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  ______________________________________________________________________

  23   Containers library                               [lib.containers]

  ______________________________________________________________________

1 This clause describes components that C++ programs may use to organize
  collections of information.

2 The  following  subclauses describe container requirements, and compo-
  nents for sequences and associative containers, as summarized in Table
  1:

                   Table 1--Containers library summary

         +------------------------------------------------------+
         |                Subclause                   Header(s) |
         +------------------------------------------------------+
         |_lib.container.requirements_ Requirements             |
         +------------------------------------------------------+
         |                                            <deque>   |
         |                                            <list>    |
         |_lib.sequences_ Sequences                   <queue>   |
         |                                            <stack>   |
         |                                            <vector>  |
         +------------------------------------------------------+
         |_lib.associative_ Associative containers    <map>     |
         |                                            <set>     |
         |_lib.template.bitset_ bitset                <bitset>  |
         +------------------------------------------------------+

  23.1  Container requirements              [lib.container.requirements]

1 Containers are objects that store other objects.  They control alloca-
  tion and deallocation of these objects through constructors,  destruc-
  tors, insert and erase operations.

2 All of the complexity requirements in this clause are stated solely in
  terms of the number of operations on the contained objects.  [Example:
  the copy constructor of type vector <vector<int> > has linear complex-
  ity, even though the complexity of copying each contained  vector<int>
  is itself linear.  ]

3 The  type of objects stored in these components must meet the require-
  ments of CopyConstructible types  (_lib.copyconstructible_),  and  the
  additional requirements of Assignable types.

4 In  Table  2,  T is the type used to instantiate the container, t is a
  value of T, and u is a value of (possibly const) T.

                     Table 2--Assignable requirements

            +------------------------------------------------+
            |expression   return type      post-condition    |
            +------------------------------------------------+
            |t = u        T&            t is equivalent to u |
            +------------------------------------------------+

5 In Table 3, X denotes a container class containing objects of type  T,
  a and b denote values of type X, u denotes an identifier and r denotes
  a value of X&.

                     Table 3--Container requirements

  ---------------------------------------------------------------------------------------------------
       expression               return type                   assertion/note            complexity
                                                            pre/post-condition
  ---------------------------------------------------------------------------------------------------
   X::value_type        T                             T is Assignable                  compile time
  ---------------------------------------------------------------------------------------------------
   X::reference         lvalue of T                                                    compile time
  ---------------------------------------------------------------------------------------------------
   X::const_reference   const lvalue of T                                              compile time
  ---------------------------------------------------------------------------------------------------
   X::iterator          iterator type pointing to T   any iterator category except     compile time
                                                      output iterator.
  ---------------------------------------------------------------------------------------------------
   X::const_iterator    iterator type pointing to     any iterator category except     compile time
                        const T                       output iterator.
  ---------------------------------------------------------------------------------------------------
   X::difference_type   signed integral type          is identical to the distance     compile time
                                                      type of X::iterator and
                                                      X::const_iterator
  ---------------------------------------------------------------------------------------------------
   X::size_type         unsigned integral type        size_type can represent any      compile time
                                                      non-negative value of differ-
                                                      ence_type
  ---------------------------------------------------------------------------------------------------
   X u;                                               post: u.size() == 0.             constant
  ---------------------------------------------------------------------------------------------------
   X();                                               X().size() == 0.                 constant
  ---------------------------------------------------------------------------------------------------
   X(a);                                              a == X(a).                       linear
  ---------------------------------------------------------------------------------------------------
   X u(a);                                            post: u == a.                    linear
   X u = a;                                           Equivalent to: X u; u = a;
  ---------------------------------------------------------------------------------------------------
   (&a)->~X();          void                          note: the destructor is ap-      linear
                                                      plied to every element of a;
                                                      all the memory is returned.
  ---------------------------------------------------------------------------------------------------
   a.begin();           iterator;                                                      constant
                        const_iterator
                        for constant a
  ---------------------------------------------------------------------------------------------------
   a.end();             iterator;                                                      constant
                        const_iterator
                        for constant a
  ---------------------------------------------------------------------------------------------------
   a == b               convertible to bool           == is an equivalence relation.   linear
                                                      a.size()==b.size()
                                                      && equal(a.begin(),

  |                                                                                                 |
  |                                                                                                 |
  |                                                                                                 |
  |                                                                                                 |
  |                                                   a.end(), b.begin())                           |
  +-------------------------------------------------------------------------------------------------+
  |a != b               convertible to bool           Equivalent to: !(a == b)         linear       |
  +-------------------------------------------------------------------------------------------------+
  |a.swap(b);           void                          swap(a,b)                        (Note A)     |
  +-------------------------------------------------------------------------------------------------+

  +---------------------------------------------------------------------------------+
  | expression      return type        operational      assertion/note   complexity |
  |                                     semantics     pre/post-condition            |
  +---------------------------------------------------------------------------------+
  |r = a        X&                                    post: r == a.      linear     |
  +---------------------------------------------------------------------------------+
  |a.size()     size_type           a.end()-a.begin()                    (Note A)   |
  +---------------------------------------------------------------------------------+
  |a.max_size() size_type           size() of the                        (Note A)   |
  |                                 largest possible                                |
  |                                 container.                                      |
  +---------------------------------------------------------------------------------+
  |a.empty()    convertible to bool a.size() == 0                        constant   |
  +---------------------------------------------------------------------------------+
  |a < b        convertible to bool lexicographical_  pre: < is defined  linear     |
  |                                 compare(a.be-     for values of T.              |
  |                                 gin(),            < is a total or-              |
  |                                 a.end(),b.be-     dering relation.              |
  |                                 gin(), b.end())                                 |
  +---------------------------------------------------------------------------------+
  |a > b        convertible to bool  b < a                               linear     |
  +---------------------------------------------------------------------------------+
  |a <= b       convertible to bool  !(a > b)                            linear     |
  +---------------------------------------------------------------------------------+
  |a >= b       convertible to bool  !(a < b)                            linear     |
  +---------------------------------------------------------------------------------+
  Notes: the algorithms swap(),  equal()  and  lexicographical_compare()
  are  defined in Clause _lib.algorithms_.  Those entries marked ``(Note
  A)'' should have constant complexity.

6 The member function size() returns the number of elements in the  con-
  tainer.   Its  semantics  is  defined  by  the  rules of constructors,
  inserts, and erases.

7 begin() returns an iterator referring to the first element in the con-
  tainer.  end() returns an iterator which is the past-the-end value for
  the container.  If the container is empty, then begin() == end();

8 Copy constructors for all container types defined in this clause  copy
  the  allocator  argument  from their respective first parameters.  All
  other constructors for these container types take an Allocator&  argu-
  ment  (_lib.allocator.requirements_).  A copy of this argument is used
  for any memory allocation performed, by these constructors and by  all
  member  functions,  during  the lifetime of each container object.  In
  all container types defined in this clause, the member get_allocator()
  returns  a  copy  of  the  Allocator  object  used  to  construct  the

  container.

9 If the iterator type of a container belongs to  the  bidirectional  or
  random  access  iterator categories (_lib.iterator.requirements_), the
  container is called reversible and satisfies the  additional  require-
  ments in Table 4:

                Table 4--Reversible container requirements

  +--------------------------------------------------------------------------------------------+
  |expression            return type                    assertion/note             complexity  |
  |                                                   pre/post-condition                       |
  +--------------------------------------------------------------------------------------------+
  |X::reverse_   iterator type pointing to T   reverse_iterator<iterator>         compile time |
  |iterator                                                                                    |
  +--------------------------------------------------------------------------------------------+
  |X::const_     iterator type pointing to     reverse_iterator<const_iterator>   compile time |
  |reverse_      const T                                                                       |
  |iterator                                                                                    |
  +--------------------------------------------------------------------------------------------+
  |a.rbegin()    reverse_iterator; const_re-   reverse_iterator(end())            constant     |
  |              verse_ iterator for con-                                                      |
  |              stant a                                                                       |
  +--------------------------------------------------------------------------------------------+
  |a.rend()      reverse_iterator; const_re-   reverse_iterator(begin())          constant     |
  |              verse_ iterator for con-                                                      |
  |              stant a                                                                       |
  +--------------------------------------------------------------------------------------------+

  23.1.1  Sequences                                [lib.sequence.reqmts]

1 A  sequence  is  a  kind  of  container that organizes a finite set of
  objects, all of the same type, into  a  strictly  linear  arrangement.
  The library provides three basic kinds of sequence containers: vector,
  list, and deque.  It also provides container  adaptors  that  make  it
  easy  to  construct abstract data types, such as stacks or queues, out
  of the basic sequence kinds (or out of other kinds of  sequences  that
  the user might define).

2 vector,  list,  and  deque  offer  the programmer different complexity
  trade-offs and should be used accordingly.   vector  is  the  type  of
  sequence  that  should  be  used by default.  list should be used when
  there are frequent insertions and deletions from  the  middle  of  the
  sequence.   deque is the data structure of choice when most insertions
  and deletions take place at  the  beginning  or  at  the  end  of  the
  sequence.

3 In Tables 5 and 6, X denotes a sequence class, a denotes value of X, i
  and j denote iterators satisfying input iterator requirements, [i,  j)
  denotes  a  valid  range,  n denotes a value of X::size_type, p and q2
  denote valid iterators to a, q and  q1  denote  valid  dereferenceable

  iterators  to a, [q1, q2) denotes a valid range, and t denotes a value
  of X::value_type.

4 The complexities of the expressions are sequence dependent.

        Table 5--Sequence requirements (in addition to container)

  +------------------------------------------------------------------------------------+
  |  expression      return type                   assertion/note                      |
  |                                               pre/post-condition                   |
  +------------------------------------------------------------------------------------+
  |X(n, t)                         post: size() == n.                                  |
  |X a(n, t);                      constructs a sequence with n copies of t.           |
  +------------------------------------------------------------------------------------+
  |X(i, j)                         post: size() == distance between i and j.           |
  |X a(i, j);                      constructs a sequence equal to the range [i,j).     |
  +------------------------------------------------------------------------------------+
  |a.insert(p,t)     iterator      inserts a copy of t before p.                       |
  +------------------------------------------------------------------------------------+
  |a.insert(p,n,t)   void          inserts n copies of t before p.                     |
  +------------------------------------------------------------------------------------+
  |a.insert(p,i,j)   void          inserts copies of elements in [i,j) before p.       |
  +------------------------------------------------------------------------------------+
  |a.erase(q)        iterator      erases the element pointed to by q.                 |
  +------------------------------------------------------------------------------------+
  |a.erase(q1,q2)    iterator      erases the elements in the range [q1,q2).           |
  +------------------------------------------------------------------------------------+
  |a.clear()         void          erase(begin(), end())                               |
  |                                post: size() == 0.                                  |
  +------------------------------------------------------------------------------------+

5 iterator and const_iterator types for sequences must be  at  least  of
  the forward iterator category.

6 The  iterator  returned  from  a.insert(p,t)  points  to the copy of t
  inserted into a.

7 The iterator returned from a.erase(q) points to  the  element  immedi-
  ately  following q prior to the element being erased.  If no such ele-
  ment exists, a.end() is returned.

8 The iterator returned by a.erase(q1,q2) points to the element  pointed
  to  by  q2  prior  to  any  elements being erased.  If no such element
  exists, a.end() is returned.

9 The operations in Table 6 are provided only  for  the  containers  for
  which they take constant time:

                  Table 6--Optional sequence operations

  +-----------------------------------------------------------------------------+
  |  expression     return type          operational             container      |
  |                                       semantics                             |
  +-----------------------------------------------------------------------------+
  |a.front()       T&; const T&     *a.begin()              vector, list, deque |
  |                for constant a                                               |
  +-----------------------------------------------------------------------------+
  |a.back()        T&; const T&     *--a.end()              vector, list, deque |
  |                for constant a                                               |
  +-----------------------------------------------------------------------------+
  |a.push_front(x) void             a.insert(a.begin(),x)   list, deque         |
  +-----------------------------------------------------------------------------+
  |a.push_back(x)  void             a.insert(a.end(),x)     vector, list, deque |
  +-----------------------------------------------------------------------------+
  |a.pop_front()   void             a.erase(a.begin())      list, deque         |
  +-----------------------------------------------------------------------------+
  |a.pop_back()    void             a.erase(--a.end())      vector, list, deque |
  +-----------------------------------------------------------------------------+
  |a[n]            T&; const T&     *(a.begin() + n)        vector, deque       |
  |                for constant a                                               |
  +-----------------------------------------------------------------------------+
  |a.at(n)         T&; const T&     *(a.begin() + n)        vector, deque       |
  |                for constant a                                               |
  +-----------------------------------------------------------------------------+

10The  member  function at() provides bounds-checked access to container
  elements.  at() throws out_of_range if n >= a.size().

  23.1.2  Associative containers                [lib.associative.reqmts]

1 Associative containers provide an ability for fast retrieval  of  data
  based  on  keys.  The library provides four basic kinds of associative
  containers: set, multiset, map and multimap.

2 Each associative containers is parameterized on Key  and  an  ordering
  relation  Compare  that induces a strict weak ordering (_lib.alg.sort-
  ing_) on elements of Key.  In addition, map and multimap associate  an
  arbitrary  type  T with the Key.  The object of type Compare is called
  the comparison object of a container.  This comparison object may be a
  pointer  to  function or an object of a type with an appropriate func-
  tion call operator.

3 The phrase ``equivalence of  keys''  means  the  equivalence  relation
  imposed  by  the  comparison and not the operator== on keys.  That is,
  two keys k1 and k2 are considered to be equivalent if for the compari-
  son object comp, comp(k1, k2) == false && comp(k2, k1) == false.

4 An  associative  container  supports  unique keys if it may contain at
  most one element for each  key.   Otherwise,  it  supports  equivalent

  keys.  set and map support unique keys.  multiset and multimap support
  equal keys.

5 For set and multiset the value type is the same as the key type.   For
  map and multimap it is equal to pair<const Key, T>.

6 iterator  of an associative container is of the bidirectional iterator
  category.

7 In Table 7, X is an associative container class, a is a  value  of  X,
  a_uniq  is  a  value  of  X when X supports unique keys, and a_eq is a
  value of X when X supports multiple keys, i and j satisfy input itera-
  tor  requirements  and  refer  to  elements of value_type, [i, j) is a
  valid range, p and q2 are valid iterators to a, q  and  q1  are  valid
  dereferenceable  iterators  to  a,  [q1,  q2) is a valid range, t is a
  value of X::value_type and k is a value of X::key_type.

  Table 7--Associative container requirements (in addition to container)

  +-----------------------------------------------------------------------------------+
  |  expression    return type              assertion/note               complexity   |
  |                                       pre/post-condition                          |
  +-----------------------------------------------------------------------------------+
  |X::key_type    Key            Key is Assignable                     compile time   |
  +-----------------------------------------------------------------------------------+
  |X::key_compare Compare        defaults to less<key_type>            compile time   |
  +-----------------------------------------------------------------------------------+
  |X:: value_com- a binary pred- is the same as key_compare for set    compile time   |
  |pare           icate type     and multiset; is an ordering relation                |
  |                              on pairs induced by the first compo-                 |
  |                              nent (i.e. Key) for map and multimap.                |
  +-----------------------------------------------------------------------------------+
  |X(c)                          constructs an empty container;        constant       |
  |X a(c);                       uses c as a comparison object                        |
  +-----------------------------------------------------------------------------------+
  |X()                           constructs an empty container;        constant       |
  |X a;                          uses Compare() as a comparison object                |
  +-----------------------------------------------------------------------------------+
  |X(i,j,c);                     constructs an empty container and in- NlogN in gen-  |
  |X a(i,j,c);                   serts elements from the range [i, j)  eral (N is the |
  |                              into it; uses c as a comparison ob-   distance from  |
  |                              ject                                  i to j);       |
  |                                                                    linear if [i,  |
  |                                                                    j) is sorted   |
  |                                                                    with val-      |
  |                                                                    ue_comp()      |
  +-----------------------------------------------------------------------------------+
  |X(i, j)                       same as above, but uses Compare() as  same as above  |
  |                              a comparison object.                                 |
  |X a(i, j);                                                                         |
  +-----------------------------------------------------------------------------------+
  |a.key_comp()   X::key_compare returns the comparison object out of  constant       |
  |                              which a was constructed.                             |
  +-----------------------------------------------------------------------------------+
  |a.value_comp() X:: value_com- returns an object of value_compare    constant       |
  |               pare           constructed out of the comparison ob-                |
  |                              ject                                                 |
  +-----------------------------------------------------------------------------------+
  |a_uniq.  in-   pair<iterator, inserts t if and only if there is no  logarithmic    |
  |sert(t)        bool>          element in the container with key                    |
  |                              equivalent to the key of t.  The bool                |
  |                              component of the returned pair indi-                 |
  |                              cates whether the insertion takes                    |
  |                              place and the iterator component of                  |
  |                              the pair points to the element with                  |
  |                              key equivalent to the key of t.                      |
  +-----------------------------------------------------------------------------------+

  -----------------------------------------------------------------------------------------
      expression     return type             assertion/note                complexity
                                           pre/post-condition
  -----------------------------------------------------------------------------------------
   a_eq.insert(t)   iterator       inserts t and returns the iterator  logarithmic
                                   pointing to the newly inserted ele-
                                   ment.
  -----------------------------------------------------------------------------------------
   a.insert(p,t)    iterator       inserts t if and only if there is   logarithmic in
                                   no element with key equivalent to   general, but amor-
                                   the key of t in containers with     tized constant if
                                   unique keys; always inserts t in    t is inserted
                                   containers with equivalent keys.    right after p.
                                   always returns the iterator point-
                                   ing to the element with key equiva-
                                   lent to the key of t.  iterator p
                                   is a hint pointing to where the in-
                                   sert should start to search.
  -----------------------------------------------------------------------------------------
   a.insert(i,j)    void           inserts the elements from the range Nlog(size()+N) (N
                                   [i, j) into the container.          is the distance
                                                                       from i to j) in
                                                                       general;
                                                                       linear if [i, j)
                                                                       is sorted accord-
                                                                       ing to val-
                                                                       ue_comp()
  -----------------------------------------------------------------------------------------
   a.erase(k)       size_type      erases all the elements in the con- log(size()) +
                                   tainer with key equivalent to k.    count(k)
                                   returns the number of erased ele-
                                   ments.
  -----------------------------------------------------------------------------------------
   a.erase(q)       void           erases the element pointed to by q. amortized constant
  -----------------------------------------------------------------------------------------
   a.erase(q1,q2)   void           erases all the elements in the      log(size())+ N
                                   range [q1, q2).                     where N is the
                                                                       distance from q1
                                                                       to q2.
  -----------------------------------------------------------------------------------------
   a.clear()        void           erase(s.begin, s.end))              log(size()) + N
                                   post: size == 0
  -----------------------------------------------------------------------------------------
   a.find(k)        iterator; con- returns an iterator pointing to an  logarithmic
                    st_iterator    element with the key equivalent to
                    for constant a k, or a.end() if such an element is
                                   not found.
  -----------------------------------------------------------------------------------------
   a.count(k)       size_type      returns the number of elements with log(size()) +
                                   key equivalent to k                 count(k)
  -----------------------------------------------------------------------------------------
   a.lower_bound(k) iterator; con-                                     logarithmic
                    st_iterator

  |                                                                                       |
  |                                                                                       |
  |                                                                                       |
  |                                                                                       |
  |                 for constant a than k.                                                |
  +---------------------------------------------------------------------------------------+
  |a.upper_bound(k) iterator; con- returns an iterator pointing to the logarithmic        |
  |                 st_iterator    first element with key greater than                    |
  |                 for constant a k.                                                     |
  +---------------------------------------------------------------------------------------+
  |a.equal_range(k) pair< itera-   equivalent to make_pair(            logarithmic        |
  |                 tor,iterator>;     a.lower_bound(k),                                  |
  |                 pair< con-         a.upper_bound(k)).                                 |
  |                 st_iterator,                                                          |
  |                 const_itera-                                                          |
  |                 tor> for con-                                                         |
  |                 stant a                                                               |
  +---------------------------------------------------------------------------------------+

8 The  fundamental  property  of  iterators of associative containers is
  that they iterate through the containers in the  non-descending  order
  of  keys  where  non-descending  is defined by the comparison that was
  used to construct them.  For any two dereferenceable iterators i and j
  such that distance from i to j is positive,
    value_comp(*j, *i) == false

9 For  associative  containers  with  unique keys the stronger condition
  holds,
    value_comp(*i, *j) != false.

10When an associative container is constructed by passing  a  comparison
  object  the  container  shall  not store a pointer or reference to the
  passed object, even if that object is passed by  reference.   When  an
  associative  container is copied, either through a copy constructor or
  an assignment operator, the target container shall then use  the  com-
  parison  object from the container being copied, as if that comparison
  object had been passed to the target container in its constructor.

