Simple Searching Techniques

Abstract

For a mapping or function to be represented by an array it is necessary that the domain type be both finite and of small enough cardinality to allow the allocation of a unique part of store for each array element. Likewise set structures, which have a small enough base type, are capable of an efficient bitstring representation in which an individual bit is allocated to each possible set element. Exceeding the restriction, as in the case of integer sets, necessitates an altogether different representation. However, in many applications the programmer cannot avoid requiring a structure representation for a function with large or infinite domain or for a set with large or infinite base type. A structural representation is only possible for sets that have only a small number of domain elements and for functions that map only a few values into significant range values. By ‘significant’ we mean differing from a specified null or default value. Such structures are known as sparse sets and arrays