24 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. All input iterators i support the expression *i, resulting in a value of some object type T, called the value type of the iterator. All output iterators support the expression *i = o where o is a value of some type that is in the set of types that are writable to the particular iterator type of i. All iterators i for which the expression (*i).m is well-defined, support 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 [tab:iterators.relations].

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.

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. [ Example: After the declaration of an uninitialized pointer x (as with int* x;), x must always be assumed to have a singular value of a pointer.  — end example ] 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. [ Note: This guarantee is not offered for default initialization, although the distinction only matters for types with trivial default constructors such as pointers or aggregates holding pointers.  — end note ] 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.268

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. [ Note: For an iterator type X there must be an instantiation of iterator_traits<X> ([iterator.traits]).  — end note ]

The Iterator requirements form the basis of the iterator concept taxonomy; every iterator satisfies the Iterator requirements. This set of requirements specifies operations for dereferencing and incrementing an iterator. Most algorithms will require additional operations to read ([input.iterators]) or write ([output.iterators]) values, or to provide a richer set of iterator movements ([forward.iterators], [bidirectional.iterators], [random.access.iterators]).)

A type X satisfies the Iterator requirements if:

• (2.1)

  X satisfies the CopyConstructible, CopyAssignable, and Destructible requirements ([utility.arg.requirements]) and lvalues of type X are swappable ([swappable.requirements]), and

• (2.2)

  the expressions in Table [tab:iterator.requirements] are valid and have the indicated semantics.

A class or pointer type X satisfies the requirements of an input iterator for the value type T if X satisfies the Iterator ([iterator.iterators]) and EqualityComparable (Table [equalitycomparable]) requirements and the expressions in Table [tab:iterator.input.requirements] are valid and have the indicated semantics.

In Table [tab:iterator.input.requirements], the term the domain of == is used in the ordinary mathematical sense to denote the set of values over which == is (required to be) defined. This set can change over time. Each algorithm places additional requirements on the domain of == for the iterator values it uses. These requirements can be inferred from the uses that algorithm makes of == and !=. [ Example: the call find(a,b,x) is defined only if the value of a has the property p defined as follows: b has property p and a value i has property p if (*i==x) or if (*i!=x and ++i has property p).  — end example ]

[ Note: For input iterators, a == b does not imply ++a == ++b. (Equality does not guarantee the substitution property or referential transparency.) Algorithms on input iterators should never attempt to pass through the same iterator twice. They should be single pass algorithms. Value type T is not required to be a CopyAssignable type (Table [copyassignable]). These algorithms can be used with istreams as the source of the input data through the istream_iterator class template.  — end note ]

A class or pointer type X satisfies the requirements of an output iterator if X satisfies the Iterator requirements ([iterator.iterators]) and the expressions in Table [tab:iterator.output.requirements] are valid and have the indicated semantics.

[ Note: The only valid use of an operator* is on the left side of the assignment statement. Assignment through the same value of the iterator happens only once. Algorithms on output iterators should never attempt to pass through the same iterator twice. They should be single pass algorithms. Equality and inequality might not be defined. Algorithms that take output iterators can be used with ostreams as the destination for placing data through the ostream_iterator class as well as with insert iterators and insert pointers.  — end note ]

A class or pointer type X satisfies the requirements of a forward iterator if

• (1.1)

  X satisfies the requirements of an input iterator ([input.iterators]),

• (1.2)

  X satisfies the DefaultConstructible requirements ([utility.arg.requirements]),

• (1.3)

  if X is a mutable iterator, reference is a reference to T; if X is a const iterator, reference is a reference to const T,

• (1.4)

  the expressions in Table [tab:iterator.forward.requirements] are valid and have the indicated semantics, and

• (1.5)

  objects of type X offer the multi-pass guarantee, described below.

The domain of == for forward iterators is that of iterators over the same underlying sequence. However, value-initialized iterators may be compared and shall compare equal to other value-initialized iterators of the same type. [ Note: value initialized iterators behave as if they refer past the end of the same empty sequence  — end note ]

Two dereferenceable iterators a and b of type X offer the multi-pass guarantee if:

• (3.1)

  a == b implies ++a == ++b and

• (3.2)

  X is a pointer type or the expression (void)++X(a), *a is equivalent to the expression *a.

[ Note: The requirement that a == b implies ++a == ++b (which is not true for input and output iterators) and the removal of the restrictions on the number of the assignments through a mutable iterator (which applies to output iterators) allows the use of multi-pass one-directional algorithms with forward iterators.  — end note ]

If a and b are equal, then either a and b are both dereferenceable or else neither is dereferenceable.