  23.2  Sequences                                        [lib.sequences]

1 Headers <deque>, <list>, <queue>, <stack>, and <vector>.

  Header <deque> synopsis

  namespace std {
    template <class T, class Allocator = allocator<T> > class deque;
    template <class T, class Allocator>
      bool operator==(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      void swap(deque<T,Allocator>& x, deque<T,Allocator>& y);
  }

  Header <list> synopsis

  namespace std {
    template <class T, class Allocator = allocator<T> > class list;
    template <class T, class Allocator>
      bool operator==(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      void swap(list<T,Allocator>& x, list<T,Allocator>& y);
  }

  Header <queue> synopsis

  namespace std {
    template <class T, class Container = deque<T> > class queue;
    template <class T, class Container>
      bool operator==(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator< (const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator!=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator> (const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator>=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator<=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container = vector<T>,
              class Compare = less<Container::value_type> >
    class priority_queue;
  }

  Header <stack> synopsis

  namespace std {
    template <class T, class Container = deque<T> > class stack;
    template <class T, class Container>
      bool operator==(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator< (const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator!=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator> (const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator>=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator<=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
  }

  Header <vector> synopsis

  namespace std {
    template <class T, class Allocator = allocator<T> > class vector;
    template <class T, class Allocator>
      bool operator==(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      void swap(vector<T,Allocator>& x, vector<T,Allocator>& y);

    template <class Allocator = allocator<bool> > class vector<bool,Allocator>;
    template <class Allocator>
      bool operator==(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator< (const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator!=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator> (const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator>=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator<=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      void swap(vector<bool,Allocator>& x, vector<bool,Allocator>& y);
  }

  23.2.1  Template class deque                               [lib.deque]

1 A deque is a kind of sequence that, like a vector (_lib.vector_), sup-
  ports random access iterators.  In addition, it supports constant time
  insert and erase operations at the beginning or the  end;  insert  and
  erase  in the middle take linear time.  That is, a deque is especially
  optimized for pushing and popping elements at the beginning  and  end.
  As with vectors, storage management is handled automatically.

2 A  deque  satisfies  all  of  the requirements of a container and of a
  reversible  container   (given   in   tables   in   clause   _lib.con-
  tainer.requirements_)  and  of  a  sequence,  including  the  optional
  sequence requirements (_lib.sequence.reqmts_).  Descriptions are  pro-
  vided  here only for operations on deque that are not described in one

  of these tables or for operations where there is  additional  semantic
  information.
  namespace std {
    template <class T, class Allocator = allocator<T> >
    class deque {
    public:
    // types:
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef T                                         value_type;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
    // _lib.deque.cons_ construct/copy/destroy:
      explicit deque(const Allocator& = Allocator());
      explicit deque(size_type n, const T& value = T(),
          const Allocator& = Allocator());
      template <class InputIterator>
        deque(InputIterator first, InputIterator last,
              const Allocator& = Allocator());
      deque(const deque<T,Allocator>& x);
     ~deque();
      deque<T,Allocator>& operator=(const deque<T,Allocator>& x);
      template <class InputIterator>
        void assign(InputIterator first, InputIterator last);
      template <class Size, class T>
        void assign(Size n, const T& t = T());
      allocator_type get_allocator() const;
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // _lib.deque.capacity_ capacity:
      size_type size() const;
      size_type max_size() const;
      void      resize(size_type sz, T c = T());
      bool      empty() const;

    // element access:
      reference       operator[](size_type n);
      const_reference operator[](size_type n) const;
      reference       at(size_type n);
      const_reference at(size_type n) const;
      reference       front();
      const_reference front() const;
      reference       back();
      const_reference back() const;
    // _lib.deque.modifiers_ modifiers:
      void push_front(const T& x);
      void push_back(const T& x);
      iterator insert(iterator position, const T& x = T());
      void     insert(iterator position, size_type n, const T& x);
      template <class InputIterator>
        void insert (iterator position, InputIterator first, InputIterator last);
      void pop_front();
      void pop_back();
      iterator erase(iterator position);
      iterator erase(iterator first, iterator last);
      void     swap(deque<T,Allocator>&);
      void     clear();
    };
    template <class T, class Allocator>
      bool operator==(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const deque<T,Allocator>& x, const deque<T,Allocator>& y);
    // specialized algorithms:
    template <class T, class Allocator>
      void swap(deque<T,Allocator>& x, deque<T,Allocator>& y);
  }

  23.2.1.1  deque constructors, copy, and               [lib.deque.cons]
       assignment

  explicit deque(const Allocator& = Allocator());

  Effects:
    Constructs an empty deque, using the specified allocator.
  Complexity:
    Constant.

  explicit deque(size_t n, const T& value = T(),
                 const Allocator& = Allocator());

  Effects:
    Constructs a deque with n copies of value, using the specified allo-
    cator.
  Complexity:
    Linear in n.

  template <class InputIterator>
    deque(InputIterator first, InputIterator last,
          const Allocator& = Allocator());

  Effects:
    Constructs  a  deque equal to the the range [first, last), using the
    specified allocator.
  Complexity:
    If the iterators first and last are forward iterators, bidirectional
    iterators,  or  random access iterators the constructor makes only N
    calls to the copy constructor, and performs no reallocations,  where
    N  is last - first.  It makes at most 2N calls to the copy construc-
    tor of T and log N reallocations if they are input iterators.1)

  template <class InputIterator>
    void assign(InputIterator first, InputIterator last);

  Effects:
        erase(begin(), end());
        insert(begin(), first, last);

  template <class Size, class T> void assign(Size n, const T& t = T());

  Effects:
        erase(begin(), end());
        insert(begin(), n, t);

  23.2.1.2  deque capacity                          [lib.deque.capacity]

  void resize(size_type sz, T c = T());

  Effects:

  _________________________
  1) The complexity is greater in the case of  input  iterators  because
  each element must be added individually: it is impossible to determine
  the distance between first abd last before doing the copying.

        if (sz > size())
          insert(end(), sz-size(), c);
        else if (sz < size())
          erase(begin()+sz, end());
        else
          ; // do nothing

  23.2.1.3  deque modifiers                        [lib.deque.modifiers]

  iterator insert(iterator position, const T& x = T());
  void     insert(iterator position, size_type n, const T& x);
  template <class InputIterator>
    void insert(iterator position,
                InputIterator first, InputIterator last);

  Effects:
    An insert in the middle of the deque invalidates all  the  iterators
    and references to elements of the deque.  An insert at either end of
    the deque invalidates all the iterators to the  deque,  but  has  no
    effect on the validity of references to elements of the deque.
  Complexity:
    In  the  worst  case,  inserting a single element into a deque takes
    time linear in the minimum of the distance from the insertion  point
    to  the  beginning  of the deque and the distance from the insertion
    point to the end of the deque.  Inserting a single element either at
    the  beginning  or  end  of  a  deque always takes constant time and
    causes a single call to the copy constructor of T.

  iterator erase(iterator position);
  iterator erase(iterator first, iterator last);

  Effects:
    An erase in the middle of the deque invalidates  all  the  iterators
    and references to elements of the deque.   An erase at either end of
    the deque invalidates only the iterators and the references  to  the
    erased elements.
  Complexity:
    The  number  of calls to the destructor is the same as the number of
    elements erased, but the number of the calls to the assignment oper-
    ator  is  at  most  equal  to  the minimum of the number of elements
    before the erased elements and  the  number  of  element  after  the
    erased elements.

  23.2.1.4  deque specialized algorithms             [lib.deque.special]

  template <class T, class Allocator>
    void swap(deque<T,Allocator>& x, deque<T,Allocator>& y);

  Effects:
        x.swap(y);

  23.2.2  Template class list                                 [lib.list]

1 A list is a kind of sequence that supports bidirectional iterators and
  allows constant time insert and erase operations anywhere  within  the
  sequence,  with storage management handled automatically.  Unlike vec-
  tors (_lib.vector_) and deques (_lib.deque_), fast  random  access  to
  list  elements is not supported, but many algorithms only need sequen-
  tial access anyway.

2 A list satisfies all of the requirements  of  a  container  and  of  a
  reversible  container  (given in two tables in _lib.container.require-
  ments_) and of a sequence, including most of the the optional sequence
  requirements  (_lib.sequence.reqmts_).   The exceptions are the opera-
  tor[]  and at member functions, which are not provided.2) Descriptions
  are provided here only for operations on list that are  not  described
  in  one  of  these  tables or for operations where there is additional
  semantic information.
  namespace std {
    template <class T, class Allocator = allocator<T> >
    class list {
    public:
    // types:
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef T                                         value_type;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
    // _lib.list.cons_ construct/copy/destroy:
      explicit list(const Allocator& = Allocator());
      explicit list(size_type n, const T& value = T(),
                    const Allocator& = Allocator());
      template <class InputIterator>
        list(InputIterator first, InputIterator last,
             const Allocator& = Allocator());
      list(const list<T,Allocator>& x);
     ~list();
      list<T,Allocator>& operator=(const list<T,Allocator>& x);
      template <class InputIterator>
        void assign(InputIterator first, InputIterator last);
      template <class Size, class T>
        void assign(Size n, const T& t = T());
      allocator_type get_allocator() const;

  _________________________
  2) These member functions are only provided by containers whose itera-
  tors are random access iterators.

