23 Algorithms library [algorithms]

23.1 General [algorithms.general]

1
#
This Clause describes components that C++ programs may use to perform algorithmic operations on containers and other sequences.
2
#
The following subclauses describe components for non-modifying sequence operations, mutating sequence operations, sorting and related operations, and algorithms from the ISO C library, as summarized in Table 81.
Table 81 — Algorithms library summary
Subclause
Header(s)
Non-modifying sequence operations
Mutating sequence operations
<algorithm>
Sorting and related operations
Generalized numeric operations
<numeric>
C library algorithms
<cstdlib>

23.2 Algorithms requirements [algorithms.requirements]

1
#
All of the algorithms are separated from the particular implementations of data structures and are parameterized by iterator types.
Because of this, they can work with program-defined data structures, as long as these data structures have iterator types satisfying the assumptions on the algorithms.
2
#
For purposes of determining the existence of data races, algorithms shall not modify objects referenced through an iterator argument unless the specification requires such modification.
3
#
Throughout this Clause, the names of template parameters are used to express type requirements.
  • (3.1)
    If an algorithm's template parameter is named InputIterator, InputIterator1, or InputIterator2, the template argument shall satisfy the Cpp17InputIterator requirements ([input.iterators]).
  • (3.2)
    If an algorithm's template parameter is named OutputIterator, OutputIterator1, or OutputIterator2, the template argument shall satisfy the Cpp17OutputIterator requirements ([output.iterators]).
  • (3.3)
    If an algorithm's template parameter is named ForwardIterator, ForwardIterator1, or ForwardIterator2, the template argument shall satisfy the Cpp17ForwardIterator requirements ([forward.iterators]).
  • (3.4)
    If an algorithm's template parameter is named BidirectionalIterator, BidirectionalIterator1, or BidirectionalIterator2, the template argument shall satisfy the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]).
  • (3.5)
    If an algorithm's template parameter is named RandomAccessIterator, RandomAccessIterator1, or RandomAccessIterator2, the template argument shall satisfy the Cpp17RandomAccessIterator requirements ([random.access.iterators]).
4
#
If an algorithm's Effects: element specifies that a value pointed to by any iterator passed as an argument is modified, then that algorithm has an additional type requirement: The type of that argument shall satisfy the requirements of a mutable iterator ([iterator.requirements]).
[ Note
:
This requirement does not affect arguments that are named OutputIterator, OutputIterator1, or OutputIterator2, because output iterators must always be mutable.
— end note
 ]
5
#
Both in-place and copying versions are provided for certain algorithms.236
When such a version is provided for algorithm it is called algorithm_­copy.
Algorithms that take predicates end with the suffix _­if (which follows the suffix _­copy).
6
#
The Predicate parameter is used whenever an algorithm expects a function object ([function.objects]) that, when applied to the result of dereferencing the corresponding iterator, returns a value testable as true.
In other words, if an algorithm takes Predicate pred as its argument and first as its iterator argument, it should work correctly in the construct pred(*first) contextually converted to bool ([conv]).
The function object pred shall not apply any non-constant function through the dereferenced iterator.
7
#
The BinaryPredicate parameter is used whenever an algorithm expects a function object that when applied to the result of dereferencing two corresponding iterators or to dereferencing an iterator and type T when T is part of the signature returns a value testable as true.
In other words, if an algorithm takes BinaryPredicate binary_­pred as its argument and first1 and first2 as its iterator arguments, it should work correctly in the construct binary_­pred(*first1, *first2) contextually converted to bool ([conv]).
BinaryPredicate always takes the first iterator's value_­type as its first argument, that is, in those cases when T value is part of the signature, it should work correctly in the construct binary_­pred(*first1, value) contextually converted to bool ([conv]).
binary_­pred shall not apply any non-constant function through the dereferenced iterators.
8
#
The parameters UnaryOperation, BinaryOperation, BinaryOperation1, and BinaryOperation2 are used whenever an algorithm expects a function object ([function.objects]).
9
#
[ Note
:
Unless otherwise specified, algorithms that take function objects as arguments are permitted to copy those function objects freely.
Programmers for whom object identity is important should consider using a wrapper class that points to a noncopied implementation object such as reference_­wrapper<T> ([refwrap]), or some equivalent solution.
— end note
 ]
10
#
When the description of an algorithm gives an expression such as *first == value for a condition, the expression shall evaluate to either true or false in boolean contexts.
11
#
In the description of the algorithms operators + and - are used for some of the iterator categories for which they do not have to be defined.
In these cases the semantics of a+n is the same as that of
X tmp = a;
advance(tmp, n);
return tmp;
and that of b-a is the same as of
return distance(a, b);
236)
The decision whether to include a copying version was usually based on complexity considerations.
When the cost of doing the operation dominates the cost of copy, the copying version is not included.
For example, sort_­copy is not included because the cost of sorting is much more significant, and users might as well do copy followed by sort.

23.3 Parallel algorithms [algorithms.parallel]

1
#
This subclause describes components that C++ programs may use to perform operations on containers and other sequences in parallel.

23.3.1 Terms and definitions [algorithms.parallel.defns]

1
#
A parallel algorithm is a function template listed in this document with a template parameter named ExecutionPolicy.
2
#
Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions:
  • (2.1)
    All operations of the categories of the iterators that the algorithm is instantiated with.
  • (2.2)
    Operations on those sequence elements that are required by its specification.
  • (2.3)
    User-provided function objects to be applied during the execution of the algorithm, if required by the specification.
  • (2.4)
    Operations on those function objects required by the specification.
    [ Note
    : — end note
     ]
These functions are herein called element access functions.
[ Example
:
The sort function may invoke the following element access functions:
  • Operations of the random-access iterator of the actual template argument (as per [random.access.iterators]), as implied by the name of the template parameter RandomAccessIterator.
  • The swap function on the elements of the sequence (as per the preconditions specified in [sort]).
  • The user-provided Compare function object.
— end example
 ]

23.3.2 Requirements on user-provided function objects [algorithms.parallel.user]

1
#
Unless otherwise specified, function objects passed into parallel algorithms as objects of type Predicate, BinaryPredicate, Compare, UnaryOperation, BinaryOperation, BinaryOperation1, BinaryOperation2, and the operators used by the analogous overloads to these parallel algorithms that could be formed by the invocation with the specified default predicate or operation (where applicable) shall not directly or indirectly modify objects via their arguments, nor shall they rely on the identity of the provided objects.

23.3.3 Effect of execution policies on algorithm execution [algorithms.parallel.exec]

1
#
Parallel algorithms have template parameters named ExecutionPolicy ([execpol]) which describe the manner in which the execution of these algorithms may be parallelized and the manner in which they apply the element access functions.
2
#
If an object is modified by an element access function, the algorithm will perform no other unsynchronized accesses to that object.
The modifying element access functions are those which are specified as modifying the object.
[ Note
:
For example, swap(), ++, --, @=, and assignments modify the object.
For the assignment and @= operators, only the left argument is modified.
— end note
 ]
3
#
Unless otherwise stated, implementations may make arbitrary copies of elements (with type T) from sequences where is_­trivially_­copy_­constructible_­v<T> and is_­trivially_­destructible_­v<T> are true.
[ Note
:
This implies that user-supplied function objects should not rely on object identity of arguments for such input sequences.
Users for whom the object identity of the arguments to these function objects is important should consider using a wrapping iterator that returns a non-copied implementation object such as reference_­wrapper<T> ([refwrap]) or some equivalent solution.
— end note
 ]
4
#
The invocations of element access functions in parallel algorithms invoked with an execution policy object of type execution​::​sequenced_­policy all occur in the calling thread of execution.
[ Note
:
The invocations are not interleaved; see [intro.execution].
— end note
 ]
5
#
The invocations of element access functions in parallel algorithms invoked with an execution policy object of type execution​::​parallel_­policy are permitted to execute in either the invoking thread of execution or in a thread of execution implicitly created by the library to support parallel algorithm execution.
If the threads of execution created by thread ([thread.thread.class]) provide concurrent forward progress guarantees ([intro.progress]), then a thread of execution implicitly created by the library will provide parallel forward progress guarantees; otherwise, the provided forward progress guarantee is implementation-defined.
Any such invocations executing in the same thread of execution are indeterminately sequenced with respect to each other.
[ Note
:
It is the caller's responsibility to ensure that the invocation does not introduce data races or deadlocks.
— end note
 ]
[ Example
: 
int a[] = {0,1};
std::vector<int> v;
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int i) {
  v.push_back(i*2+1); // incorrect: data race
});
The program above has a data race because of the unsynchronized access to the container v.
— end example
 ]
[ Example
: 
std::atomic<int> x{0};
int a[] = {1,2};
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int) {
  x.fetch_add(1, std::memory_order::relaxed);
  // spin wait for another iteration to change the value of x
  while (x.load(std::memory_order::relaxed) == 1) { } // incorrect: assumes execution order
});
The above example depends on the order of execution of the iterations, and will not terminate if both iterations are executed sequentially on the same thread of execution.
— end example
 ]
[ Example
: 
int x = 0;
std::mutex m;
int a[] = {1,2};
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int) {
  std::lock_guard<mutex> guard(m);
  ++x;
});
The above example synchronizes access to object x ensuring that it is incremented correctly.
— end example
 ]
6
#
The invocations of element access functions in parallel algorithms invoked with an execution policy of type execution​::​parallel_­unsequenced_­policy are permitted to execute in an unordered fashion in unspecified threads of execution, and unsequenced with respect to one another within each thread of execution.
These threads of execution are either the invoking thread of execution or threads of execution implicitly created by the library; the latter will provide weakly parallel forward progress guarantees.
[ Note
:
This means that multiple function object invocations may be interleaved on a single thread of execution, which overrides the usual guarantee from [intro.execution] that function executions do not interleave with one another.
— end note
 ]
Since execution​::​parallel_­unsequenced_­policy allows the execution of element access functions to be interleaved on a single thread of execution, blocking synchronization, including the use of mutexes, risks deadlock.
Thus, the synchronization with execution​::​parallel_­unsequenced_­policy is restricted as follows: A standard library function is vectorization-unsafe if it is specified to synchronize with another function invocation, or another function invocation is specified to synchronize with it, and if it is not a memory allocation or deallocation function.
Vectorization-unsafe standard library functions may not be invoked by user code called from execution​::​parallel_­unsequenced_­policy algorithms.
[ Note
:
Implementations must ensure that internal synchronization inside standard library functions does not prevent forward progress when those functions are executed by threads of execution with weakly parallel forward progress guarantees.
— end note
 ]
[ Example
: 
int x = 0;
std::mutex m;
int a[] = {1,2};
std::for_each(std::execution::par_unseq, std::begin(a), std::end(a), [&](int) {
  std::lock_guard<mutex> guard(m); // incorrect: lock_­guard constructor calls m.lock()
  ++x;
});
The above program may result in two consecutive calls to m.lock() on the same thread of execution (which may deadlock), because the applications of the function object are not guaranteed to run on different threads of execution.
— end example
 ]
[ Note
:
The semantics of the execution​::​parallel_­policy or the execution​::​parallel_­unsequenced_­policy invocation allow the implementation to fall back to sequential execution if the system cannot parallelize an algorithm invocation due to lack of resources.
— end note
 ]
7
#
If an invocation of a parallel algorithm uses threads of execution implicitly created by the library, then the invoking thread of execution will either
  • (7.1)
    temporarily block with forward progress guarantee delegation ([intro.progress]) on the completion of these library-managed threads of execution, or
  • (7.2)
    eventually execute an element access function;
the thread of execution will continue to do so until the algorithm is finished.
[ Note
:
In blocking with forward progress guarantee delegation in this context, a thread of execution created by the library is considered to have finished execution as soon as it has finished the execution of the particular element access function that the invoking thread of execution logically depends on.
— end note
 ]
8
#
The semantics of parallel algorithms invoked with an execution policy object of implementation-defined type are implementation-defined.

23.3.4 Parallel algorithm exceptions [algorithms.parallel.exceptions]

1
#
During the execution of a parallel algorithm, if temporary memory resources are required for parallelization and none are available, the algorithm throws a bad_­alloc exception.
2
#
During the execution of a parallel algorithm, if the invocation of an element access function exits via an uncaught exception, the behavior is determined by the ExecutionPolicy.

23.3.5 ExecutionPolicy algorithm overloads [algorithms.parallel.overloads]

1
#
Parallel algorithms are algorithm overloads.
Each parallel algorithm overload has an additional template type parameter named ExecutionPolicy, which is the first template parameter.
Additionally, each parallel algorithm overload has an additional function parameter of type ExecutionPolicy&&, which is the first function parameter.
[ Note
:
Not all algorithms have parallel algorithm overloads.
— end note
 ]
2
#
Unless otherwise specified, the semantics of ExecutionPolicy algorithm overloads are identical to their overloads without.
3
#
Unless otherwise specified, the complexity requirements of ExecutionPolicy algorithm overloads are relaxed from the complexity requirements of the overloads without as follows: when the guarantee says “at most expr” or “exactly expr” and does not specify the number of assignments or swaps, and expr is not already expressed with notation, the complexity of the algorithm shall be .
4
#
Parallel algorithms shall not participate in overload resolution unless is_­execution_­policy_­v<remove_­cvref_­t<ExecutionPolicy>> is true.

23.4 Header <algorithm> synopsis [algorithm.syn]

#include <initializer_list>

namespace std {
  // [alg.nonmodifying], non-modifying sequence operations
  // [alg.all_of], all of
  template<class InputIterator, class Predicate>
    constexpr bool all_of(InputIterator first, InputIterator last, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    bool all_of(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator first, ForwardIterator last, Predicate pred);

  // [alg.any_of], any of
  template<class InputIterator, class Predicate>
    constexpr bool any_of(InputIterator first, InputIterator last, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    bool any_of(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator first, ForwardIterator last, Predicate pred);

  // [alg.none_of], none of
  template<class InputIterator, class Predicate>
    constexpr bool none_of(InputIterator first, InputIterator last, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    bool none_of(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 ForwardIterator first, ForwardIterator last, Predicate pred);

  // [alg.foreach], for each
  template<class InputIterator, class Function>
    constexpr Function for_each(InputIterator first, InputIterator last, Function f);
  template<class ExecutionPolicy, class ForwardIterator, class Function>
    void for_each(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator first, ForwardIterator last, Function f);
  template<class InputIterator, class Size, class Function>
    constexpr InputIterator for_each_n(InputIterator first, Size n, Function f);
  template<class ExecutionPolicy, class ForwardIterator, class Size, class Function>
    ForwardIterator for_each_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                               ForwardIterator first, Size n, Function f);

  // [alg.find], find
  template<class InputIterator, class T>
    constexpr InputIterator find(InputIterator first, InputIterator last,
                                 const T& value);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    ForwardIterator find(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                         ForwardIterator first, ForwardIterator last,
                         const T& value);
  template<class InputIterator, class Predicate>
    constexpr InputIterator find_if(InputIterator first, InputIterator last,
                                    Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    ForwardIterator find_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                            ForwardIterator first, ForwardIterator last,
                            Predicate pred);
  template<class InputIterator, class Predicate>
    constexpr InputIterator find_if_not(InputIterator first, InputIterator last,
                                        Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    ForwardIterator find_if_not(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                ForwardIterator first, ForwardIterator last,
                                Predicate pred);

  // [alg.find.end], find end
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator1
      find_end(ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr ForwardIterator1
      find_end(ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2,
               BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator1
      find_end(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1,
           class ForwardIterator2, class BinaryPredicate>
    ForwardIterator1
      find_end(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2,
               BinaryPredicate pred);

  // [alg.find.first.of], find first
  template<class InputIterator, class ForwardIterator>
    constexpr InputIterator
      find_first_of(InputIterator first1, InputIterator last1,
                    ForwardIterator first2, ForwardIterator last2);
  template<class InputIterator, class ForwardIterator, class BinaryPredicate>
    constexpr InputIterator
      find_first_of(InputIterator first1, InputIterator last1,
                    ForwardIterator first2, ForwardIterator last2,
                    BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator1
      find_first_of(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    ForwardIterator1 first1, ForwardIterator1 last1,
                    ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1,
           class ForwardIterator2, class BinaryPredicate>
    ForwardIterator1
      find_first_of(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    ForwardIterator1 first1, ForwardIterator1 last1,
                    ForwardIterator2 first2, ForwardIterator2 last2,
                    BinaryPredicate pred);

  // [alg.adjacent.find], adjacent find
  template<class ForwardIterator>
    constexpr ForwardIterator
      adjacent_find(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class BinaryPredicate>
    constexpr ForwardIterator
      adjacent_find(ForwardIterator first, ForwardIterator last,
                    BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator
      adjacent_find(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class BinaryPredicate>
    ForwardIterator
      adjacent_find(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    ForwardIterator first, ForwardIterator last,
                    BinaryPredicate pred);

  // [alg.count], count
  template<class InputIterator, class T>
    constexpr typename iterator_traits<InputIterator>::difference_type
      count(InputIterator first, InputIterator last, const T& value);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    typename iterator_traits<ForwardIterator>::difference_type
      count(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
            ForwardIterator first, ForwardIterator last, const T& value);
  template<class InputIterator, class Predicate>
    constexpr typename iterator_traits<InputIterator>::difference_type
      count_if(InputIterator first, InputIterator last, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    typename iterator_traits<ForwardIterator>::difference_type
      count_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator first, ForwardIterator last, Predicate pred);

  // [mismatch], mismatch
  template<class InputIterator1, class InputIterator2>
    constexpr pair<InputIterator1, InputIterator2>
      mismatch(InputIterator1 first1, InputIterator1 last1,
               InputIterator2 first2);
  template<class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr pair<InputIterator1, InputIterator2>
      mismatch(InputIterator1 first1, InputIterator1 last1,
               InputIterator2 first2, BinaryPredicate pred);
  template<class InputIterator1, class InputIterator2>
    constexpr pair<InputIterator1, InputIterator2>
      mismatch(InputIterator1 first1, InputIterator1 last1,
               InputIterator2 first2, InputIterator2 last2);
  template<class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr pair<InputIterator1, InputIterator2>
      mismatch(InputIterator1 first1, InputIterator1 last1,
               InputIterator2 first2, InputIterator2 last2,
               BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    pair<ForwardIterator1, ForwardIterator2>
      mismatch(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    pair<ForwardIterator1, ForwardIterator2>
      mismatch(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    pair<ForwardIterator1, ForwardIterator2>
      mismatch(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    pair<ForwardIterator1, ForwardIterator2>
      mismatch(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2,
               BinaryPredicate pred);

  // [alg.equal], equal
  template<class InputIterator1, class InputIterator2>
    constexpr bool equal(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2);
  template<class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr bool equal(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, BinaryPredicate pred);
  template<class InputIterator1, class InputIterator2>
    constexpr bool equal(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, InputIterator2 last2);
  template<class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr bool equal(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, InputIterator2 last2,
                         BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    bool equal(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    bool equal(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    bool equal(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    bool equal(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator1 first1, ForwardIterator1 last1,
               ForwardIterator2 first2, ForwardIterator2 last2,
               BinaryPredicate pred);

  // [alg.is_permutation], is permutation
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                                  ForwardIterator2 first2);
  template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                                  ForwardIterator2 first2, BinaryPredicate pred);
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                                  ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                                  ForwardIterator2 first2, ForwardIterator2 last2,
                                  BinaryPredicate pred);

  // [alg.search], search
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator1
      search(ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr ForwardIterator1
      search(ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2,
             BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator1
      search(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
             ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    ForwardIterator1
      search(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
             ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2,
             BinaryPredicate pred);
  template<class ForwardIterator, class Size, class T>
    constexpr ForwardIterator
      search_n(ForwardIterator first, ForwardIterator last,
               Size count, const T& value);
  template<class ForwardIterator, class Size, class T, class BinaryPredicate>
    constexpr ForwardIterator
      search_n(ForwardIterator first, ForwardIterator last,
               Size count, const T& value,
               BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Size, class T>
    ForwardIterator
      search_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator first, ForwardIterator last,
               Size count, const T& value);
  template<class ExecutionPolicy, class ForwardIterator, class Size, class T,
           class BinaryPredicate>
    ForwardIterator
      search_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
               ForwardIterator first, ForwardIterator last,
               Size count, const T& value,
               BinaryPredicate pred);

  template<class ForwardIterator, class Searcher>
    constexpr ForwardIterator
      search(ForwardIterator first, ForwardIterator last, const Searcher& searcher);

  // [alg.modifying.operations], mutating sequence operations
  // [alg.copy], copy
  template<class InputIterator, class OutputIterator>
    constexpr OutputIterator copy(InputIterator first, InputIterator last,
                                  OutputIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                          ForwardIterator1 first, ForwardIterator1 last,
                          ForwardIterator2 result);
  template<class InputIterator, class Size, class OutputIterator>
    constexpr OutputIterator copy_n(InputIterator first, Size n,
                                    OutputIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class Size,
           class ForwardIterator2>
    ForwardIterator2 copy_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                            ForwardIterator1 first, Size n,
                            ForwardIterator2 result);
  template<class InputIterator, class OutputIterator, class Predicate>
    constexpr OutputIterator copy_if(InputIterator first, InputIterator last,
                                     OutputIterator result, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class Predicate>
    ForwardIterator2 copy_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                             ForwardIterator1 first, ForwardIterator1 last,
                             ForwardIterator2 result, Predicate pred);
  template<class BidirectionalIterator1, class BidirectionalIterator2>
    constexpr BidirectionalIterator2
      copy_backward(BidirectionalIterator1 first, BidirectionalIterator1 last,
                    BidirectionalIterator2 result);

  // [alg.move], move
  template<class InputIterator, class OutputIterator>
    constexpr OutputIterator move(InputIterator first, InputIterator last,
                                  OutputIterator result);
  template<class ExecutionPolicy, class ForwardIterator1,
           class ForwardIterator2>
    ForwardIterator2 move(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                          ForwardIterator1 first, ForwardIterator1 last,
                          ForwardIterator2 result);
  template<class BidirectionalIterator1, class BidirectionalIterator2>
    constexpr BidirectionalIterator2
      move_backward(BidirectionalIterator1 first, BidirectionalIterator1 last,
                    BidirectionalIterator2 result);

  // [alg.swap], swap
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator2 swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1,
                                           ForwardIterator2 first2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 swap_ranges(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                 ForwardIterator1 first1, ForwardIterator1 last1,
                                 ForwardIterator2 first2);
  template<class ForwardIterator1, class ForwardIterator2>
    constexpr void iter_swap(ForwardIterator1 a, ForwardIterator2 b);

  // [alg.transform], transform
  template<class InputIterator, class OutputIterator, class UnaryOperation>
    constexpr OutputIterator
      transform(InputIterator first, InputIterator last,
                OutputIterator result, UnaryOperation op);
  template<class InputIterator1, class InputIterator2, class OutputIterator,
           class BinaryOperation>
    constexpr OutputIterator
      transform(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, OutputIterator result,
                BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class UnaryOperation>
    ForwardIterator2
      transform(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator1 first, ForwardIterator1 last,
                ForwardIterator2 result, UnaryOperation op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class BinaryOperation>
    ForwardIterator
      transform(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator1 first1, ForwardIterator1 last1,
                ForwardIterator2 first2, ForwardIterator result,
                BinaryOperation binary_op);

  // [alg.replace], replace
  template<class ForwardIterator, class T>
    constexpr void replace(ForwardIterator first, ForwardIterator last,
                           const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    void replace(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 ForwardIterator first, ForwardIterator last,
                 const T& old_value, const T& new_value);
  template<class ForwardIterator, class Predicate, class T>
    constexpr void replace_if(ForwardIterator first, ForwardIterator last,
                              Predicate pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate, class T>
    void replace_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    ForwardIterator first, ForwardIterator last,
                    Predicate pred, const T& new_value);
  template<class InputIterator, class OutputIterator, class T>
    constexpr OutputIterator replace_copy(InputIterator first, InputIterator last,
                                          OutputIterator result,
                                          const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T>
    ForwardIterator2 replace_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                  ForwardIterator1 first, ForwardIterator1 last,
                                  ForwardIterator2 result,
                                  const T& old_value, const T& new_value);
  template<class InputIterator, class OutputIterator, class Predicate, class T>
    constexpr OutputIterator replace_copy_if(InputIterator first, InputIterator last,
                                             OutputIterator result,
                                             Predicate pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class Predicate, class T>
    ForwardIterator2 replace_copy_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                     ForwardIterator1 first, ForwardIterator1 last,
                                     ForwardIterator2 result,
                                     Predicate pred, const T& new_value);

  // [alg.fill], fill
  template<class ForwardIterator, class T>
    constexpr void fill(ForwardIterator first, ForwardIterator last, const T& value);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    void fill(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
              ForwardIterator first, ForwardIterator last, const T& value);
  template<class OutputIterator, class Size, class T>
    constexpr OutputIterator fill_n(OutputIterator first, Size n, const T& value);
  template<class ExecutionPolicy, class ForwardIterator,
           class Size, class T>
    ForwardIterator fill_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                           ForwardIterator first, Size n, const T& value);

  // [alg.generate], generate
  template<class ForwardIterator, class Generator>
    constexpr void generate(ForwardIterator first, ForwardIterator last,
                            Generator gen);
  template<class ExecutionPolicy, class ForwardIterator, class Generator>
    void generate(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator first, ForwardIterator last,
                  Generator gen);
  template<class OutputIterator, class Size, class Generator>
    constexpr OutputIterator generate_n(OutputIterator first, Size n, Generator gen);
  template<class ExecutionPolicy, class ForwardIterator, class Size, class Generator>
    ForwardIterator generate_n(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                               ForwardIterator first, Size n, Generator gen);

  // [alg.remove], remove
  template<class ForwardIterator, class T>
    constexpr ForwardIterator remove(ForwardIterator first, ForwardIterator last,
                                     const T& value);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    ForwardIterator remove(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                           ForwardIterator first, ForwardIterator last,
                           const T& value);
  template<class ForwardIterator, class Predicate>
    constexpr ForwardIterator remove_if(ForwardIterator first, ForwardIterator last,
                                        Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    ForwardIterator remove_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                              ForwardIterator first, ForwardIterator last,
                              Predicate pred);
  template<class InputIterator, class OutputIterator, class T>
    constexpr OutputIterator
      remove_copy(InputIterator first, InputIterator last,
                  OutputIterator result, const T& value);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class T>
    ForwardIterator2
      remove_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first, ForwardIterator1 last,
                  ForwardIterator2 result, const T& value);
  template<class InputIterator, class OutputIterator, class Predicate>
    constexpr OutputIterator
      remove_copy_if(InputIterator first, InputIterator last,
                     OutputIterator result, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class Predicate>
    ForwardIterator2
      remove_copy_if(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator1 first, ForwardIterator1 last,
                     ForwardIterator2 result, Predicate pred);

  // [alg.unique], unique
  template<class ForwardIterator>
    constexpr ForwardIterator unique(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class BinaryPredicate>
    constexpr ForwardIterator unique(ForwardIterator first, ForwardIterator last,
                                     BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator unique(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                           ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class BinaryPredicate>
    ForwardIterator unique(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                           ForwardIterator first, ForwardIterator last,
                           BinaryPredicate pred);
  template<class InputIterator, class OutputIterator>
    constexpr OutputIterator
      unique_copy(InputIterator first, InputIterator last,
                  OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryPredicate>
    constexpr OutputIterator
      unique_copy(InputIterator first, InputIterator last,
                  OutputIterator result, BinaryPredicate pred);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2
      unique_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first, ForwardIterator1 last,
                  ForwardIterator2 result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryPredicate>
    ForwardIterator2
      unique_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first, ForwardIterator1 last,
                  ForwardIterator2 result, BinaryPredicate pred);

  // [alg.reverse], reverse
  template<class BidirectionalIterator>
    constexpr void reverse(BidirectionalIterator first, BidirectionalIterator last);
  template<class ExecutionPolicy, class BidirectionalIterator>
    void reverse(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 BidirectionalIterator first, BidirectionalIterator last);
  template<class BidirectionalIterator, class OutputIterator>
    constexpr OutputIterator
      reverse_copy(BidirectionalIterator first, BidirectionalIterator last,
                   OutputIterator result);
  template<class ExecutionPolicy, class BidirectionalIterator, class ForwardIterator>
    ForwardIterator
      reverse_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                   BidirectionalIterator first, BidirectionalIterator last,
                   ForwardIterator result);

  // [alg.rotate], rotate
  template<class ForwardIterator>
    constexpr ForwardIterator rotate(ForwardIterator first,
                                     ForwardIterator middle,
                                     ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator rotate(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                           ForwardIterator first,
                           ForwardIterator middle,
                           ForwardIterator last);
  template<class ForwardIterator, class OutputIterator>
    constexpr OutputIterator
      rotate_copy(ForwardIterator first, ForwardIterator middle,
                  ForwardIterator last, OutputIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2
      rotate_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first, ForwardIterator1 middle,
                  ForwardIterator1 last, ForwardIterator2 result);

  // [alg.random.sample], sample
  template<class PopulationIterator, class SampleIterator,
           class Distance, class UniformRandomBitGenerator>
    SampleIterator sample(PopulationIterator first, PopulationIterator last,
                          SampleIterator out, Distance n,
                          UniformRandomBitGenerator&& g);

  // [alg.random.shuffle], shuffle
  template<class RandomAccessIterator, class UniformRandomBitGenerator>
    void shuffle(RandomAccessIterator first,
                 RandomAccessIterator last,
                 UniformRandomBitGenerator&& g);

  // [alg.shift], shift
  template<class ForwardIterator>
    constexpr ForwardIterator
      shift_left(ForwardIterator first, ForwardIterator last,
                 typename iterator_traits<ForwardIterator>::difference_type n);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator
      shift_left(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 ForwardIterator first, ForwardIterator last,
                 typename iterator_traits<ForwardIterator>::difference_type n);
  template<class ForwardIterator>
    constexpr ForwardIterator
      shift_right(ForwardIterator first, ForwardIterator last,
                  typename iterator_traits<ForwardIterator>::difference_type n);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator
      shift_right(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator first, ForwardIterator last,
                  typename iterator_traits<ForwardIterator>::difference_type n);

  // [alg.sorting], sorting and related operations
  // [alg.sort], sorting
  template<class RandomAccessIterator>
    constexpr void sort(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void sort(RandomAccessIterator first, RandomAccessIterator last,
                        Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    void sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
              RandomAccessIterator first, RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    void sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
              RandomAccessIterator first, RandomAccessIterator last,
              Compare comp);

  template<class RandomAccessIterator>
    void stable_sort(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    void stable_sort(RandomAccessIterator first, RandomAccessIterator last,
                     Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    void stable_sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     RandomAccessIterator first, RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    void stable_sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     RandomAccessIterator first, RandomAccessIterator last,
                     Compare comp);

  template<class RandomAccessIterator>
    constexpr void partial_sort(RandomAccessIterator first,
                                RandomAccessIterator middle,
                                RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void partial_sort(RandomAccessIterator first,
                                RandomAccessIterator middle,
                                RandomAccessIterator last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    void partial_sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                      RandomAccessIterator first,
                      RandomAccessIterator middle,
                      RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    void partial_sort(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                      RandomAccessIterator first,
                      RandomAccessIterator middle,
                      RandomAccessIterator last, Compare comp);
  template<class InputIterator, class RandomAccessIterator>
    constexpr RandomAccessIterator
      partial_sort_copy(InputIterator first, InputIterator last,
                        RandomAccessIterator result_first,
                        RandomAccessIterator result_last);
  template<class InputIterator, class RandomAccessIterator, class Compare>
    constexpr RandomAccessIterator
      partial_sort_copy(InputIterator first, InputIterator last,
                        RandomAccessIterator result_first,
                        RandomAccessIterator result_last,
                        Compare comp);
  template<class ExecutionPolicy, class ForwardIterator, class RandomAccessIterator>
    RandomAccessIterator
      partial_sort_copy(ExecutionPolicy&& exec,  // see [algorithms.parallel.overloads]
                        ForwardIterator first, ForwardIterator last,
                        RandomAccessIterator result_first,
                        RandomAccessIterator result_last);
  template<class ExecutionPolicy, class ForwardIterator, class RandomAccessIterator,
           class Compare>
    RandomAccessIterator
      partial_sort_copy(ExecutionPolicy&& exec,  // see [algorithms.parallel.overloads]
                        ForwardIterator first, ForwardIterator last,
                        RandomAccessIterator result_first,
                        RandomAccessIterator result_last,
                        Compare comp);
  template<class ForwardIterator>
    constexpr bool is_sorted(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class Compare>
    constexpr bool is_sorted(ForwardIterator first, ForwardIterator last,
                             Compare comp);
  template<class ExecutionPolicy, class ForwardIterator>
    bool is_sorted(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                   ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class Compare>
    bool is_sorted(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                   ForwardIterator first, ForwardIterator last,
                   Compare comp);
  template<class ForwardIterator>
    constexpr ForwardIterator
      is_sorted_until(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class Compare>
    constexpr ForwardIterator
      is_sorted_until(ForwardIterator first, ForwardIterator last,
                      Compare comp);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator
      is_sorted_until(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                      ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class Compare>
    ForwardIterator
      is_sorted_until(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                      ForwardIterator first, ForwardIterator last,
                      Compare comp);

  // [alg.nth.element], Nth element
  template<class RandomAccessIterator>
    constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                               RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                               RandomAccessIterator last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    void nth_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     RandomAccessIterator first, RandomAccessIterator nth,
                     RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    void nth_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     RandomAccessIterator first, RandomAccessIterator nth,
                     RandomAccessIterator last, Compare comp);

