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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.
To guarantee a fixed order of enumeration, ordered versions of the associative array are often used. There are two senses of an ordered dictionary: The order of enumeration is always deterministic for a given set of keys by sorting. This is the case for tree-based implementations, one representative being the <map> container of C++. [16]
In C++, the std::map class is templated which allows the data types of keys and values to be different for different map instances. For a given instance of the map class the keys must be of the same base type. The same must be true for all of the values.
The STL 'pair' can be assigned, copied and compared. The array of objects allocated in a map or hash_map (described below) are of type 'pair' by default, where all the 'first' elements act as the unique keys, each associated with their 'second' value objects. Sequences (arrays/linked lists): ordered collections vector
In C++, the Standard Template Library (STL) provides the set template class, which is typically implemented using a binary search tree (e.g. red–black tree); SGI's STL also provides the hash_set template class, which implements a set using a hash table. C++11 has support for the unordered_set template class, which is implemented using a hash ...
Objects may be accessed directly, by a language loop construct (e.g. for loop) or with an iterator. An associative container uses an associative array, map, or dictionary, composed of key-value pairs, such that each key appears at most once in the container. The key is used to find the value, the object, if it is stored in the container.
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As noted, what the axiom is saying is that, given two objects A and B, we can find a set C whose members are exactly A and B. We can use the axiom of extensionality to show that this set C is unique. We call the set C the pair of A and B, and denote it {A,B}. Thus the essence of the axiom is: Any two objects have a pair.