Tables

In computer science, a hash table, or a hash map, is a data structure that associates keys with values. The primary operation it supports efficiently is a lookup: given a key (e.g. a person's name), find the corresponding value (e.g. more...

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that person's telephone number). It works by transforming the key using a hash function into a hash, a number that the hash table uses to locate the desired value.

Time complexity and common uses of hash tables

Hash tables are often used to implement associative arrays, sets and caches. Like arrays, hash tables provide constant-time O(1) lookup on average, regardless of the number of items in the table. However, the rare worst-case lookup time can be as bad as O(n). Compared to other associative array data structures, hash tables are most useful when large numbers of records of data are to be stored, especially if the size of the data set can be predicted.

Hash tables may be used as in-memory data structures. Hash tables may also be adopted for use with persistent data structures; database indexes commonly use disk-based data structures based on hash tables.

In computer chess, a hash table is generally used to implement the transposition table.

Choosing a good hash function

A good hash function is essential for good hash table performance. A poor choice of hash function is likely to lead to clustering, in which probability of keys mapping to the same hash bucket (i.e. a collision) is significantly greater than would be expected from a random function. Nonzero probability of collisions is inevitable in any hash implementation, but usually the number of operations to resolve collisions scales linearly with the number of keys mapping to the same bucket, so excess collisions will degrade performance significantly. In addition, some hash functions are computationally expensive, so the amount of time (and, in some cases, memory) taken to compute the hash may be burdensome.

Choosing a good hash function is tricky. The literature is replete with poor choices, at least when measured by modern standards. For example, the very popular multiplicative hash advocated by Donald Knuth in The Art of Computer Programming (see reference below) has particularly poor clustering behavior. However, since poor hashing merely degrades hash table performance for particular input key distributions, such problems commonly go undetected.

The literature is similarly sparse on the criteria for choosing a hash function. Unlike most other fundamental algorithms and data structures, there is no universal consensus on what makes a "good" hash function. The remainder of this section is organized by three criteria: simplicity, speed, and strength, and will survey algorithms known to perform well by these criteria.

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