Algorithm That Synthesizes Other Algorithms for Hashing

A synthesized algorithm is guaranteed to be executable in constant time.

An algorithm that includes a collection of several subalgorithms has been devised as a means of synthesizing still other algorithms (which could include computer code) that utilize hashing to determine whether an element (typically, a number or other datum) is a member of a set (typically, a list of numbers). Each subalgorithm synthesizes an algorithm (e.g., a block of code) that maps a static set of key hashes to a somewhat linear monotonically increasing sequence of integers. The goal in formulating this mapping is to cause the length of the sequence thus generated to be as close as practicable to the original length of the set and thus to minimize gaps between the elements.