27 Iterators library [iterators]

Iterators are a generalization of pointers that allow a C++ program to work with different data structures (containers) in a uniform manner.

To be able to construct template algorithms that work correctly and efficiently on different types of data structures, the library formalizes not just the interfaces but also the semantics and complexity assumptions of iterators.

An input iterator i supports the expression *i, resulting in a value of some object type T, called the value type of the iterator.

An output iterator i has a non-empty set of types that are writable to the iterator; for each such type T, the expression *i = o is valid where o is a value of type T.

An iterator i for which the expression (*i).m is well-defined supports the expression i->m with the same semantics as (*i).m.

For every iterator type X for which equality is defined, there is a corresponding signed integer type called the difference type of the iterator.

Since iterators are an abstraction of pointers, their semantics is a generalization of most of the semantics of pointers in C++.

This ensures that every function template that takes iterators works as well with regular pointers.

This International Standard defines five categories of iterators, according to the operations defined on them: input iterators, output iterators, forward iterators, bidirectional iterators and random access iterators, as shown in Table 88.

Forward iterators satisfy all the requirements of input iterators and can be used whenever an input iterator is specified; Bidirectional iterators also satisfy all the requirements of forward iterators and can be used whenever a forward iterator is specified; Random access iterators also satisfy all the requirements of bidirectional iterators and can be used whenever a bidirectional iterator is specified.

Iterators that further satisfy the requirements of output iterators are called mutable iterators.

Nonmutable iterators are referred to as constant iterators.

In addition to the requirements in this subclause, the nested typedef-names specified in [iterator.traits] shall be provided for the iterator type.

Iterators that further satisfy the requirement that, for integral values n and dereferenceable iterator values a and (a + n), *(a + n) is equivalent to *(addressof(*a) + n), are called contiguous iterators.

Just as a regular pointer to an array guarantees that there is a pointer value pointing past the last element of the array, so for any iterator type there is an iterator value that points past the last element of a corresponding sequence.

These values are called past-the-end values.

Values of an iterator i for which the expression *i is defined are called dereferenceable.

The library never assumes that past-the-end values are dereferenceable.

Iterators can also have singular values that are not associated with any sequence.

Results of most expressions are undefined for singular values; the only exceptions are destroying an iterator that holds a singular value, the assignment of a non-singular value to an iterator that holds a singular value, and, for iterators that satisfy the DefaultConstructible requirements, using a value-initialized iterator as the source of a copy or move operation.

In these cases the singular value is overwritten the same way as any other value.

Dereferenceable values are always non-singular.

An iterator j is called reachable from an iterator i if and only if there is a finite sequence of applications of the expression ++i that makes i == j.

If j is reachable from i, they refer to elements of the same sequence.

Most of the library's algorithmic templates that operate on data structures have interfaces that use ranges.

A range is a pair of iterators that designate the beginning and end of the computation.

A range [i, i) is an empty range; in general, a range [i, j) refers to the elements in the data structure starting with the element pointed to by i and up to but not including the element pointed to by j.

Range [i, j) is valid if and only if j is reachable from i.

The result of the application of functions in the library to invalid ranges is undefined.

All the categories of iterators require only those functions that are realizable for a given category in constant time (amortized).

Therefore, requirement tables for the iterators do not have a complexity column.

Destruction of an iterator may invalidate pointers and references previously obtained from that iterator.

An invalid iterator is an iterator that may be singular.261

In the following sections, a and b denote values of type X or const X, difference_­type and reference refer to the types iterator_­traits<X>​::​difference_­type and iterator_­traits<X>​::​reference, respectively, n denotes a value of difference_­type, u, tmp, and m denote identifiers, r denotes a value of X&, t denotes a value of value type T, o denotes a value of some type that is writable to the output iterator.