    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // _lib.list.capacity_ capacity:
      bool      empty() const;
      size_type size() const;
      size_type max_size() const;
      void      resize(size_type sz, T c = T());
    // element access:
      reference       front();
      const_reference front() const;
      reference       back();
      const_reference back() const;
    // _lib.list.modifiers_ modifiers:
      void push_front(const T& x);
      void pop_front();
      void push_back(const T& x);
      void pop_back();
      iterator insert(iterator position, const T& x = T());
      void     insert(iterator position, size_type n, const T& x);
      template <class InputIterator>
        void insert(iterator position, InputIterator first,
                    InputIterator last);
      iterator erase(iterator position);
      iterator erase(iterator position, iterator last);
      void     swap(list<T,Allocator>&);
      void     clear();
    // _lib.list.ops_ list operations:
      void splice(iterator position, list<T,Allocator>& x);
      void splice(iterator position, list<T,Allocator>& x, iterator i);
      void splice(iterator position, list<T,Allocator>& x, iterator first,
                  iterator last);
      void remove(const T& value);
      template <class Predicate> void remove_if(Predicate pred);
      void unique();
      template <class BinaryPredicate> void unique(BinaryPredicate binary_pred);
      void merge(list<T,Allocator>& x);
      template <class Compare> void merge(list<T,Allocator>& x, Compare comp);
      void sort();
      template <class Compare> void sort(Compare comp);
      void reverse();
    };

    template <class T, class Allocator>
      bool operator==(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const list<T,Allocator>& x, const list<T,Allocator>& y);
    // specialized algorithms:
    template <class T, class Allocator>
      void swap(list<T,Allocator>& x, list<T,Allocator>& y);
  }

  23.2.2.1  list constructors, copy, and assignment      [lib.list.cons]

  explicit list(const Allocator& = Allocator());

  Effects:
    Constructs an empty list, using the specified allocator.
  Complexity:
    Constant.

  explicit list(size_type n, const T& value = T(),
                const Allocator& = Allocator());

  Effects:
    Constructs  a list with n copies of value, using the specified allo-
    cator.
  Complexity:
    Linear in n.

  template <class InputIterator>
  list(InputIterator first, InputIterator last,
       const Allocator& = Allocator());

  Effects:
    Constructs a list equal to the range [first, last).
  Complexity:
    Linear in first - last.

  template <class InputIterator>
    void assign(InputIterator first, InputIterator last);

  Effects:

        erase(begin(), end());
        insert(begin(), first, last);

  template <class Size, class T> void assign(Size n, const T& t = T());

  Effects:
        erase(begin(), end());
        insert(begin(), n, t);

  23.2.2.2  list capacity                            [lib.list.capacity]

  void resize(size_type sz, T c = T());

  Effects:
        if (sz > size())
          insert(end(), sz-size(), c);
        else if (sz < size())
          erase(begin()+sz, end());
        else
          ; // do nothing

  23.2.2.3  list modifiers                          [lib.list.modifiers]

  iterator insert(iterator position, const T& x = T());
  void     insert(iterator position, size_type n, const T& x);
  template <class InputIterator>
    void insert(iterator position, InputIterator first,
                InputIterator last);

  Notes:
    Does not affect the validity of iterators and references.
  Complexity:
    Insertion of a single element into a list takes  constant  time  and
    exactly  one call to the copy constructor of T.  Insertion of multi-
    ple elements into a  list  is  linear  in  the  number  of  elements
    inserted,  and  the  number of calls to the copy constructor of T is
    exactly equal to the number of elements inserted.

  iterator erase(iterator position);
  iterator erase(iterator first, iterator last);

  Effects:
    Invalidates only the iterators and references  to  the  erased  ele-
    ments.
  Complexity:
    Erasing  a single element is a constant time operation with a single
    call to the destructor of T.  Erasing a range in a  list  is  linear
    time  in  the  size  of  the  range  and  the number of calls to the
    destructor of type T is exactly equal to the size of the range.

  23.2.2.4  list operations                               [lib.list.ops]

1 Since lists allow fast insertion and erasing  from  the  middle  of  a
  list, certain operations are provided specifically for them.

2 list provides three splice operations that destructively move elements
  from one list to another.

  void splice(iterator position, list<T,Allocator>& x);

  Requires:
    &x != this.
  Effects:
    Inserts the contents of x before position and x becomes empty.
  Complexity:
    Constant time.

  void splice(iterator position, list<T,Allocator>& x, iterator i);

  Effects:
    Inserts an element pointed to by i from list x before  position  and
    removes  the element from x.  The result is unchanged if position ==
    i or position == ++i.
  Requires:
    i is a valid dereferenceable iterator of x.
  Complexity:
    Constant time.

  void splice(iterator position, list<T,Allocator>& x, iterator first,
              iterator last);

  Effects:
    Inserts elements in the range  [first,  last)  before  position  and
    removes the elements from x.
  Requires:
    [first,  last)  is  a  valid range in x.  The result is undefined if
    position is an iterator in the range [first, last).
  Complexity:
    Constant time if &x == this; otherwise, linear time.

                             void remove(const T& value);
  template <class Predicate> void remove_if(Predicate pred);

  Effects:
    Erases all the elements in the list referred by a  list  iterator  i
    for  which  the  following conditions hold: *i == value, pred(*i) !=
    false.
  Notes:
    Stable:  the relative order of the elements that are not removed  is

    the same as their relative order in the original list.
  Complexity:
    Exactly size() applications of the corresponding predicate.

                                   void unique();
  template <class BinaryPredicate> void unique(BinaryPredicate binary_pred);

  Effects:
    Eliminates all but the first element from every consecutive group of
    equal elements referred to by the iterator i in the range  [first  +
    1,  last)  for which *i == *(i-1) (for the version of unique with no
    arguments) or pred(*i, *(i - 1)) (for the version of unique  with  a
    predicate argument) holds.
  Complexity:
    If the range (last - first) is not empty, exactly (last - first) - 1
    applications of the corresponding predicate, otherwise  no  applica-
    tions of the predicate.

  void   merge(list<T,Allocator>& x);
  template <class Compare> void merge(list<T,Allocator>& x, Compare comp);

  Requires:
    comp  defines  a  strict  weak ordering (_lib.alg.sorting_), and the
    list and the argument list are both sorted according to this  order-
    ing.
  Effects:
    Merges the argument list into the list.
  Notes:
    Stable:  for equivalent elements in the two lists, the elements from
    the list always precede the elements from the argument list.   x  is
    empty after the merge.
  Complexity:
    At most size() + x.size() - 1 comparisons.

  void reverse();

  Effects:
    Reverses the order of the elements in the list.
  Complexity:
    Linear time.

                           void sort();
  template <class Compare> void sort(Compare comp);

  Requires:
    operator<  (for  the first version, or comp (for the second version)
    defines a strict weak ordering (_lib.alg.sorting_).
  Effects:
    Sorts the list according to the  operator<  or  a  Compare  function

    object.
  Notes:
    Stable:  the relative order of the equivalent elements is preserved.
  Complexity:
    Approximately NlogN comparisons, where N == size().

  23.2.2.5  list specialized algorithms               [lib.list.special]

  template <class T, class Allocator>
    void swap(list<T,Allocator>& x, list<T,Allocator>& y);

  Effects:
        x.swap(y);

  23.2.3  Container adapters                    [lib.container.adapters]

1 The container adapters each take a Container template  parameter,  and
  each constructor takes a Container reference argument.  This container
  is copied into the Container member of each adapter.

  23.2.3.1  Template class queue                             [lib.queue]

1 Any sequence supporting operations front(),  back(),  push_back()  and
  pop_front()  can  be  used  to instantiate queue.  In particular, list
  (_lib.list_) and deque (_lib.deque_) can be used.
  nmespace std {
    template <class T, class Container = deque<T> >
    class queue {
    public:
      typedef typename Container::value_type            value_type;
      typedef typename Container::size_type             size_type;
      typedef typename Container                        container_type;
    protected:
      Container c;
    public:
      explicit queue(const Container& = Container());

      bool      empty() const             { return c.empty(); }
      size_type size()  const             { return c.size(); }
      value_type&       front()           { return c.front(); }
      const value_type& front() const     { return c.front(); }
      value_type&       back()            { return c.back(); }
      const value_type& back() const      { return c.back(); }
      void push(const value_type& x)      { c.push_back(x); }
      void pop()                          { c.pop_front(); }
    };

    template <class T, class Container>
      bool operator==(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator< (const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator!=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator> (const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator>=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
    template <class T, class Container>
      bool operator<=(const queue<T, Container>& x,
                      const queue<T, Container>& y);
  }
  operator==
  Returns:
    x.c == y.c.
    operator<
  Returns:
    x.c < y.c.

  23.2.3.2  Template class priority_queue           [lib.priority.queue]

1 Any sequence with random access  iterator  and  supporting  operations
  front(),  push_back() and pop_back() can be used to instantiate prior-
  ity_queue.    In   particular,   vector   (_lib.vector_)   and   deque
  (_lib.deque_) can be used.  Instantiating priority_queue also involves
  supplying a function or function object for  making  priority  compar-
  isons;  the  library  assumes  that  the  function  or function object
  defines a strict weak ordering (_lib.alg.sorting_).
  namespace std {
    template <class T, class Container = vector<T>,
              class Compare = less<Container::value_type> >
    class priority_queue {
    public:
      typedef typename Container::value_type            value_type;
      typedef typename Container::size_type             size_type;
      typedef typename Container                        container_type;
    protected:
      Container c;
      Compare comp;
    public:
      explicit priority_queue(const Compare& x = Compare(),
                              const Container& = Container());
      template <class InputIterator>
        priority_queue(InputIterator first, InputIterator last,
                       const Compare& x = Compare(),
                       const Container& = Container());

      bool      empty() const       { return c.empty(); }
      size_type size()  const       { return c.size(); }
      const value_type& top() const { return c.front(); }
      void push(const value_type& x);
      void pop();
    };
    // no equality is provided
  }

  23.2.3.2.1  priority_queue constructors            [lib.priqueue.cons]

  priority_queue(const Compare& x = Compare(),
                 const Container& y = Container());

  Requires:
    x defines a strict weak ordering (_lib.alg.sorting_).
  Effects:
    Initializes comp with x and c  with  y;  calls  make_heap(c.begin(),
    c.end(), comp).

  template <class InputIterator>
    priority_queue(InputIterator first, InputIterator last,
                   const Compare& x = Compare(),
                   const Container& y = Container());

  Requires:
    x defines a strict weak ordering (_lib.alg.sorting_).
  Effects:
    Initializes c with y and comp with x; calls c.insert(c.end(), first,
    last); and finally calls make_heap(c.begin(), c.end(), comp).

  23.2.3.2.2  priority_queue members              [lib.priqueue.members]

  void push(const value_type& x);

  Effects:
            c.push_back(x);
            push_heap(c.begin(), c.end(), comp);

  void pop();

  Effects:
            pop_heap(c.begin(), c.end(), comp);
            c.pop_back();

  23.2.3.3  Template class stack                             [lib.stack]

1 Any sequence supporting operations back(), push_back() and  pop_back()
  can  be  used  to instantiate stack.  In particular, vector (_lib.vec-
  tor_), list (_lib.list_) and deque (_lib.deque_) can be used.
  namespace std {
    template <class T, class Container = deque<T> >
    class stack {
    public:
      typedef typename Container::value_type            value_type;
      typedef typename Container::size_type             size_type;
      typedef typename Container                        container_type;
    protected:
      Container c;
    public:
      explicit stack(const Container& = Container());

      bool      empty() const             { return c.empty(); }
      size_type size()  const             { return c.size(); }
      value_type&       top()             { return c.back(); }
      const value_type& top() const       { return c.back(); }
      void push(const value_type& x)      { c.push_back(x); }
      void pop()                          { c.pop_back(); }
    };
    template <class T, class Container>
      bool operator==(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator< (const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator!=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator> (const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator>=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
    template <class T, class Container>
      bool operator<=(const stack<T, Container>& x,
                      const stack<T, Container>& y);
  }

  23.2.4  Template class vector                             [lib.vector]

1 A vector is a kind of sequence that supports random access  iterators.
  In  addition,  it  supports (amortized) constant time insert and erase
  operations at the end; insert and erase  in  the  middle  take  linear
  time.   Storage  management is handled automatically, though hints can
  be given to improve efficiency.