  // [alg.binary.search], binary search
  template<class ForwardIterator, class T>
    constexpr ForwardIterator
      lower_bound(ForwardIterator first, ForwardIterator last,
                  const T& value);
  template<class ForwardIterator, class T, class Compare>
    constexpr ForwardIterator
      lower_bound(ForwardIterator first, ForwardIterator last,
                  const T& value, Compare comp);

  template<class ForwardIterator, class T>
    constexpr ForwardIterator
      upper_bound(ForwardIterator first, ForwardIterator last,
                  const T& value);
  template<class ForwardIterator, class T, class Compare>
    constexpr ForwardIterator
      upper_bound(ForwardIterator first, ForwardIterator last,
                  const T& value, Compare comp);

  template<class ForwardIterator, class T>
    constexpr pair<ForwardIterator, ForwardIterator>
      equal_range(ForwardIterator first, ForwardIterator last,
                  const T& value);
  template<class ForwardIterator, class T, class Compare>
    constexpr pair<ForwardIterator, ForwardIterator>
      equal_range(ForwardIterator first, ForwardIterator last,
                  const T& value, Compare comp);

  template<class ForwardIterator, class T>
    constexpr bool
      binary_search(ForwardIterator first, ForwardIterator last,
                    const T& value);
  template<class ForwardIterator, class T, class Compare>
    constexpr bool
      binary_search(ForwardIterator first, ForwardIterator last,
                    const T& value, Compare comp);

  // [alg.partitions], partitions
  template<class InputIterator, class Predicate>
    constexpr bool is_partitioned(InputIterator first, InputIterator last, Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    bool is_partitioned(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                        ForwardIterator first, ForwardIterator last, Predicate pred);

  template<class ForwardIterator, class Predicate>
    constexpr ForwardIterator partition(ForwardIterator first,
                                        ForwardIterator last,
                                        Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class Predicate>
    ForwardIterator partition(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                              ForwardIterator first,
                              ForwardIterator last,
                              Predicate pred);
  template<class BidirectionalIterator, class Predicate>
    BidirectionalIterator stable_partition(BidirectionalIterator first,
                                           BidirectionalIterator last,
                                           Predicate pred);
  template<class ExecutionPolicy, class BidirectionalIterator, class Predicate>
    BidirectionalIterator stable_partition(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                           BidirectionalIterator first,
                                           BidirectionalIterator last,
                                           Predicate pred);
  template<class InputIterator, class OutputIterator1,
           class OutputIterator2, class Predicate>
    constexpr pair<OutputIterator1, OutputIterator2>
      partition_copy(InputIterator first, InputIterator last,
                     OutputIterator1 out_true, OutputIterator2 out_false,
                     Predicate pred);
  template<class ExecutionPolicy, class ForwardIterator, class ForwardIterator1,
           class ForwardIterator2, class Predicate>
    pair<ForwardIterator1, ForwardIterator2>
      partition_copy(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator first, ForwardIterator last,
                     ForwardIterator1 out_true, ForwardIterator2 out_false,
                     Predicate pred);
  template<class ForwardIterator, class Predicate>
    constexpr ForwardIterator
      partition_point(ForwardIterator first, ForwardIterator last,
                      Predicate pred);

  // [alg.merge], merge
  template<class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator
      merge(InputIterator1 first1, InputIterator1 last1,
            InputIterator2 first2, InputIterator2 last2,
            OutputIterator result);
  template<class InputIterator1, class InputIterator2, class OutputIterator,
           class Compare>
    constexpr OutputIterator
      merge(InputIterator1 first1, InputIterator1 last1,
            InputIterator2 first2, InputIterator2 last2,
            OutputIterator result, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator>
    ForwardIterator
      merge(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
            ForwardIterator1 first1, ForwardIterator1 last1,
            ForwardIterator2 first2, ForwardIterator2 last2,
            ForwardIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class Compare>
    ForwardIterator
      merge(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
            ForwardIterator1 first1, ForwardIterator1 last1,
            ForwardIterator2 first2, ForwardIterator2 last2,
            ForwardIterator result, Compare comp);

  template<class BidirectionalIterator>
    void inplace_merge(BidirectionalIterator first,
                       BidirectionalIterator middle,
                       BidirectionalIterator last);
  template<class BidirectionalIterator, class Compare>
    void inplace_merge(BidirectionalIterator first,
                       BidirectionalIterator middle,
                       BidirectionalIterator last, Compare comp);
  template<class ExecutionPolicy, class BidirectionalIterator>
    void inplace_merge(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       BidirectionalIterator first,
                       BidirectionalIterator middle,
                       BidirectionalIterator last);
  template<class ExecutionPolicy, class BidirectionalIterator, class Compare>
    void inplace_merge(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       BidirectionalIterator first,
                       BidirectionalIterator middle,
                       BidirectionalIterator last, Compare comp);

  // [alg.set.operations], set operations
  template<class InputIterator1, class InputIterator2>
    constexpr bool includes(InputIterator1 first1, InputIterator1 last1,
                            InputIterator2 first2, InputIterator2 last2);
  template<class InputIterator1, class InputIterator2, class Compare>
    constexpr bool includes(InputIterator1 first1, InputIterator1 last1,
                            InputIterator2 first2, InputIterator2 last2,
                            Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    bool includes(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first1, ForwardIterator1 last1,
                  ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class Compare>
    bool includes(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                  ForwardIterator1 first1, ForwardIterator1 last1,
                  ForwardIterator2 first2, ForwardIterator2 last2,
                  Compare comp);

  template<class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator
      set_union(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, InputIterator2 last2,
                OutputIterator result);
  template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator
                set_union(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, InputIterator2 last2,
                OutputIterator result, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator>
    ForwardIterator
      set_union(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator1 first1, ForwardIterator1 last1,
                ForwardIterator2 first2, ForwardIterator2 last2,
                ForwardIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class Compare>
    ForwardIterator
      set_union(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                ForwardIterator1 first1, ForwardIterator1 last1,
                ForwardIterator2 first2, ForwardIterator2 last2,
                ForwardIterator result, Compare comp);

  template<class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator
      set_intersection(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2, InputIterator2 last2,
                       OutputIterator result);
  template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator
      set_intersection(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2, InputIterator2 last2,
                       OutputIterator result, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator>
    ForwardIterator
      set_intersection(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2, ForwardIterator2 last2,
                       ForwardIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class Compare>
    ForwardIterator
      set_intersection(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2, ForwardIterator2 last2,
                       ForwardIterator result, Compare comp);

  template<class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator
      set_difference(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2,
                     OutputIterator result);
  template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator
      set_difference(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2,
                     OutputIterator result, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator>
    ForwardIterator
      set_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator1 first1, ForwardIterator1 last1,
                     ForwardIterator2 first2, ForwardIterator2 last2,
                     ForwardIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class Compare>
    ForwardIterator
      set_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator1 first1, ForwardIterator1 last1,
                     ForwardIterator2 first2, ForwardIterator2 last2,
                     ForwardIterator result, Compare comp);

  template<class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator
      set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
                               InputIterator2 first2, InputIterator2 last2,
                               OutputIterator result);
  template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator
      set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
                               InputIterator2 first2, InputIterator2 last2,
                               OutputIterator result, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator>
    ForwardIterator
      set_symmetric_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                               ForwardIterator1 first1, ForwardIterator1 last1,
                               ForwardIterator2 first2, ForwardIterator2 last2,
                               ForwardIterator result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class ForwardIterator, class Compare>
    ForwardIterator
      set_symmetric_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                               ForwardIterator1 first1, ForwardIterator1 last1,
                               ForwardIterator2 first2, ForwardIterator2 last2,
                               ForwardIterator result, Compare comp);

  // [alg.heap.operations], heap operations
  template<class RandomAccessIterator>
    constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last,
                             Compare comp);

  template<class RandomAccessIterator>
    constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last,
                            Compare comp);

  template<class RandomAccessIterator>
    constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last,
                             Compare comp);

  template<class RandomAccessIterator>
    constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last,
                             Compare comp);

  template<class RandomAccessIterator>
    constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last,
                           Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    bool is_heap(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 RandomAccessIterator first, RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    bool is_heap(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                 RandomAccessIterator first, RandomAccessIterator last,
                 Compare comp);
  template<class RandomAccessIterator>
    constexpr RandomAccessIterator
      is_heap_until(RandomAccessIterator first, RandomAccessIterator last);
  template<class RandomAccessIterator, class Compare>
    constexpr RandomAccessIterator
      is_heap_until(RandomAccessIterator first, RandomAccessIterator last,
                    Compare comp);
  template<class ExecutionPolicy, class RandomAccessIterator>
    RandomAccessIterator
      is_heap_until(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    RandomAccessIterator first, RandomAccessIterator last);
  template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
    RandomAccessIterator
      is_heap_until(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                    RandomAccessIterator first, RandomAccessIterator last,
                    Compare comp);

  // [alg.min.max], minimum and maximum
  template<class T> constexpr const T& min(const T& a, const T& b);
  template<class T, class Compare>
    constexpr const T& min(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr T min(initializer_list<T> t);
  template<class T, class Compare>
    constexpr T min(initializer_list<T> t, Compare comp);

  template<class T> constexpr const T& max(const T& a, const T& b);
  template<class T, class Compare>
    constexpr const T& max(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr T max(initializer_list<T> t);
  template<class T, class Compare>
    constexpr T max(initializer_list<T> t, Compare comp);

  template<class T> constexpr pair<const T&, const T&> minmax(const T& a, const T& b);
  template<class T, class Compare>
    constexpr pair<const T&, const T&> minmax(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr pair<T, T> minmax(initializer_list<T> t);
  template<class T, class Compare>
    constexpr pair<T, T> minmax(initializer_list<T> t, Compare comp);

  template<class ForwardIterator>
    constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class Compare>
    constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last,
                                          Compare comp);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator min_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class Compare>
    ForwardIterator min_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                ForwardIterator first, ForwardIterator last,
                                Compare comp);
  template<class ForwardIterator>
    constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class Compare>
    constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last,
                                          Compare comp);
  template<class ExecutionPolicy, class ForwardIterator>
    ForwardIterator max_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class Compare>
    ForwardIterator max_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                ForwardIterator first, ForwardIterator last,
                                Compare comp);
  template<class ForwardIterator>
    constexpr pair<ForwardIterator, ForwardIterator>
      minmax_element(ForwardIterator first, ForwardIterator last);
  template<class ForwardIterator, class Compare>
    constexpr pair<ForwardIterator, ForwardIterator>
      minmax_element(ForwardIterator first, ForwardIterator last, Compare comp);
  template<class ExecutionPolicy, class ForwardIterator>
    pair<ForwardIterator, ForwardIterator>
      minmax_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class Compare>
    pair<ForwardIterator, ForwardIterator>
      minmax_element(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                     ForwardIterator first, ForwardIterator last, Compare comp);

  // [alg.clamp], bounded value
  template<class T>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi);
  template<class T, class Compare>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi, Compare comp);

  // [alg.lex.comparison], lexicographical comparison
  template<class InputIterator1, class InputIterator2>
    constexpr bool
      lexicographical_compare(InputIterator1 first1, InputIterator1 last1,
                              InputIterator2 first2, InputIterator2 last2);
  template<class InputIterator1, class InputIterator2, class Compare>
    constexpr bool
      lexicographical_compare(InputIterator1 first1, InputIterator1 last1,
                              InputIterator2 first2, InputIterator2 last2,
                              Compare comp);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    bool
      lexicographical_compare(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                              ForwardIterator1 first1, ForwardIterator1 last1,
                              ForwardIterator2 first2, ForwardIterator2 last2);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class Compare>
    bool
      lexicographical_compare(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                              ForwardIterator1 first1, ForwardIterator1 last1,
                              ForwardIterator2 first2, ForwardIterator2 last2,
                              Compare comp);

  // [alg.3way], three-way comparison algorithms
  template<class T, class U>
    constexpr auto compare_3way(const T& a, const U& b);
  template<class InputIterator1, class InputIterator2, class Cmp>
    constexpr auto
      lexicographical_compare_3way(InputIterator1 b1, InputIterator1 e1,
                                   InputIterator2 b2, InputIterator2 e2,
                                   Cmp comp)
        -> common_comparison_category_t<decltype(comp(*b1, *b2)), strong_ordering>;
  template<class InputIterator1, class InputIterator2>
    constexpr auto
      lexicographical_compare_3way(InputIterator1 b1, InputIterator1 e1,
                                   InputIterator2 b2, InputIterator2 e2);

  // [alg.permutation.generators], permutations
  template<class BidirectionalIterator>
    constexpr bool next_permutation(BidirectionalIterator first,
                                    BidirectionalIterator last);
  template<class BidirectionalIterator, class Compare>
    constexpr bool next_permutation(BidirectionalIterator first,
                                    BidirectionalIterator last, Compare comp);
  template<class BidirectionalIterator>
    constexpr bool prev_permutation(BidirectionalIterator first,
                                    BidirectionalIterator last);
  template<class BidirectionalIterator, class Compare>
    constexpr bool prev_permutation(BidirectionalIterator first,
                                    BidirectionalIterator last, Compare comp);
}

23.5 Non-modifying sequence operations [alg.nonmodifying]

23.5.1 All of [alg.all_of]

🔗
template<class InputIterator, class Predicate> constexpr bool all_of(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> bool all_of(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Returns: true if [first, last) is empty or if pred(*i) is true for every iterator i in the range [first, last), and false otherwise.
2
#
Complexity: At most last - first applications of the predicate.

23.5.2 Any of [alg.any_of]

🔗
template<class InputIterator, class Predicate> constexpr bool any_of(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> bool any_of(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Returns: false if [first, last) is empty or if there is no iterator i in the range [first, last) such that pred(*i) is true, and true otherwise.
2
#
Complexity: At most last - first applications of the predicate.

23.5.3 None of [alg.none_of]

🔗
template<class InputIterator, class Predicate> constexpr bool none_of(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> bool none_of(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Returns: true if [first, last) is empty or if pred(*i) is false for every iterator i in the range [first, last), and false otherwise.
2
#
Complexity: At most last - first applications of the predicate.

23.5.4 For each [alg.foreach]

🔗
template<class InputIterator, class Function> constexpr Function for_each(InputIterator first, InputIterator last, Function f);
1
#
Requires: Function shall satisfy the Cpp17MoveConstructible requirements (Table 25).
[ Note
:
Function need not meet the requirements of Cpp17CopyConstructible (Table 26).
— end note
 ]
2
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, last), starting from first and proceeding to last - 1.
[ Note
:
If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
3
#
Returns: f.
4
#
Complexity: Applies f exactly last - first times.
5
#
Remarks: If f returns a result, the result is ignored.
🔗
template<class ExecutionPolicy, class ForwardIterator, class Function> void for_each(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Function f);
6
#
Requires: Function shall satisfy the Cpp17CopyConstructible requirements.
7
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, last).
[ Note
:
If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
8
#
Complexity: Applies f exactly last - first times.
9
#
Remarks: If f returns a result, the result is ignored.
Implementations do not have the freedom granted under [algorithms.parallel.exec] to make arbitrary copies of elements from the input sequence.
10
#
[ Note
:
Does not return a copy of its Function parameter, since parallelization may not permit efficient state accumulation.
— end note
 ]
🔗
template<class InputIterator, class Size, class Function> constexpr InputIterator for_each_n(InputIterator first, Size n, Function f);
11
#
Requires: Function shall satisfy the Cpp17MoveConstructible requirements
[ Note
:
Function need not meet the requirements of Cpp17CopyConstructible.
— end note
 ]
12
#
Requires: n >= 0.
13
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n) in order.
[ Note
:
If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
14
#
Returns: first + n.
15
#
Remarks: If f returns a result, the result is ignored.
🔗
template<class ExecutionPolicy, class ForwardIterator, class Size, class Function> ForwardIterator for_each_n(ExecutionPolicy&& exec, ForwardIterator first, Size n, Function f);
16
#
Requires: Function shall satisfy the Cpp17CopyConstructible requirements.
17
#
Requires: n >= 0.
18
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n).
[ Note
:
If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
19
#
Returns: first + n.
20
#
Remarks: If f returns a result, the result is ignored.
Implementations do not have the freedom granted under [algorithms.parallel.exec] to make arbitrary copies of elements from the input sequence.

23.5.5 Find [alg.find]

🔗
template<class InputIterator, class T> constexpr InputIterator find(InputIterator first, InputIterator last, const T& value); template<class ExecutionPolicy, class ForwardIterator, class T> ForwardIterator find(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, const T& value); template<class InputIterator, class Predicate> constexpr InputIterator find_if(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> ForwardIterator find_if(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred); template<class InputIterator, class Predicate> constexpr InputIterator find_if_not(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> ForwardIterator find_if_not(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Returns: The first iterator i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false, pred(*i) == false.
Returns last if no such iterator is found.
2
#
Complexity: At most last - first applications of the corresponding predicate.

23.5.6 Find end [alg.find.end]

🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr ForwardIterator1 find_end(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator1 find_end(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> constexpr ForwardIterator1 find_end(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> ForwardIterator1 find_end(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Effects: Finds a subsequence of equal values in a sequence.
2
#
Returns: The last iterator i in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n < (last2 - first2), the following corresponding conditions hold: *(i + n) == *(​first2 + n), pred(*(i + n), *(first2 + n)) != false.
Returns last1 if [first2, last2) is empty or if no such iterator is found.
3
#
Complexity: At most (last2 - first2) * (last1 - first1 - (last2 - first2) + 1) applications of the corresponding predicate.

23.5.7 Find first [alg.find.first.of]

🔗
template<class InputIterator, class ForwardIterator> constexpr InputIterator find_first_of(InputIterator first1, InputIterator last1, ForwardIterator first2, ForwardIterator last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator1 find_first_of(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator, class ForwardIterator, class BinaryPredicate> constexpr InputIterator find_first_of(InputIterator first1, InputIterator last1, ForwardIterator first2, ForwardIterator last2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> ForwardIterator1 find_first_of(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Effects: Finds an element that matches one of a set of values.
2
#
Returns: The first iterator i in the range [first1, last1) such that for some iterator j in the range [first2, last2) the following conditions hold: *i == *j, pred(*i,*j) != false.
Returns last1 if [first2, last2) is empty or if no such iterator is found.
3
#
Complexity: At most (last1-first1) * (last2-first2) applications of the corresponding predicate.

23.5.8 Adjacent find [alg.adjacent.find]

🔗
template<class ForwardIterator> constexpr ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator adjacent_find(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class BinaryPredicate> constexpr ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator, class BinaryPredicate> ForwardIterator adjacent_find(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, BinaryPredicate pred);
1
#
Returns: The first iterator i such that both i and i + 1 are in the range [first, last) for which the following corresponding conditions hold: *i == *(i + 1), pred(*i, *(i + 1)) != false.
Returns last if no such iterator is found.
2
#
Complexity: For the overloads with no ExecutionPolicy, exactly min((i - first) + 1, (last - first) - 1) applications of the corresponding predicate, where i is adjacent_­find's return value.
For the overloads with an ExecutionPolicy, applications of the corresponding predicate.

23.5.9 Count [alg.count]

🔗
template<class InputIterator, class T> constexpr typename iterator_traits<InputIterator>::difference_type count(InputIterator first, InputIterator last, const T& value); template<class ExecutionPolicy, class ForwardIterator, class T> typename iterator_traits<ForwardIterator>::difference_type count(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, const T& value); template<class InputIterator, class Predicate> constexpr typename iterator_traits<InputIterator>::difference_type count_if(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> typename iterator_traits<ForwardIterator>::difference_type count_if(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Effects: Returns the number of iterators i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false.
2
#
Complexity: Exactly last - first applications of the corresponding predicate.

23.5.10 Mismatch [mismatch]

🔗
template<class InputIterator1, class InputIterator2> constexpr pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> pair<ForwardIterator1, ForwardIterator2> mismatch(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> constexpr pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> pair<ForwardIterator1, ForwardIterator2> mismatch(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, BinaryPredicate pred); template<class InputIterator1, class InputIterator2> constexpr pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> pair<ForwardIterator1, ForwardIterator2> mismatch(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> constexpr pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> pair<ForwardIterator1, ForwardIterator2> mismatch(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.
2
#
Returns: A pair of iterators first1 + n and first2 + n, where n is the smallest integer such that, respectively,
  • (2.1)
    !(*(first1 + n) == *(first2 + n)) or
  • (2.2)
    pred(*(first1 + n), *(first2 + n)) == false,
or min(last1 - first1, last2 - first2) if no such integer exists.
3
#
Complexity: At most min(last1 - first1, last2 - first2) applications of the corresponding predicate.

23.5.11 Equal [alg.equal]

🔗
template<class InputIterator1, class InputIterator2> constexpr bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool equal(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> constexpr bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> bool equal(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, BinaryPredicate pred); template<class InputIterator1, class InputIterator2> constexpr bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool equal(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> constexpr bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> bool equal(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.
2
#
Returns: If last1 - first1 != last2 - first2, return false.
Otherwise return true if for every iterator i in the range [first1, last1) the following corresponding conditions hold: *i == *(first2 + (i - first1)), pred(*i, *(first2 + (i - first1))) != false.
Otherwise, returns false.
3
#
Complexity:
  • (3.1)
    For the overloads with no ExecutionPolicy,
    • (3.1.1)
      if InputIterator1 and InputIterator2 meet the Cpp17RandomAccessIterator requirements ([random.access.iterators]) and last1 - first1 != last2 - first2, then no applications of the corresponding predicate; otherwise,
    • (3.1.2)
      at most applications of the corresponding predicate.
  • (3.2)
    For the overloads with an ExecutionPolicy,
    • (3.2.1)
      if ForwardIterator1 and ForwardIterator2 meet the Cpp17RandomAccessIterator requirements and last1 - first1 != last2 - first2, then no applications of the corresponding predicate; otherwise,
    • (3.2.2)
      applications of the corresponding predicate.

23.5.12 Is permutation [alg.is_permutation]

🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2); template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, BinaryPredicate pred); template<class ForwardIterator1, class ForwardIterator2> constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Requires: ForwardIterator1 and ForwardIterator2 shall have the same value type.
The comparison function shall be an equivalence relation.
2
#
Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.
3
#
Returns: If last1 - first1 != last2 - first2, return false.
Otherwise return true if there exists a permutation of the elements in the range [first2, first2 + (last1 - first1)), beginning with ForwardIterator2 begin, such that equal(first1, last1, begin) returns true or equal(first1, last1, begin, pred) returns true; otherwise, returns false.
4
#
Complexity: No applications of the corresponding predicate if ForwardIterator1 and ForwardIterator2 meet the requirements of random access iterators and last1 - first1 != last2 - first2.
Otherwise, exactly last1 - first1 applications of the corresponding predicate if equal(​first1, last1, first2, last2) would return true if pred was not given in the argument list or equal(first1, last1, first2, last2, pred) would return true if pred was given in the argument list; otherwise, at worst , where N has the value last1 - first1.

23.5.13 Search [alg.search]

🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator1 search(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> constexpr ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> ForwardIterator1 search(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);
1
#
Effects: Finds a subsequence of equal values in a sequence.
2
#
Returns: The first iterator i in the range [first1, last1 - (last2-first2)) such that for every non-negative integer n less than last2 - first2 the following corresponding conditions hold: *(i + n) == *(first2 + n), pred(*(i + n), *(first2 + n)) != false.
Returns first1 if [first2, last2) is empty, otherwise returns last1 if no such iterator is found.
3
#
Complexity: At most (last1 - first1) * (last2 - first2) applications of the corresponding predicate.
🔗
template<class ForwardIterator, class Size, class T> constexpr ForwardIterator search_n(ForwardIterator first, ForwardIterator last, Size count, const T& value); template<class ExecutionPolicy, class ForwardIterator, class Size, class T> ForwardIterator search_n(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Size count, const T& value); template<class ForwardIterator, class Size, class T, class BinaryPredicate> constexpr ForwardIterator search_n(ForwardIterator first, ForwardIterator last, Size count, const T& value, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator, class Size, class T, class BinaryPredicate> ForwardIterator search_n(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Size count, const T& value, BinaryPredicate pred);
4
#
Requires: The type Size shall be convertible to integral type ([conv.integral], [class.conv]).
5
#
Effects: Finds a subsequence of equal values in a sequence.
6
#
Returns: The first iterator i in the range [first, last-count) such that for every non-negative integer n less than count the following corresponding conditions hold: *(i + n) == value, pred(*(i + n),value) != false.
Returns last if no such iterator is found.
7
#
Complexity: At most last - first applications of the corresponding predicate.
🔗
template<class ForwardIterator, class Searcher> constexpr ForwardIterator search(ForwardIterator first, ForwardIterator last, const Searcher& searcher);
8
#
Effects: Equivalent to: return searcher(first, last).first;
9
#
Remarks: Searcher need not meet the Cpp17CopyConstructible requirements.

23.6 Mutating sequence operations [alg.modifying.operations]

23.6.1 Copy [alg.copy]

🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator copy(InputIterator first, InputIterator last, OutputIterator result);
1
#
Requires: result shall not be in the range [first, last).
2
#
Effects: Copies elements in the range [first, last) into the range [result, result + (last - first)) starting from first and proceeding to last.
For each non-negative integer n < (last - first), performs *(result + n) = *(first + n).
3
#
Returns: result + (last - first).
4
#
Complexity: Exactly last - first assignments.
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 copy(ExecutionPolicy&& policy, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
5
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
6
#
Effects: Copies elements in the range [first, last) into the range [result, result + (last - first)).
For each non-negative integer n < (last - first), performs *(result + n) = *(first + n).
7
#
Returns: result + (last - first).
8
#
Complexity: Exactly last - first assignments.
🔗
template<class InputIterator, class Size, class OutputIterator> constexpr OutputIterator copy_n(InputIterator first, Size n, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class Size, class ForwardIterator2> ForwardIterator2 copy_n(ExecutionPolicy&& exec, ForwardIterator1 first, Size n, ForwardIterator2 result);
9
#
Effects: For each non-negative integer , performs *(result + i) = *(first + i).
10
#
Returns: result + n.
11
#
Complexity: Exactly n assignments.
🔗
template<class InputIterator, class OutputIterator, class Predicate> constexpr OutputIterator copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Predicate> ForwardIterator2 copy_if(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, Predicate pred);
12
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
[ Note
:
For the overload with an ExecutionPolicy, there may be a performance cost if iterator_­traits<ForwardIterator1>​::​value_­type is not Cpp17MoveConstructible (Table 25).
— end note
 ]
13
#
Effects: Copies all of the elements referred to by the iterator i in the range [first, last) for which pred(*i) is true.
14
#
Returns: The end of the resulting range.
15
#
Complexity: Exactly last - first applications of the corresponding predicate.
16
#
Remarks: Stable ([algorithm.stable]).
🔗
template<class BidirectionalIterator1, class BidirectionalIterator2> constexpr BidirectionalIterator2 copy_backward(BidirectionalIterator1 first, BidirectionalIterator1 last, BidirectionalIterator2 result);
17
#
Requires: result shall not be in the range (first, last].
18
#
Effects: Copies elements in the range [first, last) into the range [result - (last-first), result) starting from last - 1 and proceeding to first.237
For each positive integer n <= (last - first), performs *(result - n) = *(last - n).
19
#
Returns: result - (last - first).
20
#
Complexity: Exactly last - first assignments.
237)
copy_­backward should be used instead of copy when last is in the range [result - (last - first), result).

23.6.2 Move [alg.move]

🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator move(InputIterator first, InputIterator last, OutputIterator result);
1
#
Requires: result shall not be in the range [first, last).
2
#
Effects: Moves elements in the range [first, last) into the range [result, result + (last - first)) starting from first and proceeding to last.
For each non-negative integer n < (last-first), performs *(result + n) = std​::​move(*(first + n)).
3
#
Returns: result + (last - first).
4
#
Complexity: Exactly last - first move assignments.
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 move(ExecutionPolicy&& policy, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
5
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
6
#
Effects: Moves elements in the range [first, last) into the range [result, result + (last - first)).
For each non-negative integer n < (last - first), performs *(result + n) = std​::​​move(*(first + n)).
7
#
Returns: result + (last - first).
8
#
Complexity: Exactly last - first assignments.
🔗
template<class BidirectionalIterator1, class BidirectionalIterator2> constexpr BidirectionalIterator2 move_backward(BidirectionalIterator1 first, BidirectionalIterator1 last, BidirectionalIterator2 result);
9
#
Requires: result shall not be in the range (first, last].
10
#
Effects: Moves elements in the range [first, last) into the range [result - (last-first), result) starting from last - 1 and proceeding to first.238
For each positive integer n <= (last - first), performs *(result - n) = std​::​move(*(last - n)).
11
#
Returns: result - (last - first).
12
#
Complexity: Exactly last - first assignments.
238)
move_­backward should be used instead of move when last is in the range [result - (last - first), result).

23.6.3 Swap [alg.swap]

🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr ForwardIterator2 swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 swap_ranges(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2);
1
#
Requires: The two ranges [first1, last1) and [first2, first2 + (last1 - first1)) shall not overlap.
*(first1 + n) shall be swappable with ([swappable.requirements]) *(first2 + n).
2
#
Effects: For each non-negative integer n < (last1 - first1) performs: swap(*(first1 + n), ​*(first2 + n)).
3
#
Returns: first2 + (last1 - first1).
4
#
Complexity: Exactly last1 - first1 swaps.
🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr void iter_swap(ForwardIterator1 a, ForwardIterator2 b);
5
#
Requires: a and b shall be dereferenceable.
*a shall be swappable with ([swappable.requirements]) *b.
6
#
Effects: As if by swap(*a, *b).

23.6.4 Transform [alg.transform]

🔗
template<class InputIterator, class OutputIterator, class UnaryOperation> constexpr OutputIterator transform(InputIterator first, InputIterator last, OutputIterator result, UnaryOperation op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class UnaryOperation> ForwardIterator2 transform(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, UnaryOperation op); template<class InputIterator1, class InputIterator2, class OutputIterator, class BinaryOperation> constexpr OutputIterator transform(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, OutputIterator result, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class BinaryOperation> ForwardIterator transform(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator result, BinaryOperation binary_op);
1
#
Requires: op and binary_­op shall not invalidate iterators or subranges, or modify elements in the ranges
  • (1.1)
    [first1, last1],
  • (1.2)
    [first2, first2 + (last1 - first1)], and
  • (1.3)
    [result, result + (last1 - first1)].239
2
#
Effects: Assigns through every iterator i in the range [result, result + (last1 - first1)) a new corresponding value equal to op(*(first1 + (i - result))) or binary_­op(*(first1 + (i - result)), *(first2 + (i - result))).
3
#
Returns: result + (last1 - first1).
4
#
Complexity: Exactly last1 - first1 applications of op or binary_­op.
This requirement also applies to the overload with an ExecutionPolicy .
5
#
Remarks: result may be equal to first in case of unary transform, or to first1 or first2 in case of binary transform.
239)
The use of fully closed ranges is intentional.

23.6.5 Replace [alg.replace]

🔗
template<class ForwardIterator, class T> constexpr void replace(ForwardIterator first, ForwardIterator last, const T& old_value, const T& new_value); template<class ExecutionPolicy, class ForwardIterator, class T> void replace(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, const T& old_value, const T& new_value); template<class ForwardIterator, class Predicate, class T> constexpr void replace_if(ForwardIterator first, ForwardIterator last, Predicate pred, const T& new_value); template<class ExecutionPolicy, class ForwardIterator, class Predicate, class T> void replace_if(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred, const T& new_value);
1
#
Requires: The expression *first = new_­value shall be valid.
2
#
Effects: Substitutes elements referred by the iterator i in the range [first, last) with new_­value, when the following corresponding conditions hold: *i == old_­value, pred(*i) != false.
3
#
Complexity: Exactly last - first applications of the corresponding predicate.
🔗
template<class InputIterator, class OutputIterator, class T> constexpr OutputIterator replace_copy(InputIterator first, InputIterator last, OutputIterator result, const T& old_value, const T& new_value); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> ForwardIterator2 replace_copy(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, const T& old_value, const T& new_value); template<class InputIterator, class OutputIterator, class Predicate, class T> constexpr OutputIterator replace_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred, const T& new_value); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Predicate, class T> ForwardIterator2 replace_copy_if(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, Predicate pred, const T& new_value);
4
#
Requires: The results of the expressions *first and new_­value shall be writable ([iterator.requirements.general]) to the result output iterator.
The ranges [first, last) and [result, result + (last - first)) shall not overlap.
5
#
Effects: Assigns to every iterator i in the range [result, result + (last - first)) either new_­value or *​(first + (i - result)) depending on whether the following corresponding conditions hold:
*(first + (i - result)) == old_value
pred(*(first + (i - result))) != false
6
#
Returns: result + (last - first).
7
#
Complexity: Exactly last - first applications of the corresponding predicate.

23.6.6 Fill [alg.fill]

🔗
template<class ForwardIterator, class T> constexpr void fill(ForwardIterator first, ForwardIterator last, const T& value); template<class ExecutionPolicy, class ForwardIterator, class T> void fill(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, const T& value); template<class OutputIterator, class Size, class T> constexpr OutputIterator fill_n(OutputIterator first, Size n, const T& value); template<class ExecutionPolicy, class ForwardIterator, class Size, class T> ForwardIterator fill_n(ExecutionPolicy&& exec, ForwardIterator first, Size n, const T& value);
1
#
Requires: The expression value shall be writable ([iterator.requirements.general]) to the output iterator.
The type Size shall be convertible to an integral type ([conv.integral], [class.conv]).
2
#
Effects: The fill algorithms assign value through all the iterators in the range [first, last).
The fill_­n algorithms assign value through all the iterators in the range [first, first + n) if n is positive, otherwise they do nothing.
3
#
Returns: fill_­n returns first + n for non-negative values of n and first for negative values.
4
#
Complexity: Exactly last - first, n, or 0 assignments, respectively.

23.6.7 Generate [alg.generate]

🔗
template<class ForwardIterator, class Generator> constexpr void generate(ForwardIterator first, ForwardIterator last, Generator gen); template<class ExecutionPolicy, class ForwardIterator, class Generator> void generate(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Generator gen); template<class OutputIterator, class Size, class Generator> constexpr OutputIterator generate_n(OutputIterator first, Size n, Generator gen); template<class ExecutionPolicy, class ForwardIterator, class Size, class Generator> ForwardIterator generate_n(ExecutionPolicy&& exec, ForwardIterator first, Size n, Generator gen);
1
#
Requires: gen takes no arguments, Size shall be convertible to an integral type ([conv.integral], [class.conv]).
2
#
Effects: The generate algorithms invoke the function object gen and assign the return value of gen through all the iterators in the range [first, last).
The generate_­n algorithms invoke the function object gen and assign the return value of gen through all the iterators in the range [first, first + n) if n is positive, otherwise they do nothing.
3
#
Returns: generate_­n returns first + n for non-negative values of n and first for negative values.
4
#
Complexity: Exactly last - first, n, or 0 invocations of gen and assignments, respectively.

23.6.8 Remove [alg.remove]

🔗
template<class ForwardIterator, class T> constexpr ForwardIterator remove(ForwardIterator first, ForwardIterator last, const T& value); template<class ExecutionPolicy, class ForwardIterator, class T> ForwardIterator remove(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class Predicate> constexpr ForwardIterator remove_if(ForwardIterator first, ForwardIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> ForwardIterator remove_if(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Requires: The type of *first shall satisfy the Cpp17MoveAssignable requirements (Table 27).
2
#
Effects: Eliminates all the elements referred to by iterator i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false.
3
#
Returns: The end of the resulting range.
4
#
Remarks: Stable ([algorithm.stable]).
5
#
Complexity: Exactly last - first applications of the corresponding predicate.
6
#
[ Note
:
Each element in the range [ret, last), where ret is the returned value, has a valid but unspecified state, because the algorithms can eliminate elements by moving from elements that were originally in that range.
— end note
 ]
🔗
template<class InputIterator, class OutputIterator, class T> constexpr OutputIterator remove_copy(InputIterator first, InputIterator last, OutputIterator result, const T& value); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> ForwardIterator2 remove_copy(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, const T& value); template<class InputIterator, class OutputIterator, class Predicate> constexpr OutputIterator remove_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Predicate> ForwardIterator2 remove_copy_if(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, Predicate pred);
7
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
The expression *result = *first shall be valid.
[ Note
:
For the overloads with an ExecutionPolicy, there may be a performance cost if iterator_­traits<ForwardIterator1>​::​value_­type is not Cpp17MoveConstructible (Table 25).
— end note
 ]
8
#
Effects: Copies all the elements referred to by the iterator i in the range [first, last) for which the following corresponding conditions do not hold: *i == value, pred(*i) != false.
9
#
Returns: The end of the resulting range.
10
#
Complexity: Exactly last - first applications of the corresponding predicate.
11
#
Remarks: Stable ([algorithm.stable]).

23.6.9 Unique [alg.unique]

🔗
template<class ForwardIterator> constexpr ForwardIterator unique(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator unique(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class BinaryPredicate> constexpr ForwardIterator unique(ForwardIterator first, ForwardIterator last, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator, class BinaryPredicate> ForwardIterator unique(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, BinaryPredicate pred);
1
#
Requires: The comparison function shall be an equivalence relation.
The type of *first shall satisfy the Cpp17MoveAssignable requirements (Table 27).
2
#
Effects: For a nonempty range, eliminates all but the first element from every consecutive group of equivalent elements referred to by the iterator i in the range [first + 1, last) for which the following conditions hold: *(i - 1) == *i or pred(*(i - 1), *i) != false.
3
#
Returns: The end of the resulting range.
4
#
Complexity: For nonempty ranges, exactly (last - first) - 1 applications of the corresponding predicate.
🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator unique_copy(InputIterator first, InputIterator last, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 unique_copy(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result); template<class InputIterator, class OutputIterator, class BinaryPredicate> constexpr OutputIterator unique_copy(InputIterator first, InputIterator last, OutputIterator result, BinaryPredicate pred); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryPredicate> ForwardIterator2 unique_copy(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryPredicate pred);
5
#
Requires:
  • (5.1)
    The comparison function shall be an equivalence relation.
  • (5.2)
    The ranges [first, last) and [result, result+(last-first)) shall not overlap.
  • (5.3)
    The expression *result = *first shall be valid.
  • (5.4)
    For the overloads with no ExecutionPolicy, let T be the value type of InputIterator.
    If InputIterator meets the Cpp17ForwardIterator requirements, then there are no additional requirements for T.
    Otherwise, if OutputIterator meets the Cpp17ForwardIterator requirements and its value type is the same as T, then T shall be Cpp17CopyAssignable (Table 28).
    Otherwise, T shall be both Cpp17CopyConstructible (Table 26) and Cpp17CopyAssignable.
    [ Note
    :
    For the overloads with an ExecutionPolicy, there may be a performance cost if the value type of ForwardIterator1 is not both Cpp17CopyConstructible and Cpp17CopyAssignable.
    — end note
     ]
6
#
Effects: Copies only the first element from every consecutive group of equal elements referred to by the iterator i in the range [first, last) for which the following corresponding conditions hold: *i == *(i - 1) or pred(*i, *(i - 1)) != false.
7
#
Returns: The end of the resulting range.
8
#
Complexity: For nonempty ranges, exactly last - first - 1 applications of the corresponding predicate.

23.6.10 Reverse [alg.reverse]

🔗
template<class BidirectionalIterator> constexpr void reverse(BidirectionalIterator first, BidirectionalIterator last); template<class ExecutionPolicy, class BidirectionalIterator> void reverse(ExecutionPolicy&& exec, BidirectionalIterator first, BidirectionalIterator last);
1
#
Requires: BidirectionalIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
2
#
Effects: For each non-negative integer i < (last - first) / 2, applies iter_­swap to all pairs of iterators first + i, (last - i) - 1.
3
#
Complexity: Exactly (last - first)/2 swaps.
🔗
template<class BidirectionalIterator, class OutputIterator> constexpr OutputIterator reverse_copy(BidirectionalIterator first, BidirectionalIterator last, OutputIterator result); template<class ExecutionPolicy, class BidirectionalIterator, class ForwardIterator> ForwardIterator reverse_copy(ExecutionPolicy&& exec, BidirectionalIterator first, BidirectionalIterator last, ForwardIterator result);
4
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
5
#
Effects: Copies the range [first, last) to the range [result, result + (last - first)) such that for every non-negative integer i < (last - first) the following assignment takes place: *(result + (last - first) - 1 - i) = *(first + i).
6
#
Returns: result + (last - first).
7
#
Complexity: Exactly last - first assignments.

23.6.11 Rotate [alg.rotate]

🔗
template<class ForwardIterator> constexpr ForwardIterator rotate(ForwardIterator first, ForwardIterator middle, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator rotate(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator middle, ForwardIterator last);
1
#
Requires: [first, middle) and [middle, last) shall be valid ranges.
ForwardIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: For each non-negative integer i < (last - first), places the element from the position first + i into position first + (i + (last - middle)) % (last - first).
3
#
Returns: first + (last - middle).
4
#
Remarks: This is a left rotate.
5
#
Complexity: At most last - first swaps.
🔗
template<class ForwardIterator, class OutputIterator> constexpr OutputIterator rotate_copy(ForwardIterator first, ForwardIterator middle, ForwardIterator last, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 rotate_copy(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 middle, ForwardIterator1 last, ForwardIterator2 result);
6
#
Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.
7
#
Effects: Copies the range [first, last) to the range [result, result + (last - first)) such that for each non-negative integer i < (last - first) the following assignment takes place: *(result + i) = *(first + (i + (middle - first)) % (last - first)).
8
#
Returns: result + (last - first).
9
#
Complexity: Exactly last - first assignments.

23.6.12 Sample [alg.random.sample]

🔗
template<class PopulationIterator, class SampleIterator, class Distance, class UniformRandomBitGenerator> SampleIterator sample(PopulationIterator first, PopulationIterator last, SampleIterator out, Distance n, UniformRandomBitGenerator&& g);
1
#
Requires:
2
#
Effects: Copies min(last - first, n) elements (the sample) from [first, last) (the population) to out such that each possible sample has equal probability of appearance.
[ Note
:
Algorithms that obtain such effects include selection sampling and reservoir sampling.
— end note
 ]
3
#
Returns: The end of the resulting sample range.
4
#
Complexity: .
5
#
Remarks:
  • (5.1)
    Stable if and only if PopulationIterator satisfies the Cpp17ForwardIterator requirements.
  • (5.2)
    To the extent that the implementation of this function makes use of random numbers, the object g shall serve as the implementation's source of randomness.

23.6.13 Shuffle [alg.random.shuffle]

🔗
template<class RandomAccessIterator, class UniformRandomBitGenerator> void shuffle(RandomAccessIterator first, RandomAccessIterator last, UniformRandomBitGenerator&& g);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type remove_­reference_­t<UniformRandomBitGenerator> shall satisfy the requirements of a uniform random bit generator ([rand.req.urng]) type whose return type is convertible to iterator_­traits<RandomAccessIterator>​::​difference_­type.
2
#
Effects: Permutes the elements in the range [first, last) such that each possible permutation of those elements has equal probability of appearance.
3
#
Complexity: Exactly (last - first) - 1 swaps.
4
#
Remarks: To the extent that the implementation of this function makes use of random numbers, the object g shall serve as the implementation's source of randomness.

23.6.14 Shift [alg.shift]

🔗
template<class ForwardIterator> constexpr ForwardIterator shift_left(ForwardIterator first, ForwardIterator last, typename iterator_traits<ForwardIterator>::difference_type n); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator shift_left(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, typename iterator_traits<ForwardIterator>::difference_type n);
1
#
Requires: The type of *first shall satisfy the Cpp17MoveAssignable requirements.
2
#
Effects: If n <= 0 or n >= last - first, does nothing.
Otherwise, moves the element from position first + n + i into position first + i for each non-negative integer i < (last - first) - n.
In the first overload case, does so in order starting from i = 0 and proceeding to i = (last - first) - n - 1.
3
#
Returns: first + (last - first - n) if n is positive and n < last - first, otherwise first if n is positive, otherwise last.
4
#
Complexity: At most (last - first) - n assignments.
🔗
template<class ForwardIterator> constexpr ForwardIterator shift_right(ForwardIterator first, ForwardIterator last, typename iterator_traits<ForwardIterator>::difference_type n); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator shift_right(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, typename iterator_traits<ForwardIterator>::difference_type n);
5
#
Requires: The type of *first shall satisfy the Cpp17MoveAssignable requirements.
ForwardIterator shall meet the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]) or the Cpp17ValueSwappable requirements.
6
#
Effects: If n <= 0 or n >= last - first, does nothing.
Otherwise, moves the element from position first + i into position first + n + i for each non-negative integer i < (last - first) - n.
In the first overload case, if ForwardIterator satisfies the Cpp17BidirectionalIterator requirements, does so in order starting from i = (last - first) - n - 1 and proceeding to i = 0.
7
#
Returns: first + n if n is positive and n < last - first, otherwise last if n is positive, otherwise first.
8
#
Complexity: At most (last - first) - n assignments or swaps.

23.7 Sorting and related operations [alg.sorting]

1
#
All the operations in [alg.sorting] have two versions: one that takes a function object of type Compare and one that uses an operator<.
2
#
Compare is a function object type ([function.objects]).
The return value of the function call operation applied to an object of type Compare, when contextually converted to bool ([conv]), yields true if the first argument of the call is less than the second, and false otherwise.
Compare comp is used throughout for algorithms assuming an ordering relation.
It is assumed that comp will not apply any non-constant function through the dereferenced iterator.
3
#
For all algorithms that take Compare, there is a version that uses operator< instead.
That is, comp(*i, *j) != false defaults to *i < *j != false.
For algorithms other than those described in [alg.binary.search], comp shall induce a strict weak ordering on the values.
4
#
The term strict refers to the requirement of an irreflexive relation (!comp(x, x) for all x), and the term weak to requirements that are not as strong as those for a total ordering, but stronger than those for a partial ordering.
If we define equiv(a, b) as !comp(a, b) && !comp(b, a), then the requirements are that comp and equiv both be transitive relations:
  • (4.1)
    comp(a, b) && comp(b, c) implies comp(a, c)
  • (4.2)
    equiv(a, b) && equiv(b, c) implies equiv(a, c)
[ Note
:
Under these conditions, it can be shown that
  • (4.3)
    equiv is an equivalence relation,
  • (4.4)
    comp induces a well-defined relation on the equivalence classes determined by equiv, and
  • (4.5)
    the induced relation is a strict total ordering.
— end note
 ]
5
#
A sequence is sorted with respect to a comparator comp if for every iterator i pointing to the sequence and every non-negative integer n such that i + n is a valid iterator pointing to an element of the sequence, comp(*(i + n), *i) == false.
6
#
A sequence [start, finish) is partitioned with respect to an expression f(e) if there exists an integer n such that for all 0 <= i < (finish - start), f(*(start + i)) is true if and only if i < n.
7
#
In the descriptions of the functions that deal with ordering relationships we frequently use a notion of equivalence to describe concepts such as stability.
The equivalence to which we refer is not necessarily an operator==, but an equivalence relation induced by the strict weak ordering.
That is, two elements a and b are considered equivalent if and only if !(a < b) && !(b < a).

23.7.1 Sorting [alg.sort]

23.7.1.1 sort [sort]

🔗
template<class RandomAccessIterator> constexpr void sort(RandomAccessIterator first, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> void sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void sort(RandomAccessIterator first, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> void sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Sorts the elements in the range [first, last).
3
#
Complexity: comparisons, where .

23.7.1.2 stable_­sort [stable.sort]

🔗
template<class RandomAccessIterator> void stable_sort(RandomAccessIterator first, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> void stable_sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> void stable_sort(RandomAccessIterator first, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> void stable_sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Sorts the elements in the range [first, last).
3
#
Complexity: At most comparisons, where , but only comparisons if there is enough extra memory.
4
#
Remarks: Stable ([algorithm.stable]).

23.7.1.3 partial_­sort [partial.sort]

🔗
template<class RandomAccessIterator> constexpr void partial_sort(RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> void partial_sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void partial_sort(RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> void partial_sort(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last, Compare comp);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Places the first middle - first sorted elements from the range [first, last) into the range [first, middle).
The rest of the elements in the range [middle, last) are placed in an unspecified order.
3
#
Complexity: Approximately (last - first) * log(middle - first) comparisons.

23.7.1.4 partial_­sort_­copy [partial.sort.copy]

🔗
template<class InputIterator, class RandomAccessIterator> constexpr RandomAccessIterator partial_sort_copy(InputIterator first, InputIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last); template<class ExecutionPolicy, class ForwardIterator, class RandomAccessIterator> RandomAccessIterator partial_sort_copy(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last); template<class InputIterator, class RandomAccessIterator, class Compare> constexpr RandomAccessIterator partial_sort_copy(InputIterator first, InputIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last, Compare comp); template<class ExecutionPolicy, class ForwardIterator, class RandomAccessIterator, class Compare> RandomAccessIterator partial_sort_copy(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last, Compare comp);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *result_­first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Places the first min(last - first, result_­last - result_­first) sorted elements into the range [result_­first, result_­first + min(last - first, result_­last - result_­first)).
3
#
Returns: The smaller of: result_­last or result_­first + (last - first).
4
#
Complexity: Approximately (last - first) * log(min(last - first, result_­last - result_­first)) comparisons.

23.7.1.5 is_­sorted [is.sorted]

🔗
template<class ForwardIterator> constexpr bool is_sorted(ForwardIterator first, ForwardIterator last);
1
#
Returns: is_­sorted_­until(first, last) == last.
🔗
template<class ExecutionPolicy, class ForwardIterator> bool is_sorted(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last);
2
#
Returns: is_­sorted_­until(std​::​forward<ExecutionPolicy>(exec), first, last) == last.
🔗
template<class ForwardIterator, class Compare> constexpr bool is_sorted(ForwardIterator first, ForwardIterator last, Compare comp);
3
#
Returns: is_­sorted_­until(first, last, comp) == last.
🔗
template<class ExecutionPolicy, class ForwardIterator, class Compare> bool is_sorted(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Compare comp);
4
#
Returns: 
is_sorted_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last
🔗
template<class ForwardIterator> constexpr ForwardIterator is_sorted_until(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator is_sorted_until(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class Compare> constexpr ForwardIterator is_sorted_until(ForwardIterator first, ForwardIterator last, Compare comp); template<class ExecutionPolicy, class ForwardIterator, class Compare> ForwardIterator is_sorted_until(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Compare comp);
5
#
Returns: If (last - first) < 2, returns last.
Otherwise, returns the last iterator i in [first, last] for which the range [first, i) is sorted.
6
#
Complexity: Linear.

23.7.2 Nth element [alg.nth.element]

🔗
template<class RandomAccessIterator> constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> void nth_element(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> void nth_element(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last, Compare comp);
1
#
Requires: RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: After nth_­element the element in the position pointed to by nth is the element that would be in that position if the whole range were sorted, unless nth == last.
Also for every iterator i in the range [first, nth) and every iterator j in the range [nth, last) it holds that: !(*j < *i) or comp(*j, *i) == false.
3
#
Complexity: For the overloads with no ExecutionPolicy, linear on average.
For the overloads with an ExecutionPolicy, applications of the predicate, and swaps, where .

23.7.3 Binary search [alg.binary.search]

1
#
All of the algorithms in this subclause are versions of binary search and assume that the sequence being searched is partitioned with respect to an expression formed by binding the search key to an argument of the implied or explicit comparison function.
They work on non-random access iterators minimizing the number of comparisons, which will be logarithmic for all types of iterators.
They are especially appropriate for random access iterators, because these algorithms do a logarithmic number of steps through the data structure.
For non-random access iterators they execute a linear number of steps.

23.7.3.1 lower_­bound [lower.bound]

🔗
template<class ForwardIterator, class T> constexpr ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class T, class Compare> constexpr ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);
1
#
Requires: The elements e of [first, last) shall be partitioned with respect to the expression e < value or comp(e, value).
2
#
Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i) the following corresponding conditions hold: *j < value or comp(*j, value) != false.
3
#
Complexity: At most comparisons.

23.7.3.2 upper_­bound [upper.bound]

🔗
template<class ForwardIterator, class T> constexpr ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class T, class Compare> constexpr ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);
1
#
Requires: The elements e of [first, last) shall be partitioned with respect to the expression !(value < e) or !comp(​value, e).
2
#
Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i) the following corresponding conditions hold: !(value < *j) or comp(value, *j) == false.
3
#
Complexity: At most comparisons.

23.7.3.3 equal_­range [equal.range]

🔗
template<class ForwardIterator, class T> constexpr pair<ForwardIterator, ForwardIterator> equal_range(ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class T, class Compare> constexpr pair<ForwardIterator, ForwardIterator> equal_range(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);
1
#
Requires: The elements e of [first, last) shall be partitioned with respect to the expressions e < value and !(value < e) or comp(e, value) and !comp(value, e).
Also, for all elements e of [first, last), e < value shall imply !(value < e) or comp(e, value) shall imply !comp(value, e).
2
#
Returns: 
make_pair(lower_bound(first, last, value),
          upper_bound(first, last, value))
or 
make_pair(lower_bound(first, last, value, comp),
          upper_bound(first, last, value, comp))
3
#
Complexity: At most comparisons.

23.7.3.4 binary_­search [binary.search]

🔗
template<class ForwardIterator, class T> constexpr bool binary_search(ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class T, class Compare> constexpr bool binary_search(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);
1
#
Requires: The elements e of [first, last) shall be partitioned with respect to the expressions e < value and !(value < e) or comp(e, value) and !comp(value, e).
Also, for all elements e of [first, last), e < value shall imply !(value < e) or comp(e, value) shall imply !comp(value, e).
2
#
Returns: true if there is an iterator i in the range [first, last) that satisfies the corresponding conditions: !(*i < value) && !(value < *i) or comp(*i, value) == false && comp(value, *i) == false.
3
#
Complexity: At most comparisons.

23.7.4 Partitions [alg.partitions]

🔗
template<class InputIterator, class Predicate> constexpr bool is_partitioned(InputIterator first, InputIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> bool is_partitioned(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
1
#
Requires: For the overload with no ExecutionPolicy, InputIterator's value type shall be convertible to Predicate's argument type.
For the overload with an ExecutionPolicy, ForwardIterator's value type shall be convertible to Predicate's argument type.
2
#
Returns: true if [first, last) is empty or if the elements e of [first, last) are partitioned with respect to the expression pred(e).
3
#
Complexity: Linear.
At most last - first applications of pred.
🔗
template<class ForwardIterator, class Predicate> constexpr ForwardIterator partition(ForwardIterator first, ForwardIterator last, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class Predicate> ForwardIterator partition(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Predicate pred);
4
#
Requires: ForwardIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
5
#
Effects: Places all the elements in the range [first, last) that satisfy pred before all the elements that do not satisfy it.
6
#
Returns: An iterator i such that for every iterator j in the range [first, i) pred(*j) != false, and for every iterator k in the range [i, last), pred(*k) == false.
7
#
Complexity: Let :
  • (7.1)
    For the overload with no ExecutionPolicy, exactly N applications of the predicate.
    At most swaps if ForwardIterator meets the Cpp17BidirectionalIterator requirements and at most N swaps otherwise.
  • (7.2)
    For the overload with an ExecutionPolicy, swaps and applications of the predicate.
🔗
template<class BidirectionalIterator, class Predicate> BidirectionalIterator stable_partition(BidirectionalIterator first, BidirectionalIterator last, Predicate pred); template<class ExecutionPolicy, class BidirectionalIterator, class Predicate> BidirectionalIterator stable_partition(ExecutionPolicy&& exec, BidirectionalIterator first, BidirectionalIterator last, Predicate pred);
8
#
Requires: BidirectionalIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
9
#
Effects: Places all the elements in the range [first, last) that satisfy pred before all the elements that do not satisfy it.
10
#
Returns: An iterator i such that for every iterator j in the range [first, i), pred(*j) != false, and for every iterator k in the range [i, last), pred(*k) == false.
The relative order of the elements in both groups is preserved.
11
#
Complexity: Let N = last - first:
  • (11.1)
    For the overload with no ExecutionPolicy, at most swaps, but only swaps if there is enough extra memory.
    Exactly N applications of the predicate.
  • (11.2)
    For the overload with an ExecutionPolicy, swaps and applications of the predicate.
🔗
template<class InputIterator, class OutputIterator1, class OutputIterator2, class Predicate> constexpr pair<OutputIterator1, OutputIterator2> partition_copy(InputIterator first, InputIterator last, OutputIterator1 out_true, OutputIterator2 out_false, Predicate pred); template<class ExecutionPolicy, class ForwardIterator, class ForwardIterator1, class ForwardIterator2, class Predicate> pair<ForwardIterator1, ForwardIterator2> partition_copy(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, ForwardIterator1 out_true, ForwardIterator2 out_false, Predicate pred);
12
#
Requires:
  • (12.1)
    For the overload with no ExecutionPolicy, InputIterator's value type shall be Cpp17CopyAssignable (Table 28), and shall be writable ([iterator.requirements.general]) to the out_­true and out_­false OutputIterators, and shall be convertible to Predicate's argument type.
  • (12.2)
    For the overload with an ExecutionPolicy, ForwardIterator's value type shall be Cpp17CopyAssignable, and shall be writable to the out_­true and out_­false ForwardIterators, and shall be convertible to Predicate's argument type.
    [ Note
    :
    There may be a performance cost if ForwardIterator's value type is not Cpp17CopyConstructible.
    — end note
     ]
  • (12.3)
    For both overloads, the input range shall not overlap with either of the output ranges.
13
#
Effects: For each iterator i in [first, last), copies *i to the output range beginning with out_­true if pred(*i) is true, or to the output range beginning with out_­false otherwise.
14
#
Returns: A pair p such that p.first is the end of the output range beginning at out_­true and p.second is the end of the output range beginning at out_­false.
15
#
Complexity: Exactly last - first applications of pred.
🔗
template<class ForwardIterator, class Predicate> constexpr ForwardIterator partition_point(ForwardIterator first, ForwardIterator last, Predicate pred);
16
#
Requires: ForwardIterator's value type shall be convertible to Predicate's argument type.
The elements e of [first, last) shall be partitioned with respect to the expression pred(e).
17
#
Returns: An iterator mid such that all_­of(first, mid, pred) and none_­of(mid, last, pred) are both true.
18
#
Complexity: applications of pred.

23.7.5 Merge [alg.merge]

🔗
template<class InputIterator1, class InputIterator2, class OutputIterator> constexpr OutputIterator merge(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator merge(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> constexpr OutputIterator merge(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator merge(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp);
1
#
Requires: The ranges [first1, last1) and [first2, last2) shall be sorted with respect to operator< or comp.
The resulting range shall not overlap with either of the original ranges.
2
#
Effects: Copies all the elements of the two ranges [first1, last1) and [first2, last2) into the range [result, result_­last), where result_­last is result + (last1 - first1) + (last2 - first2), such that the resulting range satisfies is_­sorted(result, result_­last) or is_­sorted(result, result_­last, comp), respectively.
3
#
Returns: result + (last1 - first1) + (last2 - first2).
4
#
Complexity: Let :
  • (4.1)
    For the overloads with no ExecutionPolicy, at most comparisons.
  • (4.2)
    For the overloads with an ExecutionPolicy, comparisons.
5
#
Remarks: Stable ([algorithm.stable]).
🔗
template<class BidirectionalIterator> void inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last); template<class ExecutionPolicy, class BidirectionalIterator> void inplace_merge(ExecutionPolicy&& exec, BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last); template<class BidirectionalIterator, class Compare> void inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last, Compare comp); template<class ExecutionPolicy, class BidirectionalIterator, class Compare> void inplace_merge(ExecutionPolicy&& exec, BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last, Compare comp);
6
#
Requires: The ranges [first, middle) and [middle, last) shall be sorted with respect to operator< or comp.
BidirectionalIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
7
#
Effects: Merges two sorted consecutive ranges [first, middle) and [middle, last), putting the result of the merge into the range [first, last).
The resulting range will be in non-decreasing order; that is, for every iterator i in [first, last) other than first, the condition *i < *(i - 1) or, respectively, comp(*i, *(i - 1)) will be false.
8
#
Complexity: Let :
  • (8.1)
    For the overloads with no ExecutionPolicy, if enough additional memory is available, exactly comparisons.
  • (8.2)
    For the overloads with no ExecutionPolicy if no additional memory is available, comparisons.
  • (8.3)
    For the overloads with an ExecutionPolicy, comparisons.
9
#
Remarks: Stable.

23.7.6 Set operations on sorted structures [alg.set.operations]

1
#
This subclause defines all the basic set operations on sorted structures.
They also work with multisets ([multiset]) containing multiple copies of equivalent elements.
The semantics of the set operations are generalized to multisets in a standard way by defining set_­union() to contain the maximum number of occurrences of every element, set_­intersection() to contain the minimum, and so on.

23.7.6.1 includes [includes]

🔗
template<class InputIterator1, class InputIterator2> constexpr bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool includes(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> constexpr bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Compare> bool includes(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, Compare comp);
1
#
Returns: true if [first2, last2) is empty or if every element in the range [first2, last2) is contained in the range [first1, last1).
Returns false otherwise.
2
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

23.7.6.2 set_­union [set.union]

🔗
template<class InputIterator1, class InputIterator2, class OutputIterator> constexpr OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_union(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> constexpr OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_union(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp);
1
#
Requires: The resulting range shall not overlap with either of the original ranges.
2
#
Effects: Constructs a sorted union of the elements from the two ranges; that is, the set of elements that are present in one or both of the ranges.
3
#
Returns: The end of the constructed range.
4
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.
5
#
Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then all m elements from the first range shall be copied to the output range, in order, and then elements from the second range shall be copied to the output range, in order.

23.7.6.3 set_­intersection [set.intersection]

🔗
template<class InputIterator1, class InputIterator2, class OutputIterator> constexpr OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_intersection(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> constexpr OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_intersection(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp);
1
#
Requires: The resulting range shall not overlap with either of the original ranges.
2
#
Effects: Constructs a sorted intersection of the elements from the two ranges; that is, the set of elements that are present in both of the ranges.
3
#
Returns: The end of the constructed range.
4
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.
5
#
Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, the first elements shall be copied from the first range to the output range, in order.

23.7.6.4 set_­difference [set.difference]

🔗
template<class InputIterator1, class InputIterator2, class OutputIterator> constexpr OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> constexpr OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp);
1
#
Requires: The resulting range shall not overlap with either of the original ranges.
2
#
Effects: Copies the elements of the range [first1, last1) which are not present in the range [first2, last2) to the range beginning at result.
The elements in the constructed range are sorted.
3
#
Returns: The end of the constructed range.
4
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.
5
#
Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, the last elements from [first1, last1) shall be copied to the output range.

23.7.6.5 set_­symmetric_­difference [set.symmetric.difference]

🔗
template<class InputIterator1, class InputIterator2, class OutputIterator> constexpr OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_symmetric_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> constexpr OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_symmetric_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp);
1
#
Requires: The resulting range shall not overlap with either of the original ranges.
2
#
Effects: Copies the elements of the range [first1, last1) that are not present in the range [first2, last2), and the elements of the range [first2, last2) that are not present in the range [first1, last1) to the range beginning at result.
The elements in the constructed range are sorted.
3
#
Returns: The end of the constructed range.
4
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.
5
#
Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then of those elements shall be copied to the output range: the last of these elements from [first1, last1) if , and the last of these elements from [first2, last2) if .

23.7.7 Heap operations [alg.heap.operations]

1
#
A heap is a particular organization of elements in a range between two random access iterators [a, b) such that:
  • (1.1)
    With N = b - a, for all i, , comp(a[], a[i]) is false.
  • (1.2)
    *a may be removed by pop_­heap(), or a new element added by push_­heap(), in time.
2
#
These properties make heaps useful as priority queues.
3
#
make_­heap() converts a range into a heap and sort_­heap() turns a heap into a sorted sequence.

23.7.7.1 push_­heap [push.heap]

🔗
template<class RandomAccessIterator> constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void push_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: The range [first, last - 1) shall be a valid heap.
The type of *first shall satisfy the Cpp17MoveConstructible requirements (Table 25) and the Cpp17MoveAssignable requirements (Table 27).
2
#
Effects: Places the value in the location last - 1 into the resulting heap [first, last).
3
#
Complexity: At most comparisons.

23.7.7.2 pop_­heap [pop.heap]

🔗
template<class RandomAccessIterator> constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void pop_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: The range [first, last) shall be a valid non-empty heap.
RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Swaps the value in the location first with the value in the location last - 1 and makes [first, last - 1) into a heap.
3
#
Complexity: At most comparisons.

23.7.7.3 make_­heap [make.heap]

🔗
template<class RandomAccessIterator> constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: The type of *first shall satisfy the Cpp17MoveConstructible requirements (Table 25) and the Cpp17MoveAssignable requirements (Table 27).
2
#
Effects: Constructs a heap out of the range [first, last).
3
#
Complexity: At most comparisons.

23.7.7.4 sort_­heap [sort.heap]

🔗
template<class RandomAccessIterator> constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr void sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
1
#
Requires: The range [first, last) shall be a valid heap.
RandomAccessIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
The type of *first shall satisfy the Cpp17MoveConstructible (Table 25) and Cpp17MoveAssignable (Table 27) requirements.
2
#
Effects: Sorts elements in the heap [first, last).
3
#
Complexity: At most comparisons, where .

23.7.7.5 is_­heap [is.heap]

🔗
template<class RandomAccessIterator> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);
1
#
Returns: is_­heap_­until(first, last) == last.
🔗
template<class ExecutionPolicy, class RandomAccessIterator> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);
2
#
Returns: is_­heap_­until(std​::​forward<ExecutionPolicy>(exec), first, last) == last.
🔗
template<class RandomAccessIterator, class Compare> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);
3
#
Returns: is_­heap_­until(first, last, comp) == last.
🔗
template<class ExecutionPolicy, class RandomAccessIterator, class Compare> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
4
#
Returns: 
is_heap_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last
🔗
template<class RandomAccessIterator> constexpr RandomAccessIterator is_heap_until(RandomAccessIterator first, RandomAccessIterator last); template<class ExecutionPolicy, class RandomAccessIterator> RandomAccessIterator is_heap_until(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last); template<class RandomAccessIterator, class Compare> constexpr RandomAccessIterator is_heap_until(RandomAccessIterator first, RandomAccessIterator last, Compare comp); template<class ExecutionPolicy, class RandomAccessIterator, class Compare> RandomAccessIterator is_heap_until(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last, Compare comp);
5
#
Returns: If (last - first) < 2, returns last.
Otherwise, returns the last iterator i in [first, last] for which the range [first, i) is a heap.
6
#
Complexity: Linear.

23.7.8 Minimum and maximum [alg.min.max]

🔗
template<class T> constexpr const T& min(const T& a, const T& b); template<class T, class Compare> constexpr const T& min(const T& a, const T& b, Compare comp);
1
#
Requires: For the first form, type T shall be Cpp17LessThanComparable (Table 23).
2
#
Returns: The smaller value.
3
#
Remarks: Returns the first argument when the arguments are equivalent.
4
#
Complexity: Exactly one comparison.
🔗
template<class T> constexpr T min(initializer_list<T> t); template<class T, class Compare> constexpr T min(initializer_list<T> t, Compare comp);
5
#
Requires: T shall be Cpp17CopyConstructible and t.size() > 0.
For the first form, type T shall be Cpp17LessThanComparable.
6
#
Returns: The smallest value in the initializer list.
7
#
Remarks: Returns a copy of the leftmost argument when several arguments are equivalent to the smallest.
8
#
Complexity: Exactly t.size() - 1 comparisons.
🔗
template<class T> constexpr const T& max(const T& a, const T& b); template<class T, class Compare> constexpr const T& max(const T& a, const T& b, Compare comp);
9
#
Requires: For the first form, type T shall be Cpp17LessThanComparable (Table 23).
10
#
Returns: The larger value.
11
#
Remarks: Returns the first argument when the arguments are equivalent.
12
#
Complexity: Exactly one comparison.
🔗
template<class T> constexpr T max(initializer_list<T> t); template<class T, class Compare> constexpr T max(initializer_list<T> t, Compare comp);
13
#
Requires: T shall be Cpp17CopyConstructible and t.size() > 0.
For the first form, type T shall be Cpp17LessThanComparable.
14
#
Returns: The largest value in the initializer list.
15
#
Remarks: Returns a copy of the leftmost argument when several arguments are equivalent to the largest.
16
#
Complexity: Exactly t.size() - 1 comparisons.
🔗
template<class T> constexpr pair<const T&, const T&> minmax(const T& a, const T& b); template<class T, class Compare> constexpr pair<const T&, const T&> minmax(const T& a, const T& b, Compare comp);
17
#
Requires: For the first form, type T shall be Cpp17LessThanComparable (Table 23).
18
#
Returns: pair<const T&, const T&>(b, a) if b is smaller than a, and pair<const T&, const T&>(a, b) otherwise.
19
#
Remarks: Returns pair<const T&, const T&>(a, b) when the arguments are equivalent.
20
#
Complexity: Exactly one comparison.
🔗
template<class T> constexpr pair<T, T> minmax(initializer_list<T> t); template<class T, class Compare> constexpr pair<T, T> minmax(initializer_list<T> t, Compare comp);
21
#
Requires: T shall be Cpp17CopyConstructible and t.size() > 0.
For the first form, type T shall be Cpp17LessThanComparable.
22
#
Returns: pair<T, T>(x, y), where x has the smallest and y has the largest value in the initializer list.
23
#
Remarks: x is a copy of the leftmost argument when several arguments are equivalent to the smallest.
y is a copy of the rightmost argument when several arguments are equivalent to the largest.
24
#
Complexity: At most applications of the corresponding predicate.
🔗
template<class ForwardIterator> constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator min_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class Compare> constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last, Compare comp); template<class ExecutionPolicy, class ForwardIterator, class Compare> ForwardIterator min_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Compare comp);
25
#
Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last) the following corresponding conditions hold: !(*j < *i) or comp(*j, *i) == false.
Returns last if first == last.
26
#
Complexity: Exactly applications of the corresponding comparisons.
🔗
template<class ForwardIterator> constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> ForwardIterator max_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class Compare> constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last, Compare comp); template<class ExecutionPolicy, class ForwardIterator, class Compare> ForwardIterator max_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Compare comp);
27
#
Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last) the following corresponding conditions hold: !(*i < *j) or comp(*i, *j) == false.
Returns last if first == last.
28
#
Complexity: Exactly applications of the corresponding comparisons.
🔗
template<class ForwardIterator> constexpr pair<ForwardIterator, ForwardIterator> minmax_element(ForwardIterator first, ForwardIterator last); template<class ExecutionPolicy, class ForwardIterator> pair<ForwardIterator, ForwardIterator> minmax_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class Compare> constexpr pair<ForwardIterator, ForwardIterator> minmax_element(ForwardIterator first, ForwardIterator last, Compare comp); template<class ExecutionPolicy, class ForwardIterator, class Compare> pair<ForwardIterator, ForwardIterator> minmax_element(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, Compare comp);
29
#
Returns: make_­pair(first, first) if [first, last) is empty, otherwise make_­pair(m, M), where m is the first iterator in [first, last) such that no iterator in the range refers to a smaller element, and where M is the last iterator240 in [first, last) such that no iterator in the range refers to a larger element.
30
#
Complexity: At most applications of the corresponding predicate, where N is last - first.
240)
This behavior intentionally differs from max_­element().

23.7.9 Bounded value [alg.clamp]

🔗
template<class T> constexpr const T& clamp(const T& v, const T& lo, const T& hi); template<class T, class Compare> constexpr const T& clamp(const T& v, const T& lo, const T& hi, Compare comp);
1
#
Requires: The value of lo shall be no greater than hi.
For the first form, type T shall be Cpp17LessThanComparable (Table 23).
2
#
Returns: lo if v is less than lo, hi if hi is less than v, otherwise v.
3
#
[ Note
:
If NaN is avoided, T can be a floating-point type.
— end note
 ]
4
#
Complexity: At most two comparisons.

23.7.10 Lexicographical comparison [alg.lex.comparison]

🔗
template<class InputIterator1, class InputIterator2> constexpr bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool lexicographical_compare(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> constexpr bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Compare> bool lexicographical_compare(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, Compare comp);
1
#
Returns: true if the sequence of elements defined by the range [first1, last1) is lexicographically less than the sequence of elements defined by the range [first2, last2) and false otherwise.
2
#
Complexity: At most applications of the corresponding comparison.
3
#
Remarks: If two sequences have the same number of elements and their corresponding elements (if any) are equivalent, then neither sequence is lexicographically less than the other.
If one sequence is a prefix of the other, then the shorter sequence is lexicographically less than the longer sequence.
Otherwise, the lexicographical comparison of the sequences yields the same result as the comparison of the first corresponding pair of elements that are not equivalent.
4
#
[ Example
:
The following sample implementation satisfies these requirements: 
for ( ; first1 != last1 && first2 != last2 ; ++first1, (void) ++first2) {
  if (*first1 < *first2) return true;
  if (*first2 < *first1) return false;
}
return first1 == last1 && first2 != last2;
— end example
 ]
5
#
[ Note
:
An empty sequence is lexicographically less than any non-empty sequence, but not less than any empty sequence.
— end note
 ]

23.7.11 Three-way comparison algorithms [alg.3way]

🔗
template<class T, class U> constexpr auto compare_3way(const T& a, const U& b);
1
#
Effects: Compares two values and produces a result of the strongest applicable comparison category type:
  • (1.1)
    Returns a <=> b if that expression is well-formed.
  • (1.2)
    Otherwise, if the expressions a == b and a < b are each well-formed and convertible to bool, returns strong_­ordering​::​equal when a == b is true, otherwise returns strong_­ordering​::​less when a < b is true, and otherwise returns strong_­ordering​::​greater.
  • (1.3)
    Otherwise, if the expression a == b is well-formed and convertible to bool, returns strong_­equality​::​equal when a == b is true, and otherwise returns strong_­equality​::​nonequal.
  • (1.4)
    Otherwise, the function is defined as deleted.
🔗
template<class InputIterator1, class InputIterator2, class Cmp> constexpr auto lexicographical_compare_3way(InputIterator1 b1, InputIterator1 e1, InputIterator2 b2, InputIterator2 e2, Cmp comp) -> common_comparison_category_t<decltype(comp(*b1, *b2)), strong_ordering>;
2
#
Requires: Cmp shall be a function object type whose return type is a comparison category type.
3
#
Effects: Lexicographically compares two ranges and produces a result of the strongest applicable comparison category type.
Equivalent to: 
for ( ; b1 != e1 && b2 != e2; void(++b1), void(++b2) )
  if (auto cmp = comp(*b1,*b2); cmp != 0)
    return cmp;
return b1 != e1 ? strong_ordering::greater :
       b2 != e2 ? strong_ordering::less :
                  strong_ordering::equal;
🔗
template<class InputIterator1, class InputIterator2> constexpr auto lexicographical_compare_3way(InputIterator1 b1, InputIterator1 e1, InputIterator2 b2, InputIterator2 e2);
4
#
Effects: Equivalent to: 
return lexicographical_compare_3way(b1, e1, b2, e2,
                                    [](const auto& t, const auto& u) {
                                      return compare_3way(t, u);
                                    });

23.7.12 Permutation generators [alg.permutation.generators]

🔗
template<class BidirectionalIterator> constexpr bool next_permutation(BidirectionalIterator first, BidirectionalIterator last); template<class BidirectionalIterator, class Compare> constexpr bool next_permutation(BidirectionalIterator first, BidirectionalIterator last, Compare comp);
1
#
Requires: BidirectionalIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
2
#
Effects: Takes a sequence defined by the range [first, last) and transforms it into the next permutation.
The next permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp.
3
#
Returns: true if such a permutation exists.
Otherwise, it transforms the sequence into the smallest permutation, that is, the ascendingly sorted one, and returns false.
4
#
Complexity: At most (last - first) / 2 swaps.
🔗
template<class BidirectionalIterator> constexpr bool prev_permutation(BidirectionalIterator first, BidirectionalIterator last); template<class BidirectionalIterator, class Compare> constexpr bool prev_permutation(BidirectionalIterator first, BidirectionalIterator last, Compare comp);
5
#
Requires: BidirectionalIterator shall satisfy the Cpp17ValueSwappable requirements ([swappable.requirements]).
6
#
Effects: Takes a sequence defined by the range [first, last) and transforms it into the previous permutation.
The previous permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp.
7
#
Returns: true if such a permutation exists.
Otherwise, it transforms the sequence into the largest permutation, that is, the descendingly sorted one, and returns false.
8
#
Complexity: At most (last - first) / 2 swaps.

23.8 Header <numeric> synopsis [numeric.ops.overview]

namespace std {
  // [accumulate], accumulate
  template<class InputIterator, class T>
    T accumulate(InputIterator first, InputIterator last, T init);
  template<class InputIterator, class T, class BinaryOperation>
    T accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);

  // [reduce], reduce
  template<class InputIterator>
    typename iterator_traits<InputIterator>::value_type
      reduce(InputIterator first, InputIterator last);
  template<class InputIterator, class T>
    T reduce(InputIterator first, InputIterator last, T init);
  template<class InputIterator, class T, class BinaryOperation>
    T reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator>
    typename iterator_traits<ForwardIterator>::value_type
      reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
             ForwardIterator first, ForwardIterator last);
  template<class ExecutionPolicy, class ForwardIterator, class T>
    T reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
             ForwardIterator first, ForwardIterator last, T init);
  template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation>
    T reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
             ForwardIterator first, ForwardIterator last, T init, BinaryOperation binary_op);

  // [inner.product], inner product
  template<class InputIterator1, class InputIterator2, class T>
    T inner_product(InputIterator1 first1, InputIterator1 last1,
                    InputIterator2 first2, T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T inner_product(InputIterator1 first1, InputIterator1 last1,
                    InputIterator2 first2, T init,
                    BinaryOperation1 binary_op1,
                    BinaryOperation2 binary_op2);

  // [transform.reduce], transform reduce
  template<class InputIterator1, class InputIterator2, class T>
    T transform_reduce(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2,
                       T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T transform_reduce(InputIterator1 first1, InputIterator1 last1,
                       InputIterator2 first2,
                       T init,
                       BinaryOperation1 binary_op1,
                       BinaryOperation2 binary_op2);
  template<class InputIterator, class T,
           class BinaryOperation, class UnaryOperation>
    T transform_reduce(InputIterator first, InputIterator last,
                       T init,
                       BinaryOperation binary_op, UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T>
    T transform_reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2,
                       T init);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    T transform_reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       ForwardIterator1 first1, ForwardIterator1 last1,
                       ForwardIterator2 first2,
                       T init,
                       BinaryOperation1 binary_op1,
                       BinaryOperation2 binary_op2);
  template<class ExecutionPolicy,
           class ForwardIterator, class T,
           class BinaryOperation, class UnaryOperation>
    T transform_reduce(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                       ForwardIterator first, ForwardIterator last,
                       T init,
                       BinaryOperation binary_op, UnaryOperation unary_op);

  // [partial.sum], partial sum
  template<class InputIterator, class OutputIterator>
    OutputIterator partial_sum(InputIterator first,
                               InputIterator last,
                               OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator partial_sum(InputIterator first,
                               InputIterator last,
                               OutputIterator result,
                               BinaryOperation binary_op);

  // [exclusive.scan], exclusive scan
  template<class InputIterator, class OutputIterator, class T>
    OutputIterator exclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  T init);
  template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
    OutputIterator exclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  T init, BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T>
    ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    T init);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation>
    ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    T init, BinaryOperation binary_op);

  // [inclusive.scan], inclusive scan
  template<class InputIterator, class OutputIterator>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  BinaryOperation binary_op);
  template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
    OutputIterator inclusive_scan(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  BinaryOperation binary_op, T init);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class T>
    ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                    ForwardIterator1 first, ForwardIterator1 last,
                                    ForwardIterator2 result,
                                    BinaryOperation binary_op, T init);

  // [transform.exclusive.scan], transform exclusive scan
  template<class InputIterator, class OutputIterator, class T,
           class BinaryOperation, class UnaryOperation>
    OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            T init,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2, class T,
           class BinaryOperation, class UnaryOperation>
    ForwardIterator2 transform_exclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                              ForwardIterator1 first, ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              T init,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op);

  // [transform.inclusive.scan], transform inclusive scan
  template<class InputIterator, class OutputIterator,
           class BinaryOperation, class UnaryOperation>
    OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op);
  template<class InputIterator, class OutputIterator,
           class BinaryOperation, class UnaryOperation, class T>
    OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last,
                                            OutputIterator result,
                                            BinaryOperation binary_op,
                                            UnaryOperation unary_op,
                                            T init);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class UnaryOperation>
    ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                              ForwardIterator1 first, ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op);
  template<class ExecutionPolicy,
           class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation, class UnaryOperation, class T>
    ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                              ForwardIterator1 first, ForwardIterator1 last,
                                              ForwardIterator2 result,
                                              BinaryOperation binary_op,
                                              UnaryOperation unary_op,
                                              T init);

  // [adjacent.difference], adjacent difference
  template<class InputIterator, class OutputIterator>
    OutputIterator adjacent_difference(InputIterator first,
                                       InputIterator last,
                                       OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    OutputIterator adjacent_difference(InputIterator first,
                                       InputIterator last,
                                       OutputIterator result,
                                       BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
    ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                         ForwardIterator1 first,
                                         ForwardIterator1 last,
                                         ForwardIterator2 result);
  template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
           class BinaryOperation>
    ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, // see [algorithms.parallel.overloads]
                                         ForwardIterator1 first,
                                         ForwardIterator1 last,
                                         ForwardIterator2 result,
                                         BinaryOperation binary_op);

  // [numeric.iota], iota
  template<class ForwardIterator, class T>
    void iota(ForwardIterator first, ForwardIterator last, T value);

  // [numeric.ops.gcd], greatest common divisor
  template<class M, class N>
    constexpr common_type_t<M,N> gcd(M m, N n);

  // [numeric.ops.lcm], least common multiple
  template<class M, class N>
    constexpr common_type_t<M,N> lcm(M m, N n);
}

23.9 Generalized numeric operations [numeric.ops]

1
#
[ Note
:
The use of closed ranges as well as semi-open ranges to specify requirements throughout this subclause is intentional.
— end note
 ]

23.9.1 Accumulate [accumulate]

🔗
template<class InputIterator, class T> T accumulate(InputIterator first, InputIterator last, T init); template<class InputIterator, class T, class BinaryOperation> T accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
1
#
Requires: T shall satisfy the Cpp17CopyConstructible (Table 26) and Cpp17CopyAssignable (Table 28) requirements.
In the range [first, last], binary_­op shall neither modify elements nor invalidate iterators or subranges.241
2
#
Effects: Computes its result by initializing the accumulator acc with the initial value init and then modifies it with acc = std​::​move(acc) + *i or acc = binary_­op(std​::​move(acc), *i) for every iterator i in the range [first, last) in order.242
241)
The use of fully closed ranges is intentional.
242)
accumulate is similar to the APL reduction operator and Common Lisp reduce function, but it avoids the difficulty of defining the result of reduction on an empty sequence by always requiring an initial value.

23.9.2 Reduce [reduce]

🔗
template<class InputIterator> typename iterator_traits<InputIterator>::value_type reduce(InputIterator first, InputIterator last);
1
#
Effects: Equivalent to: 
return reduce(first, last,
              typename iterator_traits<InputIterator>::value_type{});
🔗
template<class ExecutionPolicy, class ForwardIterator> typename iterator_traits<ForwardIterator>::value_type reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last);
2
#
Effects: Equivalent to: 
return reduce(std::forward<ExecutionPolicy>(exec), first, last,
              typename iterator_traits<ForwardIterator>::value_type{});
🔗
template<class InputIterator, class T> T reduce(InputIterator first, InputIterator last, T init);
3
#
Effects: Equivalent to: 
return reduce(first, last, init, plus<>());
🔗
template<class ExecutionPolicy, class ForwardIterator, class T> T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init);
4
#
Effects: Equivalent to: 
return reduce(std::forward<ExecutionPolicy>(exec), first, last, init, plus<>());
🔗
template<class InputIterator, class T, class BinaryOperation> T reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation> T reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init, BinaryOperation binary_op);
5
#
Requires:
  • (5.1)
    T shall be Cpp17MoveConstructible (Table 25).
  • (5.2)
    All of binary_­op(init, *first), binary_­op(*first, init), binary_­op(init, init), and binary_­op(*first, *first) shall be convertible to T.
  • (5.3)
    binary_­op shall neither invalidate iterators or subranges, nor modify elements in the range [first, last].
6
#
Returns: GENERALIZED_­SUM(binary_­op, init, *i, ...) for every i in [first, last).
7
#
Complexity: applications of binary_­op.
8
#
[ Note
:
The difference between reduce and accumulate is that reduce applies binary_­op in an unspecified order, which yields a nondeterministic result for non-associative or non-commutative binary_­op such as floating-point addition.
— end note
 ]

23.9.3 Inner product [inner.product]

🔗
template<class InputIterator1, class InputIterator2, class T> T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init); template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
1
#
Requires: T shall satisfy the Cpp17CopyConstructible (Table 26) and Cpp17CopyAssignable (Table 28) requirements.
In the ranges [first1, last1] and [first2, first2 + (last1 - first1)] binary_­op1 and binary_­op2 shall neither modify elements nor invalidate iterators or subranges.243
2
#
Effects: Computes its result by initializing the accumulator acc with the initial value init and then modifying it with acc = std​::​move(acc) + (*i1) * (*i2) or acc = binary_­op1(std​::​move(acc), binary_­op2(*i1, *i2)) for every iterator i1 in the range [first1, last1) and iterator i2 in the range [first2, first2 + (last1 - first1)) in order.
243)
The use of fully closed ranges is intentional.

23.9.4 Transform reduce [transform.reduce]

🔗
template<class InputIterator1, class InputIterator2, class T> T transform_reduce(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);
1
#
Effects: Equivalent to: 
return transform_reduce(first1, last1, first2, init, plus<>(), multiplies<>());
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, T init);
2
#
Effects: Equivalent to: 
return transform_reduce(std::forward<ExecutionPolicy>(exec),
                        first1, last1, first2, init, plus<>(), multiplies<>());
🔗
template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> T transform_reduce(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation1, class BinaryOperation2> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
3
#
Requires:
  • (3.1)
    T shall be Cpp17MoveConstructible (Table 25).
  • (3.2)
    All of
    • (3.2.1)
      binary_­op1(init, init),
    • (3.2.2)
      binary_­op1(init, binary_­op2(*first1, *first2)),
    • (3.2.3)
      binary_­op1(binary_­op2(*first1, *first2), init), and
    • (3.2.4)
      binary_­op1(binary_­op2(*first1, *first2), binary_­op2(*first1, *first2))
    shall be convertible to T.
  • (3.3)
    Neither binary_­op1 nor binary_­op2 shall invalidate subranges, or modify elements in the ranges [first1, last1] and [first2, first2 + (last1 - first1)].
4
#
Returns: 
GENERALIZED_SUM(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...)
for every iterator i in [first1, last1).
5
#
Complexity: applications each of binary_­op1 and binary_­op2.
🔗
template<class InputIterator, class T, class BinaryOperation, class UnaryOperation> T transform_reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op, UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator, class T, class BinaryOperation, class UnaryOperation> T transform_reduce(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last, T init, BinaryOperation binary_op, UnaryOperation unary_op);
6
#
Requires:
  • (6.1)
    T shall be Cpp17MoveConstructible (Table 25).
  • (6.2)
    All of
    • (6.2.1)
      binary_­op(init, init),
    • (6.2.2)
      binary_­op(init, unary_­op(*first)),
    • (6.2.3)
      binary_­op(unary_­op(*first), init), and
    • (6.2.4)
      binary_­op(unary_­op(*first), unary_­op(*first))
    shall be convertible to T.
  • (6.3)
    Neither unary_­op nor binary_­op shall invalidate subranges, or modify elements in the range [first, last].
7
#
Returns: 
GENERALIZED_SUM(binary_op, init, unary_op(*i), ...)
for every iterator i in [first, last).
8
#
Complexity: applications each of unary_­op and binary_­op.
9
#
[ Note
:
transform_­reduce does not apply unary_­op to init.
— end note
 ]

23.9.5 Partial sum [partial.sum]

🔗
template<class InputIterator, class OutputIterator> OutputIterator partial_sum( InputIterator first, InputIterator last, OutputIterator result); template<class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator partial_sum( InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
1
#
Requires: InputIterator's value type shall be constructible from the type of *first.
The result of the expression std​::​move(acc) + *i or binary_­op(std​::​move(acc), *i) shall be implicitly convertible to InputIterator's value type.
acc shall be writable ([iterator.requirements.general]) to the result output iterator.
In the ranges [first, last] and [result, result + (last - first)] binary_­op shall neither modify elements nor invalidate iterators or subranges.244
2
#
Effects: For a non-empty range, the function creates an accumulator acc whose type is InputIterator's value type, initializes it with *first, and assigns the result to *result.
For every iterator i in [first + 1, last) in order, acc is then modified by acc = std​::​move(acc) + *i or acc = binary_­op(std​::​move(acc), *i) and the result is assigned to *(result + (i - first)).
3
#
Returns: result + (last - first).
4
#
Complexity: Exactly (last - first) - 1 applications of the binary operation.
5
#
Remarks: result may be equal to first.
244)
The use of fully closed ranges is intentional.

23.9.6 Exclusive scan [exclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class T> OutputIterator exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init);
1
#
Effects: Equivalent to: 
return exclusive_scan(first, last, result, init, plus<>());
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T> ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init);
2
#
Effects: Equivalent to: 
return exclusive_scan(std::forward<ExecutionPolicy>(exec),
                      first, last, result, init, plus<>());
🔗
template<class InputIterator, class OutputIterator, class T, class BinaryOperation> OutputIterator exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation> ForwardIterator2 exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init, BinaryOperation binary_op);
3
#
Requires:
  • (3.1)
    T shall be Cpp17MoveConstructible (Table 25).
  • (3.2)
    All of binary_­op(init, init), binary_­op(init, *first), and binary_­op(*first, *first) shall be convertible to T.
  • (3.3)
    binary_­op shall neither invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
4
#
Effects: For each integer K in [0, last - first) assigns through result + K the value of: 
GENERALIZED_NONCOMMUTATIVE_SUM(
    binary_op, init, *(first + 0), *(first + 1), ..., *(first + K - 1))
5
#
Returns: The end of the resulting range beginning at result.
6
#
Complexity: applications of binary_­op.
7
#
Remarks: result may be equal to first.
8
#
[ Note
:
The difference between exclusive_­scan and inclusive_­scan is that exclusive_­scan excludes the input element from the sum.
If binary_­op is not mathematically associative, the behavior of exclusive_­scan may be nondeterministic.
— end note
 ]

23.9.7 Inclusive scan [inclusive.scan]

🔗
template<class InputIterator, class OutputIterator> OutputIterator inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);
1
#
Effects: Equivalent to: 
return inclusive_scan(first, last, result, plus<>());
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
2
#
Effects: Equivalent to: 
return inclusive_scan(std::forward<ExecutionPolicy>(exec), first, last, result, plus<>());
🔗
template<class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation> ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op); template<class InputIterator, class OutputIterator, class BinaryOperation, class T> OutputIterator inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, T init); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class T> ForwardIterator2 inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op, T init);
3
#
Requires:
  • (3.1)
    If init is provided, T shall be Cpp17MoveConstructible (Table 25); otherwise, ForwardIterator1's value type shall be Cpp17MoveConstructible.
  • (3.2)
    If init is provided, all of binary_­op(init, init), binary_­op(init, *first), and binary_­op(*first, *first) shall be convertible to T; otherwise, binary_­op(*first, *first) shall be convertible to ForwardIterator1's value type.
  • (3.3)
    binary_­op shall neither invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
4
#
Effects: For each integer K in [0, last - first) assigns through result + K the value of
  • (4.1)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op, init, *(first + 0), *(first + 1), ..., *(first + K))
    if init is provided, or
  • (4.2)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op, *(first + 0), *(first + 1), ..., *(first + K))
    otherwise.
5
#
Returns: The end of the resulting range beginning at result.
6
#
Complexity: applications of binary_­op.
7
#
Remarks: result may be equal to first.
8
#
[ Note
:
The difference between exclusive_­scan and inclusive_­scan is that inclusive_­scan includes the input element in the sum.
If binary_­op is not mathematically associative, the behavior of inclusive_­scan may be nondeterministic.
— end note
 ]

23.9.8 Transform exclusive scan [transform.exclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class T, class BinaryOperation, class UnaryOperation> OutputIterator transform_exclusive_scan(InputIterator first, InputIterator last, OutputIterator result, T init, BinaryOperation binary_op,UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class T, class BinaryOperation, class UnaryOperation> ForwardIterator2 transform_exclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, T init, BinaryOperation binary_op, UnaryOperation unary_op);
1
#
Requires:
  • (1.1)
    T shall be Cpp17MoveConstructible (Table 25).
  • (1.2)
    All of
    • (1.2.1)
      binary_­op(init, init),
    • (1.2.2)
      binary_­op(init, unary_­op(*first)), and
    • (1.2.3)
      binary_­op(unary_­op(*first), unary_­op(*first))
    shall be convertible to T.
  • (1.3)
    Neither unary_­op nor binary_­op shall invalidate iterators or subranges, or modify elements in the ranges [first, last] or [result, result + (last - first)].
2
#
Effects: For each integer K in [0, last - first) assigns through result + K the value of: 
GENERALIZED_NONCOMMUTATIVE_SUM(
    binary_op, init,
    unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K - 1)))
3
#
Returns: The end of the resulting range beginning at result.
4
#
Complexity: applications each of unary_­op and binary_­op.
5
#
Remarks: result may be equal to first.
6
#
[ Note
:
The difference between transform_­exclusive_­scan and transform_­inclusive_­scan is that transform_­exclusive_­scan excludes the input element from the sum.
If binary_­op is not mathematically associative, the behavior of transform_­exclusive_­scan may be nondeterministic.
transform_­exclusive_­scan does not apply unary_­op to init.
— end note
 ]

23.9.9 Transform inclusive scan [transform.inclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation> OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class UnaryOperation> ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op, UnaryOperation unary_op); template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation, class T> OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, UnaryOperation unary_op, T init); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class UnaryOperation, class T> ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op, UnaryOperation unary_op, T init);
1
#
Requires:
  • (1.1)
    If init is provided, T shall be Cpp17MoveConstructible (Table 25); otherwise, ForwardIterator1's value type shall be Cpp17MoveConstructible.
  • (1.2)
    If init is provided, all of
    • (1.2.1)
      binary_­op(init, init),
    • (1.2.2)
      binary_­op(init, unary_­op(*first)), and
    • (1.2.3)
      binary_­op(unary_­op(*first), unary_­op(*first))
    shall be convertible to T; otherwise, binary_­op(unary_­op(*first), unary_­op(*first)) shall be convertible to ForwardIterator1's value type.
  • (1.3)
    Neither unary_­op nor binary_­op shall invalidate iterators or subranges, nor modify elements in the ranges [first, last] or [result, result + (last - first)].
2
#
Effects: For each integer K in [0, last - first) assigns through result + K the value of
  • (2.1)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op, init,
        unary_­op(*(first + 0)), unary_­op(*(first + 1)), ..., unary_­op(*(first + K)))
    if init is provided, or
  • (2.2)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op,
        unary_­op(*(first + 0)), unary_­op(*(first + 1)), ..., unary_­op(*(first + K)))
    otherwise.
3
#
Returns: The end of the resulting range beginning at result.
4
#
Complexity: applications each of unary_­op and binary_­op.
5
#
Remarks: result may be equal to first.
6
#
[ Note
:
The difference between transform_­exclusive_­scan and transform_­inclusive_­scan is that transform_­inclusive_­scan includes the input element in the sum.
If binary_­op is not mathematically associative, the behavior of transform_­inclusive_­scan may be nondeterministic.
transform_­inclusive_­scan does not apply unary_­op to init.
— end note
 ]

23.9.10 Adjacent difference [adjacent.difference]

🔗
template<class InputIterator, class OutputIterator> OutputIterator adjacent_difference(InputIterator first, InputIterator last, OutputIterator result); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result); template<class InputIterator, class OutputIterator, class BinaryOperation> OutputIterator adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation> ForwardIterator2 adjacent_difference(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op);
1
#
Let T be the value type of decltype(first).
For the overloads that do not take an argument binary_­op, let binary_­op be an lvalue that denotes an object of type minus<>.
2
#
Requires:
  • (2.1)
    For the overloads with no ExecutionPolicy, T shall be Cpp17MoveAssignable (Table 27) and shall be constructible from the type of *first.
    acc (defined below) shall be writable ([iterator.requirements.general]) to the result output iterator.
    The result of the expression binary_­op(val, std​::​move(acc)) shall be writable to the result output iterator.
  • (2.2)
    For the overloads with an ExecutionPolicy, the result of the expressions binary_­op(*first, *first) and *first shall be writable to result.
  • (2.3)
    For all overloads, in the ranges [first, last] and [result, result + (last - first)], binary_­op shall neither modify elements nor invalidate iterators or subranges.245
3
#
Effects: For the overloads with no ExecutionPolicy and a non-empty range, the function creates an accumulator acc of type T, initializes it with *first, and assigns the result to *result.
For every iterator i in [first + 1, last) in order, creates an object val whose type is T, initializes it with *i, computes binary_­op(val, std​::​move(acc)), assigns the result to *(result + (i - first)), and move assigns from val to acc.
4
#
For the overloads with an ExecutionPolicy and a non-empty range, performs *result = *first.
Then, for every d in [1, last - first - 1], performs *(result + d) = binary_­op(*(first + d), *(first + (d - 1))).
5
#
Returns: result + (last - first).
6
#
Complexity: Exactly (last - first) - 1 applications of the binary operation.
7
#
Remarks: For the overloads with no ExecutionPolicy, result may be equal to first.
For the overloads with an ExecutionPolicy, the ranges [first, last) and [result, result + (last - first)) shall not overlap.
245)
The use of fully closed ranges is intentional.

23.9.11 Iota [numeric.iota]

🔗
template<class ForwardIterator, class T> void iota(ForwardIterator first, ForwardIterator last, T value);
1
#
Requires: T shall be convertible to ForwardIterator's value type.
The expression ++val, where val has type T, shall be well-formed.
2
#
Effects: For each element referred to by the iterator i in the range [first, last), assigns *i = value and increments value as if by ++value.
3
#
Complexity: Exactly last - first increments and assignments.

23.9.12 Greatest common divisor [numeric.ops.gcd]

🔗
template<class M, class N> constexpr common_type_t<M,N> gcd(M m, N n);
1
#
Requires: |m| and |n| shall be representable as a value of common_­type_­t<M, N>.
[ Note
:
These requirements ensure, for example, that gcd(m, m) is representable as a value of type M.
— end note
 ]
2
#
Remarks: If either M or N is not an integer type, or if either is cv bool, the program is ill-formed.
3
#
Returns: Zero when m and n are both zero.
Otherwise, returns the greatest common divisor of |m| and |n|.
4
#
Throws: Nothing.

23.9.13 Least common multiple [numeric.ops.lcm]

🔗
template<class M, class N> constexpr common_type_t<M,N> lcm(M m, N n);
1
#
Requires: |m| and |n| shall be representable as a value of common_­type_­t<M, N>.
The least common multiple of |m| and |n| shall be representable as a value of type common_­type_­t<M,N>.
2
#
Remarks: If either M or N is not an integer type, or if either is cv bool the program is ill-formed.
3
#
Returns: Zero when either m or n is zero.
Otherwise, returns the least common multiple of |m| and |n|.
4
#
Throws: Nothing.

23.10 C library algorithms [alg.c.library]

1
#
[ Note
:
The header <cstdlib> declares the functions described in this subclause.
— end note
 ]
🔗
void* bsearch(const void* key, const void* base, size_t nmemb, size_t size, c-compare-pred* compar); void* bsearch(const void* key, const void* base, size_t nmemb, size_t size, compare-pred* compar); void qsort(void* base, size_t nmemb, size_t size, c-compare-pred* compar); void qsort(void* base, size_t nmemb, size_t size, compare-pred* compar);
2
#
Effects: These functions have the semantics specified in the C standard library.
3
#
Remarks: The behavior is undefined unless the objects in the array pointed to by base are of trivial type.
4
#
Throws: Any exception thrown by compar() ([res.on.exception.handling]).
See also: ISO C 7.22.5.