If a and b are both dereferenceable, then a == b if and only if *a and *b are bound to the same object.

A class or pointer type X satisfies the requirements of a bidirectional iterator if, in addition to satisfying the requirements for forward iterators, the following expressions are valid as shown in Table [tab:iterator.bidirectional.requirements].

[ Note: Bidirectional iterators allow algorithms to move iterators backward as well as forward.  — end note ]

A class or pointer type X satisfies the requirements of a random access iterator if, in addition to satisfying the requirements for bidirectional iterators, the following expressions are valid as shown in Table [tab:iterator.random.access.requirements].

To implement algorithms only in terms of iterators, it is often necessary to determine the value and difference types that correspond to a particular iterator type. Accordingly, it is required that if Iterator is the type of an iterator, the types

iterator_traits<Iterator>::difference_type
iterator_traits<Iterator>::value_type
iterator_traits<Iterator>::iterator_category

be defined as the iterator's difference type, value type and iterator category, respectively. In addition, the types

iterator_traits<Iterator>::reference
iterator_traits<Iterator>::pointer

shall be defined as the iterator's reference and pointer types, that is, for an iterator object a, the same type as the type of *a and a->, respectively. In the case of an output iterator, the types

iterator_traits<Iterator>::difference_type
iterator_traits<Iterator>::value_type
iterator_traits<Iterator>::reference
iterator_traits<Iterator>::pointer

may be defined as void.

The template iterator_traits<Iterator> is defined as

namespace std {
  template<class Iterator> struct iterator_traits {
    typedef typename Iterator::difference_type difference_type;
    typedef typename Iterator::value_type value_type;
    typedef typename Iterator::pointer pointer;
    typedef typename Iterator::reference reference;
    typedef typename Iterator::iterator_category iterator_category;
  };
}

It is specialized for pointers as

namespace std {
  template<class T> struct iterator_traits<T*> {
    typedef ptrdiff_t difference_type;
    typedef T value_type;
    typedef T* pointer;
    typedef T& reference;
    typedef random_access_iterator_tag iterator_category;
  };
}

and for pointers to const as

namespace std {
  template<class T> struct iterator_traits<const T*> {
    typedef ptrdiff_t difference_type;
    typedef T value_type;
    typedef const T* pointer;
    typedef const T& reference;
    typedef random_access_iterator_tag iterator_category;
  };
}

[ Example: To implement a generic reverse function, a C++ program can do the following:

template <class BidirectionalIterator>
void reverse(BidirectionalIterator first, BidirectionalIterator last) {
  typename iterator_traits<BidirectionalIterator>::difference_type n =
    distance(first, last);
  --n;
  while(n > 0) {
    typename iterator_traits<BidirectionalIterator>::value_type
     tmp = *first;
    *first++ = *--last;
    *last = tmp;
    n -= 2;
  }
}

 — end example ]

The iterator template may be used as a base class to ease the definition of required types for new iterators.

namespace std {
  template<class Category, class T, class Distance = ptrdiff_t,
    class Pointer = T*, class Reference = T&>
  struct iterator {
    typedef T         value_type;
    typedef Distance  difference_type;
    typedef Pointer   pointer;
    typedef Reference reference;
    typedef Category  iterator_category;
  };
}

It is often desirable for a function template specialization to find out what is the most specific category of its iterator argument, so that the function can select the most efficient algorithm at compile time. To facilitate this, the library introduces category tag classes which are used as compile time tags for algorithm selection. They are: input_iterator_tag, output_iterator_tag, forward_iterator_tag, bidirectional_iterator_tag and random_access_iterator_tag. For every iterator of type Iterator, iterator_traits<Iterator>::iterator_category shall be defined to be the most specific category tag that describes the iterator's behavior.

namespace std {
  struct input_iterator_tag { };
  struct output_iterator_tag { };
  struct forward_iterator_tag: public input_iterator_tag { };
  struct bidirectional_iterator_tag: public forward_iterator_tag { };
  struct random_access_iterator_tag: public bidirectional_iterator_tag { };
}

[ Example: For a program-defined iterator BinaryTreeIterator, it could be included into the bidirectional iterator category by specializing the iterator_traits template:

template<class T> struct iterator_traits<BinaryTreeIterator<T> > {
  typedef std::ptrdiff_t difference_type;
  typedef T value_type;
  typedef T* pointer;
  typedef T& reference;
  typedef bidirectional_iterator_tag iterator_category;
};

