Associative array

Implementation

For dictionaries with very few mappings, it may make sense to implement the dictionary using an association list, which is a linked list of mappings. With this implementation, the time to perform the basic dictionary operations is linear in the total number of mappings. However, it is easy to implement and the constant factors in its running time are small.

Another very simple implementation technique, usable when the keys are restricted to a narrow range, is direct addressing into an array: the value for a given key k is stored at the array cell A[k], or if there is no mapping for k then the cell stores a special sentinel value that indicates the lack of a mapping. This technique is simple and fast, with each dictionary operation taking constant time. However, the space requirement for this structure is the size of the entire keyspace, making it impractical unless the keyspace is small.

The two major approaches for implementing dictionaries are a hash table or a search tree.

Hash table implementations

The most common general-purpose implementation of an associative array is a hash table: an array combined with a hash function that separates each key into a separate "bucket" of the array. The basic idea behind a hash table is that accessing an element of an array via its index is a simple, constant-time operation. Therefore, the average overhead of an operation for a hash table is only the computation of the key's hash, combined with accessing the corresponding bucket within the array. As such, hash tables usually perform in O(1) time, and usually outperform alternative implementations.

Hash tables must be able to handle collisions: the mapping by the hash function of two different keys to the same bucket of the array. The two most widespread approaches to this problem are separate chaining and open addressing. In separate chaining, the array does not store the value itself but stores a pointer to another container, usually an association list, that stores all the values matching the hash. By contrast, in open addressing, if a hash collision is found, the table seeks an empty spot in an array to store the value in a deterministic manner, usually by looking at the next immediate position in the array.

Open addressing has a lower cache miss ratio than separate chaining when the table is mostly empty. However, as the table becomes filled with more elements, open addressing's performance degrades exponentially. Additionally, separate chaining uses less memory in most cases, unless the entries are very small (less than four times the size of a pointer).

Tree implementations

Self-balancing binary search trees

Another common approach is to implement an associative array with a self-balancing binary search tree, such as an AVL tree or a red–black tree.

Compared to hash tables, these structures have both strengths and weaknesses. The worst-case performance of self-balancing binary search trees is significantly better than that of a hash table, with a time complexity in big O notation of O(log n). This is in contrast to hash tables, whose worst-case performance involves all elements sharing a single bucket, resulting in O(n) time complexity. In addition, and like all binary search trees, self-balancing binary search trees keep their elements in order. Thus, traversing its elements follows a least-to-greatest pattern, whereas traversing a hash table can result in elements being in seemingly random order. Because they are in order, tree-based maps can also satisfy range queries (find all values between two bounds) whereas a hashmap can only find exact values. However, hash tables have a much better average-case time complexity than self-balancing binary search trees of O(1), and their worst-case performance is highly unlikely when a good hash function is used.

A self-balancing binary search tree can be used to implement the buckets for a hash table that uses separate chaining. This allows for average-case constant lookup, but assures a worst-case performance of O(log n). However, this introduces extra complexity into the implementation and may cause even worse performance for smaller hash tables, where the time spent inserting into and balancing the tree is greater than the time needed to perform a linear search on all elements of a linked list or similar data structure.

Other trees

Associative arrays may also be stored in unbalanced binary search trees or in data structures specialized to a particular type of keys such as radix trees, tries, Judy arrays, or van Emde Boas trees, though the relative performance of these implementations varies. For instance, Judy trees have been found to perform less efficiently than hash tables, while carefully selected hash tables generally perform more efficiently than adaptive radix trees, with potentially greater restrictions on the data types they can handle. The advantages of these alternative structures come from their ability to handle additional associative array operations, such as finding the mapping whose key is the closest to a queried key when the query is absent in the set of mappings.

Comparison

Ordered dictionary

The basic definition of a dictionary does not mandate an order. To guarantee a fixed order of enumeration, ordered versions of the associative array are often used. There are two senses of an ordered dictionary:

• The order of enumeration is always deterministic for a given set of keys by sorting. This is the case for tree-based implementations, one representative being the std::map (a tree map) container of C++.
• The order of enumeration is key-independent and is instead based on the order of insertion. This is the case for the "ordered dictionary" in .NET Framework, the LinkedHashMap of Java and Python.

The latter is more common. Such ordered dictionaries can be implemented using an association list, by overlaying a doubly linked list on top of a normal dictionary, or by moving the actual data out of the sparse (unordered) array and into a dense insertion-ordered one.

Language support

Associative arrays can be implemented in any programming language as a package and many language systems provide them as part of their standard library. In some languages, they are not only built into the standard system, but have special syntax, often using array-like subscripting.

Built-in syntactic support for associative arrays was introduced in 1969 by SNOBOL4, under the name "table". TMG offered tables with string keys and integer values. MUMPS made multi-dimensional associative arrays, optionally persistent, its key data structure. SETL supported them as one possible implementation of sets and maps. Most modern scripting languages, starting with AWK and including Rexx, Perl, PHP, Tcl, JavaScript, Maple, Python, Ruby, Wolfram Language, Go, and Lua, support associative arrays as a primary container type. In many more languages, they are available as library functions without special syntax.

In Smalltalk, Objective-C, .NET, Python, REALbasic, Swift, VBA and Delphi they are called dictionaries; in Perl and Ruby they are called hashes; in C++, C#, Java, Go, Clojure, Scala, OCaml, Haskell they are called maps (see map (C++), unordered_map (C++), and Map); in Common Lisp and Windows PowerShell, they are called hash tables (since both typically use this implementation); in Maple and Lua, they are called tables. In PHP and R, all arrays can be associative, except that the keys are limited to integers and strings. In JavaScript (see also JSON), all objects behave as associative arrays with string-valued keys, while the Map and WeakMap types take arbitrary objects as keys. In Lua, they are used as the primitive building block for all data structures. In Visual FoxPro, they are called Collections. The D language also supports associative arrays.

Permanent storage

Many programs using associative arrays will need to store that data in a more permanent form, such as a computer file. A common solution to this problem is a generalized concept known as archiving or serialization, which produces a text or binary representation of the original objects that can be written directly to a file. This is most commonly implemented in the underlying object model, like .Net or Cocoa, which includes standard functions that convert the internal data into text. The program can create a complete text representation of any group of objects by calling these methods, which are almost always already implemented in the base associative array class.

For programs that use very large data sets, this sort of individual file storage is not appropriate, and a database management system (DB) is required. Some DB systems natively store associative arrays by serializing the data and then storing that serialized data and the key. Individual arrays can then be loaded or saved from the database using the key to refer to them. These key–value stores have been used for many years and have a history as long as that of the more common relational database (RDBs), but a lack of standardization, among other reasons, limited their use to certain niche roles. RDBs were used for these roles in most cases, although saving objects to a RDB can be complicated, a problem known as object-relational impedance mismatch.

After approximately 2010, the need for high-performance databases suitable for cloud computing and more closely matching the internal structure of the programs using them led to a renaissance in the key–value store market. These systems can store and retrieve associative arrays in a native fashion, which can greatly improve performance in common web-related workflows.