2 A vector satisfies all of the requirements of a  container  and  of  a
  reversible      container      (given     in     two     tables     in

  _lib.container.requirements_) and of a sequence, including most of the
  optional  sequence  requirements  (_lib.sequence.reqmts_).  The excep-
  tions are the push_front and pop_front member functions, which are not
  provided.   Descriptions are provided here only for operations on vec-
  tor that are not described in one of these tables  or  for  operations
  where there is additional semantic information.
  namespace std {
    template <class T, class Allocator = allocator<T> >
    class vector {
    public:
    // types:
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef T                                         value_type;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
    // _lib.vector.cons_ construct/copy/destroy:
      explicit vector(const Allocator& = Allocator());
      explicit vector(size_type n, const T& value = T(),
          const Allocator& = Allocator());
      template <class InputIterator>
        vector(InputIterator first, InputIterator last,
          const Allocator& = Allocator());
      vector(const vector<T,Allocator>& x);
     ~vector();
      vector<T,Allocator>& operator=(const vector<T,Allocator>& x);
      template <class InputIterator>
        void assign(InputIterator first, InputIterator last);
      template <class Size, class U> void assign(Size n, const U& u = U());
      allocator_type get_allocator() const;
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // _lib.vector.capacity_ capacity:
      size_type size() const;
      size_type max_size() const;
      void      resize(size_type sz, T c = T());
      size_type capacity() const;
      bool      empty() const;
      void      reserve(size_type n);

    // element access:
      reference       operator[](size_type n);
      const_reference operator[](size_type n) const;
      const_reference at(size_type n) const;
      reference       at(size_type n);
      reference       front();
      const_reference front() const;
      reference       back();
      const_reference back() const;
    // _lib.vector.modifiers_ modifiers:
      void push_back(const T& x);
      void pop_back();
      iterator insert(iterator position, const T& x = T());
      void     insert(iterator position, size_type n, const T& x);
      template <class InputIterator>
          void insert(iterator position, InputIterator first, InputIterator last);
      iterator erase(iterator position);
      iterator erase(iterator first, iterator last);
      void     swap(vector<T,Allocator>&);
      void     clear();
    };
    template <class T, class Allocator>
      bool operator==(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator< (const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator!=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator> (const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator>=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    template <class T, class Allocator>
      bool operator<=(const vector<T,Allocator>& x, const vector<T,Allocator>& y);
    // specialized algorithms:
    template <class T, class Allocator>
      void swap(vector<T,Allocator>& x, vector<T,Allocator>& y);
  }

  23.2.4.1  vector constructors, copy, and             [lib.vector.cons]
       assignment

  vector(const Allocator& = Allocator());
  explicit vector(size_type n, const T& value = T(),
                  const Allocator& = Allocator());
  template <class InputIterator>
    vector(InputIterator first, InputIterator last,
           const Allocator& = Allocator());
  vector(const vector<T,Allocator>& x);

  Complexity:
    The constructor template <class InputIterator>  vector(InputIterator
    first,   InputIterator   last)  makes  only  N  calls  to  the  copy

    constructor of T (where N is the distance between  first  and  last)
    and  no  reallocations  if  iterators first and last are of forward,
    bidirectional, or random access categories.   It  does  at  most  2N
    calls  to  the  copy constructor of T and logN reallocations if they
    are just input iterators, since it is impossible  to  determine  the
    distance between first and last and then do copying.

  template <class InputIterator>
    void assign(InputIterator first, InputIterator last);

  Effects:
        erase(begin(), end());
        insert(begin(), first, last);

  template <class Size, class U> void assign(Size n, const U& u = U());

  Effects:
        erase(begin(), end());
        insert(begin(), n, t);

  23.2.4.2  vector capacity                        [lib.vector.capacity]

  size_type capacity() const;

  Returns:
    The  total  number  of  elements  that  the  vector can hold without
    requiring reallocation.

  void reserve(size_type n);

  Effects:
    A directive that informs a vector of a planned change  in  size,  so
    that  it  can  manage  the  storage  allocation  accordingly.  After
    reserve(), capacity() is greater or equal to the argument of reserve
    if  reallocation  happens; and equal to the previous value of capac-
    ity() otherwise.  Reallocation happens at this point if and only  if
    the current capacity is less than the argument of reserve().
  Complexity:
    It does not change the size of the sequence and takes at most linear
    time in the size of the sequence.
  Notes:
    Reallocation invalidates all the references, pointers, and iterators
    referring to the elements in the sequence.  It is guaranteed that no
    reallocation takes place during insertions that happen after a  call
    to reserve() until the time when an insertion would make the size of
    the vector greater than the size specified in the most  recent  call
    to reserve().

  void resize(size_type sz, T c = T());

  Effects:
        if (sz > size())
          insert(end(), sz-size(), c);
        else if (sz < size())
          erase(begin()+sz, end());
        else
          ; // do nothing

  23.2.4.3  vector modifiers                      [lib.vector.modifiers]

  iterator insert(iterator position, const T& x = T());
  void     insert(iterator position, size_type n, const T& x);
  template <class InputIterator>
    void insert(iterator position, InputIterator first, InputIterator last);

  Notes:
    Causes  reallocation  if the new size is greater than the old capac-
    ity.  If no reallocation happens, all the iterators  and  references
    before the insertion point remain valid.
  Complexity:
    If first and last are forward iterators, bidirectional iterators, or
    random access iterators, the complexity is linear in the  number  of
    elements  in the range [first, last) plus the distance to the end of
    the vector.  If they are input iterators, the complexity is  propor-
    tional  to  the  number of elements in the range [first, last) times
    the distance to the end of the vector.

  iterator erase(iterator position);
  iterator erase(iterator first, iterator last);

  Effects:
    Invalidates all the iterators and references after the point of  the
    erase.
  Complexity:
    The  destructor of T is called the number of times equal to the num-
    ber of the elements erased, but the  assignment  operator  of  T  is
    called  the  number  of times equal to the number of elements in the
    vector after the erased elements.

  23.2.4.4  vector specialized algorithms           [lib.vector.special]

  template <class T, class Allocator>
    void swap(vector<T,Allocator>& x, vector<T,Allocator>& y);

  Effects:
        x.swap(y);

  23.2.5  Class vector<bool>                           [lib.vector.bool]

1 To optimize space allocation, a specialization of vector for bool ele-
  ments is provided:
  namespace std {
    template <class Allocator = allocator<bool> >
    class vector<bool, Allocator> {
    public:
    // types:
      typedef bool                                      const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef bool                                      value_type;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
    // bit reference:
      class reference {
       friend class vector;
       reference();
      public:
       ~reference();
        operator bool() const;
        reference& operator=(const bool x);
        reference& operator=(const reference& x);
        void flip();      // flips the bit
      };
    // construct/copy/destroy:
      explicit vector(const Allocator& = Allocator());
      explicit vector(size_type n, const bool& value = bool(),
                      const Allocator& = Allocator());
      template <class InputIterator>
        vector(InputIterator first, InputIterator last,
          const Allocator& = Allocator());
      vector(const vector<bool,Allocator>& x);
     ~vector();
      vector<bool,Allocator>& operator=(const vector<bool,Allocator>& x);
      template <class InputIterator>
        void assign(InputIterator first, InputIterator last);
      template <class Size, class U> void assign(Size n, const U& u = U());
      allocator_type get_allocator() const;
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;

    // capacity:
      size_type size() const;
      size_type max_size() const;
      void      resize(size_type sz, bool c = false);
      size_type capacity() const;
      bool      empty() const;
      void      reserve(size_type n);
    // element access:
      reference       operator[](size_type n);
      const_reference operator[](size_type n) const;
      const_reference at(size_type n) const;
      reference       at(size_type n);
      reference       front();
      const_reference front() const;
      reference       back();
      const_reference back() const;
    // modifiers:
      void push_back(const bool& x);
      void pop_back();
      iterator insert(iterator position, const bool& x = bool());
      void     insert (iterator position, size_type n, const bool& x);
      template <class InputIterator>
          void insert (iterator position, InputIterator first, InputIterator last);
      iterator erase(iterator position);
      iterator erase(iterator first, iterator last);
      void swap(vector<bool,Allocator>&);
      static void swap(reference x, reference y);
      void flip();        // flips all bits
      void clear();
    };
    template <class Allocator>
      bool operator==(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator< (const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator!=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator> (const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator>=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    template <class Allocator>
      bool operator<=(const vector<bool,Allocator>& x,
                      const vector<bool,Allocator>& y);
    // specialized algorithms:
    template <class Allocator>
      void swap(vector<bool,Allocator>& x, vector<bool,Allocator>& y);
  }

2 reference  is  a  class that simulates the behavior of references of a
  single bit in vector<bool>.

  23.3  Associative containers                         [lib.associative]

1 Headers <map> and <set>:

  Header <map> synopsis

  namespace std {
    template <class Key, class T, class Compare = less<Key>,
              class Allocator = allocator<T> >
      class map;
    template <class Key, class T, class Compare, class Allocator>
      bool operator==(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator< (const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator!=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator> (const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator>=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator<=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      void swap(map<Key,T,Compare,Allocator>& x,
                map<Key,T,Compare,Allocator>& y);

    template <class Key, class T, class Compare = less<Key>,
              class Allocator = allocator<T> >
      class multimap;
    template <class Key, class T, class Compare, class Allocator>
      bool operator==(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator< (const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator!=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator> (const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator>=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator<=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      void swap(multimap<Key,T,Compare,Allocator>& x,
                multimap<Key,T,Compare,Allocator>& y);
  }

  Header <set> synopsis

  namespace std {
    template <class Key, class Compare = less<Key>,
              class Allocator = allocator<Key> >
      class set;
    template <class Key, class Compare, class Allocator>
      bool operator==(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator< (const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator!=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator> (const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator>=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator<=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      void swap(set<Key,Compare,Allocator>& x,
                set<Key,Compare,Allocator>& y);

    template <class Key, class Compare = less<Key>,
              class Allocator = allocator<Key> >
      class multiset;
    template <class Key, class Compare, class Allocator>
      bool operator==(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator< (const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator!=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator> (const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator>=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator<=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      void swap(multiset<Key,Compare,Allocator>& x,
                multiset<Key,Compare,Allocator>& y);
  }

  23.3.1  Template class map                                   [lib.map]

1 A map is a kind of associative container  that  supports  unique  keys
  (contains  at  most  one  of  each  key  value)  and provides for fast
  retrieval of values of another type T based on the keys.  Map supports
  bidirectional iterators.

2 A  map  satisfies  all  of  the  requirements  of a container and of a
  reversible container (_lib.container.requirements_) and of an associa-
  tive  container  (_lib.associative.reqmts_).  A map also provides most
  operations described in (_lib.associative.reqmts_)  for  unique  keys.
  This means that a map supports the a_uniq operations in (_lib.associa-
  tive.reqmts_) but not the  a_eq  operations.   For  a  map<Key,T>  the
  key_type is Key and the value_type is pair<const Key,T>.  Descriptions
  are provided here only for operations on map that are not described in
  one of those tables or for operations where there is additional seman-
  tic information.

  namespace std {
    template <class Key, class T, class Compare = less<Key>,
              class Allocator = allocator<T> >
    class map {
    public:
    // types:
      typedef Key                                       key_type;
      typedef T                                         mapped_type;
      typedef pair<const Key, T>                        value_type;
      typedef Compare                                   key_compare;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef Allocator::pointer                        pointer;
      typedef Allocator::const_pointer                  const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
      class value_compare
        : public binary_function<value_type,value_type,bool> {
      friend class map;
      protected:
        Compare comp;
        value_compare(Compare c) : comp(c) {}
      public:
        bool operator()(const value_type& x, const value_type& y) const {
          return comp(x.first, y.first);
        }
      };
    // _lib.map.cons_ construct/copy/destroy:
      explicit map(const Compare& comp = Compare(), const Allocator& = Allocator());
      template <class InputIterator>
        map(InputIterator first, InputIterator last,
            const Compare& comp = Compare(), const Allocator& = Allocator());
      map(const map<Key,T,Compare,Allocator>& x);
     ~map();
      map<Key,T,Compare,Allocator>&
        operator=(const map<Key,T,Compare,Allocator>& x);
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // capacity:
      bool      empty() const;
      size_type size() const;
      size_type max_size() const;

    // _lib.map.access_ element access:
      reference operator[](const key_type& x);
    // modifiers:
      pair<iterator, bool> insert(const value_type& x);
      iterator             insert(iterator position, const value_type& x);
      template <class InputIterator>
        void insert(InputIterator first, InputIterator last);
      void      erase(iterator position);
      size_type erase(const key_type& x);
      void      erase(iterator first, iterator last);
      void swap(map<Key,T,Compare,Allocator>&);
      void clear();
    // observers:
      key_compare   key_comp() const;
      value_compare value_comp() const;
    // _lib.map.ops_ map operations:
      iterator       find(const key_type& x);
      const_iterator find(const key_type& x) const;
      size_type      count(const key_type& x) const;
      iterator       lower_bound(const key_type& x);
      const_iterator lower_bound(const key_type& x) const;
      iterator       upper_bound(const key_type& x);
      const_iterator upper_bound(const key_type& x) const;
      pair<iterator,iterator>             equal_range(const key_type& x);
      pair<const_iterator,const_iterator> equal_range(const key_type& x) const;
    };
    template <class Key, class T, class Compare, class Allocator>
      bool operator==(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator< (const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator!=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator> (const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator>=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator<=(const map<Key,T,Compare,Allocator>& x,
                      const map<Key,T,Compare,Allocator>& y);
    // specialized algorithms:
    template <class Key, class T, class Compare, class Allocator>
      void swap(map<Key,T,Compare,Allocator>& x,
                map<Key,T,Compare,Allocator>& y);
  }

  23.3.1.1  map constructors, copy, and assignment        [lib.map.cons]

  explicit map(const Compare& comp = Compare(),
               const Allocator& = Allocator());

  Effects:
    Constructs an empty map using the specified  comparison  object  and
    allocator.
  Complexity:
    Constant.

  template <class InputIterator>
    map(InputIterator first, InputIterator last,
        const Compare& comp = Compare(), const Allocator& = Allocator());

  Effects:
    Constructs  an  empty  map using the specified comparison object and
    allocator, and inserts elements from the range [first, last).
  Complexity:
    Linear in N if the range [first, last) is already sorted using  comp
    and otherwise N log N, where N is last - first.

  23.3.1.2  map element access                          [lib.map.access]

  reference operator[](const key_type& x);

  Returns:
    (*((insert(make_pair(x, T()))).first)).second.

  23.3.1.3  map operations                                 [lib.map.ops]

  iterator       find(const key_type& x);
  const_iterator find(const key_type& x) const;

  iterator       lower_bound(const key_type& x);
  const_iterator lower_bound(const key_type& x) const;

  iterator       upper_bound(const key_type& x);
  const_iterator upper_bound(const key_type &x) const;

  pair<iterator, iterator>
    equal_range(const_key_type &x);
  pair<const_iterator, const_iterator>
    equal_range(const key_type& x) const;

    The  find, lower_bound, upper_bound and equal_range member functions
  each have two versions, one const and the other  non-const.   In  each
  case  the  behavior  of the two functions is identical except that the
  const version returns a const_iterator and the  non-const  version  an
  iterator.  See for a description of the behavior of these functions.

  23.3.1.4  map specialized algorithms                 [lib.map.special]

  template <class Key, class T, class Compare, class Allocator>
    void swap(map<Key,T,Compare,Allocator>& x,
              map<Key,T,Compare,Allocator>& y);

  Effects:
        x.swap(y);

  23.3.2  Template class multimap                         [lib.multimap]

1 A multimap is a kind of associative container that supports equivalent
  keys (possibly containing multiple copies of the same key  value)  and
  provides  for  fast retrieval of values of another type T based on the
  keys.  Multimap supports bidirectional iterators.

2 A multimap satisfies all of the requirements of a container and  of  a
  reversible container (_lib.container.requirements_) and of an associa-
  tive container (_lib.associative.reqmts_).  A multimap  also  provides
  most  operations  described  in  (_lib.associative.reqmts_)  for equal
  keys.  This means that a multimap  supports  the  a_eq  operations  in
  (_lib.associative.reqmts_)  but not the a_uniq operations.  For a mul-
  timap<Key,T> the key_type is Key  and  the  value_type  is  pair<const
  Key,T>.   Descriptions  are  provided here only for operations on mul-
  timap that are not described in one of those tables or for  operations
  where there is additional semantic information.

  namespace std {
    template <class Key, class T, class Compare = less<Key>,
              class Allocator = allocator<T> >
    class multimap {
    public:
    // types:
      typedef Key                                       key_type;
      typedef T                                         mapped_type;
      typedef pair<const Key,T>                         value_type;
      typedef Compare                                   key_compare;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
      class value_compare
        : public binary_function<value_type,value_type,bool> {
      friend class multimap;
      protected:
        Compare comp;
        value_compare(Compare c) : comp(c) {}
      public:
        bool operator()(const value_type& x, const value_type& y) const {
          return comp(x.first, y.first);
        }
      };
    // construct/copy/destroy:
      explicit multimap(const Compare& comp = Compare(),
                        const Allocator& = Allocator());
      template <class InputIterator>
        multimap(InputIterator first, InputIterator last,
                 const Compare& comp = Compare(), const Allocator& = Allocator());
      multimap(const multimap<Key,T,Compare,Allocator>& x);
     ~multimap();
      multimap<Key,T,Compare,Allocator>&
        operator=(const multimap<Key,T,Compare,Allocator>& x);
      allocator_type get_allocator() const;
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;

    // capacity:
      bool           empty() const;
      size_type      size() const;
      size_type      max_size() const;
    // modifiers:
      iterator insert(const value_type& x);
      iterator insert(iterator position, const value_type& x);
      template <class InputIterator>
        void insert(InputIterator first, InputIterator last);
      void      erase(iterator position);
      size_type erase(const key_type& x);
      void      erase(iterator first, iterator last);
      void swap(multimap<Key,T,Compare,Allocator>&);
      void clear();
    // observers:
      key_compare    key_comp() const;
      value_compare  value_comp() const;
    // map operations:
      iterator       find(const key_type& x);
      const_iterator find(const key_type& x) const;
      size_type      count(const key_type& x) const;
      iterator       lower_bound(const key_type& x);
      const_iterator lower_bound(const key_type& x) const;
      iterator       upper_bound(const key_type& x);
      const_iterator upper_bound(const key_type& x) const;
      pair<iterator,iterator>             equal_range(const key_type& x);
      pair<const_iterator,const_iterator> equal_range(const key_type& x) const;
    };
    template <class Key, class T, class Compare, class Allocator>
      bool operator==(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator< (const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator!=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator> (const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator>=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    template <class Key, class T, class Compare, class Allocator>
      bool operator<=(const multimap<Key,T,Compare,Allocator>& x,
                      const multimap<Key,T,Compare,Allocator>& y);
    // specialized algorithms:
    template <class Key, class T, class Compare, class Allocator>
      void swap(multimap<Key,T,Compare,Allocator>& x,
                multimap<Key,T,Compare,Allocator>& y);
  }

  23.3.2.1  multimap constructors                    [lib.multimap.cons]

  explicit multimap(const Compare& comp = Compare(),
                    const Allocator& = Allocator());

  Effects:
    Constructs  an  empty multimap using the specified comparison object
    and allocator.
  Complexity:
    Constant.

  template <class InputIterator>
    multimap(InputIterator first, InputIterator last,
             const Compare& comp = Compare(),
             const Allocator& = Allocator()0;

  Effects:
    Constructs an empty multimap using the specified  comparison  object
    and allocator, and inserts elements from the range [first, last).
  Complexity:
    Linear  in  N  if  the range [first, last).  is already sorted using
    comp and otherwise N log N, where N is last - first.

  23.3.2.2  multimap operations                       [lib.multimap.ops]

  iterator       find(const key_type &x);
  const_iterator find(const key_type& x) const;

  iterator       lower_bound(const key_type& x);
  const_iterator lower_bound(const key_type& x) const;

  pair<iterator, iterator>
    equal_range(const key_type& x);
  pair<const_iterator, const_iterator>
    equal_range(const_key_type& x) const;

   The find, lower_bound, upper_bound, and equal_range member  functions
  each have two versions, one const and one non-const.  In each case the
  behavior of the two versions is identical except that the  const  ver-
  sion  returns  a const_iterator and the non-const version an iterator.
  See for a description of the behavior of these functions.

  23.3.2.3  multimap specialized algorithms       [lib.multimap.special]

  template <class Key, class T, class Compare, class Allocator>
    void swap(multimap<Key,T,Compare,Allocator>& x,
              multimap<Key,T,Compare,Allocator>& y);

  Effects:
        x.swap(y);

  23.3.3  Template class set                                   [lib.set]

1 A set is a kind of associative container  that  supports  unique  keys
  (contains  at  most  one  of  each  key  value)  and provides for fast
  retrieval of the keys themselves.  Set supports  bidirectional  itera-
  tors.

2 A  set  satisfies  all  of  the  requirements  of a container and of a
  reversible container (_lib.container.requirements_), and of  an  asso-
  ciative  container  (_lib.associative.reqmts_).   A  set also provides
  most operations described  in  (_lib.associative.reqmts_)  for  unique
  keys.   This  means  that  a  set  supports  the  a_uniq operations in
  (_lib.associative.reqmts_)  but  not  the  a_eq  operations.   For   a
  set<Key>  both  the key_type and value_type are Key.  Descriptions are
  provided here only for operations on set that are not described in one
  of  these tables and for operations where there is additional semantic
  information.
  namespace std {
    template <class Key, class Compare = less<Key>,
              class Allocator = allocator<Key> >
    class set {
    public:
    // types:
      typedef Key                                       key_type;
      typedef Key                                       value_type;
      typedef Compare                                   key_compare;
      typedef Compare                                   value_compare;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;

    // _lib.set.cons_ construct/copy/destroy:
      explicit set(const Compare& comp = Compare(), const Allocator& = Allocator());
      template <class InputIterator>
        set(InputIterator first, InputIterator last,
            const Compare& comp = Compare(), const Allocator& = Allocator());
      set(const set<Key,Compare,Allocator>& x);
     ~set();
      set<Key,Compare,Allocator>& operator=(const set<Key,Compare,Allocator>& x);
      allocator_type get_allocator() const;
    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // capacity:
      bool          empty() const;
      size_type     size() const;
      size_type     max_size() const;
    // modifiers:
      pair<iterator,bool> insert(const value_type& x);
      iterator             insert(iterator position, const value_type& x);
      template <class InputIterator>
          void insert(InputIterator first, InputIterator last);
      void      erase(iterator position);
      size_type erase(const key_type& x);
      void      erase(iterator first, iterator last);
      void swap(set<Key,Compare,Allocator>&);
      void clear();
    // observers:
      key_compare   key_comp() const;
      value_compare value_comp() const;
    // set operations:
      iterator  find(const key_type& x) const;
      size_type count(const key_type& x) const;
      iterator  lower_bound(const key_type& x) const;
      iterator  upper_bound(const key_type& x) const;
      pair<iterator,iterator> equal_range(const key_type& x) const;
    };

    template <class Key, class Compare, class Allocator>
      bool operator==(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator< (const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator!=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator> (const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator>=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator<=(const set<Key,Compare,Allocator>& x,
                      const set<Key,Compare,Allocator>& y);
    // specialized algorithms:
    template <class Key, class Compare, class Allocator>
      void swap(set<Key,Compare,Allocator>& x,
                set<Key,Compare,Allocator>& y);
  }

  23.3.3.1  set constructors, copy, and assignment        [lib.set.cons]

  explicit set(const Compare& comp = Compare(),
               const Allocator& = Allocator());

  Effects:
    Constructs an empty set using the specified comparison  objects  and
    allocator.
  Complexity:
    Constant.

  template <class INputIterator>
    set(InputIterator first, last,
        const COmpare& comp = Compare(), const Allocator& = Allocator());

  set  using  the specified comparison object and allocator, and inserts
  elements from the range [first, last).
  Complexity:
    Linear in N if the range [first, last) is already sorted using  comp
    and otherwise N log N, where N is last - first.

  23.3.3.2  set specialized algorithms                 [lib.set.special]

  template <class Key, class Compare, class Allocator>
    void swap(set<Key,Compare,Allocator>& x,
              set<Key,Compare,Allocator>& y);

  Effects:
        x.swap(y);

  23.3.4  Template class multiset                         [lib.multiset]

1 A multiset is a kind of associative container that supports equivalent
  keys (possibly contains multiple copies of the  same  key  value)  and
  provides for fast retrieval of the keys themselves.  Multiset supports
  bidirectional iterators.

2 A multiset satisfies all of the requirements of a container and  of  a
  reversible  container  (_lib.container.requirements_), and of an asso-
  ciative container (_lib.associative.reqmts_).  multiset also  provides
  most  operations described in (_lib.associative.reqmts_) for duplicate
  keys.  This means that a multiset  supports  the  a_eu  operations  in
  (_lib.associative.reqmts_)  but not the a_uniq operations.  For a mul-
  tiset<Key> both the key_type and value_type are Key.  Descriptions are
  provided  here  only for operations on multiset that are not described
  in one of these tables and for operations where  there  is  additional
  semantic information.
  namespace std {
    template <class Key, class Compare = less<Key>,
              class Allocator = allocator<Key> >
    class multiset {
    public:
    // types:
      typedef Key                                       key_type;
      typedef Key                                       value_type;
      typedef Compare                                   key_compare;
      typedef Compare                                   value_compare;
      typedef Allocator                                 allocator_type;
      typedef typename Allocator::reference             reference;
      typedef typename Allocator::const_reference       const_reference;
      typedef implementation defined                    iterator;       // See _lib.container.requirements_
      typedef implementation defined                    const_iterator; // See _lib.container.requirements_
      typedef typename Allocator::size_type             size_type;
      typedef typename Allocator::difference_type       difference_type;
      typedef typename Allocator::pointer               pointer;
      typedef typename Allocator::const_pointer         const_pointer;
      typedef std::reverse_iterator<iterator>           reverse_iterator;
      typedef std::reverse_iterator<const_iterator>     const_reverse_iterator;
    // construct/copy/destroy:
      explicit multiset(const Compare& comp = Compare(),
                        const Allocator& = Allocator());
      template <class InputIterator>
        multiset(InputIterator first, InputIterator last,
                 const Compare& comp = Compare(), const Allocator& = Allocator());
      multiset(const multiset<Key,Compare,Allocator>& x);
     ~multiset();
      multiset<Key,Compare,Allocator>&
          operator=(const multiset<Key,Compare,Allocator>& x);
      allocator_type get_allocator() const;

    // iterators:
      iterator               begin();
      const_iterator         begin() const;
      iterator               end();
      const_iterator         end() const;
      reverse_iterator       rbegin();
      const_reverse_iterator rbegin() const;
      reverse_iterator       rend();
      const_reverse_iterator rend() const;
    // capacity:
      bool          empty() const;
      size_type     size() const;
      size_type     max_size() const;
    // modifiers:
      iterator insert(const value_type& x);
      iterator insert(iterator position, const value_type& x);
      template <class InputIterator>
        void insert(InputIterator first, InputIterator last);
      void      erase(iterator position);
      size_type erase(const key_type& x);
      void      erase(iterator first, iterator last);
      void swap(multiset<Key,Compare,Allocator>&);
      void clear();
    // observers:
      key_compare   key_comp() const;
      value_compare value_comp() const;
    // set operations:
      iterator  find(const key_type& x) const;
      size_type count(const key_type& x) const;
      iterator  lower_bound(const key_type& x) const;
      iterator  upper_bound(const key_type& x) const;
      pair<iterator,iterator> equal_range(const key_type& x) const;
    };
    template <class Key, class Compare, class Allocator>
      bool operator==(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator< (const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator!=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator> (const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator>=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);
    template <class Key, class Compare, class Allocator>
      bool operator<=(const multiset<Key,Compare,Allocator>& x,
                      const multiset<Key,Compare,Allocator>& y);

    // specialized algorithms:
    template <class Key, class Compare, class Allocator>
      void swap(multiset<Key,Compare,Allocator>& x,
                multiset<Key,Compare,Allocator>& y);
  }

  23.3.4.1  multiset constructors                    [lib.multiset.cons]

  explicit multiset(const Compare& comp = Compare(),
                    const Allocator& = Allocator());

  Effects:
    Constructs  an  empty  set using the specified comparison object and
    allocator.
  Complexity:
    Constant.

  template <class InputIterator>
    multiset(InputIterator first, last,
             const Compare& comp = Compare(), const Allocator& = Allocator());

  Effects:
    Constructs an empty multiset using the specified  comparison  object
    and allocator, and inserts elements from the range [first, last).
  Complexity:
    Linear  in N if the range [first, last) is already sorted using comp
    and otherwise N log N, where N is last - first.

  23.3.4.2  multiset specialized algorithms       [lib.multiset.special]

  template <class Key, class Compare, class Allocator>
    void swap(multiset<Key,Compare,Allocator>& x,
              multiset<Key,Compare,Allocator>& y);

  Effects:
        x.swap(y);

  23.3.5  Template class bitset                    [lib.template.bitset]

  Header <bitset> synopsis

  #include <cstddef>      // for size_t
  #include <string>
  #include <stdexcept>    // for invalid_argument, out_of_range, overflow_error
  #include <iosfwd>       // for istream, ostream
  namespace std {
    template <size_t N> class bitset;

    // _lib.bitset.operators_ bitset operations:
    template <size_t N> bitset<N> operator&(const bitset<N>&, const bitset<N>&);
    template <size_t N> bitset<N> operator|(const bitset<N>&, const bitset<N>&);
    template <size_t N> bitset<N> operator^(const bitset<N>&, const bitset<N>&);
    template <class charT, class traits, size_t N>
      basic_istream<charT, traits>&
      operator>>(basic_istream<charT, traits>& is, bitset<N>& x);
    template <class charT, class traits, size_t N>
      basic_ostream<charT, traits>&
      operator<<(basic_ostream<charT, traits>& os, const bitset<N>& x);
  }

1 The header <bitset> defines a template class and several related func-
  tions  for representing and manipulating fixed-size sequences of bits.
  namespace std {
    template<size_t N> class bitset {
    public:
    // bit reference:
      class reference {
        friend class bitset;
        reference();
      public:
       ~reference();
        reference& operator=(bool x);           // for b[i] = x;
        reference& operator=(const reference&); // for b[i] = b[j];
        bool operator~() const;                 // flips the bit
        operator bool() const;                  // for x = b[i];
        reference& flip();                      // for b[i].flip();
      };
    // _lib.bitset.cons_ constructors:
      bitset();
      bitset(unsigned long val);
      template<class charT, class traits, class Allocator>
        explicit bitset(
          const basic_string<charT,traits,Allocator>& str,
          typename basic_string<charT,traits,Allocator>::size_type pos = 0,
          typename basic_string<charT,traits,Allocator>::size_type n =
            basic_string<charT,traits,Allocator>::npos);
    // _lib.bitset.members_ bitset operations:
      bitset<N>& operator&=(const bitset<N>& rhs);
      bitset<N>& operator|=(const bitset<N>& rhs);
      bitset<N>& operator^=(const bitset<N>& rhs);
      bitset<N>& operator<<=(size_t pos);
      bitset<N>& operator>>=(size_t pos);
      bitset<N>& set();
      bitset<N>& set(size_t pos, int val = true);
      bitset<N>& reset();
      bitset<N>& reset(size_t pos);
      bitset<N>  operator~() const;
      bitset<N>& flip();
      bitset<N>& flip(size_t pos);
    // element access:
      reference operator[](size_t pos);   // for b[i];

      unsigned long  to_ulong() const;
      template <class charT, class traits, class Allocator>
        basic_string<charT, traits, Allocator> to_string() const;
      size_t count() const;
      size_t size()  const;
      bool operator==(const bitset<N>& rhs) const;
      bool operator!=(const bitset<N>& rhs) const;
      bool test(size_t pos) const;
      bool any() const;
      bool none() const;
      bitset<N> operator<<(size_t pos) const;
      bitset<N> operator>>(size_t pos) const;
    };
  }

2 The template class bitset<N> describes an  object  that  can  store  a
  sequence consisting of a fixed number of bits, N.

3 Each  bit  represents  either the value zero (reset) or one (set).  To
  toggle a bit is to change the value zero to one, or the value  one  to
  zero.   Each  bit  has  a  non-negative position pos.  When converting
  between an object of class bitset<N> and  a  value  of  some  integral
  type,  bit  position  pos  corresponds to the bit value 1 << pos.  The
  integral value corresponding to two or more bits is the sum  of  their
  bit values.

4 The  functions  described  in this subclause can report three kinds of
  errors, each associated with a distinct exception:

  --an invalid-argument error is  associated  with  exceptions  of  type
    invalid_argument (_lib.invalid.argument_);

  --an   out-of-range  error  is  associated  with  exceptions  of  type
    out_of_range (_lib.out.of.range_);

  --an overflow error  is  associated  with  exceptions  of  type  over-
    flow_error (_lib.overflow.error_).

  23.3.5.1  bitset constructors                        [lib.bitset.cons]

  bitset();

  Effects:
    Constructs  an  object  of class bitset<N>, initializing all bits to
    zero.

  bitset(unsigned long val);

  Effects:
    Constructs an object of class bitset<N>, initializing  the  first  M
    bit  positions  to  the  corresponding  bit values in val.  M is the

    smaller of N and the value CHAR_BIT * sizeof (unsigned long).3)
    If M < N, remaining bit positions are initialized to zero.

  template <class charT, class traits, class Allocator>
  explicit
  bitset(const basic_string<charT, traits, Allocator>& str,
         basic_string<charT, traits, Allocator>::size_type pos = 0,
         basic_string<charT, traits, Allocator>::size_type n =
           basic_string<charT, traits, Allocator>::npos);

  Requires:
    pos <= str.size().
  Throws:
    out_of_range if pos > str.size().
  Effects:
    Determines  the  effective length rlen of the initializing string as
    the smaller of n and str.size() - pos.
    The function then throws invalid_argument if any of the rlen charac-
    ters in str beginning at position pos is other than 0 or 1.
    Otherwise,  the  function  constructs  an object of class bitset<N>,
    initializing the first M bit positions to values determined from the
    corresponding  characters  in the string str.  M is the smaller of N
    and rlen.

1 An element of the constructed string has value zero if the correspond-
  ing character in str, beginning at position pos, is 0.  Otherwise, the
  element has the value one.  Character position pos + M - 1 corresponds
  to  bit position zero.  Subsequent decreasing character positions cor-
  respond to increasing bit positions.

2 If M < N, remaining bit positions are initialized to zero.

  23.3.5.2  bitset members                          [lib.bitset.members]

  bitset<N>& operator&=(const bitset<N>& rhs);

  Effects:
    Clears each bit in *this for which the corresponding bit in  rhs  is
    clear, and leaves all other bits unchanged.
  Returns:
    *this.

  bitset<N>& operator|=(const bitset<N>& rhs);

  Effects:
    Sets  each  bit  in  *this for which the corresponding bit in rhs is
  _________________________
  3) The macro CHAR_BIT is defined in <climits>  (_lib.support.limits_).

    set, and leaves all other bits unchanged.
  Returns:
    *this.

  bitset<N>& operator^=(const bitset<N>& rhs);

  Effects:
    Toggles each bit in *this for which the corresponding bit in rhs  is
    set, and leaves all other bits unchanged.
  Returns:
    *this.

  bitset<N>& operator<<=(size_t pos);

  Effects:
    Replaces  each bit at position I in *this with a value determined as
    follows:

  --If I < pos, the new value is zero;

  --If I >= pos, the new value is the previous value of the bit at posi-
    tion I - pos.
  Returns:
    *this.

  bitset<N>& operator>>=(size_t pos);

  Effects:
    Replaces  each bit at position I in *this with a value determined as
    follows:

  --If pos >= N - I, the new value is zero;

  --If pos < N - I, the new value is the previous value of  the  bit  at
    position I + pos.
  Returns:
    *this.

  bitset<N>& set();

  Effects:
    Sets all bits in *this.
  Returns:
    *this.

  bitset<N>& set(size_t pos, int val = 1);

  Requires:
    pos is valid
  Throws:
    out_of_range if pos does not correspond to a valid bit position.
  Effects:
    Stores  a  new value in the bit at position pos in *this.  If val is
    nonzero, the stored value is one, otherwise it is zero.
  Returns:
    *this.

  bitset<N>& reset();

  Effects:
    Resets all bits in *this.
  Returns:
    *this.

  bitset<N>& reset(size_t pos);

  Requires:
    pos is valid
  Throws:
    out_of_range if pos does not correspond to a valid bit position.
  Effects:
    Resets the bit at position pos in *this.
  Returns:
    *this.

  bitset<N> operator~() const;

  Effects:
    Constructs an object x of class bitset<N> and  initializes  it  with
    *this.
  Returns:
    x.flip().

  bitset<N>& flip();

  Effects:
    Toggles all bits in *this.
  Returns:
    *this.

  bitset<N>& flip(size_t pos);

  Requires:
    pos is valid

  Throws:
    out_of_range if pos does not correspond to a valid bit position.
  Effects:
    Toggles the bit at position pos in *this.
  Returns:
    *this.

  unsigned long to_ulong() const;

  Throws:
    overflow_error  if the integral value x corresponding to the bits in
    *this cannot be represented as type unsigned long.
  Returns:
    x.

  template <class charT, class traits, class Allocator>
  basic_string<charT, traits, Allocator> to_string() const;

  Effects:
    Constructs a string object of the appropriate type  and  initializes
    it to a string of length N characters.  Each character is determined
    by the value of its corresponding bit position in *this.   Character
    position  N  -  1  corresponds  to  bit  position  zero.  Subsequent
    decreasing character positions correspond to  increasing  bit  posi-
    tions.   Bit  value  zero  becomes  the  character  0, bit value one
    becomes the character 1.
  Returns:
    The created object.

  size_t count() const;

  Returns:
    A count of the number of bits set in *this.

  size_t size() const;

  Returns:
    N.

  bool operator==(const bitset<N>& rhs) const;

  Returns:
    A nonzero value if the value of each bit in *this equals  the  value
    of the corresponding bit in rhs.

  bool operator!=(const bitset<N>& rhs) const;

  Returns:
    A nonzero value if !(*this == rhs).

  bool test(size_t pos) const;

  Requires:
    pos is valid
  Throws:
    out_of_range if pos does not correspond to a valid bit position.
  Returns:
    true if the bit at position pos in *this has the value one.

  bool any() const;

  Returns:
    true if any bit in *this is one.

  bool none() const;

  Returns:
    true if no bit in *this is one.

  bitset<N> operator<<(size_t pos) const;

  Returns:
    bitset<N>(*this) <<= pos.

  bitset<N> operator>>(size_t pos) const;

  Returns:
    bitset<N>(*this) >>= pos.

  23.3.5.3  bitset operators                      [lib.bitset.operators]

  bitset<N> operator&(const bitset<N>& lhs, const bitset<N>& rhs);

  Returns:
    bitset<N>(lhs) &= rhs.

  bitset<N> operator|(const bitset<N>& lhs, const bitset<N>& rhs);

  Returns:
    bitset<N>(lhs) |= rhs.

  bitset<N> operator^(const bitset<N>& lhs, const bitset<N>& rhs);

  Returns:
    bitset<N>(lhs) ^= rhs.

  template <class charT, class traits, size_t N>
    basic_istream<charT, traits>&
    operator>>(basic_istream<charT, traits>& is, bitset<N>& x);

1 A formatted input function (_lib.istream.formatted_).
  Effects:
    Extracts  up  to  N  (single-byte) characters from is.  Stores these
    characters in a temporary object str of type string, then  evaluates
    the  expression  x  =  bitset<N>(str).  Characters are extracted and
    stored until any of the following occurs:

  --N characters have been extracted and stored;

  --end-of-file occurs on the input sequence;

  --the next input character is neither 0 or 1 (in which case the  input
    character is not extracted).

2 If  no  characters  are stored in str, calls is.setstate(ios::failbit)
  (which may throw ios_base::failure (_lib.iostate.flags_).
  Returns:
    is.

  template <class charT, class traits, size_t N>
    basic_ostream<charT, traits>&
    operator<<(basic_ostream<charT, traits>& os, const bitset<N>& x);

  Returns:
    os      <<       x.to_string<charT,traits,allocator<charT>       >()
    (_lib.ostream.formatted_).