Memoization

In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing in a general top-down parsing algorithm that accommodates ambiguity and left recursion in polynomial time and space. Although related to caching, memoization refers to a specific case of this optimization, distinguishing it from forms of caching such as buffering or page replacement. In the context of some logic programming languages, memoization is also known as tabling; see also lookup table.

The term "memoization" was coined by Donald Michie in 1968 and is derived from the Latin word "memorandum" ("to be remembered"), usually truncated as "memo" in the English language, and thus carries the meaning of "turning [the results of] a function into something to be remembered." While "memoization" might be confused with "memorization" (because they are etymological cognates), "memoization" has a specialized meaning in computing.

A memoized function "remembers" the results corresponding to some set of specific inputs. Subsequent calls with remembered inputs return the remembered result rather than recalculating it, thus eliminating the primary cost of a call with given parameters from all but the first call made to the function with those parameters. The set of remembered associations may be a fixed-size set controlled by a replacement algorithm or a fixed set, depending on the nature of the function and its use. A function can only be memoized if it is referentially transparent; that is, only if calling the function has exactly the same effect as replacing that function call with its return value. (Special case exceptions to this restriction exist, however.) While related to lookup tables, since memoization often uses such tables in its implementation, memoization populates its cache of results transparently on the fly, as needed, rather than in advance.

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