Associative array

In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms, an associative array is a function with finite domain.^[1] It supports 'lookup', 'remove', and 'insert' operations.

The dictionary problem is the classic problem of designing efficient data structures that implement associative arrays.^[2] The two major solutions to the dictionary problem are hash tables and search trees.^[3]^[4]^[5]^[6] It is sometimes also possible to solve the problem using directly addressed arrays, binary search trees, or other more specialized structures.

Many programming languages include associative arrays as primitive data types, while many other languages provide software libraries that support associative arrays. Content-addressable memory is a form of direct hardware-level support for associative arrays.

Associative arrays have many applications including such fundamental programming patterns as memoization and the decorator pattern.^[7]

The name does not come from the associative property known in mathematics. Rather, it arises from the association of values with keys. It is not to be confused with associative processors.

^ Collins, Graham; Syme, Donald (1995). "A theory of finite maps". Higher Order Logic Theorem Proving and Its Applications. Lecture Notes in Computer Science. 971: 122–137. doi:10.1007/3-540-60275-5_61. ISBN 978-3-540-60275-0.
^ Andersson, Arne (1989). "Optimal Bounds on the Dictionary Problem". Proc. Symposium on Optimal Algorithms. Lecture Notes in Computer Science. 401. Springer Verlag: 106–114. doi:10.1007/3-540-51859-2_10. ISBN 978-3-540-51859-4.
^ Cite error: The named reference gt was invoked but never defined (see the help page).
^ Cite error: The named reference ms was invoked but never defined (see the help page).
^ Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001), "11 Hash Tables", Introduction to Algorithms (2nd ed.), MIT Press and McGraw-Hill, pp. 221–252, ISBN 0-262-03293-7.
^ Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., and Tarjan, R. E. 1994. "Dynamic Perfect Hashing: Upper and Lower Bounds" Archived 2016-03-04 at the Wayback Machine. SIAM J. Comput. 23, 4 (Aug. 1994), 738-761. http://portal.acm.org/citation.cfm?id=182370 doi:10.1137/S0097539791194094
^ Goodrich & Tamassia (2006), pp. 597–599.

[1] Collins, Graham; Syme, Donald (1995). "A theory of finite maps". Higher Order Logic Theorem Proving and Its Applications. Lecture Notes in Computer Science. 971: 122–137. doi:10.1007/3-540-60275-5_61. ISBN 978-3-540-60275-0.

[2] Andersson, Arne (1989). "Optimal Bounds on the Dictionary Problem". Proc. Symposium on Optimal Algorithms. Lecture Notes in Computer Science. 401. Springer Verlag: 106–114. doi:10.1007/3-540-51859-2_10. ISBN 978-3-540-51859-4.

[gt-3] Cite error: The named reference gt was invoked but never defined (see the help page).

[ms-4] Cite error: The named reference ms was invoked but never defined (see the help page).

[clrs-5] Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001), "11 Hash Tables", Introduction to Algorithms (2nd ed.), MIT Press and McGraw-Hill, pp. 221–252, ISBN 0-262-03293-7.

[dietzfelbinger-6] Dietzfelbinger, M., Karlin, A., Mehlhorn, K., Meyer auf der Heide, F., Rohnert, H., and Tarjan, R. E. 1994. "Dynamic Perfect Hashing: Upper and Lower Bounds" Archived 2016-03-04 at the Wayback Machine. SIAM J. Comput. 23, 4 (Aug. 1994), 738-761. http://portal.acm.org/citation.cfm?id=182370 doi:10.1137/S0097539791194094

[decorator-7] Goodrich & Tamassia (2006), pp. 597–599.

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