Typically, however, it would be easier to derive BinaryTreeIterator<T> from iterator<bidirectional_iterator_tag,T,ptrdiff_t,T*,T&>.  — end example ]

[ Example: If evolve() is well defined for bidirectional iterators, but can be implemented more efficiently for random access iterators, then the implementation is as follows:

template <class BidirectionalIterator>
inline void
evolve(BidirectionalIterator first, BidirectionalIterator last) {
  evolve(first, last,
    typename iterator_traits<BidirectionalIterator>::iterator_category());
}

template <class BidirectionalIterator>
void evolve(BidirectionalIterator first, BidirectionalIterator last,
  bidirectional_iterator_tag) {
  // more generic, but less efficient algorithm
}

template <class RandomAccessIterator>
void evolve(RandomAccessIterator first, RandomAccessIterator last,
  random_access_iterator_tag) {
  // more efficient, but less generic algorithm
}

 — end example ]

[ Example: If a C++ program wants to define a bidirectional iterator for some data structure containing double and such that it works on a large memory model of the implementation, it can do so with:

class MyIterator :
  public iterator<bidirectional_iterator_tag, double, long, T*, T&> {
  // code implementing ++, etc.
};

Then there is no need to specialize the iterator_traits template.  — end example ]

Since only random access iterators provide + and - operators, the library provides two function templates advance and distance. These function templates use + and - for random access iterators (and are, therefore, constant time for them); for input, forward and bidirectional iterators they use ++ to provide linear time implementations.

template <class InputIterator, class Distance> void advance(InputIterator& i, Distance n);

Class template reverse_iterator is an iterator adaptor that iterates from the end of the sequence defined by its underlying iterator to the beginning of that sequence. The fundamental relation between a reverse iterator and its corresponding iterator i is established by the identity: &*(reverse_iterator(i)) == &*(i - 1).

To make it possible to deal with insertion in the same way as writing into an array, a special kind of iterator adaptors, called insert iterators, are provided in the library. With regular iterator classes,

while (first != last) *result++ = *first++;

causes a range [first,last) to be copied into a range starting with result. The same code with result being an insert iterator will insert corresponding elements into the container. This device allows all of the copying algorithms in the library to work in the insert mode instead of the regular overwrite mode.

An insert iterator is constructed from a container and possibly one of its iterators pointing to where insertion takes place if it is neither at the beginning nor at the end of the container. Insert iterators satisfy the requirements of output iterators. operator* returns the insert iterator itself. The assignment operator=(const T& x) is defined on insert iterators to allow writing into them, it inserts x right before where the insert iterator is pointing. In other words, an insert iterator is like a cursor pointing into the container where the insertion takes place. back_insert_iterator inserts elements at the end of a container, front_insert_iterator inserts elements at the beginning of a container, and insert_iterator inserts elements where the iterator points to in a container. back_inserter, front_inserter, and inserter are three functions making the insert iterators out of a container.

Class template move_iterator is an iterator adaptor with the same behavior as the underlying iterator except that its indirection operator implicitly converts the value returned by the underlying iterator's indirection operator to an rvalue reference. Some generic algorithms can be called with move iterators to replace copying with moving.

[ Example:

list<string> s;
// populate the list s
vector<string> v1(s.begin(), s.end());          // copies strings into v1
vector<string> v2(make_move_iterator(s.begin()),
                  make_move_iterator(s.end())); // moves strings into v2

 — end example ]

The class template istream_iterator is an input iterator ([input.iterators]) that reads (using operator>>) successive elements from the input stream for which it was constructed. After it is constructed, and every time ++ is used, the iterator reads and stores a value of T. If the iterator fails to read and store a value of T (fail() on the stream returns true), the iterator becomes equal to the end-of-stream iterator value. The constructor with no arguments istream_iterator() always constructs an end-of-stream input iterator object, which is the only legitimate iterator to be used for the end condition. The result of operator* on an end-of-stream iterator is not defined. For any other iterator value a const T& is returned. The result of operator-> on an end-of-stream iterator is not defined. For any other iterator value a const T* is returned. The behavior of a program that applies operator++() to an end-of-stream iterator is undefined. It is impossible to store things into istream iterators.

