Advanced Data Structures and Implementation Questions

Deep and practical expertise in advanced data structures, their implementation details, performance characteristics, and selection for both algorithmic problems and production systems. Topics include arrays and dynamic arrays, strings, linked lists, stacks and queues, hash tables, heaps and priority queues, various tree forms including binary search trees and balanced trees, tries or prefix trees, segment trees and binary indexed trees or fenwick trees, union find or disjoint set union, suffix arrays, and advanced graph representations. Candidates should be able to implement core structures from first principles, demonstrate interfaces and invariants, reason about insertion deletion search traversal and iteration costs including worst case average case and amortized analysis, and discuss memory management and ownership in low level languages such as C and C plus plus as well as safe memory and reference use in managed languages. Evaluation also covers trade offs between contiguous and pointer based layouts, cache friendliness, concurrency considerations, selection of structures based on access patterns update frequency and memory constraints, handling of edge cases, testing and performance tuning for realistic inputs, and applying structures to problems such as top K queries prefix search connectivity range queries caches and union operations.

HardSystem Design

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You must design data structures to support neighborhood queries and incremental edge updates for large sparse graphs used in GNN training across multiple GPUs. Describe partitioning (edge-cut vs vertex-cut), storage formats (CSR/CSC/COO), halo exchange strategies, and how to maintain consistency and efficiency when edges are added/removed during training.

EasyTechnical

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Explain collision resolution strategies for hash tables (separate chaining, linear probing, quadratic probing, double hashing). For an AI feature store that maps strings (tokens) to IDs and needs fast lookups and inserts in memory, compare these strategies in terms of memory overhead, cache behavior, expected and worst-case lookup time, deletion handling, and resizing strategy. Recommend a strategy for low-latency lookups.

HardSystem Design

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Design an Approximate Nearest Neighbor (ANN) index for high-dimensional embeddings (dimensions ~ 512) that balances query latency (<10ms), memory footprint, and support for dynamic inserts/deletes. Compare HNSW, Product Quantization (IVF+PQ), and tree-based approaches. Propose a data-structure choice for a production embedding store and describe how you'd handle updates and sharding.

MediumTechnical

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Implement Disjoint Set Union (Union-Find) with rollbacks: support make_set, union(a,b), find(a), and snapshot()/rollback() to revert to a previous snapshot. This is useful for offline dynamic connectivity queries. Provide C++ implementation details and complexity analysis.

EasyTechnical

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Implement a dynamic array (vector) from first principles in C++ that supports: push_back, pop_back, operator[], size(), capacity(), reserve(n), and clear(). Use RAII for memory management, provide strong exception-safety guarantees, and ensure amortized O(1) push_back by using a doubling growth strategy. Describe iterator invalidation rules and how your implementation handles move semantics. Provide simple usage examples showing correctness.

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