Hsets

Hsets are hash-based sets, a data structure used in computer science to store unique elements with fast access. They are typically implemented using a hash table or similar structure that maps elements to buckets. An Hset provides typical set operations such as add (insert), remove, and contains (membership test), with an emphasis on average-case constant time performance.

Key properties include that elements are unique within the collection and the structure is usually unordered. Iteration order is not guaranteed and may depend on the hash function and insertion sequence. The memory footprint includes storage for elements plus the hash table structure. Performance depends on the quality of the hash function and the load factor; operations are amortized to O(1), with worst-case O(n) in degenerate collision scenarios.

Implementation details involve how collisions are resolved, commonly via chaining (linked lists or trees in buckets) or open addressing. The table is resized when the load factor exceeds a threshold to maintain speed. Many programming languages implement Hsets as built-in types, often under the names HashSet or unordered_set. They typically require elements to be hashable and comparable for equality, aligning with the language’s hashing and equality rules.

Variants and related concepts distinguish hash-based from tree-based sets, the latter being ordered and offering logarithmic time guarantees and sorted iteration. Some Hsets support thread-safety or immutable/persistent variants, which preserve previous versions after updates.

Applications include deduplication, fast membership queries in graphs and databases, caches, and algorithms that rely on distinguishing distinct elements. See also: hash table, set (abstract data type), hash function, unordered collection.