hash table

(data structure)

Definition: A dictionary in which keys are mapped to array positions by hash functions. Having the keys of more than one item map to the same position is called a collision. There are many collision resolution schemes, but they may be divided into open addressing, chaining, and keeping one special overflow area. Perfect hashing avoids collisions, but may be time-consuming to create.

Also known as scatter storage.

Specialization (... is a kind of me.)
perfect hashing, dynamic hashing, 2-left hashing, cuckoo hashing, 2-choice hashing, hashbelt.

Aggregate parent (I am a part of or used in ...)

Aggregate child (... is a part of or used in me.)
load factor, hash table delete, collision resolution: coalesced chaining, linear probing, double hashing, quadratic probing, uniform hashing, simple uniform hashing, separate chaining, direct chaining, clustering.

See also Bloom filter, huge sparse array.

Note: Complexity depends on the hash function and collision resolution scheme, but may be constant (Θ(1)) if the table is big enough or grows. Some open addressing schemes suffer from clustering more than others.

The table may be an array of buckets, to handle some numbers of collisions easily, but some provision must still be made for bucket overflow.

Author: PEB


direct chaining: (C). Bro. David Carlson's tutorial and code (C++). linear probing hashing: insert (C), look up (C). Direct chaining: explanations, diagrams, and code (Visual Basic). Mark Nelson's tutorial to using C++ Hash Table Memoization: [for] Simplifying Dynamic Programming (C++).

More information

explanation and example of hashing and various collision resolution techniques.

Historical Note
"The idea of hashing appears to have been originated by H. P. Luhn, who wrote an internal IBM memorandum in January 1953" [Knuth98, 3:547, Sect. 6.4]. He continues with more than a page of history.

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 20 April 2022.
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Cite this as:
Paul E. Black, "hash table", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 20 April 2022. (accessed TODAY) Available from: