int) -> List[Any]Your algorithm should use O(k) memory and guarantee equal probability for each item.
EasyTechnical
0 practiced
Explain prefix sums (cumulative sums) and how they can be used to answer range sum queries in O(1) after O(n) preprocessing. Then extend the idea to 2D prefix sums and describe a use-case in image processing or heatmaps.
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