21 Containers library [containers]

21.1 General [containers.general]

This Clause describes components that C++ programs may use to organize collections of information.
The following subclauses describe container requirements, and components for sequence containers and associative containers, as summarized in Table 63.
Table 63 — Containers library summary
Subclause
Header(s)
Requirements
Sequence containers
<array>
<deque>
<forward_­list>
<list>
<vector>
Associative containers
<map>
<set>
Unordered associative containers
<unordered_­map>
<unordered_­set>
Container adaptors
<queue>
<stack>
Views
<span>

21.2 Container requirements [container.requirements]

21.2.1 General container requirements [container.requirements.general]

Containers are objects that store other objects.
They control allocation and deallocation of these objects through constructors, destructors, insert and erase operations.
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 complexity, even though the complexity of copying each contained vector<int> is itself linear.
end example
]
For the components affected by this subclause that declare an allocator_­type, objects stored in these components shall be constructed using the function allocator_­traits<allocator_­type>​::​rebind_­traits<U>​::​​construct and destroyed using the function allocator_­traits<allocator_­type>​::​rebind_­traits<U>​::​​destroy, where U is either allocator_­type::value_­type or an internal type used by the container.
These functions are called only for the container's element type, not for internal types used by the container.
[Note
:
This means, for example, that a node-based container might need to construct nodes containing aligned buffers and call construct to place the element into the buffer.
end note
]
In Tables 64, 65, and 66 X denotes a container class containing objects of type T, a and b denote values of type X, u denotes an identifier, r denotes a non-const value of type X, and rv denotes a non-const rvalue of type X.
Table 64 — Container requirements
Expression
Return type
Operational
Assertion/note
Complexity
semantics
pre-/post-condition
X::value_­type
T
Requires:  T is Cpp17Erasable from X (see [container.requirements.general], below)
compile time
X::reference
T&
compile time
X::const_­reference
const T&
compile time
X::iterator
iterator type whose value type is T
any iterator category that meets the forward iterator requirements.
convertible to X::const_­iterator.
compile time
X::const_­iterator
constant iterator type whose value type is T
any iterator category that meets the forward iterator requirements.
compile time
X::difference_­type
signed integer type
is identical to the difference type of X::iterator and X::const_­iterator
compile time
X::size_­type
unsigned integer type
size_­type can represent any non-negative value of difference_­type
compile time
X u;
Ensures: u.empty()
constant
X()
Ensures: X().empty()
constant
X(a)
Requires: T is Cpp17CopyInsertable into X (see below).

Ensures: a == X(a).
linear
X u(a);
X u = a;
Requires: T is Cpp17CopyInsertable into X (see below).

Ensures: u == a
linear
X u(rv);
X u = rv;
Ensures: u shall be equal to the value that rv had before this construction
(Note B)
a = rv
X&
All existing elements of a are either move assigned to or destroyed
a shall be equal to the value that rv had before this assignment
linear
(&a)->~X()
void
the destructor is applied to every element of a; any memory obtained is deallocated.
linear
a.begin()
iterator; const_­iterator for constant a
constant
a.end()
iterator; const_­iterator for constant a
constant
a.cbegin()
const_­iterator
const_­cast<​X const&>(a).begin();
constant
a.cend()
const_­iterator
const_­cast<​X const&>(a).end();
constant
a == b
convertible to bool
== is an equivalence relation.
equal(​a.begin(), a.end(), b.begin(), b.end())
Requires:  T is Cpp17EqualityComparable
Constant if a.size() != b.size(), linear otherwise
a != b
convertible to bool
Equivalent to !(a == b)
linear
a.swap(b)
void
exchanges the contents of a and b
(Note A)
swap(a, b)
void
Equivalent to a.swap(b)
(Note A)
r = a
X&
Ensures: r == a.
linear
a.size()
size_­type
distance(​a.begin(), a.end())
constant
a.max_­size()
size_­type
distance(​begin(), end()) for the largest possible container
constant
a.empty()
convertible to bool
a.begin() == a.end()
constant
Those entries marked “(Note A)” or “(Note B)” have linear complexity for array and have constant complexity for all other standard containers.
[Note
:
The algorithm equal() is defined in [algorithms].
end note
]
The member function size() returns the number of elements in the container.
The number of elements is defined by the rules of constructors, inserts, and erases.
begin() returns an iterator referring to the first element in the container.
end() returns an iterator which is the past-the-end value for the container.
If the container is empty, then begin() == end().
In the expressions
i == j
i != j
i < j
i <= j
i >= j
i > j
i - j
where i and j denote objects of a container's iterator type, either or both may be replaced by an object of the container's const_­iterator type referring to the same element with no change in semantics.
Unless otherwise specified, all containers defined in this clause obtain memory using an allocator (see [allocator.requirements]).
[Note
:
In particular, containers and iterators do not store references to allocated elements other than through the allocator's pointer type, i.e., as objects of type P or pointer_­traits<P>::template rebind<unspecified>, where P is allocator_­traits<allocator_­type>::pointer.
end note
]
Copy constructors for these container types obtain an allocator by calling allocator_­traits<allocator_­type>::select_­on_­container_­copy_­construction on the allocator belonging to the container being copied.
Move constructors obtain an allocator by move construction from the allocator belonging to the container being moved.
Such move construction of the allocator shall not exit via an exception.
All other constructors for these container types take a const allocator_­type& argument.
[Note
:
If an invocation of a constructor uses the default value of an optional allocator argument, then the allocator type must support value-initialization.
end note
]
A copy of this allocator is used for any memory allocation and element construction performed, by these constructors and by all member functions, during the lifetime of each container object or until the allocator is replaced.
The allocator may be replaced only via assignment or swap().
Allocator replacement is performed by copy assignment, move assignment, or swapping of the allocator only if allocator_­traits<allocator_­type>::propagate_­on_­container_­copy_­assignment::value, allocator_­traits<allocator_­type>::propagate_­on_­container_­move_­assignment::value, or allocator_­traits<allocator_­type>::propagate_­on_­container_­swap::value is true within the implementation of the corresponding container operation.
In all container types defined in this Clause, the member get_­allocator() returns a copy of the allocator used to construct the container or, if that allocator has been replaced, a copy of the most recent replacement.
The expression a.swap(b), for containers a and b of a standard container type other than array, shall exchange the values of a and b without invoking any move, copy, or swap operations on the individual container elements.
Lvalues of any Compare, Pred, or Hash types belonging to a and b shall be swappable and shall be exchanged by calling swap as described in [swappable.requirements].
If allocator_­traits<allocator_­type>::propagate_­on_­container_­swap::value is true, then lvalues of type allocator_­type shall be swappable and the allocators of a and b shall also be exchanged by calling swap as described in [swappable.requirements].
Otherwise, the allocators shall not be swapped, and the behavior is undefined unless a.get_­allocator() == b.get_­allocator().
Every iterator referring to an element in one container before the swap shall refer to the same element in the other container after the swap.
It is unspecified whether an iterator with value a.end() before the swap will have value b.end() after the swap.
If the iterator type of a container belongs to the bidirectional or random access iterator categories, the container is called reversible and satisfies the additional requirements in Table 65.
Table 65 — Reversible container requirements
Expression
Return type
Assertion/note
Complexity
pre-/post-condition
X::reverse_­iterator
iterator type whose value type is T
reverse_­iterator<iterator>
compile time
X::const_­reverse_­iterator
constant iterator type whose value type is T
reverse_­iterator<const_­iterator>
compile time
a.rbegin()
reverse_­iterator; const_­reverse_­iterator for constant a
reverse_­iterator(end())
constant
a.rend()
reverse_­iterator; const_­reverse_­iterator for constant a
reverse_­iterator(begin())
constant
a.crbegin()
const_­reverse_­iterator
const_­cast<X const&>(a).rbegin()
constant
a.crend()
const_­reverse_­iterator
const_­cast<X const&>(a).rend()
constant
Unless otherwise specified (see [associative.reqmts.except], [unord.req.except], [deque.modifiers], and [vector.modifiers]) all container types defined in this Clause meet the following additional requirements:
  • if an exception is thrown by an insert() or emplace() function while inserting a single element, that function has no effects.
  • if an exception is thrown by a push_­back(), push_­front(), emplace_­back(), or emplace_­front() function, that function has no effects.
  • no erase(), clear(), pop_­back() or pop_­front() function throws an exception.
  • no copy constructor or assignment operator of a returned iterator throws an exception.
  • no swap() function throws an exception.
  • no swap() function invalidates any references, pointers, or iterators referring to the elements of the containers being swapped.
    [Note
    :
    The end() iterator does not refer to any element, so it may be invalidated.
    end note
    ]
Unless otherwise specified (either explicitly or by defining a function in terms of other functions), invoking a container member function or passing a container as an argument to a library function shall not invalidate iterators to, or change the values of, objects within that container.
A contiguous container is a container that supports random access iterators and whose member types iterator and const_­iterator are contiguous iterators.
Table 66 lists operations that are provided for some types of containers but not others.
Those containers for which the listed operations are provided shall implement the semantics described in Table 66 unless otherwise stated.
Table 66 — Optional container operations
Expression
Return type
Operational
Assertion/note
Complexity
semantics
pre-/post-condition
a < b
convertible to bool
lexicographical_­compare( a.begin(), a.end(), b.begin(), b.end())
Requires: < is defined for values of T.
< is a total ordering relationship.
linear
a > b
convertible to bool
b < a
linear
a <= b
convertible to bool
!(a > b)
linear
a >= b
convertible to bool
!(a < b)
linear
[Note
:
The algorithm lexicographical_­compare() is defined in [algorithms].
end note
]
All of the containers defined in this Clause and in [basic.string] except array meet the additional requirements of an allocator-aware container, as described in Table 67.
Given an allocator type A and given a container type X having a value_­type identical to T and an allocator_­type identical to allocator_­traits<A>::rebind_­alloc<T> and given an lvalue m of type A, a pointer p of type T*, an expression v of type (possibly const) T, and an rvalue rv of type T, the following terms are defined.
If X is not allocator-aware, the terms below are defined as if A were allocator<T> — no allocator object needs to be created and user specializations of allocator<T> are not instantiated:
  • T is Cpp17DefaultInsertable into X means that the following expression is well-formed:
    allocator_traits<A>::construct(m, p)
    
  • An element of X is default-inserted if it is initialized by evaluation of the expression
    allocator_traits<A>::construct(m, p)
    
    where p is the address of the uninitialized storage for the element allocated within X.
  • T is Cpp17MoveInsertable into X means that the following expression is well-formed:
    allocator_traits<A>::construct(m, p, rv)
    
    and its evaluation causes the following postcondition to hold: The value of *p is equivalent to the value of rv before the evaluation.
    [Note
    :
    rv remains a valid object.
    Its state is unspecified
    end note
    ]
  • T is Cpp17CopyInsertable into X means that, in addition to T being Cpp17MoveInsertable into X, the following expression is well-formed:
    allocator_traits<A>::construct(m, p, v)
    
    and its evaluation causes the following postcondition to hold: The value of v is unchanged and is equivalent to *p.
  • T is Cpp17EmplaceConstructible into X from args, for zero or more arguments args, means that the following expression is well-formed:
    allocator_traits<A>::construct(m, p, args)
    
  • T is Cpp17Erasable from X means that the following expression is well-formed:
    allocator_traits<A>::destroy(m, p)
    
[Note
:
A container calls allocator_­traits<A>::construct(m, p, args) to construct an element at p using args, with m == get_­allocator().
The default construct in allocator will call ::new((void*)p) T(args), but specialized allocators may choose a different definition.
end note
]
In Table 67, X denotes an allocator-aware container class with a value_­type of T using allocator of type A, u denotes a variable, a and b denote non-const lvalues of type X, t denotes an lvalue or a const rvalue of type X, rv denotes a non-const rvalue of type X, and m is a value of type A.
Table 67 — Allocator-aware container requirements
Expression
Return type
Assertion/note
Complexity
pre-/post-condition
allocator_­type
A
Requires: allocator_­type::value_­type is the same as X::value_­type.
compile time
get_­- allocator()
A
constant
X()
X u;
Requires:  A is Cpp17DefaultConstructible.

Ensures: u.empty() returns true, u.get_­allocator() == A()
constant
X(m)
Ensures: u.empty() returns true,
constant
X u(m);
u.get_­allocator() == m
X(t, m)
X u(t, m);
Requires:  T is Cpp17CopyInsertable into X.

Ensures: u == t, u.get_­allocator() == m
linear
X(rv)
X u(rv);
Ensures: u shall have the same elements as rv had before this construction; the value of u.get_­allocator() shall be the same as the value of rv.get_­allocator() before this construction.
constant
X(rv, m)
X u(rv, m);
Requires:  T is Cpp17MoveInsertable into X.

Ensures: u shall have the same elements, or copies of the elements, that rv had before this construction, u.get_­allocator() == m
constant if m == rv.get_­allocator(), otherwise linear
a = t
X&
Requires:  T is Cpp17CopyInsertable into X and Cpp17CopyAssignable.

Ensures: a == t
linear
a = rv
X&
Requires:  If allocator_­-
traits<allocator_­type>
::propagate_­on_­container_­-
move_­assignment::value is
false, T is Cpp17MoveInsertable into X and Cpp17MoveAssignable.
All existing elements of a are either move assigned to or destroyed.

Ensures: a shall be equal to the value that rv had before this assignment.
linear
a.swap(b)
void
exchanges the contents of a and b
constant
The behavior of certain container member functions and deduction guides depends on whether types qualify as input iterators or allocators.
The extent to which an implementation determines that a type cannot be an input iterator is unspecified, except that as a minimum integral types shall not qualify as input iterators.
Likewise, the extent to which an implementation determines that a type cannot be an allocator is unspecified, except that as a minimum a type A shall not qualify as an allocator unless it satisfies both of the following conditions:

21.2.2 Container data races [container.requirements.dataraces]

For purposes of avoiding data races, implementations shall consider the following functions to be const: begin, end, rbegin, rend, front, back, data, find, lower_­bound, upper_­bound, equal_­range, at and, except in associative or unordered associative containers, operator[].
Notwithstanding [res.on.data.races], implementations are required to avoid data races when the contents of the contained object in different elements in the same container, excepting vector<bool>, are modified concurrently.
[Note
:
For a vector<int> x with a size greater than one, x[1] = 5 and *x.begin() = 10 can be executed concurrently without a data race, but x[0] = 5 and *x.begin() = 10 executed concurrently may result in a data race.
As an exception to the general rule, for a vector<bool> y, y[0] = true may race with y[1] = true.
end note
]

21.2.3 Sequence containers [sequence.reqmts]

A sequence container organizes a finite set of objects, all of the same type, into a strictly linear arrangement.
The library provides four basic kinds of sequence containers: vector, forward_­list, list, and deque.
In addition, array is provided as a sequence container which provides limited sequence operations because it has a fixed number of elements.
The library also provides container adaptors that make it easy to construct abstract data types, such as stacks or queues, out of the basic sequence container kinds (or out of other kinds of sequence containers that the user might define).
[Note
:
The sequence containers offer the programmer different complexity trade-offs and should be used accordingly.
vector is the type of sequence container that should be used by default.
array should be used when the container has a fixed size known during translation.
list or forward_­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.
When choosing a container, remember vector is best; leave a comment to explain if you choose from the rest!
end note
]
In Tables 68 and 69, X denotes a sequence container class, a denotes a value of type X containing elements of type T, u denotes the name of a variable being declared, A denotes X::allocator_­type if the qualified-id X::allocator_­type is valid and denotes a type ([temp.deduct]) and allocator<T> if it doesn't, i and j denote iterators satisfying input iterator requirements and refer to elements implicitly convertible to value_­type, [i, j) denotes a valid range, il designates an object of type initializer_­list<value_­type>, n denotes a value of type X::size_­type, p denotes a valid constant iterator to a, q denotes a valid dereferenceable constant iterator to a, [q1, q2) denotes a valid range of constant iterators in a, t denotes an lvalue or a const rvalue of X::value_­type, and rv denotes a non-const rvalue of X::value_­type.
Args denotes a template parameter pack; args denotes a function parameter pack with the pattern Args&&.
The complexities of the expressions are sequence dependent.
Table 68 — Sequence container requirements (in addition to container)
Expression
Return type
Assertion/note
pre-/post-condition
X(n, t)
X u(n, t);
Requires:  T shall be Cpp17CopyInsertable into X.

Ensures: distance(begin(), end()) == n
Constructs a sequence container with n copies of t
X(i, j)
X u(i, j);
Requires:  T shall be Cpp17EmplaceConstructible into X from *i.
For vector, if the iterator does not meet the Cpp17ForwardIterator requirements ([forward.iterators]), T shall also be Cpp17MoveInsertable into X.
Each iterator in the range [i, j) shall be dereferenced exactly once.

Ensures: distance(begin(), end()) == distance(i, j)
Constructs a sequence container equal to the range [i, j)
X(il)
Equivalent to X(il.begin(), il.end())
a = il
X&
Requires:  T is Cpp17CopyInsertable into X and Cpp17CopyAssignable.
Assigns the range [il.begin(), il.end()) into a.
All existing elements of a are either assigned to or destroyed.

Returns:  *this.
a.emplace(p, args)
iterator
Requires:  T is Cpp17EmplaceConstructible into X from args.
For vector and deque, T is also Cpp17MoveInsertable into X and Cpp17MoveAssignable.
Effects:  Inserts an object of type T constructed with std::forward<​Args​>(​args)... before p.
[Note
:
args may directly or indirectly refer to a value in a.
end note
]
a.insert(p,t)
iterator
Requires:  T shall be Cpp17CopyInsertable into X.
For vector and deque, T shall also be Cpp17CopyAssignable.

Effects:  Inserts a copy of t before p.
a.insert(p,rv)
iterator
Requires:  T shall be Cpp17MoveInsertable into X.
For vector and deque, T shall also be Cpp17MoveAssignable.

Effects:  Inserts a copy of rv before p.
a.insert(p,n,t)
iterator
Requires:  T shall be Cpp17CopyInsertable into X and Cpp17CopyAssignable.

Inserts n copies of t before p.
a.insert(p,i,j)
iterator
Requires:  T shall be Cpp17EmplaceConstructible into X from *i.
For vector and deque, T shall also be Cpp17MoveInsertable into X, Cpp17MoveConstructible, Cpp17MoveAssignable, and swappable ([swappable.requirements]).
Each iterator in the range [i, j) shall be dereferenced exactly once.

Requires: i and j are not iterators into a.

Inserts copies of elements in [i, j) before p
a.insert(p, il)
iterator
a.insert(p, il.begin(), il.end()).
a.erase(q)
iterator
Requires:  For vector and deque, T shall be Cpp17MoveAssignable.

Effects:  Erases the element pointed to by q.
a.erase(q1,q2)
iterator
Requires:  For vector and deque, T shall be Cpp17MoveAssignable.

Effects:  Erases the elements in the range [q1, q2).
a.clear()
void
Destroys all elements in a.
Invalidates all references, pointers, and iterators referring to the elements of a and may invalidate the past-the-end iterator.

Ensures: a.empty() returns true.

Complexity: Linear.
a.assign(i,j)
void
Requires:  T shall be Cpp17EmplaceConstructible into X from *i and assignable from *i.
For vector, if the iterator does not meet the forward iterator requirements, T shall also be Cpp17MoveInsertable into X.

Each iterator in the range [i, j) shall be dereferenced exactly once.

Requires: i, j are not iterators into a.

Replaces elements in a with a copy of [i, j).

Invalidates all references, pointers and iterators referring to the elements of a.
For vector and deque, also invalidates the past-the-end iterator.
a.assign(il)
void
a.assign(il.begin(), il.end()).
a.assign(n,t)
void
Requires:  T shall be Cpp17CopyInsertable into X and Cpp17CopyAssignable.

Requires: t is not a reference into a.

Replaces elements in a with n copies of t.

Invalidates all references, pointers and iterators referring to the elements of a.
For vector and deque, also invalidates the past-the-end iterator.
The iterator returned from a.insert(p, t) points to the copy of t inserted into a.
The iterator returned from a.insert(p, rv) points to the copy of rv inserted into a.
The iterator returned from a.insert(p, n, t) points to the copy of the first element inserted into a, or p if n == 0.
The iterator returned from a.insert(p, i, j) points to the copy of the first element inserted into a, or p if i == j.
The iterator returned from a.insert(p, il) points to the copy of the first element inserted into a, or p if il is empty.
The iterator returned from a.emplace(p, args) points to the new element constructed from args into a.
The iterator returned from a.erase(q) points to the element immediately following q prior to the element being erased.
If no such element exists, a.end() is returned.
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.
For every sequence container defined in this Clause and in [strings]:
  • If the constructor
    template<class InputIterator>
      X(InputIterator first, InputIterator last,
        const allocator_type& alloc = allocator_type());
    
    is called with a type InputIterator that does not qualify as an input iterator, then the constructor shall not participate in overload resolution.
  • If the member functions of the forms:
    template<class InputIterator>
      return-type F(const_iterator p,
                    InputIterator first, InputIterator last);       // such as insert
    
    template<class InputIterator>
      return-type F(InputIterator first, InputIterator last);       // such as append, assign
    
    template<class InputIterator>
      return-type F(const_iterator i1, const_iterator i2,
                    InputIterator first, InputIterator last);       // such as replace
    
    are called with a type InputIterator that does not qualify as an input iterator, then these functions shall not participate in overload resolution.
  • A deduction guide for a sequence container shall not participate in overload resolution if it has an InputIterator template parameter and a type that does not qualify as an input iterator is deduced for that parameter, or if it has an Allocator template parameter and a type that does not qualify as an allocator is deduced for that parameter.
Table 69 lists operations that are provided for some types of sequence containers but not others.
An implementation shall provide these operations for all container types shown in the “container” column, and shall implement them so as to take amortized constant time.
Table 69 — Optional sequence container operations
Expression
Return type
Operational semantics
Container
a.front()
reference; const_­reference for constant a
*a.begin()
basic_­string, array, deque, forward_­list, list, vector
a.back()
reference; const_­reference for constant a
{ auto tmp = a.end();
--tmp;
return *tmp; }
basic_­string, array, deque, list, vector
a.emplace_­front(args)
reference
Prepends an object of type T constructed with std::forward<​Args​>(​args)....

Requires:  T shall be Cpp17EmplaceConstructible into X from args.

Returns: a.front().
deque, forward_­list, list
a.emplace_­back(args)
reference
Appends an object of type T constructed with std::forward<​Args​>(​args)....

Requires:  T shall be Cpp17EmplaceConstructible into X from args.
For vector, T shall also be Cpp17MoveInsertable into X.

Returns: a.back().
deque, list, vector
a.push_­front(t)
void
Prepends a copy of t.

Requires:  T shall be Cpp17CopyInsertable into X.
deque, forward_­list, list
a.push_­front(rv)
void
Prepends a copy of rv.

Requires:  T shall be Cpp17MoveInsertable into X.
deque, forward_­list, list
a.push_­back(t)
void
Appends a copy of t.

Requires:  T shall be Cpp17CopyInsertable into X.
basic_­string, deque, list, vector
a.push_­back(rv)
void
Appends a copy of rv.

Requires:  T shall be Cpp17MoveInsertable into X.
basic_­string, deque, list, vector
a.pop_­front()
void
Destroys the first element.

Requires:  a.empty() shall be false.
deque, forward_­list, list
a.pop_­back()
void
Destroys the last element.

Requires:  a.empty() shall be false.
basic_­string, deque, list, vector
a[n]
reference; const_­reference for constant a
*(a.begin() + n)
basic_­string, array, deque, vector
a.at(n)
reference; const_­reference for constant a
*(a.begin() + n)
basic_­string, array, deque, vector
The member function at() provides bounds-checked access to container elements.
at() throws out_­of_­range if n >= a.size().

21.2.4 Node handles [container.node]

21.2.4.1 Overview [container.node.overview]

A node handle is an object that accepts ownership of a single element from an associative container ([associative.reqmts]) or an unordered associative container ([unord.req]).
It may be used to transfer that ownership to another container with compatible nodes.
Containers with compatible nodes have the same node handle type.
Elements may be transferred in either direction between container types in the same row of Table 70.
Table 70 — Container types with compatible nodes
map<K, T, C1, A>
map<K, T, C2, A>
map<K, T, C1, A>
multimap<K, T, C2, A>
set<K, C1, A>
set<K, C2, A>
set<K, C1, A>
multiset<K, C2, A>
unordered_­map<K, T, H1, E1, A>
unordered_­map<K, T, H2, E2, A>
unordered_­map<K, T, H1, E1, A>
unordered_­multimap<K, T, H2, E2, A>
unordered_­set<K, H1, E1, A>
unordered_­set<K, H2, E2, A>
unordered_­set<K, H1, E1, A>
unordered_­multiset<K, H2, E2, A>
If a node handle is not empty, then it contains an allocator that is equal to the allocator of the container when the element was extracted.
If a node handle is empty, it contains no allocator.
Class node-handle is for exposition only.
If a user-defined specialization of pair exists for pair<const Key, T> or pair<Key, T>, where Key is the container's key_­type and T is the container's mapped_­type, the behavior of operations involving node handles is undefined.
template<unspecified>
class node-handle {
public:
  // These type declarations are described in Tables 71 and 72.
  using value_type     = see below;     // not present for map containers
  using key_type       = see below;     // not present for set containers
  using mapped_type    = see below;     // not present for set containers
  using allocator_type = see below;

private:
  using container_node_type = unspecified;
  using ator_traits = allocator_traits<allocator_type>;

  typename ator_traits::rebind_traits<container_node_type>::pointer ptr_;
  optional<allocator_type> alloc_;

public:
  // [container.node.cons], constructors, copy, and assignment
  constexpr node-handle() noexcept : ptr_(), alloc_() {}
  node-handle(node-handle&&) noexcept;
  node-handle& operator=(node-handle&&);

  // [container.node.dtor], destructor
  ~node-handle();

  // [container.node.observers], observers
  value_type& value() const;            // not present for map containers
  key_type& key() const;                // not present for set containers
  mapped_type& mapped() const;          // not present for set containers

  allocator_type get_allocator() const;
  explicit operator bool() const noexcept;
  [[nodiscard]] bool empty() const noexcept;

  // [container.node.modifiers], modifiers
  void swap(node-handle&)
    noexcept(ator_traits::propagate_on_container_swap::value ||
             ator_traits::is_always_equal::value);

  friend void swap(node-handle& x, node-handle& y) noexcept(noexcept(x.swap(y))) {
    x.swap(y);
  }
};

21.2.4.2 Constructors, copy, and assignment [container.node.cons]

node-handle(node-handle&& nh) noexcept;
Effects: Constructs a node-handle object initializing ptr_­ with nh.ptr_­.
Move constructs alloc_­ with nh.alloc_­.
Assigns nullptr to nh.ptr_­ and assigns nullopt to nh.alloc_­.
node-handle& operator=(node-handle&& nh);
Requires: Either !alloc_­, or ator_­traits::propagate_­on_­container_­move_­assignment is true, or alloc_­ == nh.alloc_­.
Effects:
  • If ptr_­ != nullptr, destroys the value_­type subobject in the container_­node_­type object pointed to by ptr_­ by calling ator_­traits::destroy, then deallocates ptr_­ by calling ator_­traits::rebind_­traits<container_­node_­type>::deallocate.
  • Assigns nh.ptr_­ to ptr_­.
  • If !alloc_ or ator_­traits::propagate_­on_­container_­move_­assignment is true, move assigns nh.alloc_­ to alloc_­.
  • Assigns nullptr to nh.ptr_­ and assigns nullopt to nh.alloc_­.
Returns: *this.
Throws: Nothing.

21.2.4.3 Destructor [container.node.dtor]

~node-handle();
Effects: If ptr_­ != nullptr, destroys the value_­type subobject in the container_­node_­type object pointed to by ptr_­ by calling ator_­traits::destroy, then deallocates ptr_­ by calling ator_­traits::rebind_­traits<container_­node_­type>::deallocate.

21.2.4.4 Observers [container.node.observers]

value_type& value() const;
Requires: empty() == false.
Returns: A reference to the value_­type subobject in the container_­node_­type object pointed to by ptr_­.
Throws: Nothing.
key_type& key() const;
Requires: empty() == false.
Returns: A non-const reference to the key_­type member of the value_­type subobject in the container_­node_­type object pointed to by ptr_­.
Throws: Nothing.
Remarks: Modifying the key through the returned reference is permitted.
mapped_type& mapped() const;
Requires: empty() == false.
Returns: A reference to the mapped_­type member of the value_­type subobject in the container_­node_­type object pointed to by ptr_­.
Throws: Nothing.
allocator_type get_allocator() const;
Requires: empty() == false.
Returns: *alloc_­.
Throws: Nothing.
explicit operator bool() const noexcept;
Returns: ptr_­ != nullptr.
[[nodiscard]] bool empty() const noexcept;
Returns: ptr_­ == nullptr.

21.2.4.5 Modifiers [container.node.modifiers]

void swap(node-handle& nh) noexcept(ator_traits::propagate_on_container_swap::value || ator_traits::is_always_equal::value);
Requires: !alloc_­, or !nh.alloc_­, or ator_­traits::propagate_­on_­container_­swap is true, or alloc_­ == nh.alloc_­.
Effects: Calls swap(ptr_­, nh.ptr_­).
If !alloc_­, or !nh.alloc_­, or ator_­traits::propagate_­on_­container_­swap is true calls swap(alloc_­, nh.alloc_­).

21.2.5 Insert return type [container.insert.return]

The associative containers with unique keys and the unordered containers with unique keys have a member function insert that returns a nested type insert_­return_­type.
That return type is a specialization of the template specified in this subclause.
template<class Iterator, class NodeType>
struct insert-return-type
{
  Iterator position;
  bool     inserted;
  NodeType node;
};
The name insert-return-type is exposition only.
insert-return-type has the template parameters, data members, and special members specified above.
It has no base classes or members other than those specified.

21.2.6 Associative containers [associative.reqmts]

Associative containers provide fast retrieval of data based on keys.
The library provides four basic kinds of associative containers: set, multiset, map and multimap.
Each associative container is parameterized on Key and an ordering relation Compare that induces a strict weak ordering on elements of Key.
In addition, map and multimap associate an arbitrary mapped type T with the Key.
The object of type Compare is called the comparison object of a container.
The phrase “equivalence of keys” means the equivalence relation imposed by the comparison object.
That is, two keys k1 and k2 are considered to be equivalent if for the comparison object comp, comp(k1, k2) == false && comp(k2, k1) == false.
[Note
:
This is not necessarily the same as the result of k1 == k2.
end note
]
For any two keys k1 and k2 in the same container, calling comp(k1, k2) shall always return the same value.
An associative container supports unique keys if it may contain at most one element for each key.
Otherwise, it supports equivalent keys.
The set and map classes support unique keys; the multiset and multimap classes support equivalent keys.
For multiset and multimap, insert, emplace, and erase preserve the relative ordering of equivalent elements.
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>.
iterator of an associative container is of the bidirectional iterator category.
For associative containers where the value type is the same as the key type, both iterator and const_­iterator are constant iterators.
It is unspecified whether or not iterator and const_­iterator are the same type.
[Note
:
iterator and const_­iterator have identical semantics in this case, and iterator is convertible to const_­iterator.
Users can avoid violating the one-definition rule by always using const_­iterator in their function parameter lists.
end note
]
The associative containers meet all the requirements of Allocator-aware containers, except that for map and multimap, the requirements placed on value_­type in Table 67 apply instead to key_­type and mapped_­type.
[Note
:
For example, in some cases key_­type and mapped_­type are required to be Cpp17CopyAssignable even though the associated value_­type, pair<const key_­type, mapped_­type>, is not Cpp17CopyAssignable.
end note
]
In Table 71, X denotes an associative container class, a denotes a value of type X, a2 denotes a value of a type with nodes compatible with type X (Table 70), b denotes a possibly const value of type X, u denotes the name of a variable being declared, a_­uniq denotes a value of type X when X supports unique keys, a_­eq denotes a value of type X when X supports multiple keys, a_­tran denotes a possibly const value of type X when the qualified-id X::key_­compare::is_­transparent is valid and denotes a type ([temp.deduct]), i and j satisfy input iterator requirements and refer to elements implicitly convertible to value_­type, [i, j) denotes a valid range, p denotes a valid constant iterator to a, q denotes a valid dereferenceable constant iterator to a, r denotes a valid dereferenceable iterator to a, [q1, q2) denotes a valid range of constant iterators in a, il designates an object of type initializer_­list<value_­type>, t denotes a value of type X::value_­type, k denotes a value of type X::key_­type and c denotes a possibly const value of type X::key_­compare; kl is a value such that a is partitioned ([alg.sorting]) with respect to c(r, kl), with r the key value of e and e in a; ku is a value such that a is partitioned with respect to !c(ku, r); ke is a value such that a is partitioned with respect to c(r, ke) and !c(ke, r), with c(r, ke) implying !c(ke, r).
A denotes the storage allocator used by X, if any, or allocator<X::value_­type> otherwise, m denotes an allocator of a type convertible to A, and nh denotes a non-const rvalue of type X::node_­type.
Table 71 — Associative container requirements (in addition to container)
Expression
Return type
Assertion/note
Complexity
pre-/post-condition
X::key_­type
Key
compile time
X::mapped_­type (map and multimap only)
T
compile time
X::value_­type (set and multiset only)
Key
Requires:  value_­type is Cpp17Erasable from X
compile time
X::value_­type (map and multimap only)
pair<const Key, T>
Requires:  value_­type is Cpp17Erasable from X
compile time
X::key_­compare
Compare
Requires:  key_­compare is Cpp17CopyConstructible.
compile time
X::value_­compare
a binary predicate type
is the same as key_­compare for set and multiset; is an ordering relation on pairs induced by the first component (i.e., Key) for map and multimap.
compile time
X::node_­type
a specialization of a node-handle class template, such that the public nested types are the same types as the corresponding types in X.
compile time
X(c)
X u(c);
Effects:  Constructs an empty container.
Uses a copy of c as a comparison object.
constant
X()
X u;
Requires:  key_­compare is Cpp17DefaultConstructible.

Effects:  Constructs an empty container.
Uses Compare() as a comparison object
constant
X(i,j,c)
X u(i,j,c);
Requires:  value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Constructs an empty container and inserts elements from the range [i, j) into it; uses c as a comparison object.
in general, where N has the value distance(i, j); linear if [i, j) is sorted with value_­comp()
X(i,j)
X u(i,j);
Requires:  key_­compare is Cpp17DefaultConstructible.
value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Same as above, but uses Compare() as a comparison object.
same as above
X(il)
same as X(il.begin(), il.end())
same as X(il.begin(), il.end())
X(il,c)
same as X(il.begin(), il.end(), c)
same as X(il.begin(), il.end(), c)
a = il
X&
Requires:  value_­type is Cpp17CopyInsertable into X and Cpp17CopyAssignable.

Effects: Assigns the range [il.begin(), il.end()) into a.
All existing elements of a are either assigned to or destroyed.
in general, where N has the value il.size() + a.size(); linear if [il.begin(), il.end()) is sorted with value_­comp()
b.key_­comp()
X::key_­compare
returns the comparison object out of which b was constructed.
constant
b.value_­comp()
X::value_­compare
returns an object of value_­compare constructed out of the comparison object
constant
a_­uniq.​emplace(​args)
pair<​iterator, bool>
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from args.

Effects:  Inserts a value_­type object t constructed with std::forward<​Args​>(​args)... if and only if there is no element in the container with key equivalent to the key of t.
The bool component of the returned pair is true if and only if the insertion takes place, and the iterator component of the pair points to the element with key equivalent to the key of t.
logarithmic
a_­eq.​emplace(​args)
iterator
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from args.

Effects:  Inserts a value_­type object t constructed with std::forward<​Args​>(​args)... and returns the iterator pointing to the newly inserted element.
If a range containing elements equivalent to t exists in a_­eq, t is inserted at the end of that range.
logarithmic
a.emplace_­hint(​p, args)
iterator
equivalent to a.emplace( std::forward<​Args​>(​args)...).
Return value is an iterator pointing to the element with the key equivalent to the newly inserted element.
The element is inserted as close as possible to the position just prior to p.
logarithmic in general, but amortized constant if the element is inserted right before p
a_­uniq.​insert(​t)
pair<​iterator, bool>
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects:  Inserts t if and only if there is no element in the container with key equivalent to the key of t.
The bool component of the returned pair is true if and only if the insertion takes place, and the iterator component of the pair points to the element with key equivalent to the key of t.
logarithmic
a_­eq.​insert(​t)
iterator
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects:  Inserts t and returns the iterator pointing to the newly inserted element.
If a range containing elements equivalent to t exists in a_­eq, t is inserted at the end of that range.
logarithmic
a.​insert(​p, t)
iterator
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects:  Inserts t if and only if there is no element with key equivalent to the key of t in containers with unique keys; always inserts t in containers with equivalent keys.
Always returns the iterator pointing to the element with key equivalent to the key of t.
t is inserted as close as possible to the position just prior to p.
logarithmic in general, but amortized constant if t is inserted right before p.
a.​insert(​i, j)
void
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from *i.

Requires: i, j are not iterators into a.
inserts each element from the range [i, j) if and only if there is no element with key equivalent to the key of that element in containers with unique keys; always inserts that element in containers with equivalent keys.
, where N has the value distance(i, j)
a.​insert(​il)
void
equivalent to a.insert(il.begin(), il.end())
a_­uniq.​insert(​nh)
insert_­return_­type
Requires: nh is empty or a_­uniq.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect.
Otherwise, inserts the element owned by nh if and only if there is no element in the container with a key equivalent to nh.key().

Ensures: If nh is empty, inserted is false, position is end(), and node is empty.
Otherwise if the insertion took place, inserted is true, position points to the inserted element, and node is empty; if the insertion failed, inserted is false, node has the previous value of nh, and position points to an element with a key equivalent to nh.key().
logarithmic
a_­eq.​insert(​nh)
iterator
Requires: nh is empty or a_­eq.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect and returns a_­eq.end().
Otherwise, inserts the element owned by nh and returns an iterator pointing to the newly inserted element.
If a range containing elements with keys equivalent to nh.key() exists in a_­eq, the element is inserted at the end of that range.

Ensures: nh is empty.
logarithmic
a.​insert(​p, nh)
iterator
Requires: nh is empty or a.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect and returns a.end().
Otherwise, inserts the element owned by nh if and only if there is no element with key equivalent to nh.key() in containers with unique keys; always inserts the element owned by nh in containers with equivalent keys.
Always returns the iterator pointing to the element with key equivalent to nh.key().
The element is inserted as close as possible to the position just prior to p.

Ensures: nh is empty if insertion succeeds, unchanged if insertion fails.
logarithmic in general, but amortized constant if the element is inserted right before p.
a.​extract(​k)
node_­type
removes the first element in the container with key equivalent to k.
Returns a node_­type owning the element if found, otherwise an empty node_­type.
log(a.size())
a.​extract(​q)
node_­type
removes the element pointed to by q.
Returns a node_­type owning that element.
amortized constant
a.merge(a2)
void
Requires: a.get_­allocator() == a2.get_­allocator().

Attempts to extract each element in a2 and insert it into a using the comparison object of a.
In containers with unique keys, if there is an element in a with key equivalent to the key of an element from a2, then that element is not extracted from a2.

Ensures: Pointers and references to the transferred elements of a2 refer to those same elements but as members of a.
Iterators referring to the transferred elements will continue to refer to their elements, but they now behave as iterators into a, not into a2.

Throws: Nothing unless the comparison object throws.
, where N has the value a2.size().
a.erase(k)
size_­type
erases all elements in the container with key equivalent to k.
returns the number of erased elements.
a.erase(q)
iterator
erases the element pointed to by q.
Returns an iterator pointing to the element immediately following q prior to the element being erased.
If no such element exists, returns a.end().
amortized constant
a.erase(r)
iterator
erases the element pointed to by r.
Returns an iterator pointing to the element immediately following r prior to the element being erased.
If no such element exists, returns a.end().
amortized constant
a.erase(
q1, q2)
iterator
erases all the elements in the range [q1, q2).
Returns an iterator pointing to the element pointed to by q2 prior to any elements being erased.
If no such element exists, a.end() is returned.
, where N has the value distance(q1, q2).
a.clear()
void
a.erase(a.begin(),a.end())
Ensures: a.empty() returns true.
linear in a.size().
b.find(k)
iterator; const_­iterator for constant b.
returns an iterator pointing to an element with the key equivalent to k, or b.end() if such an element is not found
logarithmic
a_­tran.
find(ke)
iterator; const_­iterator for constant a_­tran.
returns an iterator pointing to an element with key r such that !c(r, ke) && !c(ke, r), or a_­tran.end() if such an element is not found
logarithmic
b.count(k)
size_­type
returns the number of elements with key equivalent to k
a_­tran.
count(ke)
size_­type
returns the number of elements with key r such that !c(r, ke) && !c(ke, r)
b.
contains(k)
bool
equivalent to b.find(k) != b.end()
logarithmic
a_­tran.
contains(ke)
bool
equivalent to a_­tran.find(ke) != a_­tran.end()
logarithmic
b.lower_­bound(k)
iterator; const_­iterator for constant b.
returns an iterator pointing to the first element with key not less than k, or b.end() if such an element is not found.
logarithmic
a_­tran.
lower_­bound(kl)
iterator; const_­iterator for constant a_­tran.
returns an iterator pointing to the first element with key r such that !c(r, kl), or a_­tran.end() if such an element is not found.
logarithmic
b.upper_­bound(k)
iterator; const_­iterator for constant b.
returns an iterator pointing to the first element with key greater than k, or b.end() if such an element is not found.
logarithmic
a_­tran.
upper_­bound(ku)
iterator; const_­iterator for constant a_­tran.
returns an iterator pointing to the first element with key r such that c(ku, r), or a_­tran.end() if such an element is not found.
logarithmic
b.equal_­range(k)
pair<​iterator, iterator>; pair<​const_­iterator, const_­iterator> for constant b.
equivalent to make_­pair(b.lower_­bound(k), b.upper_­bound(k)).
logarithmic
a_­tran.
equal_­range(ke)
pair<​iterator, iterator>; pair<​const_­iterator, const_­iterator> for constant a_­tran.
equivalent to make_­pair(
a_­tran.lower_­bound(ke), a_­tran.upper_­bound(ke)).
logarithmic
The insert and emplace members shall not affect the validity of iterators and references to the container, and the erase members shall invalidate only iterators and references to the erased elements.
The extract members invalidate only iterators to the removed element; pointers and references to the removed element remain valid.
However, accessing the element through such pointers and references while the element is owned by a node_­type is undefined behavior.
References and pointers to an element obtained while it is owned by a node_­type are invalidated if the element is successfully inserted.
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, the following condition holds:
value_comp(*j, *i) == false
For associative containers with unique keys the stronger condition holds:
value_comp(*i, *j) != false
When 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 comparison object from the container being copied, as if that comparison object had been passed to the target container in its constructor.
The member function templates find, count, contains, lower_­bound, upper_­bound, and equal_­range shall not participate in overload resolution unless the qualified-id Compare::is_­transparent is valid and denotes a type ([temp.deduct]).
A deduction guide for an associative container shall not participate in overload resolution if any of the following are true:
  • It has an InputIterator template parameter and a type that does not qualify as an input iterator is deduced for that parameter.
  • It has an Allocator template parameter and a type that does not qualify as an allocator is deduced for that parameter.
  • It has a Compare template parameter and a type that qualifies as an allocator is deduced for that parameter.

21.2.6.1 Exception safety guarantees [associative.reqmts.except]

For associative containers, no clear() function throws an exception.
erase(k) does not throw an exception unless that exception is thrown by the container's Compare object (if any).
For associative containers, if an exception is thrown by any operation from within an insert or emplace function inserting a single element, the insertion has no effect.
For associative containers, no swap function throws an exception unless that exception is thrown by the swap of the container's Compare object (if any).

21.2.7 Unordered associative containers [unord.req]

Unordered associative containers provide an ability for fast retrieval of data based on keys.
The worst-case complexity for most operations is linear, but the average case is much faster.
The library provides four unordered associative containers: unordered_­set, unordered_­map, unordered_­multiset, and unordered_­multimap.
Unordered associative containers conform to the requirements for Containers, except that the expressions a == b and a != b have different semantics than for the other container types.
Each unordered associative container is parameterized by Key, by a function object type Hash that meets the Cpp17Hash requirements ([hash.requirements]) and acts as a hash function for argument values of type Key, and by a binary predicate Pred that induces an equivalence relation on values of type Key.
Additionally, unordered_­map and unordered_­multimap associate an arbitrary mapped type T with the Key.
The container's object of type Hash — denoted by hash — is called the hash function of the container.
The container's object of type Pred — denoted by pred — is called the key equality predicate of the container.
Two values k1 and k2 of type Key are considered equivalent if the container's key equality predicate returns true when passed those values.
If k1 and k2 are equivalent, the container's hash function shall return the same value for both.
[Note
:
Thus, when an unordered associative container is instantiated with a non-default Pred parameter it usually needs a non-default Hash parameter as well.
end note
]
For any two keys k1 and k2 in the same container, calling pred(k1, k2) shall always return the same value.
For any key k in a container, calling hash(k) shall always return the same value.
An unordered associative container supports unique keys if it may contain at most one element for each key.
Otherwise, it supports equivalent keys.
unordered_­set and unordered_­map support unique keys.
unordered_­multiset and unordered_­multimap support equivalent keys.
In containers that support equivalent keys, elements with equivalent keys are adjacent to each other in the iteration order of the container.
Thus, although the absolute order of elements in an unordered container is not specified, its elements are grouped into equivalent-key groups such that all elements of each group have equivalent keys.
Mutating operations on unordered containers shall preserve the relative order of elements within each equivalent-key group unless otherwise specified.
For unordered_­set and unordered_­multiset the value type is the same as the key type.
For unordered_­map and unordered_­multimap it is pair<const Key, T>.
For unordered containers where the value type is the same as the key type, both iterator and const_­iterator are constant iterators.
It is unspecified whether or not iterator and const_­iterator are the same type.
[Note
:
iterator and const_­iterator have identical semantics in this case, and iterator is convertible to const_­iterator.
Users can avoid violating the one-definition rule by always using const_­iterator in their function parameter lists.
end note
]
The elements of an unordered associative container are organized into buckets.
Keys with the same hash code appear in the same bucket.
The number of buckets is automatically increased as elements are added to an unordered associative container, so that the average number of elements per bucket is kept below a bound.
Rehashing invalidates iterators, changes ordering between elements, and changes which buckets elements appear in, but does not invalidate pointers or references to elements.
For unordered_­multiset and unordered_­multimap, rehashing preserves the relative ordering of equivalent elements.
The unordered associative containers meet all the requirements of Allocator-aware containers, except that for unordered_­map and unordered_­multimap, the requirements placed on value_­type in Table 67 apply instead to key_­type and mapped_­type.
[Note
:
For example, key_­type and mapped_­type are sometimes required to be Cpp17CopyAssignable even though the associated value_­type, pair<const key_­type, mapped_­type>, is not Cpp17CopyAssignable.
end note
]
In Table 72: X denotes an unordered associative container class, a denotes a value of type X, a2 denotes a value of a type with nodes compatible with type X (Table 70), b denotes a possibly const value of type X, a_­uniq denotes a value of type X when X supports unique keys, a_­eq denotes a value of type X when X supports equivalent keys, i and j denote input iterators that refer to value_­type, [i, j) denotes a valid range, p and q2 denote valid constant iterators to a, q and q1 denote valid dereferenceable constant iterators to a, r denotes a valid dereferenceable iterator to a, [q1, q2) denotes a valid range in a, il denotes a value of type initializer_­list<value_­type>, t denotes a value of type X::value_­type, k denotes a value of type key_­type, hf denotes a possibly const value of type hasher, eq denotes a possibly const value of type key_­equal, n denotes a value of type size_­type, z denotes a value of type float, and nh denotes a non-const rvalue of type X::node_­type.
Table 72 — Unordered associative container requirements (in addition to container)
Expression
Return type
Assertion/note
Complexity
pre-/post-condition
X::key_­type
Key
compile time
X::mapped_­type (unordered_­map and unordered_­multimap only)
T
compile time
X::value_­type (unordered_­set and unordered_­multiset only)
Key
Requires:  value_­type is Cpp17Erasable from X
compile time
X::value_­type (unordered_­map and unordered_­multimap only)
pair<const Key, T>
Requires:  value_­type is Cpp17Erasable from X
compile time
X::hasher
Hash
Hash shall be a unary function object type such that the expression hf(k) has type size_­t.
compile time
X::key_­equal
Pred
Requires:  Pred is Cpp17CopyConstructible.

Pred shall be a binary predicate that takes two arguments of type Key.
Pred is an equivalence relation.
compile time
X::local_­iterator
An iterator type whose category, value type, difference type, and pointer and reference types are the same as X::iterator's.
A local_­iterator object may be used to iterate through a single bucket, but may not be used to iterate across buckets.
compile time
X::const_­local_­iterator
An iterator type whose category, value type, difference type, and pointer and reference types are the same as X::const_­iterator's.
A const_­local_­iterator object may be used to iterate through a single bucket, but may not be used to iterate across buckets.
compile time
X::node_­type
a specialization of a node-handle class template, such that the public nested types are the same types as the corresponding types in X.
compile time
X(n, hf, eq)
X a(n, hf, eq);
X
Effects:  Constructs an empty container with at least n buckets, using hf as the hash function and eq as the key equality predicate.
X(n, hf)
X a(n, hf);
X
Requires:  key_­equal is Cpp17DefaultConstructible.

Effects:  Constructs an empty container with at least n buckets, using hf as the hash function and key_­equal() as the key equality predicate.
X(n)
X a(n);
X
Requires:  hasher and key_­equal are Cpp17DefaultConstructible.

Effects:  Constructs an empty container with at least n buckets, using hasher() as the hash function and key_­equal() as the key equality predicate.
X()
X a;
X
Requires:  hasher and key_­equal are Cpp17DefaultConstructible.

Effects:  Constructs an empty container with an unspecified number of buckets, using hasher() as the hash function and key_­equal() as the key equality predicate.
constant
X(i, j, n, hf, eq)
X a(i, j, n, hf, eq);
X
Requires:  value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Constructs an empty container with at least n buckets, using hf as the hash function and eq as the key equality predicate, and inserts elements from [i, j) into it.
Average case (N is distance(i, j)), worst case
X(i, j, n, hf)
X a(i, j, n, hf);
X
Requires:  key_­equal is Cpp17DefaultConstructible.
value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Constructs an empty container with at least n buckets, using hf as the hash function and key_­equal() as the key equality predicate, and inserts elements from [i, j) into it.
Average case (N is distance(i, j)), worst case
X(i, j, n)
X a(i, j, n);
X
Requires:  hasher and key_­equal are Cpp17DefaultConstructible.
value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Constructs an empty container with at least n buckets, using hasher() as the hash function and key_­equal() as the key equality predicate, and inserts elements from [i, j) into it.
Average case (N is distance(i, j)), worst case
X(i, j)
X a(i, j);
X
Requires:  hasher and key_­equal are Cpp17DefaultConstructible.
value_­type is Cpp17EmplaceConstructible into X from *i.

Effects:  Constructs an empty container with an unspecified number of buckets, using hasher() as the hash function and key_­equal() as the key equality predicate, and inserts elements from [i, j) into it.
Average case (N is distance(i, j)), worst case
X(il)
X
Same as X(il.begin(), il.end()).
Same as X(il.begin(), il.end()).
X(il, n)
X
Same as X(il.begin(), il.end(), n).
Same as X(il.begin(), il.end(), n).
X(il, n, hf)
X
Same as X(il.begin(), il.end(), n, hf).
Same as X(il.begin(), il.end(), n, hf).
X(il, n, hf, eq)
X
Same as X(il.begin(), il.end(), n, hf, eq).
Same as X(il.begin(), il.end(), n, hf, eq).
X(b)
X a(b);
X
Copy constructor.
In addition to the requirements of Table 64, copies the hash function, predicate, and maximum load factor.
Average case linear in b.size(), worst case quadratic.
a = b
X&
Copy assignment operator.
In addition to the requirements of Table 64, copies the hash function, predicate, and maximum load factor.
Average case linear in b.size(), worst case quadratic.
a = il
X&
Requires:  value_­type is Cpp17CopyInsertable into X and Cpp17CopyAssignable.

Effects:  Assigns the range [il.begin(), il.end()) into a.
All existing elements of a are either assigned to or destroyed.
Same as a = X(il).
b.hash_­function()
hasher
Returns b's hash function.
constant
b.key_­eq()
key_­equal
Returns b's key equality predicate.
constant
a_­uniq. emplace(args)
pair<iterator, bool>
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from args.

Effects:  Inserts a value_­type object t constructed with std::forward<​Args​>(​args)... if and only if there is no element in the container with key equivalent to the key of t.
The bool component of the returned pair is true if and only if the insertion takes place, and the iterator component of the pair points to the element with key equivalent to the key of t.
Average case , worst case .
a_­eq.emplace(args)
iterator
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from args.

Effects:  Inserts a value_­type object t constructed with std::forward<​Args>(​args)... and returns the iterator pointing to the newly inserted element.
Average case , worst case .
a.emplace_­hint(p, args)
iterator
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from args.

Effects:  Equivalent to a.emplace( std::forward<​Args>(​args)...).
Return value is an iterator pointing to the element with the key equivalent to the newly inserted element.
The const_­iterator p is a hint pointing to where the search should start.
Implementations are permitted to ignore the hint.
Average case , worst case .
a_­uniq.insert(t)
pair<iterator, bool>
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects:  Inserts t if and only if there is no element in the container with key equivalent to the key of t.
The bool component of the returned pair indicates whether the insertion takes place, and the iterator component points to the element with key equivalent to the key of t.
Average case , worst case .
a_­eq.insert(t)
iterator
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects:  Inserts t, and returns an iterator pointing to the newly inserted element.
Average case , worst case .
a.insert(p, t)
iterator
Requires:  If t is a non-const rvalue, value_­type shall be Cpp17MoveInsertable into X; otherwise, value_­type shall be Cpp17CopyInsertable into X.

Effects: Equivalent to a.insert(t).
Return value is an iterator pointing to the element with the key equivalent to that of t.
The iterator p is a hint pointing to where the search should start.
Implementations are permitted to ignore the hint.
Average case , worst case .
a.insert(i, j)
void
Requires:  value_­type shall be Cpp17EmplaceConstructible into X from *i.

Requires: i and j are not iterators in a.

Effects: Equivalent to a.insert(t) for each element in [i,j).
Average case , where N is distance(i, j).
Worst case .
a.insert(il)
void
Same as a.insert(il.begin(), il.end()).
Same as a.insert( il.begin(), il.end()).
a_­uniq.
insert(nh)
insert_­return_­type
Requires: nh is empty or a_­uniq.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect.
Otherwise, inserts the element owned by nh if and only if there is no element in the container with a key equivalent to nh.key().

Ensures: If nh is empty, inserted is false, position is end(), and node is empty.
Otherwise if the insertion took place, inserted is true, position points to the inserted element, and node is empty; if the insertion failed, inserted is false, node has the previous value of nh, and position points to an element with a key equivalent to nh.key().
Average case , worst case .
a_­eq.
insert(nh)
iterator
Requires: nh is empty or a_­eq.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect and returns a_­eq.end().
Otherwise, inserts the element owned by nh and returns an iterator pointing to the newly inserted element.

Ensures: nh is empty.
Average case , worst case .
a.insert(q, nh)
iterator
Requires: nh is empty or a.get_­allocator() == nh.get_­allocator().

Effects: If nh is empty, has no effect and returns a.end().
Otherwise, inserts the element owned by nh if and only if there is no element with key equivalent to nh.key() in containers with unique keys; always inserts the element owned by nh in containers with equivalent keys.
Always returns the iterator pointing to the element with key equivalent to nh.key().
The iterator q is a hint pointing to where the search should start.
Implementations are permitted to ignore the hint.

Ensures: nh is empty if insertion succeeds, unchanged if insertion fails.
Average case , worst case .
a.extract(k)
node_­type
Removes an element in the container with key equivalent to k.
Returns a node_­type owning the element if found, otherwise an empty node_­type.
Average case , worst case .
a.extract(q)
node_­type
Removes the element pointed to by q.
Returns a node_­type owning that element.
Average case , worst case .
a.merge(a2)
void
Requires: a.get_­allocator() == a2.get_­allocator().

Attempts to extract each element in a2 and insert it into a using the hash function and key equality predicate of a.
In containers with unique keys, if there is an element in a with key equivalent to the key of an element from a2, then that element is not extracted from a2.
Ensures: Pointers and references to the transferred elements of a2 refer to those same elements but as members of a.
Iterators referring to the transferred elements and all iterators referring to a will be invalidated, but iterators to elements remaining in a2 will remain valid.
Average case , where N is a2.size().
Worst case .
a.erase(k)
size_­type
Erases all elements with key equivalent to k.
Returns the number of elements erased.
Average case .
Worst case .
a.erase(q)
iterator
Erases the element pointed to by q.
Returns the iterator immediately following q prior to the erasure.
Average case , worst case .
a.erase(r)
iterator
Erases the element pointed to by r.
Returns the iterator immediately following r prior to the erasure.
Average case , worst case .
a.erase(q1, q2)
iterator
Erases all elements in the range [q1, q2).
Returns the iterator immediately following the erased elements prior to the erasure.
Average case linear in distance(q1, q2), worst case .
a.clear()
void
Erases all elements in the container.
Ensures: a.empty() returns true
Linear in a.size().
b.find(k)
iterator;
const_­iterator for const b.
Returns an iterator pointing to an element with key equivalent to k, or b.end() if no such element exists.
Average case , worst case .
b.count(k)
size_­type
Returns the number of elements with key equivalent to k.
Average case , worst case .
b.contains(k)
bool
Equivalent to b.find(k) != b.end()
Average case , worst case .
b.equal_­range(k)
pair<iterator, iterator>;
pair<const_­iterator, const_­iterator> for const b.
Returns a range containing all elements with keys equivalent to k.
Returns make_­pair(b.end(), b.end()) if no such elements exist.
Average case .
Worst case .
b.bucket_­count()
size_­type
Returns the number of buckets that b contains.
Constant
b.max_­bucket_­count()
size_­type
Returns an upper bound on the number of buckets that b might ever contain.
Constant
b.bucket(k)
size_­type
Requires: b.bucket_­count() > 0.

Returns the index of the bucket in which elements with keys equivalent to k would be found, if any such element existed.
Ensures: the return value shall be in the range [0, b.bucket_­count()).
Constant
b.bucket_­size(n)
size_­type
Requires: n shall be in the range [0, b.bucket_­count()).
Returns the number of elements in the n bucket.
b.begin(n)
local_­iterator;
const_­local_­iterator for const b.
Requires: n shall be in the range [0, b.bucket_­count()).
b.begin(n) returns an iterator referring to the first element in the bucket.
If the bucket is empty, then b.begin(n) == b.end(n).
Constant
b.end(n)
local_­iterator;
const_­local_­iterator for const b.
Requires: n shall be in the range [0, b.bucket_­count()).
b.end(n) returns an iterator which is the past-the-end value for the bucket.
Constant
b.cbegin(n)
const_­local_­iterator
Requires: n shall be in the range [0, b.bucket_­count()).
b.cbegin(n) returns an iterator referring to the first element in the bucket.
If the bucket is empty, then b.cbegin(n) == b.cend(n).
Constant
b.cend(n)
const_­local_­iterator
Requires: n shall be in the range [0, b.bucket_­count()).
b.cend(n) returns an iterator which is the past-the-end value for the bucket.
Constant
b.load_­factor()
float
Returns the average number of elements per bucket.
Constant
b.max_­load_­factor()
float
Returns a positive number that the container attempts to keep the load factor less than or equal to.
The container automatically increases the number of buckets as necessary to keep the load factor below this number.
Constant
a.max_­load_­factor(z)
void
Requires: z shall be positive.
May change the container's maximum load factor, using z as a hint.
Constant
a.rehash(n)
void
Ensures: a.bucket_­count() >= a.size() / a.max_­load_­factor() and a.bucket_­count() >= n.
Average case linear in a.size(), worst case quadratic.
a.reserve(n)
void
Same as a.rehash(ceil(n / a.max_­load_­factor())).
Average case linear in a.size(), worst case quadratic.
Two unordered containers a and b compare equal if a.size() == b.size() and, for every equivalent-key group [Ea1, Ea2) obtained from a.equal_­range(Ea1), there exists an equivalent-key group [Eb1, Eb2) obtained from b.equal_­range(Ea1), such that is_­permutation(Ea1, Ea2, Eb1, Eb2) returns true.
For unordered_­set and unordered_­map, the complexity of operator== (i.e., the number of calls to the == operator of the value_­type, to the predicate returned by key_­eq(), and to the hasher returned by hash_­function()) is proportional to N in the average case and to in the worst case, where N is a.
size().
For unordered_­multiset and unordered_­multimap, the complexity of operator== is proportional to in the average case and to in the worst case, where N is a.size(), and is the size of the equivalent-key group in a.
However, if the respective elements of each corresponding pair of equivalent-key groups and are arranged in the same order (as is commonly the case, e.g., if a and b are unmodified copies of the same container), then the average-case complexity for unordered_­multiset and unordered_­multimap becomes proportional to N (but worst-case complexity remains , e.g., for a pathologically bad hash function). The behavior of a program that uses operator== or operator!= on unordered containers is undefined unless the Pred function object has the same behavior for both containers and the equality comparison function for Key is a refinement230 of the partition into equivalent-key groups produced by Pred.
The iterator types iterator and const_­iterator of an unordered associative container are of at least the forward iterator category.
For unordered associative containers where the key type and value type are the same, both iterator and const_­iterator are constant iterators.
The insert and emplace members shall not affect the validity of references to container elements, but may invalidate all iterators to the container.
The erase members shall invalidate only iterators and references to the erased elements, and preserve the relative order of the elements that are not erased.
The insert and emplace members shall not affect the validity of iterators if (N+n) <= z * B, where N is the number of elements in the container prior to the insert operation, n is the number of elements inserted, B is the container's bucket count, and z is the container's maximum load factor.
The extract members invalidate only iterators to the removed element, and preserve the relative order of the elements that are not erased; pointers and references to the removed element remain valid.
However, accessing the element through such pointers and references while the element is owned by a node_­type is undefined behavior.
References and pointers to an element obtained while it is owned by a node_­type are invalidated if the element is successfully inserted.
A deduction guide for an unordered associative container shall not participate in overload resolution if any of the following are true:
  • It has an InputIterator template parameter and a type that does not qualify as an input iterator is deduced for that parameter.
  • It has an Allocator template parameter and a type that does not qualify as an allocator is deduced for that parameter.
  • It has a Hash template parameter and an integral type or a type that qualifies as an allocator is deduced for that parameter.
  • It has a Pred template parameter and a type that qualifies as an allocator is deduced for that parameter.
Equality comparison is a refinement of partitioning if no two objects that compare equal fall into different partitions.

21.2.7.1 Exception safety guarantees [unord.req.except]

For unordered associative containers, no clear() function throws an exception.
erase(k) does not throw an exception unless that exception is thrown by the container's Hash or Pred object (if any).
For unordered associative containers, if an exception is thrown by any operation other than the container's hash function from within an insert or emplace function inserting a single element, the insertion has no effect.
For unordered associative containers, no swap function throws an exception unless that exception is thrown by the swap of the container's Hash or Pred object (if any).
For unordered associative containers, if an exception is thrown from within a rehash() function other than by the container's hash function or comparison function, the rehash() function has no effect.

