Explain the concept of Hash Tables and their collision resolution techniques.

Instruction: Discuss the structure of Hash Tables, how they function for data storage and retrieval, and explain at least two methods used to resolve collisions within them.

Context: This question is designed to test the candidate's understanding of Hash Tables, a fundamental data structure used for efficient data retrieval. Candidates should explain the basic principle of using hash functions to map keys to table indices and discuss collision scenarios where two keys hash to the same index. They are expected to describe at least two collision resolution techniques, such as chaining or open addressing, and explain how these methods work to maintain efficient access and storage in the face of collisions.

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Official answer

A hash table maps a key's hash to a bucket or probe sequence and stores key-value entries. Different keys can collide; a hash is not a unique identity. Lookup must compare keys according to the table's equality rule, and equal keys must have compatible hashes.

Two common collision strategies are separate chaining, where a bucket holds several entries, and open addressing, where colliding entries occupy other slots along a probe sequence. Chaining can use lists or other bucket structures. Open addressing needs a search procedure consistent with insertion and deletion; simply clearing a deleted slot can break a probe chain, so implementations use tombstones or a suitable repair strategy.

With suitable hashing and controlled load, operations can have expected O(1) cost; pathological collisions can make them O(n). Resizing also costs work, commonly accounted for amortized over updates. Keep hashing/equality costs in the model for long or complex keys.

Choose a load policy and probe strategy from the workload and security requirements. Open addressing can improve locality but is not universally more memory-efficient or faster. Test colliding keys, repeated updates, deletion, resizing and missing-key lookup, rather than assuming collisions are exceptional.

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