Two end-of-stream iterators are always equal. An end-of-stream iterator is not equal to a non-end-of-stream iterator. Two non-end-of-stream iterators are equal when they are constructed from the same stream.

namespace std {
  template <class T, class charT = char, class traits = char_traits<charT>,
      class Distance = ptrdiff_t>
  class istream_iterator:
    public iterator<input_iterator_tag, T, Distance, const T*, const T&> {
  public:
    typedef charT char_type;
    typedef traits traits_type;
    typedef basic_istream<charT,traits> istream_type;
    see below istream_iterator();
    istream_iterator(istream_type& s);
    istream_iterator(const istream_iterator& x) = default;
   ~istream_iterator() = default;

    const T& operator*() const;
    const T* operator->() const;
    istream_iterator<T,charT,traits,Distance>& operator++();
    istream_iterator<T,charT,traits,Distance>  operator++(int);
  private:
    basic_istream<charT,traits>* in_stream; // exposition only
    T value;                                // exposition only
  };

  template <class T, class charT, class traits, class Distance>
    bool operator==(const istream_iterator<T,charT,traits,Distance>& x,
            const istream_iterator<T,charT,traits,Distance>& y);
  template <class T, class charT, class traits, class Distance>
    bool operator!=(const istream_iterator<T,charT,traits,Distance>& x,
            const istream_iterator<T,charT,traits,Distance>& y);
}

ostream_iterator writes (using operator<<) successive elements onto the output stream from which it was constructed. If it was constructed with charT* as a constructor argument, this string, called a delimiter string, is written to the stream after every T is written. It is not possible to get a value out of the output iterator. Its only use is as an output iterator in situations like

while (first != last)
  *result++ = *first++;

ostream_iterator is defined as:

namespace std {
  template <class T, class charT = char, class traits = char_traits<charT> >
  class ostream_iterator:
    public iterator<output_iterator_tag, void, void, void, void> {
  public:
    typedef charT char_type;
    typedef traits traits_type;
    typedef basic_ostream<charT,traits> ostream_type;
    ostream_iterator(ostream_type& s);
    ostream_iterator(ostream_type& s, const charT* delimiter);
    ostream_iterator(const ostream_iterator<T,charT,traits>& x);
   ~ostream_iterator();
    ostream_iterator<T,charT,traits>& operator=(const T& value);

    ostream_iterator<T,charT,traits>& operator*();
    ostream_iterator<T,charT,traits>& operator++();
    ostream_iterator<T,charT,traits>& operator++(int);
  private:
    basic_ostream<charT,traits>* out_stream;  // exposition only
    const charT* delim;                       // exposition only
  };
}

The class template istreambuf_iterator defines an input iterator ([input.iterators]) that reads successive characters from the streambuf for which it was constructed. operator* provides access to the current input character, if any. [ Note: operator-> may return a proxy.  — end note ] Each time operator++ is evaluated, the iterator advances to the next input character. If the end of stream is reached (streambuf_type::sgetc() returns traits::eof()), the iterator becomes equal to the end-of-stream iterator value. The default constructor istreambuf_iterator() and the constructor istreambuf_iterator(0) both construct an end-of-stream iterator object suitable for use as an end-of-range. All specializations of istreambuf_iterator shall have a trivial copy constructor, a constexpr default constructor, and a trivial destructor.

The result of operator*() on an end-of-stream iterator is undefined. For any other iterator value a char_type value is returned. It is impossible to assign a character via an input iterator.

namespace std {
  template<class charT, class traits = char_traits<charT> >
  class istreambuf_iterator
     : public iterator<input_iterator_tag, charT,
                       typename traits::off_type, unspecified, charT> {
  public:
    typedef charT                         char_type;
    typedef traits                        traits_type;
    typedef typename traits::int_type     int_type;
    typedef basic_streambuf<charT,traits> streambuf_type;
    typedef basic_istream<charT,traits>   istream_type;

    class proxy;                          // exposition only

    constexpr istreambuf_iterator() noexcept;
    istreambuf_iterator(const istreambuf_iterator&) noexcept = default;
    ~istreambuf_iterator() = default;
    istreambuf_iterator(istream_type& s) noexcept;
    istreambuf_iterator(streambuf_type* s) noexcept;
    istreambuf_iterator(const proxy& p) noexcept;
    charT operator*() const;
    pointer operator->() const;
    istreambuf_iterator<charT,traits>& operator++();
    proxy operator++(int);
    bool equal(const istreambuf_iterator& b) const;
  private:
    streambuf_type* sbuf_;                // exposition only
  };

  template <class charT, class traits>
    bool operator==(const istreambuf_iterator<charT,traits>& a,
            const istreambuf_iterator<charT,traits>& b);
  template <class charT, class traits>
    bool operator!=(const istreambuf_iterator<charT,traits>& a,
            const istreambuf_iterator<charT,traits>& b);
}

The class template ostreambuf_iterator writes successive characters onto the output stream from which it was constructed. It is not possible to get a character value out of the output iterator.