21.3 Sequence containers [sequences]

21.3.1 In general [sequences.general]

The headers <array>, <deque>, <forward_­list>, <list>, and <vector> define class templates that meet the requirements for sequence containers.
The following exposition-only alias template may appear in deduction guides for sequence containers:
template<class InputIterator>
  using iter-value-type = typename iterator_traits<InputIterator>::value_type;  // exposition only

21.3.2 Header <array> synopsis [array.syn]

#include <initializer_list>

namespace std {
  // [array], class template array
  template<class T, size_t N> struct array;

  template<class T, size_t N>
    constexpr bool operator==(const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    constexpr bool operator!=(const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    constexpr bool operator< (const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    constexpr bool operator> (const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    constexpr bool operator<=(const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    constexpr bool operator>=(const array<T, N>& x, const array<T, N>& y);
  template<class T, size_t N>
    void swap(array<T, N>& x, array<T, N>& y) noexcept(noexcept(x.swap(y)));

  template<class T> class tuple_size;
  template<size_t I, class T> class tuple_element;
  template<class T, size_t N>
    struct tuple_size<array<T, N>>;
  template<size_t I, class T, size_t N>
    struct tuple_element<I, array<T, N>>;
  template<size_t I, class T, size_t N>
    constexpr T& get(array<T, N>&) noexcept;
  template<size_t I, class T, size_t N>
    constexpr T&& get(array<T, N>&&) noexcept;
  template<size_t I, class T, size_t N>
    constexpr const T& get(const array<T, N>&) noexcept;
  template<size_t I, class T, size_t N>
    constexpr const T&& get(const array<T, N>&&) noexcept;
}

21.3.3 Header <deque> synopsis [deque.syn]

#include <initializer_list>

namespace std {
  // [deque], class template deque
  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)
      noexcept(noexcept(x.swap(y)));

  namespace pmr {
    template<class T>
      using deque = std::deque<T, polymorphic_allocator<T>>;
  }
}

21.3.4 Header <forward_­list> synopsis [forward_list.syn]

#include <initializer_list>

namespace std {
  // [forwardlist], class template forward_­list
  template<class T, class Allocator = allocator<T>> class forward_list;

  template<class T, class Allocator>
    bool operator==(const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);
  template<class T, class Allocator>
    bool operator!=(const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);
  template<class T, class Allocator>
    bool operator< (const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);
  template<class T, class Allocator>
    bool operator> (const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);
  template<class T, class Allocator>
    bool operator<=(const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);
  template<class T, class Allocator>
    bool operator>=(const forward_list<T, Allocator>& x, const forward_list<T, Allocator>& y);

  template<class T, class Allocator>
    void swap(forward_list<T, Allocator>& x, forward_list<T, Allocator>& y)
      noexcept(noexcept(x.swap(y)));

  namespace pmr {
    template<class T>
      using forward_list = std::forward_list<T, polymorphic_allocator<T>>;
  }
}

21.3.5 Header <list> synopsis [list.syn]

#include <initializer_list>

namespace std {
  // [list], class template list
  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)
      noexcept(noexcept(x.swap(y)));

  namespace pmr {
    template<class T>
      using list = std::list<T, polymorphic_allocator<T>>;
  }
}

21.3.6 Header <vector> synopsis [vector.syn]

#include <initializer_list>

namespace std {
  // [vector], class template vector
  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)
      noexcept(noexcept(x.swap(y)));

  // [vector.bool], class vector<bool>
  template<class Allocator> class vector<bool, Allocator>;

  // hash support
  template<class T> struct hash;
  template<class Allocator> struct hash<vector<bool, Allocator>>;

  namespace pmr {
    template<class T>
      using vector = std::vector<T, polymorphic_allocator<T>>;
  }
}

21.3.7 Class template array [array]

21.3.7.1 Overview [array.overview]

The header <array> defines a class template for storing fixed-size sequences of objects.
An array is a contiguous container.
An instance of array<T, N> stores N elements of type T, so that size() == N is an invariant.
An array is an aggregate that can be list-initialized with up to N elements whose types are convertible to T.
An array satisfies all of the requirements of a container and of a reversible container ([container.requirements]), except that a default constructed array object is not empty and that swap does not have constant complexity.
An array satisfies some of the requirements of a sequence container.
Descriptions are provided here only for operations on array that are not described in one of these tables and for operations where there is additional semantic information.
The types iterator and const_­iterator satisfy the constexpr iterator requirements ([iterator.requirements.general]).
namespace std {
  template<class T, size_t N>
  struct array {
    // types
    using value_type             = T;
    using pointer                = T*;
    using const_pointer          = const T*;
    using reference              = T&;
    using const_reference        = const T&;
    using size_type              = size_t;
    using difference_type        = ptrdiff_t;
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;

    // no explicit construct/copy/destroy for aggregate type

    void fill(const T& u);
    void swap(array&) noexcept(is_nothrow_swappable_v<T>);

    // iterators
    constexpr iterator               begin() noexcept;
    constexpr const_iterator         begin() const noexcept;
    constexpr iterator               end() noexcept;
    constexpr const_iterator         end() const noexcept;

    constexpr reverse_iterator       rbegin() noexcept;
    constexpr const_reverse_iterator rbegin() const noexcept;
    constexpr reverse_iterator       rend() noexcept;
    constexpr const_reverse_iterator rend() const noexcept;

    constexpr const_iterator         cbegin() const noexcept;
    constexpr const_iterator         cend() const noexcept;
    constexpr const_reverse_iterator crbegin() const noexcept;
    constexpr const_reverse_iterator crend() const noexcept;

    // capacity
    [[nodiscard]] constexpr bool empty() const noexcept;
    constexpr size_type size() const noexcept;
    constexpr size_type max_size() const noexcept;

    // element access
    constexpr reference       operator[](size_type n);
    constexpr const_reference operator[](size_type n) const;
    constexpr reference       at(size_type n);
    constexpr const_reference at(size_type n) const;
    constexpr reference       front();
    constexpr const_reference front() const;
    constexpr reference       back();
    constexpr const_reference back() const;

    constexpr T *       data() noexcept;
    constexpr const T * data() const noexcept;
  };

  template<class T, class... U>
    array(T, U...) -> array<T, 1 + sizeof...(U)>;
}

21.3.7.2 Constructors, copy, and assignment [array.cons]

The conditions for an aggregate shall be met.
Class array relies on the implicitly-declared special member functions ([class.default.ctor], [class.dtor], and [class.copy.ctor]) to conform to the container requirements table in [container.requirements].
In addition to the requirements specified in the container requirements table, the implicit move constructor and move assignment operator for array require that T be Cpp17MoveConstructible or Cpp17MoveAssignable, respectively.
template<class T, class... U> array(T, U...) -> array<T, 1 + sizeof...(U)>;
Requires: (is_­same_­v<T, U> && ...) is true.
Otherwise the program is ill-formed.

21.3.7.3 Member functions [array.members]

constexpr size_type size() const noexcept;
Returns: N.
constexpr T* data() noexcept; constexpr const T* data() const noexcept;
Returns: A pointer such that [data(), data() + size()) is a valid range.
For a non-empty array, data() == addressof(front()).
void fill(const T& u);
Effects: As if by fill_­n(begin(), N, u).
void swap(array& y) noexcept(is_nothrow_swappable_v<T>);
Effects: Equivalent to swap_­ranges(begin(), end(), y.begin()).
[Note
:
Unlike the swap function for other containers, array::swap takes linear time, may exit via an exception, and does not cause iterators to become associated with the other container.
end note
]

21.3.7.4 Specialized algorithms [array.special]

template<class T, size_t N> void swap(array<T, N>& x, array<T, N>& y) noexcept(noexcept(x.swap(y)));
Remarks: This function shall not participate in overload resolution unless N == 0 or is_­swappable_­v<T> is true.
Effects: As if by x.swap(y).
Complexity: Linear in N.

21.3.7.5 Zero-sized arrays [array.zero]

array shall provide support for the special case N == 0.
In the case that N == 0, begin() == end() == unique value.
The return value of data() is unspecified.
The effect of calling front() or back() for a zero-sized array is undefined.
Member function swap() shall have a non-throwing exception specification.

21.3.7.6 Tuple interface [array.tuple]

template<class T, size_t N> struct tuple_size<array<T, N>> : integral_constant<size_t, N> { };
tuple_element<I, array<T, N>>::type
Requires: I < N.
The program is ill-formed if I is out of bounds.
Value: The type T.
template<size_t I, class T, size_t N> constexpr T& get(array<T, N>& a) noexcept; template<size_t I, class T, size_t N> constexpr T&& get(array<T, N>&& a) noexcept; template<size_t I, class T, size_t N> constexpr const T& get(const array<T, N>& a) noexcept; template<size_t I, class T, size_t N> constexpr const T&& get(const array<T, N>&& a) noexcept;
Requires: I < N.
The program is ill-formed if I is out of bounds.
Returns: A reference to the I element of a, where indexing is zero-based.

21.3.8 Class template deque [deque]

21.3.8.1 Overview [deque.overview]

A deque is a sequence container that supports random access iterators ([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.
Storage management is handled automatically.
A deque satisfies all of the requirements of a container, of a reversible container (given in tables in [container.requirements]), of a sequence container, including the optional sequence container requirements ([sequence.reqmts]), and of an allocator-aware container (Table 67).
Descriptions are provided 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
    using value_type             = T;
    using allocator_type         = Allocator;
    using pointer                = typename allocator_traits<Allocator>::pointer;
    using const_pointer          = typename allocator_traits<Allocator>::const_pointer;
    using reference              = value_type&;
    using const_reference        = const value_type&;
    using size_type              = implementation-defined; // see [container.requirements]
    using difference_type        = implementation-defined; // see [container.requirements]
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;

    // [deque.cons], construct/copy/destroy
    deque() : deque(Allocator()) { }
    explicit deque(const Allocator&);
    explicit deque(size_type n, const Allocator& = Allocator());
    deque(size_type n, const T& value, const Allocator& = Allocator());
    template<class InputIterator>
      deque(InputIterator first, InputIterator last, const Allocator& = Allocator());
    deque(const deque& x);
    deque(deque&&);
    deque(const deque&, const Allocator&);
    deque(deque&&, const Allocator&);
    deque(initializer_list<T>, const Allocator& = Allocator());

    ~deque();
    deque& operator=(const deque& x);
    deque& operator=(deque&& x)
      noexcept(allocator_traits<Allocator>::is_always_equal::value);
    deque& operator=(initializer_list<T>);
    template<class InputIterator>
      void assign(InputIterator first, InputIterator last);
    void assign(size_type n, const T& t);
    void assign(initializer_list<T>);
    allocator_type get_allocator() const noexcept;

    // iterators
    iterator               begin() noexcept;
    const_iterator         begin() const noexcept;
    iterator               end() noexcept;
    const_iterator         end() const noexcept;
    reverse_iterator       rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
    reverse_iterator       rend() noexcept;
    const_reverse_iterator rend() const noexcept;

    const_iterator         cbegin() const noexcept;
    const_iterator         cend() const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend() const noexcept;

    // [deque.capacity], capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type size() const noexcept;
    size_type max_size() const noexcept;
    void      resize(size_type sz);
    void      resize(size_type sz, const T& c);
    void      shrink_to_fit();

    // 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;

    // [deque.modifiers], modifiers
    template<class... Args> reference emplace_front(Args&&... args);
    template<class... Args> reference emplace_back(Args&&... args);
    template<class... Args> iterator emplace(const_iterator position, Args&&... args);

    void push_front(const T& x);
    void push_front(T&& x);
    void push_back(const T& x);
    void push_back(T&& x);

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

    void pop_front();
    void pop_back();

    iterator erase(const_iterator position);
    iterator erase(const_iterator first, const_iterator last);
    void     swap(deque&)
      noexcept(allocator_traits<Allocator>::is_always_equal::value);
    void     clear() noexcept;
  };

  template<class InputIterator, class Allocator = allocator<iter-value-type<InputIterator>>>
    deque(InputIterator, InputIterator, Allocator = Allocator())
      -> deque<iter-value-type<InputIterator>, Allocator>;

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

21.3.8.2 Constructors, copy, and assignment [deque.cons]

explicit deque(const Allocator&);
Effects: Constructs an empty deque, using the specified allocator.
Complexity: Constant.
explicit deque(size_type n, const Allocator& = Allocator());
Effects: Constructs a deque with n default-inserted elements using the specified allocator.
Requires: T shall be Cpp17DefaultInsertable into *this.
Complexity: Linear in n.
deque(size_type n, const T& value, const Allocator& = Allocator());
Effects: Constructs a deque with n copies of value, using the specified allocator.
Requires: T shall be Cpp17CopyInsertable into *this.
Complexity: Linear in n.
template<class InputIterator> deque(InputIterator first, InputIterator last, const Allocator& = Allocator());
Effects: Constructs a deque equal to the range [first, last), using the specified allocator.
Complexity: Linear in distance(first, last).

21.3.8.3 Capacity [deque.capacity]

void resize(size_type sz);
Effects: If sz < size(), erases the last size() - sz elements from the sequence.
Otherwise, appends sz - size() default-inserted elements to the sequence.
Requires: T shall be Cpp17MoveInsertable and Cpp17DefaultInsertable into *this.
void resize(size_type sz, const T& c);
Effects: If sz < size(), erases the last size() - sz elements from the sequence.
Otherwise, appends sz - size() copies of c to the sequence.
Requires: T shall be Cpp17CopyInsertable into *this.
void shrink_to_fit();
Requires: T shall be Cpp17MoveInsertable into *this.
Effects: shrink_­to_­fit is a non-binding request to reduce memory use but does not change the size of the sequence.
[Note
:
The request is non-binding to allow latitude for implementation-specific optimizations.
end note
]
If an exception is thrown other than by the move constructor of a non-Cpp17CopyInsertable T there are no effects.
Complexity: Linear in the size of the sequence.
Remarks: shrink_­to_­fit invalidates all the references, pointers, and iterators referring to the elements in the sequence as well as the past-the-end iterator.

21.3.8.4 Modifiers [deque.modifiers]

iterator insert(const_iterator position, const T& x); iterator insert(const_iterator position, T&& x); iterator insert(const_iterator position, size_type n, const T& x); template<class InputIterator> iterator insert(const_iterator position, InputIterator first, InputIterator last); iterator insert(const_iterator position, initializer_list<T>); template<class... Args> reference emplace_front(Args&&... args); template<class... Args> reference emplace_back(Args&&... args); template<class... Args> iterator emplace(const_iterator position, Args&&... args); void push_front(const T& x); void push_front(T&& x); void push_back(const T& x); void push_back(T&& x);
Effects: An insertion in the middle of the deque invalidates all the iterators and references to elements of the deque.
An insertion 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.
Remarks: If an exception is thrown other than by the copy constructor, move constructor, assignment operator, or move assignment operator of T there are no effects.
If an exception is thrown while inserting a single element at either end, there are no effects.
Otherwise, if an exception is thrown by the move constructor of a non-Cpp17CopyInsertable T, the effects are unspecified.
Complexity: The complexity is linear in the number of elements inserted plus the lesser of the distances to the beginning and 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 a constructor of T.
iterator erase(const_iterator position); iterator erase(const_iterator first, const_iterator last); void pop_front(); void pop_back();
Effects: An erase operation that erases the last element of a deque invalidates only the past-the-end iterator and all iterators and references to the erased elements.
An erase operation that erases the first element of a deque but not the last element invalidates only iterators and references to the erased elements.
An erase operation that erases neither the first element nor the last element of a deque invalidates the past-the-end iterator and all iterators and references to all the elements of the deque.
[Note
:
pop_­front and pop_­back are erase operations.
end note
]
Complexity: The number of calls to the destructor of T is the same as the number of elements erased, but the number of calls to the assignment operator of T is no more than the lesser of the number of elements before the erased elements and the number of elements after the erased elements.
Throws: Nothing unless an exception is thrown by the assignment operator of T.

21.3.9 Class template forward_­list [forwardlist]

21.3.9.1 Overview [forwardlist.overview]

A forward_­list is a container that supports forward iterators and allows constant time insert and erase operations anywhere within the sequence, with storage management handled automatically.
Fast random access to list elements is not supported.
[Note
:
It is intended that forward_­list have zero space or time overhead relative to a hand-written C-style singly linked list.
Features that would conflict with that goal have been omitted.
end note
]
A forward_­list satisfies all of the requirements of a container (Table 64), except that the size() member function is not provided and operator== has linear complexity.
A forward_­list also satisfies all of the requirements for an allocator-aware container (Table 67).
In addition, a forward_­list provides the assign member functions (Table 68) and several of the optional container requirements (Table 69).
Descriptions are provided here only for operations on forward_­list that are not described in that table or for operations where there is additional semantic information.
[Note
:
Modifying any list requires access to the element preceding the first element of interest, but in a forward_­list there is no constant-time way to access a preceding element.
For this reason, ranges that are modified, such as those supplied to erase and splice, must be open at the beginning.
end note
]
namespace std {
  template<class T, class Allocator = allocator<T>>
  class forward_list {
  public:
    // types
    using value_type      = T;
    using allocator_type  = Allocator;
    using pointer         = typename allocator_traits<Allocator>::pointer;
    using const_pointer   = typename allocator_traits<Allocator>::const_pointer;
    using reference       = value_type&;
    using const_reference = const value_type&;
    using size_type       = implementation-defined; // see [container.requirements]
    using difference_type = implementation-defined; // see [container.requirements]
    using iterator        = implementation-defined; // see [container.requirements]
    using const_iterator  = implementation-defined; // see [container.requirements]

    // [forwardlist.cons], construct/copy/destroy
    forward_list() : forward_list(Allocator()) { }
    explicit forward_list(const Allocator&);
    explicit forward_list(size_type n, const Allocator& = Allocator());
    forward_list(size_type n, const T& value, const Allocator& = Allocator());
    template<class InputIterator>
      forward_list(InputIterator first, InputIterator last, const Allocator& = Allocator());
    forward_list(const forward_list& x);
    forward_list(forward_list&& x);
    forward_list(const forward_list& x, const Allocator&);
    forward_list(forward_list&& x, const Allocator&);
    forward_list(initializer_list<T>, const Allocator& = Allocator());
    ~forward_list();
    forward_list& operator=(const forward_list& x);
    forward_list& operator=(forward_list&& x)
      noexcept(allocator_traits<Allocator>::is_always_equal::value);
    forward_list& operator=(initializer_list<T>);
    template<class InputIterator>
      void assign(InputIterator first, InputIterator last);
    void assign(size_type n, const T& t);
    void assign(initializer_list<T>);
    allocator_type get_allocator() const noexcept;

    // [forwardlist.iter], iterators
    iterator before_begin() noexcept;
    const_iterator before_begin() const noexcept;
    iterator begin() noexcept;
    const_iterator begin() const noexcept;
    iterator end() noexcept;
    const_iterator end() const noexcept;

    const_iterator cbegin() const noexcept;
    const_iterator cbefore_begin() const noexcept;
    const_iterator cend() const noexcept;

    // capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type max_size() const noexcept;

    // [forwardlist.access], element access
    reference front();
    const_reference front() const;

    // [forwardlist.modifiers], modifiers
    template<class... Args> reference emplace_front(Args&&... args);
    void push_front(const T& x);
    void push_front(T&& x);
    void pop_front();

    template<class... Args> iterator emplace_after(const_iterator position, Args&&... args);
    iterator insert_after(const_iterator position, const T& x);
    iterator insert_after(const_iterator position, T&& x);

    iterator insert_after(const_iterator position, size_type n, const T& x);
    template<class InputIterator>
      iterator insert_after(const_iterator position, InputIterator first, InputIterator last);
    iterator insert_after(const_iterator position, initializer_list<T> il);

    iterator erase_after(const_iterator position);
    iterator erase_after(const_iterator position, const_iterator last);
    void swap(forward_list&)
      noexcept(allocator_traits<Allocator>::is_always_equal::value);

    void resize(size_type sz);
    void resize(size_type sz, const value_type& c);
    void clear() noexcept;

    // [forwardlist.ops], forward_­list operations
    void splice_after(const_iterator position, forward_list& x);
    void splice_after(const_iterator position, forward_list&& x);
    void splice_after(const_iterator position, forward_list& x, const_iterator i);
    void splice_after(const_iterator position, forward_list&& x, const_iterator i);
    void splice_after(const_iterator position, forward_list& x,
                      const_iterator first, const_iterator last);
    void splice_after(const_iterator position, forward_list&& x,
                      const_iterator first, const_iterator last);

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

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

    void merge(forward_list& x);
    void merge(forward_list&& x);
    template<class Compare> void merge(forward_list& x, Compare comp);
    template<class Compare> void merge(forward_list&& x, Compare comp);

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

    void reverse() noexcept;
  };

  template<class InputIterator, class Allocator = allocator<iter-value-type<InputIterator>>>
    forward_list(InputIterator, InputIterator, Allocator = Allocator())
      -> forward_list<iter-value-type<InputIterator>, Allocator>;

  // swap
  template<class T, class Allocator>
    void swap(forward_list<T, Allocator>& x, forward_list<T, Allocator>& y)
      noexcept(noexcept(x.swap(y)));
}
An incomplete type T may be used when instantiating forward_­list if the allocator satisfies the allocator completeness requirements.
T shall be complete before any member of the resulting specialization of forward_­list is referenced.

21.3.9.2 Constructors, copy, and assignment [forwardlist.cons]

explicit forward_list(const Allocator&);
Effects: Constructs an empty forward_­list object using the specified allocator.
Complexity: Constant.
explicit forward_list(size_type n, const Allocator& = Allocator());
Effects: Constructs a forward_­list object with n default-inserted elements using the specified allocator.
Requires: T shall be Cpp17DefaultInsertable into *this.
Complexity: Linear in n.
forward_list(size_type n, const T& value, const Allocator& = Allocator());
Effects: Constructs a forward_­list object with n copies of value using the specified allocator.
Requires: T shall be Cpp17CopyInsertable into *this.
Complexity: Linear in n.
template<class InputIterator> forward_list(InputIterator first, InputIterator last, const Allocator& = Allocator());
Effects: Constructs a forward_­list object equal to the range [first, last).
Complexity: Linear in distance(first, last).

21.3.9.3 Iterators [forwardlist.iter]

iterator before_begin() noexcept; const_iterator before_begin() const noexcept; const_iterator cbefore_begin() const noexcept;
Returns: A non-dereferenceable iterator that, when incremented, is equal to the iterator returned by begin().
Effects: cbefore_­begin() is equivalent to const_­cast<forward_­list const&>(*this).before_­begin().
Remarks: before_­begin() == end() shall equal false.

21.3.9.4 Element access [forwardlist.access]

reference front(); const_reference front() const;
Returns: *begin()

21.3.9.5 Modifiers [forwardlist.modifiers]

None of the overloads of insert_­after shall affect the validity of iterators and references, and erase_­after shall invalidate only iterators and references to the erased elements.
If an exception is thrown during insert_­after there shall be no effect.
Inserting n elements into a forward_­list is linear in n, and the number of calls to the copy or move constructor of T is exactly equal to n.
Erasing n elements from a forward_­list is linear in n and the number of calls to the destructor of type T is exactly equal to n.
template<class... Args> reference emplace_front(Args&&... args);
Effects: Inserts an object of type value_­type constructed with value_­type(std::forward<Args>(​args)...) at the beginning of the list.
void push_front(const T& x); void push_front(T&& x);
Effects: Inserts a copy of x at the beginning of the list.
void pop_front();
Effects: As if by erase_­after(before_­begin()).
iterator insert_after(const_iterator position, const T& x); iterator insert_after(const_iterator position, T&& x);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
Effects: Inserts a copy of x after position.
Returns: An iterator pointing to the copy of x.
iterator insert_after(const_iterator position, size_type n, const T& x);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
Effects: Inserts n copies of x after position.
Returns: An iterator pointing to the last inserted copy of x or position if n == 0.
template<class InputIterator> iterator insert_after(const_iterator position, InputIterator first, InputIterator last);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
first and last are not iterators in *this.
Effects: Inserts copies of elements in [first, last) after position.
Returns: An iterator pointing to the last inserted element or position if first == last.
iterator insert_after(const_iterator position, initializer_list<T> il);
Effects: insert_­after(p, il.begin(), il.end()).
Returns: An iterator pointing to the last inserted element or position if il is empty.
template<class... Args> iterator emplace_after(const_iterator position, Args&&... args);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
Effects: Inserts an object of type value_­type constructed with value_­type(std::forward<Args>(​args)...) after position.
Returns: An iterator pointing to the new object.
iterator erase_after(const_iterator position);
Requires: The iterator following position is dereferenceable.
Effects: Erases the element pointed to by the iterator following position.
Returns: An iterator pointing to the element following the one that was erased, or end() if no such element exists.
Throws: Nothing.
iterator erase_after(const_iterator position, const_iterator last);
Requires: All iterators in the range (position, last) are dereferenceable.
Effects: Erases the elements in the range (position, last).
Returns: last.
Throws: Nothing.
void resize(size_type sz);
Effects: If sz < distance(begin(), end()), erases the last distance(begin(), end()) - sz elements from the list.
Otherwise, inserts sz - distance(begin(), end()) default-inserted elements at the end of the list.
Requires: T shall be Cpp17DefaultInsertable into *this.
void resize(size_type sz, const value_type& c);
Effects: If sz < distance(begin(), end()), erases the last distance(begin(), end()) - sz elements from the list.
Otherwise, inserts sz - distance(begin(), end()) copies of c at the end of the list.
Requires: T shall be Cpp17CopyInsertable into *this.
void clear() noexcept;
Effects: Erases all elements in the range [begin(), end()).
Remarks: Does not invalidate past-the-end iterators.

21.3.9.6 Operations [forwardlist.ops]

In this subclause, arguments for a template parameter named Predicate or BinaryPredicate shall satisfy the corresponding requirements in [algorithms.requirements].
For merge and sort, the definitions and requirements in [alg.sorting] apply.
void splice_after(const_iterator position, forward_list& x); void splice_after(const_iterator position, forward_list&& x);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
get_­allocator() == x.get_­allocator().
addressof(x) != this.
Effects: Inserts the contents of x after position, and x becomes empty.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Throws: Nothing.
Complexity:
void splice_after(const_iterator position, forward_list& x, const_iterator i); void splice_after(const_iterator position, forward_list&& x, const_iterator i);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
The iterator following i is a dereferenceable iterator in x.
get_­allocator() == x.get_­allocator().
Effects: Inserts the element following i into *this, following position, and removes it from x.
The result is unchanged if position == i or position == ++i.
Pointers and references to *++i continue to refer to the same element but as a member of *this.
Iterators to *++i continue to refer to the same element, but now behave as iterators into *this, not into x.
Throws: Nothing.
Complexity:
void splice_after(const_iterator position, forward_list& x, const_iterator first, const_iterator last); void splice_after(const_iterator position, forward_list&& x, const_iterator first, const_iterator last);
Requires: position is before_­begin() or is a dereferenceable iterator in the range [begin(), end()).
(first, last) is a valid range in x, and all iterators in the range (first, last) are dereferenceable.
position is not an iterator in the range (first, last).
get_­allocator() == x.get_­allocator().
Effects: Inserts elements in the range (first, last) after position and removes the elements from x.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Complexity:
size_type remove(const T& value); template<class Predicate> size_type remove_if(Predicate pred);
Effects: Erases all the elements in the list referred to by a list iterator i for which the following conditions hold: *i == value (for remove()), pred(*i) is true (for remove_­if()).
Invalidates only the iterators and references to the erased elements.
Returns: The number of elements erased.
Throws: Nothing unless an exception is thrown by the equality comparison or the predicate.
Remarks: Stable.
Complexity: Exactly distance(begin(), end()) applications of the corresponding predicate.
size_type unique(); template<class BinaryPredicate> size_type unique(BinaryPredicate pred);
Effects: Erases 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 with no arguments) or pred(*i, *(i - 1)) (for the version with a predicate argument) holds.
Invalidates only the iterators and references to the erased elements.
Returns: The number of elements erased.
Throws: Nothing unless an exception is thrown by the equality comparison or the predicate.
Complexity: If the range [first, last) is not empty, exactly (last - first) - 1 applications of the corresponding predicate, otherwise no applications of the predicate.
void merge(forward_list& x); void merge(forward_list&& x); template<class Compare> void merge(forward_list& x, Compare comp); template<class Compare> void merge(forward_list&& x, Compare comp);
Requires: *this and x are both sorted with respect to the comparator operator< (for the first two overloads) or comp (for the last two overloads), and get_­allocator() == x.get_­allocator() is true.
Effects: Merges the two sorted ranges [begin(), end()) and [x.begin(), x.end()).
x is empty after the merge.
If an exception is thrown other than by a comparison there are no effects.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Remarks: Stable.
The behavior is undefined if get_­allocator() != x.get_­allocator().
Complexity: At most distance(begin(), end()) + distance(x.begin(), x.end()) - 1 comparisons.
void sort(); template<class Compare> void sort(Compare comp);
Effects: Sorts the list according to the operator< or the comp function object.
If an exception is thrown, the order of the elements in *this is unspecified.
Does not affect the validity of iterators and references.
Remarks: Stable.
Complexity: Approximately comparisons, where N is distance(begin(), end()).
void reverse() noexcept;
Effects: Reverses the order of the elements in the list.
Does not affect the validity of iterators and references.
Complexity: Linear time.

21.3.10 Class template list [list]

21.3.10.1 Overview [list.overview]

A list is a sequence container that supports bidirectional iterators and allows constant time insert and erase operations anywhere within the sequence, with storage management handled automatically.
Unlike vectors and deques, fast random access to list elements is not supported, but many algorithms only need sequential access anyway.
A list satisfies all of the requirements of a container, of a reversible container (given in two tables in [container.requirements]), of a sequence container, including most of the optional sequence container requirements ([sequence.reqmts]), and of an allocator-aware container (Table 67).
The exceptions are the operator[] and at member functions, which are not provided.231
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
    using value_type             = T;
    using allocator_type         = Allocator;
    using pointer                = typename allocator_traits<Allocator>::pointer;
    using const_pointer          = typename allocator_traits<Allocator>::const_pointer;
    using reference              = value_type&;
    using const_reference        = const value_type&;
    using size_type              = implementation-defined; // see [container.requirements]
    using difference_type        = implementation-defined; // see [container.requirements]
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;

    // [list.cons], construct/copy/destroy
    list() : list(Allocator()) { }
    explicit list(const Allocator&);
    explicit list(size_type n, const Allocator& = Allocator());
    list(size_type n, const T& value, const Allocator& = Allocator());
    template<class InputIterator>
      list(InputIterator first, InputIterator last, const Allocator& = Allocator());
    list(const list& x);
    list(list&& x);
    list(const list&, const Allocator&);
    list(list&&, const Allocator&);
    list(initializer_list<T>, const Allocator& = Allocator());
    ~list();
    list& operator=(const list& x);
    list& operator=(list&& x)
      noexcept(allocator_traits<Allocator>::is_always_equal::value);
    list& operator=(initializer_list<T>);
    template<class InputIterator>
      void assign(InputIterator first, InputIterator last);
    void assign(size_type n, const T& t);
    void assign(initializer_list<T>);
    allocator_type get_allocator() const noexcept;

    // iterators
    iterator               begin() noexcept;
    const_iterator         begin() const noexcept;
    iterator               end() noexcept;
    const_iterator         end() const noexcept;
    reverse_iterator       rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
    reverse_iterator       rend() noexcept;
    const_reverse_iterator rend() const noexcept;

    const_iterator         cbegin() const noexcept;
    const_iterator         cend() const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend() const noexcept;

    // [list.capacity], capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type size() const noexcept;
    size_type max_size() const noexcept;
    void      resize(size_type sz);
    void      resize(size_type sz, const T& c);

    // element access
    reference       front();
    const_reference front() const;
    reference       back();
    const_reference back() const;

    // [list.modifiers], modifiers
    template<class... Args> reference emplace_front(Args&&... args);
    template<class... Args> reference emplace_back(Args&&... args);
    void push_front(const T& x);
    void push_front(T&& x);
    void pop_front();
    void push_back(const T& x);
    void push_back(T&& x);
    void pop_back();

    template<class... Args> iterator emplace(const_iterator position, Args&&... args);
    iterator insert(const_iterator position, const T& x);
    iterator insert(const_iterator position, T&& x);
    iterator insert(const_iterator position, size_type n, const T& x);
    template<class InputIterator>
      iterator insert(const_iterator position, InputIterator first, InputIterator last);
    iterator insert(const_iterator position, initializer_list<T> il);

    iterator erase(const_iterator position);
    iterator erase(const_iterator position, const_iterator last);
    void     swap(list&) noexcept(allocator_traits<Allocator>::is_always_equal::value);
    void     clear() noexcept;

    // [list.ops], list operations
    void splice(const_iterator position, list& x);
    void splice(const_iterator position, list&& x);
    void splice(const_iterator position, list& x, const_iterator i);
    void splice(const_iterator position, list&& x, const_iterator i);
    void splice(const_iterator position, list& x, const_iterator first, const_iterator last);
    void splice(const_iterator position, list&& x, const_iterator first, const_iterator last);

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

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

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

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

    void reverse() noexcept;
  };

  template<class InputIterator, class Allocator = allocator<iter-value-type<InputIterator>>>
    list(InputIterator, InputIterator, Allocator = Allocator())
      -> list<iter-value-type<InputIterator>, Allocator>;

  // swap
  template<class T, class Allocator>
    void swap(list<T, Allocator>& x, list<T, Allocator>& y)
      noexcept(noexcept(x.swap(y)));
}
An incomplete type T may be used when instantiating list if the allocator satisfies the allocator completeness requirements.
T shall be complete before any member of the resulting specialization of list is referenced.
These member functions are only provided by containers whose iterators are random access iterators.

21.3.10.2 Constructors, copy, and assignment [list.cons]

explicit list(const Allocator&);
Effects: Constructs an empty list, using the specified allocator.
Complexity: Constant.
explicit list(size_type n, const Allocator& = Allocator());
Effects: Constructs a list with n default-inserted elements using the specified allocator.
Requires: T shall be Cpp17DefaultInsertable into *this.
Complexity: Linear in n.
list(size_type n, const T& value, const Allocator& = Allocator());
Effects: Constructs a list with n copies of value, using the specified allocator.
Requires: T shall be Cpp17CopyInsertable into *this.
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 distance(first, last).

21.3.10.3 Capacity [list.capacity]

void resize(size_type sz);
Effects: If size() < sz, appends sz - size() default-inserted elements to the sequence.
If sz <= size(), equivalent to:
list<T>::iterator it = begin();
advance(it, sz);
erase(it, end());
Requires: T shall be Cpp17DefaultInsertable into *this.
void resize(size_type sz, const T& c);
Effects: As if by:
if (sz > size())
  insert(end(), sz-size(), c);
else if (sz < size()) {
  iterator i = begin();
  advance(i, sz);
  erase(i, end());
}
else
  ;                 // do nothing
Requires: T shall be Cpp17CopyInsertable into *this.

21.3.10.4 Modifiers [list.modifiers]

iterator insert(const_iterator position, const T& x); iterator insert(const_iterator position, T&& x); iterator insert(const_iterator position, size_type n, const T& x); template<class InputIterator> iterator insert(const_iterator position, InputIterator first, InputIterator last); iterator insert(const_iterator position, initializer_list<T>); template<class... Args> reference emplace_front(Args&&... args); template<class... Args> reference emplace_back(Args&&... args); template<class... Args> iterator emplace(const_iterator position, Args&&... args); void push_front(const T& x); void push_front(T&& x); void push_back(const T& x); void push_back(T&& x);
Remarks: Does not affect the validity of iterators and references.
If an exception is thrown there are no effects.
Complexity: Insertion of a single element into a list takes constant time and exactly one call to a constructor of T.
Insertion of multiple elements into a list is linear in the number of elements inserted, and the number of calls to the copy constructor or move constructor of T is exactly equal to the number of elements inserted.
iterator erase(const_iterator position); iterator erase(const_iterator first, const_iterator last); void pop_front(); void pop_back(); void clear() noexcept;
Effects: Invalidates only the iterators and references to the erased elements.
Throws: Nothing.
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.

21.3.10.5 Operations [list.ops]

Since lists allow fast insertion and erasing from the middle of a list, certain operations are provided specifically for them.232
In this subclause, arguments for a template parameter named Predicate or BinaryPredicate shall satisfy the corresponding requirements in [algorithms.requirements].
For merge and sort, the definitions and requirements in [alg.sorting] apply.
list provides three splice operations that destructively move elements from one list to another.
The behavior of splice operations is undefined if get_­allocator() != x.get_­allocator().
void splice(const_iterator position, list& x); void splice(const_iterator position, list&& x);
Requires: addressof(x) != this.
Effects: Inserts the contents of x before position and x becomes empty.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Throws: Nothing.
Complexity: Constant time.
void splice(const_iterator position, list& x, const_iterator i); void splice(const_iterator position, list&& x, const_iterator i);
Requires: i is a valid dereferenceable iterator of x.
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.
Pointers and references to *i continue to refer to this same element but as a member of *this.
Iterators to *i (including i itself) continue to refer to the same element, but now behave as iterators into *this, not into x.
Throws: Nothing.
Complexity: Constant time.
void splice(const_iterator position, list& x, const_iterator first, const_iterator last); void splice(const_iterator position, list&& x, const_iterator first, const_iterator last);
Requires: [first, last) is a valid range in x.
The program has undefined behavior if position is an iterator in the range [first, last).
Effects: Inserts elements in the range [first, last) before position and removes the elements from x.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Throws: Nothing.
Complexity: Constant time if &x == this; otherwise, linear time.
size_type remove(const T& value); template<class Predicate> size_type remove_if(Predicate pred);
Effects: Erases all the elements in the list referred to by a list iterator i for which the following conditions hold: *i == value, pred(*i) != false.
Invalidates only the iterators and references to the erased elements.
Returns: The number of elements erased.
Throws: Nothing unless an exception is thrown by *i == value or pred(*i) != false.
Remarks: Stable.
Complexity: Exactly size() applications of the corresponding predicate.
size_type unique(); template<class BinaryPredicate> size_type unique(BinaryPredicate binary_pred);
Effects: Erases 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.
Invalidates only the iterators and references to the erased elements.
Returns: The number of elements erased.
Throws: Nothing unless an exception is thrown by *i == *(i-1) or pred(*i, *(i - 1))
Complexity: If the range [first, last) is not empty, exactly (last - first) - 1 applications of the corresponding predicate, otherwise no applications of the predicate.
void merge(list& x); void merge(list&& x); template<class Compare> void merge(list& x, Compare comp); template<class Compare> void merge(list&& x, Compare comp);
Requires: Both the list and the argument list shall be sorted with respect to the comparator operator< (for the first two overloads) or comp (for the last two overloads).
Effects: If addressof(x) == this, does nothing; otherwise, merges the two sorted ranges [begin(), end()) and [x.​begin(), x.end()).
The result is a range in which the elements will be sorted in non-decreasing order according to the ordering defined by comp; that is, for every iterator i, in the range other than the first, the condition comp(*i, *(i - 1)) will be false.
Pointers and references to the moved elements of x now refer to those same elements but as members of *this.
Iterators referring to the moved elements will continue to refer to their elements, but they now behave as iterators into *this, not into x.
Remarks: Stable ([algorithm.stable]).
If addressof(x) != this, the range [x.begin(), x.end()) is empty after the merge.
No elements are copied by this operation.
The behavior is undefined if get_­allocator() != x.get_­allocator().
Complexity: At most size() + x.size() - 1 applications of comp if addressof(x) != this; otherwise, no applications of comp are performed.
If an exception is thrown other than by a comparison there are no effects.
void reverse() noexcept;
Effects: Reverses the order of the elements in the list.
Does not affect the validity of iterators and references.
Complexity: Linear time.
void sort(); template<class Compare> void sort(Compare comp);
Effects: Sorts the list according to the operator< or a Compare function object.
If an exception is thrown, the order of the elements in *this is unspecified.
Does not affect the validity of iterators and references.
Remarks: Stable.
Complexity: Approximately comparisons, where N == size().
As specified in [allocator.requirements], the requirements in this Clause apply only to lists whose allocators compare equal.

21.3.11 Class template vector [vector]

21.3.11.1 Overview [vector.overview]

A vector is a sequence container that 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.
A vector satisfies all of the requirements of a container and of a reversible container (given in two tables in [container.requirements]), of a sequence container, including most of the optional sequence container requirements ([sequence.reqmts]), of an allocator-aware container (Table 67), and, for an element type other than bool, of a contiguous container.
The exceptions are the push_­front, pop_­front, and emplace_­front member functions, which are not provided.
Descriptions are provided here only for operations on vector 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
    using value_type             = T;
    using allocator_type         = Allocator;
    using pointer                = typename allocator_traits<Allocator>::pointer;
    using const_pointer          = typename allocator_traits<Allocator>::const_pointer;
    using reference              = value_type&;
    using const_reference        = const value_type&;
    using size_type              = implementation-defined; // see [container.requirements]
    using difference_type        = implementation-defined; // see [container.requirements]
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;

    // [vector.cons], construct/copy/destroy
    vector() noexcept(noexcept(Allocator())) : vector(Allocator()) { }
    explicit vector(const Allocator&) noexcept;
    explicit vector(size_type n, const Allocator& = Allocator());
    vector(size_type n, const T& value, const Allocator& = Allocator());
    template<class InputIterator>
      vector(InputIterator first, InputIterator last, const Allocator& = Allocator());
    vector(const vector& x);
    vector(vector&&) noexcept;
    vector(const vector&, const Allocator&);
    vector(vector&&, const Allocator&);
    vector(initializer_list<T>, const Allocator& = Allocator());
    ~vector();
    vector& operator=(const vector& x);
    vector& operator=(vector&& x)
      noexcept(allocator_traits<Allocator>::propagate_on_container_move_assignment::value ||
               allocator_traits<Allocator>::is_always_equal::value);
    vector& operator=(initializer_list<T>);
    template<class InputIterator>
      void assign(InputIterator first, InputIterator last);
    void assign(size_type n, const T& u);
    void assign(initializer_list<T>);
    allocator_type get_allocator() const noexcept;

    // iterators
    iterator               begin() noexcept;
    const_iterator         begin() const noexcept;
    iterator               end() noexcept;
    const_iterator         end() const noexcept;
    reverse_iterator       rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
    reverse_iterator       rend() noexcept;
    const_reverse_iterator rend() const noexcept;

    const_iterator         cbegin() const noexcept;
    const_iterator         cend() const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend() const noexcept;

    // [vector.capacity], capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type size() const noexcept;
    size_type max_size() const noexcept;
    size_type capacity() const noexcept;
    void      resize(size_type sz);
    void      resize(size_type sz, const T& c);
    void      reserve(size_type n);
    void      shrink_to_fit();

    // 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;

    // [vector.data], data access
    T*       data() noexcept;
    const T* data() const noexcept;

    // [vector.modifiers], modifiers
    template<class... Args> reference emplace_back(Args&&... args);
    void push_back(const T& x);
    void push_back(T&& x);
    void pop_back();

    template<class... Args> iterator emplace(const_iterator position, Args&&... args);
    iterator insert(const_iterator position, const T& x);
    iterator insert(const_iterator position, T&& x);
    iterator insert(const_iterator position, size_type n, const T& x);
    template<class InputIterator>
      iterator insert(const_iterator position, InputIterator first, InputIterator last);
    iterator insert(const_iterator position, initializer_list<T> il);
    iterator erase(const_iterator position);
    iterator erase(const_iterator first, const_iterator last);
    void     swap(vector&)
      noexcept(allocator_traits<Allocator>::propagate_on_container_swap::value ||
               allocator_traits<Allocator>::is_always_equal::value);
    void     clear() noexcept;
  };

  template<class InputIterator, class Allocator = allocator<iter-value-type<InputIterator>>>
    vector(InputIterator, InputIterator, Allocator = Allocator())
      -> vector<iter-value-type<InputIterator>, Allocator>;

  // swap
  template<class T, class Allocator>
    void swap(vector<T, Allocator>& x, vector<T, Allocator>& y)
      noexcept(noexcept(x.swap(y)));
}
An incomplete type T may be used when instantiating vector if the allocator satisfies the allocator completeness requirements.
T shall be complete before any member of the resulting specialization of vector is referenced.

21.3.11.2 Constructors, copy, and assignment [vector.cons]

explicit vector(const Allocator&) noexcept;
Effects: Constructs an empty vector, using the specified allocator.
Complexity: Constant.
explicit vector(size_type n, const Allocator& = Allocator());
Effects: Constructs a vector with n default-inserted elements using the specified allocator.
Requires: T shall be Cpp17DefaultInsertable into *this.
Complexity: Linear in n.
vector(size_type n, const T& value, const Allocator& = Allocator());
Effects: Constructs a vector with n copies of value, using the specified allocator.
Requires: T shall be Cpp17CopyInsertable into *this.
Complexity: Linear in n.
template<class InputIterator> vector(InputIterator first, InputIterator last, const Allocator& = Allocator());
Effects: Constructs a vector equal to the range [first, last), using the specified allocator.
Complexity: 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 makes order N calls to the copy constructor of T and order logN reallocations if they are just input iterators.

21.3.11.3 Capacity [vector.capacity]

size_type capacity() const noexcept;
Returns: The total number of elements that the vector can hold without requiring reallocation.
Complexity: Constant time.
void reserve(size_type n);
Requires: T shall be Cpp17MoveInsertable into *this.
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 capacity() otherwise.
Reallocation happens at this point if and only if the current capacity is less than the argument of reserve().
If an exception is thrown other than by the move constructor of a non-Cpp17CopyInsertable type, there are no effects.
Complexity: It does not change the size of the sequence and takes at most linear time in the size of the sequence.
Throws: length_­error if n > max_­size().233
Remarks: Reallocation invalidates all the references, pointers, and iterators referring to the elements in the sequence.
No reallocation shall take 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 value of capacity().
void shrink_to_fit();
Requires: T shall be Cpp17MoveInsertable into *this.
Effects: shrink_­to_­fit is a non-binding request to reduce capacity() to size().
[Note
:
The request is non-binding to allow latitude for implementation-specific optimizations.
end note
]
It does not increase capacity(), but may reduce capacity() by causing reallocation.
If an exception is thrown other than by the move constructor of a non-Cpp17CopyInsertable T there are no effects.
Complexity: Linear in the size of the sequence.
Remarks: Reallocation invalidates all the references, pointers, and iterators referring to the elements in the sequence as well as the past-the-end iterator.
If no reallocation happens, they remain valid.
void swap(vector& x) noexcept(allocator_traits<Allocator>::propagate_on_container_swap::value || allocator_traits<Allocator>::is_always_equal::value);
Effects: Exchanges the contents and capacity() of *this with that of x.
Complexity: Constant time.
void resize(size_type sz);
Effects: If sz < size(), erases the last size() - sz elements from the sequence.
Otherwise, appends sz - size() default-inserted elements to the sequence.
Requires: T shall be Cpp17MoveInsertable and Cpp17DefaultInsertable into *this.
Remarks: If an exception is thrown other than by the move constructor of a non-Cpp17CopyInsertable T there are no effects.
void resize(size_type sz, const T& c);
Effects: If sz < size(), erases the last size() - sz elements from the sequence.
Otherwise, appends sz - size() copies of c to the sequence.
Requires: T shall be Cpp17CopyInsertable into *this.
Remarks: If an exception is thrown there are no effects.
reserve() uses Allocator::allocate() which may throw an appropriate exception.

21.3.11.4 Data [vector.data]

T* data() noexcept; const T* data() const noexcept;
Returns: A pointer such that [data(), data() + size()) is a valid range.
For a non-empty vector, data() == addressof(front()).
Complexity: Constant time.

21.3.11.5 Modifiers [vector.modifiers]

iterator insert(const_iterator position, const T& x); iterator insert(const_iterator position, T&& x); iterator insert(const_iterator position, size_type n, const T& x); template<class InputIterator> iterator insert(const_iterator position, InputIterator first, InputIterator last); iterator insert(const_iterator position, initializer_list<T>); template<class... Args> reference emplace_back(Args&&... args); template<class... Args> iterator emplace(const_iterator position, Args&&... args); void push_back(const T& x); void push_back(T&& x);
Remarks: Causes reallocation if the new size is greater than the old capacity.
Reallocation invalidates all the references, pointers, and iterators referring to the elements in the sequence.
If no reallocation happens, all the iterators and references before the insertion point remain valid.
If an exception is thrown other than by the copy constructor, move constructor, assignment operator, or move assignment operator of T or by any InputIterator operation there are no effects.
If an exception is thrown while inserting a single element at the end and T is Cpp17CopyInsertable or is_­nothrow_­move_­constructible_­v<T> is true, there are no effects.
Otherwise, if an exception is thrown by the move constructor of a non-Cpp17CopyInsertable T, the effects are unspecified.
Complexity: The complexity is linear in the number of elements inserted plus the distance to the end of the vector.
iterator erase(const_iterator position); iterator erase(const_iterator first, const_iterator last); void pop_back();
Effects: Invalidates iterators and references at or after the point of the erase.
Complexity: The destructor of T is called the number of times equal to the number 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.
Throws: Nothing unless an exception is thrown by the assignment operator or move assignment operator of T.

21.3.12 Class vector<bool> [vector.bool]

To optimize space allocation, a specialization of vector for bool elements is provided:
namespace std {
  template<class Allocator>
  class vector<bool, Allocator> {
  public:
    // types
    using value_type             = bool;
    using allocator_type         = Allocator;
    using pointer                = implementation-defined;
    using const_pointer          = implementation-defined;
    using const_reference        = bool;
    using size_type              = implementation-defined; // see [container.requirements]
    using difference_type        = implementation-defined; // see [container.requirements]
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;

    // bit reference
    class reference {
      friend class vector;
      reference() noexcept;
    public:
      reference(const reference&) = default;
      ~reference();
      operator bool() const noexcept;
      reference& operator=(const bool x) noexcept;
      reference& operator=(const reference& x) noexcept;
      void flip() noexcept;     // flips the bit
    };

    // construct/copy/destroy
    vector() : vector(Allocator()) { }
    explicit vector(const Allocator&);
    explicit vector(size_type n, const Allocator& = Allocator());
    vector(size_type n, const bool& value, const Allocator& = Allocator());
    template<class InputIterator>
      vector(InputIterator first, InputIterator last, const Allocator& = Allocator());
    vector(const vector& x);
    vector(vector&& x);
    vector(const vector&, const Allocator&);
    vector(vector&&, const Allocator&);
    vector(initializer_list<bool>, const Allocator& = Allocator()));
    ~vector();
    vector& operator=(const vector& x);
    vector& operator=(vector&& x);
    vector& operator=(initializer_list<bool>);
    template<class InputIterator>
      void assign(InputIterator first, InputIterator last);
    void assign(size_type n, const bool& t);
    void assign(initializer_list<bool>);
    allocator_type get_allocator() const noexcept;

    // iterators
    iterator               begin() noexcept;
    const_iterator         begin() const noexcept;
    iterator               end() noexcept;
    const_iterator         end() const noexcept;
    reverse_iterator       rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
    reverse_iterator       rend() noexcept;
    const_reverse_iterator rend() const noexcept;

    const_iterator         cbegin() const noexcept;
    const_iterator         cend() const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend() const noexcept;

    // capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type size() const noexcept;
    size_type max_size() const noexcept;
    size_type capacity() const noexcept;
    void      resize(size_type sz, bool c = false);
    void      reserve(size_type n);
    void      shrink_to_fit();

    // 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
    template<class... Args> reference emplace_back(Args&&... args);
    void push_back(const bool& x);
    void pop_back();
    template<class... Args> iterator emplace(const_iterator position, Args&&... args);
    iterator insert(const_iterator position, const bool& x);
    iterator insert(const_iterator position, size_type n, const bool& x);
    template<class InputIterator>
      iterator insert(const_iterator position, InputIterator first, InputIterator last);
    iterator insert(const_iterator position, initializer_list<bool> il);

    iterator erase(const_iterator position);
    iterator erase(const_iterator first, const_iterator last);
    void swap(vector&);
    static void swap(reference x, reference y) noexcept;
    void flip() noexcept;       // flips all bits
    void clear() noexcept;
  };
}
Unless described below, all operations have the same requirements and semantics as the primary vector template, except that operations dealing with the bool value type map to bit values in the container storage and allocator_­traits​::​construct is not used to construct these values.
There is no requirement that the data be stored as a contiguous allocation of bool values.
A space-optimized representation of bits is recommended instead.
reference is a class that simulates the behavior of references of a single bit in vector<bool>.
The conversion function returns true when the bit is set, and false otherwise.
The assignment operator sets the bit when the argument is (convertible to) true and clears it otherwise.
flip reverses the state of the bit.
void flip() noexcept;
Effects: Replaces each element in the container with its complement.
static void swap(reference x, reference y) noexcept;
Effects: Exchanges the contents of x and y as if by:
bool b = x;
x = y;
y = b;
template<class Allocator> struct hash<vector<bool, Allocator>>;
The specialization is enabled ([unord.hash]).

21.4 Associative containers [associative]

21.4.1 In general [associative.general]

The header <map> defines the class templates map and multimap; the header <set> defines the class templates set and multiset.
The following exposition-only alias templates may appear in deduction guides for associative containers:
template<class InputIterator>
  using iter-value-type =
    typename iterator_traits<InputIterator>::value_type;                // exposition only
template<class InputIterator>
  using iter-key-type = remove_const_t<
    typename iterator_traits<InputIterator>::value_type::first_type>;   // exposition only
template<class InputIterator>
  using iter-mapped-type =
    typename iterator_traits<InputIterator>::value_type::second_type;   // exposition only
template<class InputIterator>
  using iter-to-alloc-type = pair<
    add_const_t<typename iterator_traits<InputIterator>::value_type::first_type>,
    typename iterator_traits<InputIterator>::value_type::second_type>;  // exposition only

21.4.2 Header <map> synopsis [associative.map.syn]

#include <initializer_list>

namespace std {
  // [map], class template map
  template<class Key, class T, class Compare = less<Key>,
           class Allocator = allocator<pair<const Key, 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)
      noexcept(noexcept(x.swap(y)));

  // [multimap], class template multimap
  template<class Key, class T, class Compare = less<Key>,
           class Allocator = allocator<pair<const Key, 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)
      noexcept(noexcept(x.swap(y)));

  namespace pmr {
    template<class Key, class T, class Compare = less<Key>>
      using map = std::map<Key, T, Compare,
                           polymorphic_allocator<pair<const Key, T>>>;

    template<class Key, class T, class Compare = less<Key>>
      using multimap = std::multimap<Key, T, Compare,
                                     polymorphic_allocator<pair<const Key, T>>>;
  }
}

21.4.3 Header <set> synopsis [associative.set.syn]

#include <initializer_list>

namespace std {
  // [set], class template set
  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)
      noexcept(noexcept(x.swap(y)));

  // [multiset], class template multiset
  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)
      noexcept(noexcept(x.swap(y)));

  namespace pmr {
    template<class Key, class Compare = less<Key>>
      using set = std::set<Key, Compare, polymorphic_allocator<Key>>;

    template<class Key, class Compare = less<Key>>
      using multiset = std::multiset<Key, Compare, polymorphic_allocator<Key>>;
  }
}

21.4.4 Class template map [map]

21.4.4.1 Overview [map.overview]

A map is an 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.
The map class supports bidirectional iterators.
A map satisfies all of the requirements of a container, of a reversible container ([container.requirements]), of an associative container ([associative.reqmts]), and of an allocator-aware container (Table 67).
A map also provides most operations described in [associative.reqmts] for unique keys.
This means that a map supports the a_­uniq operations in [associative.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 semantic information.
namespace std {
  template<class Key, class T, class Compare = less<Key>,
           class Allocator = allocator<pair<const Key, T>>>
  class map {
  public:
    // types
    using key_type               = Key;
    using mapped_type            = T;
    using value_type             = pair<const Key, T>;
    using key_compare            = Compare;
    using allocator_type         = Allocator;
    using pointer                = typename allocator_traits<Allocator>::pointer;
    using const_pointer          = typename allocator_traits<Allocator>::const_pointer;
    using reference              = value_type&;
    using const_reference        = const value_type&;
    using size_type              = implementation-defined; // see [container.requirements]
    using difference_type        = implementation-defined; // see [container.requirements]
    using iterator               = implementation-defined; // see [container.requirements]
    using const_iterator         = implementation-defined; // see [container.requirements]
    using reverse_iterator       = std::reverse_iterator<iterator>;
    using const_reverse_iterator = std::reverse_iterator<const_iterator>;
    using node_type              = unspecified;
    using insert_return_type     = insert-return-type<iterator, node_type>;

    class value_compare {
      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);
      }
    };

    // [map.cons], construct/copy/destroy
    map() : map(Compare()) { }
    explicit map(const Compare& comp, const Allocator& = Allocator());
    template<class InputIterator>
      map(InputIterator first, InputIterator last,
          const Compare& comp = Compare(), const Allocator& = Allocator());
    map(const map& x);
    map(map&& x);
    explicit map(const Allocator&);
    map(const map&, const Allocator&);
    map(map&&, const Allocator&);
    map(initializer_list<value_type>,
      const Compare& = Compare(),
      const Allocator& = Allocator());
    template<class InputIterator>
      map(InputIterator first, InputIterator last, const Allocator& a)
        : map(first, last, Compare(), a) { }
    map(initializer_list<value_type> il, const Allocator& a)
      : map(il, Compare(), a) { }
    ~map();
    map& operator=(const map& x);
    map& operator=(map&& x)
      noexcept(allocator_traits<Allocator>::is_always_equal::value &&
               is_nothrow_move_assignable_v<Compare>);
    map& operator=(initializer_list<value_type>);
    allocator_type get_allocator() const noexcept;

    // iterators
    iterator               begin() noexcept;
    const_iterator         begin() const noexcept;
    iterator               end() noexcept;
    const_iterator         end() const noexcept;

    reverse_iterator       rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
    reverse_iterator       rend() noexcept;
    const_reverse_iterator rend() const noexcept;

    const_iterator         cbegin() const noexcept;
    const_iterator         cend() const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend() const noexcept;

    // capacity
    [[nodiscard]] bool empty() const noexcept;
    size_type size() const noexcept;
    size_type max_size() const noexcept;

    // [map.access], element access
    mapped_type& operator[](const key_type& x);
    mapped_type& operator[](key_type&& x);
    mapped_type&       at(const key_type& x);
    const mapped_type& at(const key_type& x) const;

    // [map.modifiers], modifiers
    template<class... Args> pair<iterator, bool> emplace(Args&&... args);
    template<class... Args> iterator emplace_hint(const_iterator position, Args&&... args);
    pair<iterator, bool> insert(const value_type& x);
    pair<iterator, bool> insert(value_type&& x);
    template<class P> pair<iterator, bool> insert(P&& x);
    iterator insert(const_iterator position, const value_type& x);
    iterator insert(const_iterator position, value_type&& x);
    template<class P>
      iterator insert(const_iterator position, P&&);
    template<class InputIterator>
      void insert(InputIterator first, InputIterator last);
    void insert(initializer_list<value_type>);

    node_type extract(const_iterator position);
    node_type extract(const key_type& x);
    insert_return_type insert(node_type&& nh);
    iterator           insert(const_iterator hint, node_type&& nh);

    template<class... Args>
      pair<iterator, bool> try_emplace(const key_type& k, Args&&... args);
    template<class... Args>
      pair<iterator, bool> try_emplace(key_type&& k, Args&&... args);
    template<class... Args>
      iterator try_emplace(const_iterator hint, const key_type& k, Args&&... args);
    template<class... Args>
      iterator try_emplace(const_iterator hint, key_type&& k, Args&&... args);
    template<class M>
      pair<iterator, bool> insert_or_assign(const key_type& k, M&& obj);
    template<class M>
      pair<iterator, bool> insert_or_assign(key_type&& k, M&& obj);
    template<class M>
      iterator insert_or_assign(const_iterator hint, const key_type& k, M&& obj);
    template<class M>
      iterator insert_or_assign(const_iterator hint, key_type&& k, M&& obj);

    iterator  erase(iterator position);
    iterator  erase(const_iterator position);
    size_type erase(const key_type& x);
    iterator  erase(const_iterator first, const_iterator last);
    void      swap(map&)
      noexcept(allocator_traits<Allocator>::is_always_equal::value &&
               is_nothrow_swappable_v<Compare>);
    void      clear() noexcept;

    template<class C2>
      void merge(map<Key, T, C2, Allocator>& source);
    template<class C2>
      void merge(map<Key, T, C2, Allocator>&& source);
    template<class C2>
      void merge(multimap<Key, T, C2, Allocator>& source);
    template<class C2>
      void merge(multimap<Key, T, C2, Allocator>&& source);

    // 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;
    template<class K> iterator       find(const K& x);
    template<class K> const_iterator find(const K& x) const;

    size_type      count(const key_type& x) const;
    template<class K> size_type count(const K& x) const;

    bool           contains(const key_type& x) const;
    template<class K> bool contains(const K& x) const;

    iterator       lower_bound(const key_type& x);
    const_iterator lower_bound(const key_type& x) const;
    template<class K> iterator       lower_bound(const K& x);
    template<class K> const_iterator lower_bound(const K& x) const;

    iterator       upper_bound(const key_type& x);
    const_iterator upper_bound(const key_type& x) const;
    template<class K> iterator       upper_bound(const K& x);
    template<class K> const_iterator upper_bound(const K& 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 K>
      pair<iterator, iterator>             equal_range(const K& x);
    template<class K>
      pair<const_iterator, const_iterator> equal_range(const K& x) const;
  };

  template<class InputIterator, class Compare = less<iter-key-type<InputIterator>>,
           class Allocator = allocator<iter-to-alloc-type<InputIterator>>>
    map(InputIterator, InputIterator, Compare = Compare(), Allocator = Allocator())
      -> map<iter-key-type<InputIterator>, iter-mapped-type<InputIterator>, Compare, Allocator>;

  template<class Key, class T, class Compare = less<Key>,
           class Allocator = allocator<pair<const Key, T>>>
    map(initializer_list<pair<const Key, T>>, Compare = Compare(), Allocator = Allocator())
      -> map<Key, T, Compare, Allocator>;

  template<class InputIterator, class Allocator>
    map(InputIterator, InputIterator, Allocator)
      -> map<iter-key-type<InputIterator>, iter-mapped-type<InputIterator>,
             less<iter-key-type<InputIterator>>, Allocator>;

  template<class Key, class T, class Allocator>
    map(initializer_list<pair<const Key, T>>, Allocator) -> map<Key, T, less<Key>, Allocator>;

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

21.4.4.2 Constructors, copy, and assignment [map.cons]

explicit map(const Compare& comp, 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 , where N is last - first.

21.4.4.3 Element access [map.access]

mapped_type& operator[](const key_type& x);
Effects: Equivalent to: return try_­emplace(x).first->second;
mapped_type& operator[](key_type&& x);
Effects: Equivalent to: return try_­emplace(move(x)).first->second;
mapped_type& at(const key_type& x); const mapped_type& at(const key_type& x) const;
Returns: A reference to the mapped_­type corresponding to x in *this.
Throws: An exception object of type out_­of_­range if no such element is present.
Complexity: Logarithmic.

21.4.4.4 Modifiers [map.modifiers]

template<class P> pair<iterator, bool> insert(P&& x); template<class P> iterator insert(const_iterator position, P&& x);
Effects: The first form is equivalent to return emplace(std::forward<P>(x)).
The second form is equivalent to return emplace_­hint(position, std::forward<P>(x)).
Remarks: These signatures shall not participate in overload resolution unless is_­constructible_­v<value_­type, P&&> is true.
template<class... Args> pair<iterator, bool> try_emplace(const key_type& k, Args&&... args); template<class... Args> iterator try_emplace(const_iterator hint, const key_type& k, Args&&... args);
Requires: value_­type shall be Cpp17EmplaceConstructible into map from piecewise_­construct, forward_­as_­tuple(k), forward_­as_­tuple(std: