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Showing content from https://cplusplus.com/reference/iterator/ below:

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Iterator definitions

An iterator is any object that, pointing to some element in a range of elements (such as an array or a container), has the ability to iterate through the elements of that range using a set of operators (with at least the increment (++) and dereference (*) operators).

The most obvious form of iterator is a pointer: A pointer can point to elements in an array, and can iterate through them using the increment operator (++). But other kinds of iterators are possible. For example, each container type (such as a list) has a specific iterator type designed to iterate through its elements.

Notice that while a pointer is a form of iterator, not all iterators have the same functionality of pointers; Depending on the properties supported by iterators, they are classified into five different categories:

Iterator categories Iterators are classified into five categories depending on the functionality they implement:
Input and output iterators are the most limited types of iterators: they can perform sequential single-pass input or output operations.

Forward iterators have all the functionality of input iterators and -if they are not constant iterators- also the functionality of output iterators, although they are limited to one direction in which to iterate through a range (forward). All standard containers support at least forward iterator types.

Bidirectional iterators are like forward iterators but can also be iterated through backwards.

Random-access iterators implement all the functionality of bidirectional iterators, and also have the ability to access ranges non-sequentially: distant elements can be accessed directly by applying an offset value to an iterator without iterating through all the elements in between. These iterators have a similar functionality to standard pointers (pointers are iterators of this category).

The properties of each iterator category are:

category properties valid expressions all categories copy-constructible, copy-assignable and destructible

X b(a);

  b = a;

Can be incremented

++a

  a++

Random Access Bidirectional Forward Input Supports equality/inequality comparisons

a == b

  a != b

Can be dereferenced as an rvalue *a
a->m Output Can be dereferenced as an lvalue
(only for mutable iterator types) *a = t
*a++ = t default-constructible X a;
X() Multi-pass: neither dereferencing nor incrementing affects dereferenceability { b=a; *a++; *b; } Can be decremented --a
a--
*a-- Supports arithmetic operators + and - a + n
n + a
a - n
a - b Supports inequality comparisons (<, >, <= and >=) between iterators a < b
a > b
a <= b
a >= b Supports compound assignment operations += and -= a += n
a -= n Supports offset dereference operator ([]) a[n]

Where X is an iterator type, a and b are objects of this iterator type, t is an object of the type pointed by the iterator type, and n is an integer value.

For more details, see the references for input iterator, output iterator, forward iterator, bidirectional iterator and random-access iterator.

FunctionsIterator operations:

advance: Advance iterator (function template)

distance: Return distance between iterators (function template)

begin: Iterator to beginning (function template)

end: Iterator to end (function template)

prev: Get iterator to previous element (function template)

next: Get iterator to next element (function template)

Iterator generators:

back_inserter: Construct back insert iterator (function template)

front_inserter: Constructs front insert iterator (function template)

inserter: Construct insert iterator (function template)

make_move_iterator: Construct move iterator (function template)

Classes

iterator: Iterator base class (class template)

iterator_traits: Iterator traits (class template)

Predefined iterators

reverse_iterator: Reverse iterator (class template)

move_iterator: Move iterator (class template)

back_insert_iterator: Back insert iterator (class template)

front_insert_iterator: Front insert iterator (class template)

insert_iterator: Insert iterator (class template)

istream_iterator: Istream iterator (class template)

ostream_iterator: Ostream iterator (class template)

istreambuf_iterator: Input stream buffer iterator (class template)

ostreambuf_iterator: Output stream buffer iterator (class template)

Category tags

input_iterator_tag: Input iterator category (class)

output_iterator_tag: Output iterator category (class)

forward_iterator_tag: Forward iterator category (class)

bidirectional_iterator_tag: Bidirectional iterator category (class)

random_access_iterator_tag: Random-access iterator category (class)

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