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Pairing function. Function uniquely mapping two numbers into a single number. In mathematics, a pairing function is a process to uniquely encode two natural numbers into a single natural number. [1] Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.
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 ...
similar to a set, multiset, map, or multimap, respectively, but implemented using a hash table; keys are not ordered, but a hash function must exist for the key type. These types were left out of the C++ standard; similar containers were standardized in C++11, but with different names (unordered_set and unordered_map). Other types of containers ...
[2] [3] [4] Functionally, the mutator pop can be interpreted as the pair of selectors (pick, rest), where rest returns the set consisting of all elements except for the arbitrary element. [5] Can be interpreted in terms of iterate. [a] map(F,S): returns the set of distinct values resulting from applying function F to each element of S.
The C++ Standard Library is based upon conventions introduced by the Standard Template Library (STL), and has been influenced by research in generic programming and developers of the STL such as Alexander Stepanov and Meng Lee. [4] [5] Although the C++ Standard Library and the STL share many features, neither is a strict superset of the other.
In C++, associative containers are a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. [ 1] Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard ...
In the above example, IIf is a ternary function, but not a ternary operator. As a function, the values of all three portions are evaluated before the function call occurs. This imposed limitations, and in Visual Basic .Net 9.0, released with Visual Studio 2008, an actual conditional operator was introduced, using the If keyword instead of IIf ...
A set with precisely two elements is also called a 2-set or (rarely) a binary set. An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple ...