25 Algorithms library [algorithms]

25.1 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 91.
Table 91: Algorithms library summary   [tab:algorithms.summary]
Subclause
Header
Algorithms requirements
Parallel algorithms
Non-modifying sequence operations
<algorithm>
Mutating sequence operations
Sorting and related operations
Generalized numeric operations
<numeric>
Specialized <memory> algorithms
<memory>
C library algorithms
<cstdlib>

25.2 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
#
The entities defined in the std​::​ranges namespace in this Clause are not found by argument-dependent name lookup ([basic.lookup.argdep]).
When found by unqualified ([basic.lookup.unqual]) name lookup for the postfix-expression in a function call ([expr.call]), they inhibit argument-dependent name lookup.
[ Example
: 
void foo() {
  using namespace std::ranges;
  std::vector<int> vec{1,2,3};
  find(begin(vec), end(vec), 2);        // #1
}
The function call expression at #1 invokes std​::​ranges​::​find, not std​::​find, despite that (a) the iterator type returned from begin(vec) and end(vec) may be associated with namespace std and (b) std​::​find is more specialized ([temp.func.order]) than std​::​ranges​::​find since the former requires its first two parameters to have the same type.
— end example
 ]
3
#
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.
4
#
Throughout this Clause, where the template parameters are not constrained, the names of template parameters are used to express type requirements.
  • (4.1)
    If an algorithm's template parameter is named InputIterator, InputIterator1, or InputIterator2, the template argument shall meet the Cpp17InputIterator requirements ([input.iterators]).
  • (4.2)
    If an algorithm's template parameter is named OutputIterator, OutputIterator1, or OutputIterator2, the template argument shall meet the Cpp17OutputIterator requirements ([output.iterators]).
  • (4.3)
    If an algorithm's template parameter is named ForwardIterator, ForwardIterator1, or ForwardIterator2, the template argument shall meet the Cpp17ForwardIterator requirements ([forward.iterators]).
  • (4.4)
    If an algorithm's template parameter is named NoThrowForwardIterator, the template argument shall meet the Cpp17ForwardIterator requirements ([forward.iterators]), and is required to have the property that no exceptions are thrown from increment, assignment, or comparison of, or indirection through, valid iterators.
  • (4.5)
    If an algorithm's template parameter is named BidirectionalIterator, BidirectionalIterator1, or BidirectionalIterator2, the template argument shall meet the Cpp17BidirectionalIterator requirements ([bidirectional.iterators]).
  • (4.6)
    If an algorithm's template parameter is named RandomAccessIterator, RandomAccessIterator1, or RandomAccessIterator2, the template argument shall meet the Cpp17RandomAccessIterator requirements ([random.access.iterators]).
5
#
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 meet 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, nor does it affect arguments that are constrained, for which mutability requirements are expressed explicitly.
— end note
 ]
6
#
Both in-place and copying versions are provided for certain algorithms.230
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).
7
#
When not otherwise constrained, 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 with value type T, 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.
Given a glvalue u of type (possibly const) T that designates the same object as *first, pred(u) shall be a valid expression that is equal to pred(*first).
8
#
When not otherwise constrained, 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 with respective value types T1 and T2, it should work correctly in the construct binary_­pred(*first1, *first2) contextually converted to bool ([conv]).
Unless otherwise specified, 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.
Given a glvalue u of type (possibly const) T1 that designates the same object as *first1, and a glvalue v of type (possibly const) T2 that designates the same object as *first2, binary_­pred(u, *first2), binary_­pred(*first1, v), and binary_­pred(u, v) shall each be a valid expression that is equal to binary_­pred(*first1, *first2), and binary_­pred(u, value) shall be a valid expression that is equal to binary_­pred(*first1, value).
9
#
The parameters UnaryOperation, BinaryOperation, BinaryOperation1, and BinaryOperation2 are used whenever an algorithm expects a function object ([function.objects]).
10
#
[ 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
 ]
11
#
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.
12
#
In the description of the algorithms, operator + is used for some of the iterator categories for which it does not have to be defined.
In these cases the semantics of a + n are the same as those of 
auto tmp = a;
for (; n < 0; ++n) --tmp;
for (; n > 0; --n) ++tmp;
return tmp;
Similarly, operator - is used for some combinations of iterators and sentinel types for which it does not have to be defined.
If [a, b) denotes a range, the semantics of b - a in these cases are the same as those of 
iter_difference_t<decltype(a)> n = 0;
for (auto tmp = a; tmp != b; ++tmp) ++n;
return n;
and if [b, a) denotes a range, the same as those of 
iter_difference_t<decltype(b)> n = 0;
for (auto tmp = b; tmp != a; ++tmp) --n;
return n;
13
#
In the description of algorithm return values, a sentinel value s denoting the end of a range [i, s) is sometimes returned where an iterator is expected.
In these cases, the semantics are as if the sentinel is converted into an iterator using ranges​::​next(i, s).
14
#
Overloads of algorithms that take range arguments ([range.range]) behave as if they are implemented by calling ranges​::​begin and ranges​::​end on the range(s) and dispatching to the overload in namespace ranges that takes separate iterator and sentinel arguments.
15
#
The number and order of deducible template parameters for algorithm declarations are unspecified, except where explicitly stated otherwise.
[ Note
:
Consequently, the algorithms may not be called with explicitly-specified template argument lists.
— end note
 ]
230)
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.
⮥

25.3 Parallel algorithms [algorithms.parallel]

25.3.1 Preamble [algorithms.parallel.defns]

1
#
Subclause [algorithms.parallel] describes components that C++ programs may use to perform operations on containers and other sequences in parallel.
2
#
A parallel algorithm is a function template listed in this document with a template parameter named ExecutionPolicy.
3
#
Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions:
  • (3.1)
    All operations of the categories of the iterators that the algorithm is instantiated with.
  • (3.2)
    Operations on those sequence elements that are required by its specification.
  • (3.3)
    User-provided function objects to be applied during the execution of the algorithm, if required by the specification.
  • (3.4)
    Operations on those function objects required by the specification.
    [ Note
    : See [algorithms.requirements]. — 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
 ]
4
#
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.
[ 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;
void f() {
  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
 ]

25.3.2 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.

25.3.3 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​::​unsequenced_­policy are permitted to execute in an unordered fashion in the calling thread of execution, unsequenced with respect to one another in the calling thread of execution.
[ 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 overlap with one another.
— end note
 ]
The behavior of a program is undefined if it invokes a vectorization-unsafe standard library function from user code called from a execution​::​unsequenced_­policy algorithm.
[ Note
:
Because execution​::​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.
— end note
 ]
6
#
The invocations of element access functions in parallel algorithms invoked with an execution policy object of type execution​::​parallel_­policy are permitted to execute either in 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]) or jthread ([thread.jthread.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
 ]
7
#
The invocations of element access functions in parallel algorithms invoked with an execution policy object 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 overlap with one another.
— end note
 ]
The behavior of a program is undefined if it invokes a vectorization-unsafe standard library function from user code called from a execution​::​parallel_­unsequenced_­policy algorithm.
[ Note
:
Because 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.
— end note
 ]
8
#
[ Note
:
The semantics of invocation with execution​::​unsequenced_­policy, execution​::​parallel_­policy, or execution​::​parallel_­unsequenced_­policy allow the implementation to fall back to sequential execution if the system cannot parallelize an algorithm invocation, e.g., due to lack of resources.
— end note
 ]
9
#
If an invocation of a parallel algorithm uses threads of execution implicitly created by the library, then the invoking thread of execution will either
  • (9.1)
    temporarily block with forward progress guarantee delegation ([intro.progress]) on the completion of these library-managed threads of execution, or
  • (9.2)
    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
 ]
10
#
The semantics of parallel algorithms invoked with an execution policy object of implementation-defined type are implementation-defined.

25.3.4 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.

25.3.5 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.

25.4 Header <algorithm> synopsis [algorithm.syn]

#include <initializer_list>

namespace std {
  namespace ranges {
    // [algorithms.results], algorithm result types
    template<class I, class F>
      struct in_fun_result;

    template<class I1, class I2>
      struct in_in_result;

    template<class I, class O>
      struct in_out_result;

    template<class I1, class I2, class O>
      struct in_in_out_result;

    template<class I, class O1, class O2>
      struct in_out_out_result;

    template<class T>
      struct min_max_result;

    template<class I>
      struct in_found_result;
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool all_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool all_of(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool any_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool any_of(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool none_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool none_of(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class I, class F>
      using for_each_result = in_fun_result<I, F>;

    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirectly_unary_invocable<projected<I, Proj>> Fun>
      constexpr for_each_result<I, Fun>
        for_each(I first, S last, Fun f, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
      constexpr for_each_result<borrowed_iterator_t<R>, Fun>
        for_each(R&& r, Fun f, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class F>
      using for_each_n_result = in_fun_result<I, F>;

    template<input_iterator I, class Proj = identity,
             indirectly_unary_invocable<projected<I, Proj>> Fun>
      constexpr for_each_n_result<I, Fun>
        for_each_n(I first, iter_difference_t<I> n, Fun f, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr I find(I first, S last, const T& value, Proj proj = {});
    template<input_range R, class T, class Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T*>
      constexpr borrowed_iterator_t<R>
        find(R&& r, const T& value, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr I find_if(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr borrowed_iterator_t<R>
        find_if(R&& r, Pred pred, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr I find_if_not(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr borrowed_iterator_t<R>
        find_if_not(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
      constexpr subrange<I1>
        find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_range R2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr borrowed_subrange_t<R1>
        find_end(R1&& r1, R2&& r2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1, forward_iterator I2, sentinel_for<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
      constexpr I1 find_first_of(I1 first1, S1 last1, I2 first2, S2 last2,
                                 Pred pred = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, forward_range R2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr borrowed_iterator_t<R1>
        find_first_of(R1&& r1, R2&& r2,
                      Pred pred = {},
                      Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_binary_predicate<projected<I, Proj>,
                                       projected<I, Proj>> Pred = ranges::equal_to>
      constexpr I adjacent_find(I first, S last, Pred pred = {},
                                Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_binary_predicate<projected<iterator_t<R>, Proj>,
                                       projected<iterator_t<R>, Proj>> Pred = ranges::equal_to>
      constexpr borrowed_iterator_t<R>
        adjacent_find(R&& r, Pred pred = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr iter_difference_t<I>
        count(I first, S last, const T& value, Proj proj = {});
    template<input_range R, class T, class Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T*>
      constexpr range_difference_t<R>
        count(R&& r, const T& value, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr iter_difference_t<I>
        count_if(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr range_difference_t<R>
        count_if(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class I1, class I2>
      using mismatch_result = in_in_result<I1, I2>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
      constexpr mismatch_result<I1, I2>
        mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
        mismatch(R1&& r1, R2&& r2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
      constexpr bool equal(I1 first1, S1 last1, I2 first2, S2 last2,
                           Pred pred = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr bool equal(R1&& r1, R2&& r2, Pred pred = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2,
             sentinel_for<I2> S2, class Proj1 = identity, class Proj2 = identity,
             indirect_equivalence_relation<projected<I1, Proj1>,
                                           projected<I2, Proj2>> Pred = ranges::equal_to>
      constexpr bool is_permutation(I1 first1, S1 last1, I2 first2, S2 last2,
                                    Pred pred = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_range R2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_equivalence_relation<projected<iterator_t<R1>, Proj1>,
                                           projected<iterator_t<R2>, Proj2>>
               Pred = ranges::equal_to>
      constexpr bool is_permutation(R1&& r1, R2&& r2, Pred pred = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1, forward_iterator I2,
             sentinel_for<I2> S2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
      constexpr subrange<I1>
        search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
               Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_range R2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr borrowed_subrange_t<R1>
        search(R1&& r1, R2&& r2, Pred pred = {},
               Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T,
             class Pred = ranges::equal_to, class Proj = identity>
      requires indirectly_comparable<I, const T*, Pred, Proj>
      constexpr subrange<I>
        search_n(I first, S last, iter_difference_t<I> count,
                 const T& value, Pred pred = {}, Proj proj = {});
    template<forward_range R, class T, class Pred = ranges::equal_to,
             class Proj = identity>
      requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
      constexpr borrowed_subrange_t<R>
        search_n(R&& r, range_difference_t<R> count,
                 const T& value, Pred pred = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using copy_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr copy_result<I, O>
        copy(I first, S last, O result);
    template<input_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr copy_result<borrowed_iterator_t<R>, O>
        copy(R&& r, O 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);

  namespace ranges {
    template<class I, class O>
      using copy_n_result = in_out_result<I, O>;

    template<input_iterator I, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr copy_n_result<I, O>
        copy_n(I first, iter_difference_t<I> n, O 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);

  namespace ranges {
    template<class I, class O>
      using copy_if_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr copy_if_result<I, O>
        copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr copy_if_result<borrowed_iterator_t<R>, O>
        copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }

  template<class BidirectionalIterator1, class BidirectionalIterator2>
    constexpr BidirectionalIterator2
      copy_backward(BidirectionalIterator1 first, BidirectionalIterator1 last,
                    BidirectionalIterator2 result);

  namespace ranges {
    template<class I1, class I2>
      using copy_backward_result = in_out_result<I1, I2>;

    template<bidirectional_iterator I1, sentinel_for<I1> S1, bidirectional_iterator I2>
      requires indirectly_copyable<I1, I2>
      constexpr copy_backward_result<I1, I2>
        copy_backward(I1 first, S1 last, I2 result);
    template<bidirectional_range R, bidirectional_iterator I>
      requires indirectly_copyable<iterator_t<R>, I>
      constexpr copy_backward_result<borrowed_iterator_t<R>, I>
        copy_backward(R&& r, I 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);

  namespace ranges {
    template<class I, class O>
      using move_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_movable<I, O>
      constexpr move_result<I, O>
        move(I first, S last, O result);
    template<input_range R, weakly_incrementable O>
      requires indirectly_movable<iterator_t<R>, O>
      constexpr move_result<borrowed_iterator_t<R>, O>
        move(R&& r, O result);
  }

  template<class BidirectionalIterator1, class BidirectionalIterator2>
    constexpr BidirectionalIterator2
      move_backward(BidirectionalIterator1 first, BidirectionalIterator1 last,
                    BidirectionalIterator2 result);

  namespace ranges {
    template<class I1, class I2>
      using move_backward_result = in_out_result<I1, I2>;

    template<bidirectional_iterator I1, sentinel_for<I1> S1, bidirectional_iterator I2>
      requires indirectly_movable<I1, I2>
      constexpr move_backward_result<I1, I2>
        move_backward(I1 first, S1 last, I2 result);
    template<bidirectional_range R, bidirectional_iterator I>
      requires indirectly_movable<iterator_t<R>, I>
      constexpr move_backward_result<borrowed_iterator_t<R>, I>
        move_backward(R&& r, I 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);

  namespace ranges {
    template<class I1, class I2>
      using swap_ranges_result = in_in_result<I1, I2>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2>
      requires indirectly_swappable<I1, I2>
      constexpr swap_ranges_result<I1, I2>
        swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2);
    template<input_range R1, input_range R2>
      requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
      constexpr swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
        swap_ranges(R1&& r1, R2&& r2);
  }

  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 first1, InputIterator last1,
                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 first1, ForwardIterator1 last1,
                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);

  namespace ranges {
    template<class I, class O>
      using unary_transform_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
             copy_constructible F, class Proj = identity>
      requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
      constexpr unary_transform_result<I, O>
        transform(I first1, S last1, O result, F op, Proj proj = {});
    template<input_range R, weakly_incrementable O, copy_constructible F,
             class Proj = identity>
      requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
      constexpr unary_transform_result<borrowed_iterator_t<R>, O>
        transform(R&& r, O result, F op, Proj proj = {});

    template<class I1, class I2, class O>
      using binary_transform_result = in_in_out_result<I1, I2, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, copy_constructible F, class Proj1 = identity,
             class Proj2 = identity>
      requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                             projected<I2, Proj2>>>
      constexpr binary_transform_result<I1, I2, O>
        transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             copy_constructible F, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                             projected<iterator_t<R2>, Proj2>>>
      constexpr binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
        transform(R1&& r1, R2&& r2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class T1, class T2, class Proj = identity>
      requires indirectly_writable<I, const T2&> &&
               indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr I
        replace(I first, S last, const T1& old_value, const T2& new_value, Proj proj = {});
    template<input_range R, class T1, class T2, class Proj = identity>
      requires indirectly_writable<iterator_t<R>, const T2&> &&
               indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T1*>
      constexpr borrowed_iterator_t<R>
        replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_writable<I, const T&>
      constexpr I replace_if(I first, S last, Pred pred, const T& new_value, Proj proj = {});
    template<input_range R, class T, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_writable<iterator_t<R>, const T&>
      constexpr borrowed_iterator_t<R>
        replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using replace_copy_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, class T1, class T2,
             output_iterator<const T2&> O, class Proj = identity>
      requires indirectly_copyable<I, O> &&
               indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr replace_copy_result<I, O>
        replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});
    template<input_range R, class T1, class T2, output_iterator<const T2&> O,
             class Proj = identity>
      requires indirectly_copyable<iterator_t<R>, O> &&
               indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T1*>
      constexpr replace_copy_result<borrowed_iterator_t<R>, O>
        replace_copy(R&& r, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});

    template<class I, class O>
      using replace_copy_if_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, class T, output_iterator<const T&> O,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr replace_copy_if_result<I, O>
        replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                        Proj proj = {});
    template<input_range R, class T, output_iterator<const T&> O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr replace_copy_if_result<borrowed_iterator_t<R>, O>
        replace_copy_if(R&& r, O result, Pred pred, const T& new_value,
                        Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class T, output_iterator<const T&> O, sentinel_for<O> S>
      constexpr O fill(O first, S last, const T& value);
    template<class T, output_range<const T&> R>
      constexpr borrowed_iterator_t<R> fill(R&& r, const T& value);
    template<class T, output_iterator<const T&> O>
      constexpr O fill_n(O first, iter_difference_t<O> 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);

  namespace ranges {
    template<input_or_output_iterator O, sentinel_for<O> S, copy_constructible F>
      requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
      constexpr O generate(O first, S last, F gen);
    template<class R, copy_constructible F>
      requires invocable<F&> && output_range<R, invoke_result_t<F&>>
      constexpr borrowed_iterator_t<R> generate(R&& r, F gen);
    template<input_or_output_iterator O, copy_constructible F>
      requires invocable<F&> && indirectly_writable<O, invoke_result_t<F&>>
      constexpr O generate_n(O first, iter_difference_t<O> n, F 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);

  namespace ranges {
    template<permutable I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr subrange<I> remove(I first, S last, const T& value, Proj proj = {});
    template<forward_range R, class T, class Proj = identity>
      requires permutable<iterator_t<R>> &&
               indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T*>
      constexpr borrowed_subrange_t<R>
        remove(R&& r, const T& value, Proj proj = {});
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr subrange<I> remove_if(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      constexpr borrowed_subrange_t<R>
        remove_if(R&& r, Pred pred, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using remove_copy_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class T,
             class Proj = identity>
      requires indirectly_copyable<I, O> &&
               indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr remove_copy_result<I, O>
        remove_copy(I first, S last, O result, const T& value, Proj proj = {});
    template<input_range R, weakly_incrementable O, class T, class Proj = identity>
      requires indirectly_copyable<iterator_t<R>, O> &&
               indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<R>, Proj>, const T*>
      constexpr remove_copy_result<borrowed_iterator_t<R>, O>
        remove_copy(R&& r, O result, const T& value, Proj proj = {});

    template<class I, class O>
      using remove_copy_if_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr remove_copy_if_result<I, O>
        remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr remove_copy_if_result<borrowed_iterator_t<R>, O>
        remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
      constexpr subrange<I> unique(I first, S last, C comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires permutable<iterator_t<R>>
      constexpr borrowed_subrange_t<R>
        unique(R&& r, C comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using unique_copy_result = in_out_result<I, O>;

    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class Proj = identity,
             indirect_equivalence_relation<projected<I, Proj>> C = ranges::equal_to>
      requires indirectly_copyable<I, O> &&
               (forward_iterator<I> ||
                (input_iterator<O> && same_as<iter_value_t<I>, iter_value_t<O>>) ||
                indirectly_copyable_storable<I, O>)
      constexpr unique_copy_result<I, O>
        unique_copy(I first, S last, O result, C comp = {}, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_equivalence_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires indirectly_copyable<iterator_t<R>, O> &&
               (forward_iterator<iterator_t<R>> ||
                (input_iterator<O> && same_as<range_value_t<R>, iter_value_t<O>>) ||
                indirectly_copyable_storable<iterator_t<R>, O>)
      constexpr unique_copy_result<borrowed_iterator_t<R>, O>
        unique_copy(R&& r, O result, C comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S>
      requires permutable<I>
      constexpr I reverse(I first, S last);
    template<bidirectional_range R>
      requires permutable<iterator_t<R>>
      constexpr borrowed_iterator_t<R> reverse(R&& r);
  }

  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);

  namespace ranges {
    template<class I, class O>
      using reverse_copy_result = in_out_result<I, O>;

    template<bidirectional_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr reverse_copy_result<I, O>
        reverse_copy(I first, S last, O result);
    template<bidirectional_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr reverse_copy_result<borrowed_iterator_t<R>, O>
        reverse_copy(R&& r, O 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);

  namespace ranges {
    template<permutable I, sentinel_for<I> S>
      constexpr subrange<I> rotate(I first, I middle, S last);
    template<forward_range R>
      requires permutable<iterator_t<R>>
      constexpr borrowed_subrange_t<R> rotate(R&& r, iterator_t<R> middle);
  }

  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);

  namespace ranges {
    template<class I, class O>
      using rotate_copy_result = in_out_result<I, O>;

    template<forward_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr rotate_copy_result<I, O>
        rotate_copy(I first, I middle, S last, O result);
    template<forward_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr rotate_copy_result<borrowed_iterator_t<R>, O>
        rotate_copy(R&& r, iterator_t<R> middle, O 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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S,
             weakly_incrementable O, class Gen>
      requires (forward_iterator<I> || random_access_iterator<O>) &&
               indirectly_copyable<I, O> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      O sample(I first, S last, O out, iter_difference_t<I> n, Gen&& g);
    template<input_range R, weakly_incrementable O, class Gen>
      requires (forward_range<R> || random_access_iterator<O>) &&
               indirectly_copyable<iterator_t<R>, O> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      O sample(R&& r, O out, range_difference_t<R> n, Gen&& g);
  }

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

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Gen>
      requires permutable<I> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      I shuffle(I first, S last, Gen&& g);
    template<random_access_range R, class Gen>
      requires permutable<iterator_t<R>> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      borrowed_iterator_t<R> shuffle(R&& r, Gen&& 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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        sort(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        sort(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      I stable_sort(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      borrowed_iterator_t<R>
        stable_sort(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        partial_sort(R&& r, iterator_t<R> middle, Comp comp = {},
                     Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using partial_sort_copy_result = in_out_result<I, O>;

    template<input_iterator I1, sentinel_for<I1> S1,
             random_access_iterator I2, sentinel_for<I2> S2,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_copyable<I1, I2> && sortable<I2, Comp, Proj2> &&
               indirect_strict_weak_order<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
      constexpr partial_sort_copy_result<I1, I2>
        partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last,
                          Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, random_access_range R2, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
               sortable<iterator_t<R2>, Comp, Proj2> &&
               indirect_strict_weak_order<Comp, projected<iterator_t<R1>, Proj1>,
                                          projected<iterator_t<R2>, Proj2>>
      constexpr partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
        partial_sort_copy(R1&& r, R2&& result_r, Comp comp = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr bool is_sorted(I first, S last, Comp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr bool is_sorted(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr I is_sorted_until(I first, S last, Comp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr borrowed_iterator_t<R>
        is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr I lower_bound(I first, S last, const T& value, Comp comp = {},
                              Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr borrowed_iterator_t<R>
        lower_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr I upper_bound(I first, S last, const T& value, Comp comp = {}, Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr borrowed_iterator_t<R>
        upper_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr subrange<I>
        equal_range(I first, S last, const T& value, Comp comp = {}, Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr borrowed_subrange_t<R>
        equal_range(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr bool binary_search(I first, S last, const T& value, Comp comp = {},
                                   Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr bool binary_search(R&& r, const T& value, Comp comp = {},
                                   Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool is_partitioned(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool is_partitioned(R&& r, Pred pred, Proj proj = {});
  }

  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);

  namespace ranges {
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr subrange<I>
        partition(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      constexpr borrowed_subrange_t<R>
        partition(R&& r, Pred pred, Proj proj = {});
  }

  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);

  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires permutable<I>
      subrange<I> stable_partition(I first, S last, Pred pred, Proj proj = {});
    template<bidirectional_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      borrowed_subrange_t<R> stable_partition(R&& r, Pred pred, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I, class O1, class O2>
      using partition_copy_result = in_out_out_result<I, O1, O2>;

    template<input_iterator I, sentinel_for<I> S,
             weakly_incrementable O1, weakly_incrementable O2,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
      constexpr partition_copy_result<I, O1, O2>
        partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                       Proj proj = {});
    template<input_range R, weakly_incrementable O1, weakly_incrementable O2,
             class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O1> &&
               indirectly_copyable<iterator_t<R>, O2>
      constexpr partition_copy_result<borrowed_iterator_t<R>, O1, O2>
        partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});
  }

  template<class ForwardIterator, class Predicate>
    constexpr ForwardIterator
      partition_point(ForwardIterator first, ForwardIterator last,
                      Predicate pred);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr I partition_point(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr borrowed_iterator_t<R>
        partition_point(R&& r, Pred pred, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class I1, class I2, class O>
      using merge_result = in_in_out_result<I1, I2, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Comp = ranges::less, class Proj1 = identity,
             class Proj2 = identity>
      requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr merge_result<I1, I2, O>
        merge(I1 first1, S1 last1, I2 first2, S2 last2, O result,
              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
        merge(R1&& r1, R2&& r2, O result,
              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      I inplace_merge(I first, I middle, S last, Comp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      borrowed_iterator_t<R>
        inplace_merge(R&& r, iterator_t<R> middle, Comp comp = {},
                      Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
               ranges::less>
      constexpr bool includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, class Proj1 = identity,
             class Proj2 = identity,
             indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                        projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
      constexpr bool includes(R1&& r1, R2&& r2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<class I1, class I2, class O>
      using set_union_result = in_in_out_result<I1, I2, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_union_result<I1, I2, O>
        set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
        set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<class I1, class I2, class O>
      using set_intersection_result = in_in_out_result<I1, I2, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_intersection_result<I1, I2, O>
        set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                         Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
        set_intersection(R1&& r1, R2&& r2, O result,
                         Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<class I, class O>
      using set_difference_result = in_out_result<I, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_difference_result<I1, O>
        set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                       Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_difference_result<borrowed_iterator_t<R1>, O>
        set_difference(R1&& r1, R2&& r2, O result,
                       Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  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);

  namespace ranges {
    template<class I1, class I2, class O>
      using set_symmetric_difference_result = in_in_out_result<I1, I2, O>;

    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_symmetric_difference_result<I1, I2, O>
        set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                 Comp comp = {}, Proj1 proj1 = {},
                                 Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_symmetric_difference_result<borrowed_iterator_t<R1>,
                                                borrowed_iterator_t<R2>, O>
        set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        push_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        push_heap(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        pop_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        pop_heap(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        make_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        make_heap(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr I
        sort_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Comp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr borrowed_iterator_t<R>
        sort_heap(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr bool is_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr bool is_heap(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr I is_heap_until(I first, S last, Comp comp = {}, Proj proj = {});
    template<random_access_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr borrowed_iterator_t<R>
        is_heap_until(R&& r, Comp comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr const T& min(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr T min(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr range_value_t<R>
        min(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr const T& max(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr T max(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr range_value_t<R>
        max(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class T>
      using minmax_result = min_max_result<T>;

    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr minmax_result<const T&>
        minmax(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr minmax_result<T>
        minmax(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr minmax_result<range_value_t<R>>
        minmax(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr I min_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr borrowed_iterator_t<R>
        min_element(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

 namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr I max_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr borrowed_iterator_t<R>
        max_element(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I>
      using minmax_element_result = min_max_result<I>;

    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
      constexpr minmax_element_result<I>
        minmax_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr minmax_element_result<borrowed_iterator_t<R>>
        minmax_element(R&& r, Comp comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
      constexpr const T&
        clamp(const T& v, const T& lo, const T& hi, Comp comp = {}, Proj proj = {});
  }

  // [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);

  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
               ranges::less>
      constexpr bool
        lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
                                Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, class Proj1 = identity,
             class Proj2 = identity,
             indirect_strict_weak_order<projected<iterator_t<R1>, Proj1>,
                                        projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
      constexpr bool
        lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});
  }

  // [alg.three.way], three-way comparison algorithms
  template<class InputIterator1, class InputIterator2, class Cmp>
    constexpr auto
      lexicographical_compare_three_way(InputIterator1 b1, InputIterator1 e1,
                                        InputIterator2 b2, InputIterator2 e2,
                                        Cmp comp)
        -> decltype(comp(*b1, *b2));
  template<class InputIterator1, class InputIterator2>
    constexpr auto
      lexicographical_compare_three_way(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);

  namespace ranges {
    template<class I>
      using next_permutation_result = in_found_result<I>;

    template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr next_permutation_result<I>
        next_permutation(I first, S last, Comp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr next_permutation_result<borrowed_iterator_t<R>>
        next_permutation(R&& r, Comp comp = {}, Proj proj = {});
  }

  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);

  namespace ranges {
    template<class I>
      using prev_permutation_result = in_found_result<I>;

    template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<I, Comp, Proj>
      constexpr prev_permutation_result<I>
        prev_permutation(I first, S last, Comp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Comp = ranges::less,
             class Proj = identity>
      requires sortable<iterator_t<R>, Comp, Proj>
      constexpr prev_permutation_result<borrowed_iterator_t<R>>
        prev_permutation(R&& r, Comp comp = {}, Proj proj = {});
  }
}

25.5 Algorithm result types [algorithms.results]

1
#
Each of the class templates specified in this subclause has the template parameters, data members, and special members specified below, and has no base classes or members other than those specified.
namespace std::ranges {
  template<class I, class F>
  struct in_fun_result {
    [[no_unique_address]] I in;
    [[no_unique_address]] F fun;

    template<class I2, class F2>
      requires convertible_to<const I&, I2> && convertible_to<const F&, F2>
    constexpr operator in_fun_result<I2, F2>() const & {
      return {in, fun};
    }

    template<class I2, class F2>
      requires convertible_to<I, I2> && convertible_to<F, F2>
    constexpr operator in_fun_result<I2, F2>() && {
      return {std::move(in), std::move(fun)};
    }
  };

  template<class I1, class I2>
  struct in_in_result {
    [[no_unique_address]] I1 in1;
    [[no_unique_address]] I2 in2;

    template<class II1, class II2>
      requires convertible_to<const I1&, II1> && convertible_to<const I2&, II2>
    constexpr operator in_in_result<II1, II2>() const & {
      return {in1, in2};
    }

    template<class II1, class II2>
      requires convertible_to<I1, II1> && convertible_to<I2, II2>
    constexpr operator in_in_result<II1, II2>() && {
      return {std::move(in1), std::move(in2)};
    }
  };

  template<class I, class O>
  struct in_out_result {
    [[no_unique_address]] I in;
    [[no_unique_address]] O out;

    template<class I2, class O2>
      requires convertible_to<const I&, I2> && convertible_to<const O&, O2>
    constexpr operator in_out_result<I2, O2>() const & {
      return {in, out};
    }

    template<class I2, class O2>
      requires convertible_to<I, I2> && convertible_to<O, O2>
    constexpr operator in_out_result<I2, O2>() && {
      return {std::move(in), std::move(out)};
    }
  };

  template<class I1, class I2, class O>
  struct in_in_out_result {
    [[no_unique_address]] I1 in1;
    [[no_unique_address]] I2 in2;
    [[no_unique_address]] O  out;

    template<class II1, class II2, class OO>
      requires convertible_to<const I1&, II1> &&
               convertible_to<const I2&, II2> &&
               convertible_to<const O&, OO>
    constexpr operator in_in_out_result<II1, II2, OO>() const & {
      return {in1, in2, out};
    }

    template<class II1, class II2, class OO>
      requires convertible_to<I1, II1> &&
               convertible_to<I2, II2> &&
               convertible_to<O, OO>
    constexpr operator in_in_out_result<II1, II2, OO>() && {
      return {std::move(in1), std::move(in2), std::move(out)};
    }
  };

  template<class I, class O1, class O2>
  struct in_out_out_result {
    [[no_unique_address]] I  in;
    [[no_unique_address]] O1 out1;
    [[no_unique_address]] O2 out2;

    template<class II, class OO1, class OO2>
      requires convertible_to<const I&, II> &&
               convertible_to<const O1&, OO1> &&
               convertible_to<const O2&, OO2>
    constexpr operator in_out_out_result<II, OO1, OO2>() const & {
      return {in, out1, out2};
    }

    template<class II, class OO1, class OO2>
      requires convertible_to<I, II> &&
               convertible_to<O1, OO1> &&
               convertible_to<O2, OO2>
    constexpr operator in_out_out_result<II, OO1, OO2>() && {
      return {std::move(in), std::move(out1), std::move(out2)};
    }
  };

  template<class T>
  struct min_max_result {
    [[no_unique_address]] T min;
    [[no_unique_address]] T max;

    template<class T2>
      requires convertible_to<const T&, T2>
    constexpr operator min_max_result<T2>() const & {
      return {min, max};
    }

    template<class T2>
      requires convertible_to<T, T2>
    constexpr operator min_max_result<T2>() && {
      return {std::move(min), std::move(max)};
    }
  };

  template<class I>
  struct in_found_result {
    [[no_unique_address]] I in;
    bool found;

    template<class I2>
      requires convertible_to<const I&, I2>
    constexpr operator in_found_result<I2>() const & {
      return {in, found};
    }
    template<class I2>
      requires convertible_to<I, I2>
    constexpr operator in_found_result<I2>() && {
      return {std::move(in), found};
    }
  };
}

25.6 Non-modifying sequence operations [alg.nonmodifying]

25.6.1 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); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr bool ranges::all_of(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr bool ranges::all_of(R&& r, Pred pred, Proj proj = {});
1
#
Let E be:
  • (1.1)
    pred(*i) for the overloads in namespace std;
  • (1.2)
    invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.
2
#
Returns: false if E is false for some iterator i in the range [first, last), and true otherwise.
3
#
Complexity: At most last - first applications of the predicate and any projection.

25.6.2 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); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr bool ranges::any_of(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr bool ranges::any_of(R&& r, Pred pred, Proj proj = {});
1
#
Let E be:
  • (1.1)
    pred(*i) for the overloads in namespace std;
  • (1.2)
    invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.
2
#
Returns: true if E is true for some iterator i in the range [first, last), and false otherwise.
3
#
Complexity: At most last - first applications of the predicate and any projection.

25.6.3 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); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr bool ranges::none_of(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr bool ranges::none_of(R&& r, Pred pred, Proj proj = {});
1
#
Let E be:
  • (1.1)
    pred(*i) for the overloads in namespace std;
  • (1.2)
    invoke(pred, invoke(proj, *i)) for the overloads in namespace ranges.
2
#
Returns: false if E is true for some iterator i in the range [first, last), and true otherwise.
3
#
Complexity: At most last - first applications of the predicate and any projection.

25.6.4 For each [alg.foreach]

🔗
template<class InputIterator, class Function> constexpr Function for_each(InputIterator first, InputIterator last, Function f);
1
#
Preconditions: Function meets the Cpp17MoveConstructible requirements (Table 28).
[ Note
:
Function need not meet the requirements of Cpp17CopyConstructible (Table 29).
— 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 meets 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
#
Preconditions: Function meets 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 meets 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<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirectly_­unary_­invocable<projected<I, Proj>> Fun> constexpr ranges::for_each_result<I, Fun> ranges::for_each(I first, S last, Fun f, Proj proj = {}); template<input_­range R, class Proj = identity, indirectly_­unary_­invocable<projected<iterator_t<R>, Proj>> Fun> constexpr ranges::for_each_result<borrowed_iterator_t<R>, Fun> ranges::for_each(R&& r, Fun f, Proj proj = {});
11
#
Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, last), starting from first and proceeding to last - 1.
[ Note
:
If the result of invoke(proj, *i) is a mutable reference, f may apply non-constant functions.
— end note
 ]
12
#
Returns: {last, std​::​move(f)}.
13
#
Complexity: Applies f and proj exactly last - first times.
14
#
Remarks: If f returns a result, the result is ignored.
15
#
[ Note
:
The overloads in namespace ranges require Fun to model copy_­constructible.
— end note
 ]
🔗
template<class InputIterator, class Size, class Function> constexpr InputIterator for_each_n(InputIterator first, Size n, Function f);
16
#
Mandates: The type Size is convertible to an integral type ([conv.integral], [class.conv]).
17
#
Preconditions: Function meets the Cpp17MoveConstructible requirements.
[ Note
:
Function need not meet the requirements of Cpp17CopyConstructible.
— end note
 ]
18
#
Preconditions: n >= 0 is true.
19
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n) in order.
[ Note
:
If the type of first meets the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
20
#
Returns: first + n.
21
#
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);
22
#
Mandates: The type Size is convertible to an integral type ([conv.integral], [class.conv]).
23
#
Preconditions: Function meets the Cpp17CopyConstructible requirements.
24
#
Preconditions: n >= 0 is true.
25
#
Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n).
[ Note
:
If the type of first meets the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.
— end note
 ]
26
#
Returns: first + n.
27
#
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.
🔗
template<input_iterator I, class Proj = identity, indirectly_­unary_­invocable<projected<I, Proj>> Fun> constexpr ranges::for_each_n_result<I, Fun> ranges::for_each_n(I first, iter_difference_t<I> n, Fun f, Proj proj = {});
28
#
Preconditions: n >= 0 is true.
29
#
Effects: Calls invoke(f, invoke(proj, *i)) for every iterator i in the range [first, first + n) in order.
[ Note
:
If the result of invoke(proj, *i) is a mutable reference, f may apply non-constant functions.
— end note
 ]
30
#
Returns: {first + n, std​::​move(f)}.
31
#
Remarks: If f returns a result, the result is ignored.
32
#
[ Note
:
The overload in namespace ranges requires Fun to model copy_­constructible.
— end note
 ]

25.6.5 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); template<input_­iterator I, sentinel_­for<I> S, class T, class Proj = identity> requires indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T*> constexpr I ranges::find(I first, S last, const T& value, Proj proj = {}); template<input_­range R, class T, class Proj = identity> requires indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*> constexpr borrowed_iterator_t<R> ranges::find(R&& r, const T& value, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr I ranges::find_if(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr borrowed_iterator_t<R> ranges::find_if(R&& r, Pred pred, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr I ranges::find_if_not(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr borrowed_iterator_t<R> ranges::find_if_not(R&& r, Pred pred, Proj proj = {});
1
#
Let E be:
  • (1.1)
    *i == value for find;
  • (1.2)
    pred(*i) != false for find_­if;
  • (1.3)
    pred(*i) == false for find_­if_­not;
  • (1.4)
    bool(invoke(proj, *i) == value) for ranges​::​find;
  • (1.5)
    bool(invoke(pred, invoke(proj, *i))) for ranges​::​find_­if;
  • (1.6)
    bool(!invoke(pred, invoke(proj, *i))) for ranges​::​find_­if_­not.
2
#
Returns: The first iterator i in the range [first, last) for which E is true.
Returns last if no such iterator is found.
3
#
Complexity: At most last - first applications of the corresponding predicate and any projection.

25.6.6 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); template<forward_­iterator I1, sentinel_­for<I1> S1, forward_­iterator I2, sentinel_­for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<I1, I2, Pred, Proj1, Proj2> constexpr subrange<I1> ranges::find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<forward_­range R1, forward_­range R2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2> constexpr borrowed_subrange_t<R1> ranges::find_end(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let:
  • (1.1)
    pred be equal_­to{} for the overloads with no parameter pred;
  • (1.2)
    E be:
    • (1.2.1)
      pred(*(i + n), *(first2 + n)) for the overloads in namespace std;
    • (1.2.2)
      invoke(pred, invoke(proj1, *(i + n)), invoke(proj2, *(first2 + n))) for the overloads in namespace ranges;
  • (1.3)
    i be last1 if [first2, last2) is empty, or if (last2 - first2) > (last1 - first1) is true, or if there is no iterator in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n < (last2 - first2), E is true. Otherwise i is the last such iterator in [first1, last1 - (last2 - first2)).
2
#
Returns:
  • (2.1)
    i for the overloads in namespace std.
  • (2.2)
    {i, i + (i == last1 ? 0 : last2 - first2)} for the overloads in namespace ranges.
3
#
Complexity: At most (last2 - first2) * (last1 - first1 - (last2 - first2) + 1) applications of the corresponding predicate and any projections.

25.6.7 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); template<input_­iterator I1, sentinel_­for<I1> S1, forward_­iterator I2, sentinel_­for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<I1, I2, Pred, Proj1, Proj2> constexpr I1 ranges::find_first_of(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, forward_­range R2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2> constexpr borrowed_iterator_t<R1> ranges::find_first_of(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let E be:
  • (1.1)
    *i == *j for the overloads with no parameter pred;
  • (1.2)
    pred(*i, *j) != false for the overloads with a parameter pred and no parameter proj1;
  • (1.3)
    bool(invoke(pred, invoke(proj1, *i), invoke(proj2, *j))) for the overloads with parameters pred and proj1.
2
#
Effects: Finds an element that matches one of a set of values.
3
#
Returns: The first iterator i in the range [first1, last1) such that for some iterator j in the range [first2, last2) E holds.
Returns last1 if [first2, last2) is empty or if no such iterator is found.
4
#
Complexity: At most (last1-first1) * (last2-first2) applications of the corresponding predicate and any projections.

25.6.8 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); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­binary_­predicate<projected<I, Proj>, projected<I, Proj>> Pred = ranges::equal_to> constexpr I ranges::adjacent_find(I first, S last, Pred pred = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­binary_­predicate<projected<iterator_t<R>, Proj>, projected<iterator_t<R>, Proj>> Pred = ranges::equal_to> constexpr borrowed_iterator_t<R> ranges::adjacent_find(R&& r, Pred pred = {}, Proj proj = {});
1
#
Let E be:
  • (1.1)
    *i == *(i + 1) for the overloads with no parameter pred;
  • (1.2)
    pred(*i, *(i + 1)) != false for the overloads with a parameter pred and no parameter proj;
  • (1.3)
    bool(invoke(pred, invoke(proj, *i), invoke(proj, *(i + 1)))) for the overloads with both parameters pred and proj.
2
#
Returns: The first iterator i such that both i and i + 1 are in the range [first, last) for which E holds.
Returns last if no such iterator is found.
3
#
Complexity: For the overloads with no ExecutionPolicy, exactly
applications of the corresponding predicate, where i is adjacent_­find's return value.
For the overloads with an ExecutionPolicy, applications of the corresponding predicate, and no more than twice as many applications of any projection.

25.6.9 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); template<input_­iterator I, sentinel_­for<I> S, class T, class Proj = identity> requires indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T*> constexpr iter_difference_t<I> ranges::count(I first, S last, const T& value, Proj proj = {}); template<input_­range R, class T, class Proj = identity> requires indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*> constexpr range_difference_t<R> ranges::count(R&& r, const T& value, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr iter_difference_t<I> ranges::count_if(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr range_difference_t<R> ranges::count_if(R&& r, Pred pred, Proj proj = {});
1
#
Let E be:
  • (1.1)
    *i == value for the overloads with no parameter pred or proj;
  • (1.2)
    pred(*i) != false for the overloads with a parameter pred but no parameter proj;
  • (1.3)
    invoke(proj, *i) == value for the overloads with a parameter proj but no parameter pred;
  • (1.4)
    bool(invoke(pred, invoke(proj, *i))) for the overloads with both parameters proj and pred.
2
#
Effects: Returns the number of iterators i in the range [first, last) for which E holds.
3
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.

25.6.10 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<I1, I2, Pred, Proj1, Proj2> constexpr ranges::mismatch_result<I1, I2> ranges::mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2> constexpr ranges::mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>> ranges::mismatch(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let last2 be first2 + (last1 - first1) for the overloads with no parameter last2 or r2.
2
#
Let E be:
  • (2.1)
    !(*(first1 + n) == *(first2 + n)) for the overloads with no parameter pred;
  • (2.2)
    pred(*(first1 + n), *(first2 + n)) == false for the overloads with a parameter pred and no parameter proj1;
  • (2.3)
    !invoke(pred, invoke(proj1, *(first1 + n)), invoke(proj2, *(first2 + n))) for the overloads with both parameters pred and proj1.
3
#
Let N be .
4
#
Returns: { first1 + n, first2 + n }, where n is the smallest integer in [0, N) such that E holds, or N if no such integer exists.
5
#
Complexity: At most N applications of the corresponding predicate and any projections.

25.6.11 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<I1, I2, Pred, Proj1, Proj2> constexpr bool ranges::equal(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2> constexpr bool ranges::equal(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let:
  • (1.1)
    last2 be first2 + (last1 - first1) for the overloads with no parameter last2 or r2;
  • (1.2)
    pred be equal_­to{} for the overloads with no parameter pred;
  • (1.3)
    E be:
    • (1.3.1)
      pred(*i, *(first2 + (i - first1))) for the overloads with no parameter proj1;
    • (1.3.2)
      invoke(pred, invoke(proj1, *i), invoke(proj2, *(first2 + (i - first1)))) for the overloads with parameter proj1.
2
#
Returns: If last1 - first1 != last2 - first2, return false.
Otherwise return true if E holds for every iterator i in the range [first1, last1) Otherwise, returns false.
3
#
Complexity: If the types of first1, last1, first2, and last2: and last1 - first1 != last2 - first2, then no applications of the corresponding predicate and each projection; otherwise,
  • (3.3)
    For the overloads with no ExecutionPolicy, at most applications of the corresponding predicate and any projections.
  • (3.4)
    For the overloads with an ExecutionPolicy, applications of the corresponding predicate.

25.6.12 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
#
Mandates: ForwardIterator1 and ForwardIterator2 have the same value type.
2
#
Preconditions: The comparison function is an equivalence relation.
3
#
Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.
4
#
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.
5
#
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.
🔗
template<forward_­iterator I1, sentinel_­for<I1> S1, forward_­iterator I2, sentinel_­for<I2> S2, class Proj1 = identity, class Proj2 = identity, indirect_­equivalence_­relation<projected<I1, Proj1>, projected<I2, Proj2>> Pred = ranges::equal_to> constexpr bool ranges::is_permutation(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<forward_­range R1, forward_­range R2, class Proj1 = identity, class Proj2 = identity, indirect_­equivalence_­relation<projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to> constexpr bool ranges::is_permutation(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
6
#
Returns: If last1 - first1 != last2 - first2, return false.
Otherwise return true if there exists a permutation of the elements in the range [first2, last2), bounded by [pfirst, plast), such that ranges​::​equal(first1, last1, pfirst, plast, pred, proj1, proj2) returns true; otherwise, returns false.
7
#
Complexity: No applications of the corresponding predicate and projections if:
  • (7.1)
    S1 and I1 model sized_­sentinel_­for<S1, I1>,
  • (7.2)
    S2 and I2 model sized_­sentinel_­for<S2, I2>, and
  • (7.3)
    last1 - first1 != last2 - first2.
Otherwise, exactly last1 - first1 applications of the corresponding predicate and projections if ranges​::​equal(​first1, last1, first2, last2, pred, proj1, proj2) would return true; otherwise, at worst , where N has the value last1 - first1.

25.6.13 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
#
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.
2
#
Complexity: At most (last1 - first1) * (last2 - first2) applications of the corresponding predicate.
🔗
template<forward_­iterator I1, sentinel_­for<I1> S1, forward_­iterator I2, sentinel_­for<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<I1, I2, Pred, Proj1, Proj2> constexpr subrange<I1> ranges::search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<forward_­range R1, forward_­range R2, class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity> requires indirectly_­comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2> constexpr borrowed_subrange_t<R1> ranges::search(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
3
#
Returns:
  • (3.1)
    {i, i + (last2 - first2)}, where i is the first iterator in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n less than last2 - first2 the condition 
    bool(invoke(pred, invoke(proj1, *(i + n)), invoke(proj2, *(first2 + n))))
    is true.
  • (3.2)
    Returns {last1, last1} if no such iterator exists.
4
#
Complexity: At most (last1 - first1) * (last2 - first2) applications of the corresponding predicate and projections.
🔗
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);
5
#
Mandates: The type Size is convertible to an integral type ([conv.integral], [class.conv]).
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<forward_­iterator I, sentinel_­for<I> S, class T, class Pred = ranges::equal_to, class Proj = identity> requires indirectly_­comparable<I, const T*, Pred, Proj> constexpr subrange<I> ranges::search_n(I first, S last, iter_difference_t<I> count, const T& value, Pred pred = {}, Proj proj = {}); template<forward_­range R, class T, class Pred = ranges::equal_to, class Proj = identity> requires indirectly_­comparable<iterator_t<R>, const T*, Pred, Proj> constexpr borrowed_subrange_t<R> ranges::search_n(R&& r, range_difference_t<R> count, const T& value, Pred pred = {}, Proj proj = {});
8
#
Returns: {i, i + count} where i is the first iterator in the range [first, last - count) such that for every non-negative integer n less than count, the following condition holds: invoke(pred, invoke(proj, *(i + n)), value).
Returns {last, last} if no such iterator is found.
9
#
Complexity: At most last - first applications of the corresponding predicate and projection.
🔗
template<class ForwardIterator, class Searcher> constexpr ForwardIterator search(ForwardIterator first, ForwardIterator last, const Searcher& searcher);
10
#
Effects: Equivalent to: return searcher(first, last).first;
11
#
Remarks: Searcher need not meet the Cpp17CopyConstructible requirements.

25.7 Mutating sequence operations [alg.modifying.operations]

25.7.1 Copy [alg.copy]

🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator copy(InputIterator first, InputIterator last, OutputIterator result); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O> requires indirectly_­copyable<I, O> constexpr ranges::copy_result<I, O> ranges::copy(I first, S last, O result); template<input_­range R, weakly_­incrementable O> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::copy_result<borrowed_iterator_t<R>, O> ranges::copy(R&& r, O result);
1
#
Let N be last - first.
2
#
Preconditions: result is not in the range [first, last).
3
#
Effects: Copies elements in the range [first, last) into the range [result, result + N) starting from first and proceeding to last.
For each non-negative integer , performs *(result + n) = *(first + n).
4
#
Returns:
  • (4.1)
    result + N for the overload in namespace std.
  • (4.2)
    {last, result + N} for the overloads in namespace ranges.
5
#
Complexity: Exactly N assignments.
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 copy(ExecutionPolicy&& policy, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
6
#
Preconditions: The ranges [first, last) and [result, result + (last - first)) do not overlap.
7
#
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).
8
#
Returns: result + (last - first).
9
#
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); template<input_­iterator I, weakly_­incrementable O> requires indirectly_­copyable<I, O> constexpr ranges::copy_n_result<I, O> ranges::copy_n(I first, iter_difference_t<I> n, O result);
10
#
Let N be .
11
#
Mandates: The type Size is convertible to an integral type ([conv.integral], [class.conv]).
12
#
Effects: For each non-negative integer , performs *(result + i) = *(first + i).
13
#
Returns:
  • (13.1)
    result + N for the overloads in namespace std.
  • (13.2)
    {first + N, result + N} for the overload in namespace ranges.
14
#
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); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires indirectly_­copyable<I, O> constexpr ranges::copy_if_result<I, O> ranges::copy_if(I first, S last, O result, Pred pred, Proj proj = {}); template<input_­range R, weakly_­incrementable O, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::copy_if_result<borrowed_iterator_t<R>, O> ranges::copy_if(R&& r, O result, Pred pred, Proj proj = {});
15
#
Let E be:
  • (15.1)
    bool(pred(*i)) for the overloads in namespace std;
  • (15.2)
    bool(invoke(pred, invoke(proj, *i))) for the overloads in namespace ranges,
and N be the number of iterators i in the range [first, last) for which the condition E holds.
16
#
Preconditions: The ranges [first, last) and [result, result + (last - first)) do 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 28).
— end note
 ]
17
#
Effects: Copies all of the elements referred to by the iterator i in the range [first, last) for which E is true.
18
#
Returns:
  • (18.1)
    result + N for the overloads in namespace std.
  • (18.2)
    {last, result + N} for the overloads in namespace ranges.
19
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.
20
#
Remarks: Stable ([algorithm.stable]).
🔗
template<class BidirectionalIterator1, class BidirectionalIterator2> constexpr BidirectionalIterator2 copy_backward(BidirectionalIterator1 first, BidirectionalIterator1 last, BidirectionalIterator2 result); template<bidirectional_­iterator I1, sentinel_­for<I1> S1, bidirectional_­iterator I2> requires indirectly_­copyable<I1, I2> constexpr ranges::copy_backward_result<I1, I2> ranges::copy_backward(I1 first, S1 last, I2 result); template<bidirectional_­range R, bidirectional_­iterator I> requires indirectly_­copyable<iterator_t<R>, I> constexpr ranges::copy_backward_result<borrowed_iterator_t<R>, I> ranges::copy_backward(R&& r, I result);
21
#
Let N be last - first.
22
#
Preconditions: result is not in the range (first, last].
23
#
Effects: Copies elements in the range [first, last) into the range [result - N, result) starting from last - 1 and proceeding to first.231
For each positive integer , performs *(result - n) = *(last - n).
24
#
Returns:
  • (24.1)
    result - N for the overload in namespace std.
  • (24.2)
    {last, result - N} for the overloads in namespace ranges.
25
#
Complexity: Exactly N assignments.
231)
copy_­backward should be used instead of copy when last is in the range [result - N, result).
⮥

25.7.2 Move [alg.move]

🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator move(InputIterator first, InputIterator last, OutputIterator result); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O> requires indirectly_­movable<I, O> constexpr ranges::move_result<I, O> ranges::move(I first, S last, O result); template<input_­range R, weakly_­incrementable O> requires indirectly_­movable<iterator_t<R>, O> constexpr ranges::move_result<borrowed_iterator_t<R>, O> ranges::move(R&& r, O result);
1
#
Let E be
  • (1.1)
    std​::​move(*(first + n)) for the overload in namespace std;
  • (1.2)
    ranges​::​iter_­move(first + n) for the overloads in namespace ranges.
Let N be last - first.
2
#
Preconditions: result is not in the range [first, last).
3
#
Effects: Moves elements in the range [first, last) into the range [result, result + N) starting from first and proceeding to last.
For each non-negative integer , performs *(result + n) = E.
4
#
Returns:
  • (4.1)
    result + N for the overload in namespace std.
  • (4.2)
    {last, result + N} for the overloads in namespace ranges.
5
#
Complexity: Exactly N assignments.
🔗
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> ForwardIterator2 move(ExecutionPolicy&& policy, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result);
6
#
Let N be last - first.
7
#
Preconditions: The ranges [first, last) and [result, result + N) do not overlap.
8
#
Effects: Moves elements in the range [first, last) into the range [result, result + N).
For each non-negative integer , performs *(result + n) = std​::​​move(*(first + n)).
9
#
Returns: result + N.
10
#
Complexity: Exactly N assignments.
🔗
template<class BidirectionalIterator1, class BidirectionalIterator2> constexpr BidirectionalIterator2 move_backward(BidirectionalIterator1 first, BidirectionalIterator1 last, BidirectionalIterator2 result); template<bidirectional_­iterator I1, sentinel_­for<I1> S1, bidirectional_­iterator I2> requires indirectly_­movable<I1, I2> constexpr ranges::move_backward_result<I1, I2> ranges::move_backward(I1 first, S1 last, I2 result); template<bidirectional_­range R, bidirectional_­iterator I> requires indirectly_­movable<iterator_t<R>, I> constexpr ranges::move_backward_result<borrowed_iterator_t<R>, I> ranges::move_backward(R&& r, I result);
11
#
Let E be
  • (11.1)
    std​::​move(*(last - n)) for the overload in namespace std;
  • (11.2)
    ranges​::​iter_­move(last - n) for the overloads in namespace ranges.
Let N be last - first.
12
#
Preconditions: result is not in the range (first, last].
13
#
Effects: Moves elements in the range [first, last) into the range [result - N, result) starting from last - 1 and proceeding to first.232
For each positive integer , performs *(result - n) = E.
14
#
Returns:
  • (14.1)
    result - N for the overload in namespace std.
  • (14.2)
    {last, result - N} for the overloads in namespace ranges.
15
#
Complexity: Exactly N assignments.
232)
move_­backward should be used instead of move when last is in the range [result - N, result).
⮥

25.7.3 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2> requires indirectly_­swappable<I1, I2> constexpr ranges::swap_ranges_result<I1, I2> ranges::swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2); template<input_­range R1, input_range R2> requires indirectly_­swappable<iterator_t<R1>, iterator_t<R2>> constexpr ranges::swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>> ranges::swap_ranges(R1&& r1, R2&& r2);
1
#
Let:
  • (1.1)
    last2 be first2 + (last1 - first1) for the overloads with no parameter named last2;
  • (1.2)
    M be .
2
#
Preconditions: The two ranges [first1, last1) and [first2, last2) do not overlap.
For the overloads in namespace std, *(first1 + n) is swappable with ([swappable.requirements]) *(first2 + n).
3
#
Effects: For each non-negative integer performs:
  • (3.1)
    swap(*(first1 + n), *(first2 + n)) for the overloads in namespace std;
  • (3.2)
    ranges​::​iter_­swap(first1 + n, first2 + n) for the overloads in namespace ranges.
4
#
Returns:
  • (4.1)
    last2 for the overloads in namespace std.
  • (4.2)
    {first1 + M, first2 + M} for the overloads in namespace ranges.
5
#
Complexity: Exactly M swaps.
🔗
template<class ForwardIterator1, class ForwardIterator2> constexpr void iter_swap(ForwardIterator1 a, ForwardIterator2 b);
6
#
Preconditions: a and b are dereferenceable.
*a is swappable with ([swappable.requirements]) *b.
7
#
Effects: As if by swap(*a, *b).

25.7.4 Transform [alg.transform]

🔗
template<class InputIterator, class OutputIterator, class UnaryOperation> constexpr OutputIterator transform(InputIterator first1, InputIterator last1, OutputIterator result, UnaryOperation op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class UnaryOperation> ForwardIterator2 transform(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, 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); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O, copy_­constructible F, class Proj = identity> requires indirectly_­writable<O, indirect_result_t<F&, projected<I, Proj>>> constexpr ranges::unary_transform_result<I, O> ranges::transform(I first1, S last1, O result, F op, Proj proj = {}); template<input_­range R, weakly_­incrementable O, copy_­constructible F, class Proj = identity> requires indirectly_­writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>> constexpr ranges::unary_transform_result<borrowed_iterator_t<R>, O> ranges::transform(R&& r, O result, F op, Proj proj = {}); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, copy_­constructible F, class Proj1 = identity, class Proj2 = identity> requires indirectly_­writable<O, indirect_result_t<F&, projected<I1, Proj1>, projected<I2, Proj2>>> constexpr ranges::binary_transform_result<I1, I2, O> ranges::transform(I1 first1, S1 last1, I2 first2, S2 last2, O result, F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, copy_­constructible F, class Proj1 = identity, class Proj2 = identity> requires indirectly_­writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>>> constexpr ranges::binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O> ranges::transform(R1&& r1, R2&& r2, O result, F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let:
  • (1.1)
    last2 be first2 + (last1 - first1) for the overloads with parameter first2 but no parameter last2;
  • (1.2)
    N be last1 - first1 for unary transforms, or for binary transforms;
  • (1.3)
    E be
    • (1.3.1)
      op(*(first1 + (i - result))) for unary transforms defined in namespace std;
    • (1.3.2)
      binary_­op(*(first1 + (i - result)), *(first2 + (i - result))) for binary transforms defined in namespace std;
    • (1.3.3)
      invoke(op, invoke(proj, *(first1 + (i - result)))) for unary transforms defined in namespace ranges;
    • (1.3.4)
      invoke(binary_­op, invoke(proj1, *(first1 + (i - result))), invoke(proj2,
      *(first2 + (i - result))))       for binary transforms defined in namespace ranges.
2
#
Preconditions: op and binary_­op do not invalidate iterators or subranges, nor modify elements in the ranges
3
#
Effects: Assigns through every iterator i in the range [result, result + N) a new corresponding value equal to E.
4
#
Returns:
  • (4.1)
    result + N for the overloads defined in namespace std.
  • (4.2)
    {first1 + N, result + N} for unary transforms defined in namespace ranges.
  • (4.3)
    {first1 + N, first2 + N, result + N} for binary transforms defined in namespace ranges.
5
#
Complexity: Exactly N applications of op or binary_­op, and any projections.
This requirement also applies to the overload with an ExecutionPolicy.
6
#
Remarks: result may be equal to first1 or first2.
233)
The use of fully closed ranges is intentional.
⮥

25.7.5 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); template<input_­iterator I, sentinel_­for<I> S, class T1, class T2, class Proj = identity> requires indirectly_­writable<I, const T2&> && indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T1*> constexpr I ranges::replace(I first, S last, const T1& old_value, const T2& new_value, Proj proj = {}); template<input_­range R, class T1, class T2, class Proj = identity> requires indirectly_­writable<iterator_t<R>, const T2&> && indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*> constexpr borrowed_iterator_t<R> ranges::replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, class T, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires indirectly_­writable<I, const T&> constexpr I ranges::replace_if(I first, S last, Pred pred, const T& new_value, Proj proj = {}); template<input_­range R, class T, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires indirectly_­writable<iterator_t<R>, const T&> constexpr borrowed_iterator_t<R> ranges::replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});
1
#
Let E be
  • (1.1)
    bool(*i == old_­value) for replace;
  • (1.2)
    bool(pred(*i)) for replace_­if;
  • (1.3)
    bool(invoke(proj, *i) == old_­value) for ranges​::​replace;
  • (1.4)
    bool(invoke(pred, invoke(proj, *i))) for ranges​::​replace_­if.
2
#
Mandates: new_­value is writable ([iterator.requirements.general]) to first.
3
#
Effects: Substitutes elements referred by the iterator i in the range [first, last) with new_­value, when E is true.
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.
🔗
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); template<input_­iterator I, sentinel_­for<I> S, class T1, class T2, output_­iterator<const T2&> O, class Proj = identity> requires indirectly_­copyable<I, O> && indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T1*> constexpr ranges::replace_copy_result<I, O> ranges::replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value, Proj proj = {}); template<input_­range R, class T1, class T2, output_­iterator<const T2&> O, class Proj = identity> requires indirectly_­copyable<iterator_t<R>, O> && indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T1*> constexpr ranges::replace_copy_result<borrowed_iterator_t<R>, O> ranges::replace_copy(R&& r, O result, const T1& old_value, const T2& new_value, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, class T, output_­iterator<const T&> O, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires indirectly_­copyable<I, O> constexpr ranges::replace_copy_if_result<I, O> ranges::replace_copy_if(I first, S last, O result, Pred pred, const T& new_value, Proj proj = {}); template<input_­range R, class T, output_­iterator<const T&> O, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::replace_copy_if_result<borrowed_iterator_t<R>, O> ranges::replace_copy_if(R&& r, O result, Pred pred, const T& new_value, Proj proj = {});
6
#
Let E be
  • (6.1)
    bool(*(first + (i - result)) == old_­value) for replace_­copy;
  • (6.2)
    bool(pred(*(first + (i - result)))) for replace_­copy_­if;
  • (6.3)
    bool(invoke(proj, *(first + (i - result))) == old_­value) for ranges​::​replace_­copy;
  • (6.4)
    bool(invoke(pred, invoke(proj, *(first + (i - result))))) for ranges​::​replace_­copy_­if.
7
#
Mandates: The results of the expressions *first and new_­value are writable ([iterator.requirements.general]) to result.
8
#
Preconditions: The ranges [first, last) and [result, result + (last - first)) do not overlap.
9
#
Effects: Assigns through every iterator i in the range [result, result + (last - first)) a new corresponding value
  • (9.1)
    new_­value if E is true or
  • (9.2)
    *(first + (i - result)) otherwise.
10
#
Returns:
  • (10.1)
    result + (last - first) for the overloads in namespace std.
  • (10.2)
    {last, result + (last - first)} for the overloads in namespace ranges.
11
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.

25.7.6 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); template<class T, output_­iterator<const T&> O, sentinel_­for<O> S> constexpr O ranges::fill(O first, S last, const T& value); template<class T, output_­range<const T&> R> constexpr borrowed_iterator_t<R> ranges::fill(R&& r, const T& value); template<class T, output_­iterator<const T&> O> constexpr O ranges::fill_n(O first, iter_difference_t<O> n, const T& value);
1
#
Let N be for the fill_­n algorithms, and last - first for the fill algorithms.
2
#
Mandates: The expression value is writable ([iterator.requirements.general]) to the output iterator.
The type Size is convertible to an integral type ([conv.integral], [class.conv]).
3
#
Effects: Assigns value through all the iterators in the range [first, first + N).
4
#
Returns: first + N.
5
#
Complexity: Exactly N assignments.

25.7.7 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); template<input_­or_­output_­iterator O, sentinel_­for<O> S, copy_­constructible F> requires invocable<F&> && indirectly_­writable<O, invoke_result_t<F&>> constexpr O ranges::generate(O first, S last, F gen); template<class R, copy_­constructible F> requires invocable<F&> && output_­range<R, invoke_result_t<F&>> constexpr borrowed_iterator_t<R> ranges::generate(R&& r, F gen); template<input_­or_­output_­iterator O, copy_­constructible F> requires invocable<F&> && indirectly_­writable<O, invoke_result_t<F&>> constexpr O ranges::generate_n(O first, iter_difference_t<O> n, F gen);
1
#
Let N be for the generate_­n algorithms, and last - first for the generate algorithms.
2
#
Mandates: Size is convertible to an integral type ([conv.integral], [class.conv]).
3
#
Effects: Assigns the result of successive evaluations of gen() through each iterator in the range [first, first + N).
4
#
Returns: first + N.
5
#
Complexity: Exactly N evaluations of gen() and assignments.

25.7.8 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); template<permutable I, sentinel_­for<I> S, class T, class Proj = identity> requires indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T*> constexpr subrange<I> ranges::remove(I first, S last, const T& value, Proj proj = {}); template<forward_­range R, class T, class Proj = identity> requires permutable<iterator_t<R>> && indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*> constexpr borrowed_subrange_t<R> ranges::remove(R&& r, const T& value, Proj proj = {}); template<permutable I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr subrange<I> ranges::remove_if(I first, S last, Pred pred, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires permutable<iterator_t<R>> constexpr borrowed_subrange_t<R> ranges::remove_if(R&& r, Pred pred, Proj proj = {});
1
#
Let E be
  • (1.1)
    bool(*i == value) for remove;
  • (1.2)
    bool(pred(*i)) for remove_­if;
  • (1.3)
    bool(invoke(proj, *i) == value) for ranges​::​remove;
  • (1.4)
    bool(invoke(pred, invoke(proj, *i))) for ranges​::​remove_­if.
2
#
Preconditions: For the algorithms in namespace std, the type of *first meets the Cpp17MoveAssignable requirements (Table 30).
3
#
Effects: Eliminates all the elements referred to by iterator i in the range [first, last) for which E holds.
4
#
Returns: Let j be the end of the resulting range.
Returns:
  • (4.1)
    j for the overloads in namespace std.
  • (4.2)
    {j, last} for the overloads in namespace ranges.
5
#
Remarks: Stable ([algorithm.stable]).
6
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.
7
#
[ 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); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O, class T, class Proj = identity> requires indirectly_­copyable<I, O> && indirect_­binary_­predicate<ranges::equal_to, projected<I, Proj>, const T*> constexpr ranges::remove_copy_result<I, O> ranges::remove_copy(I first, S last, O result, const T& value, Proj proj = {}); template<input_­range R, weakly_­incrementable O, class T, class Proj = identity> requires indirectly_­copyable<iterator_t<R>, O> && indirect_­binary_­predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*> constexpr ranges::remove_copy_result<borrowed_iterator_t<R>, O> ranges::remove_copy(R&& r, O result, const T& value, Proj proj = {}); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires indirectly_­copyable<I, O> constexpr ranges::remove_copy_if_result<I, O> ranges::remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {}); template<input_­range R, weakly_­incrementable O, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::remove_copy_if_result<borrowed_iterator_t<R>, O> ranges::remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});
8
#
Let E be
  • (8.1)
    bool(*i == value) for remove_­copy;
  • (8.2)
    bool(pred(*i)) for remove_­copy_­if;
  • (8.3)
    bool(invoke(proj, *i) == value) for ranges​::​remove_­copy;
  • (8.4)
    bool(invoke(pred, invoke(proj, *i))) for ranges​::​remove_­copy_­if.
9
#
Let N be the number of elements in [first, last) for which E is false.
10
#
Mandates: *first is writable ([iterator.requirements.general]) to result.
11
#
Preconditions: The ranges [first, last) and [result, result + (last - first)) do not overlap.
[ Note
:
For the overloads with an ExecutionPolicy, there may be a performance cost if iterator_­traits<ForwardIterator1>​::​value_­type does not meet the Cpp17MoveConstructible (Table 28) requirements.
— end note
 ]
12
#
Effects: Copies all the elements referred to by the iterator i in the range [first, last) for which E is false.
13
#
Returns:
  • (13.1)
    result + N, for the algorithms in namespace std.
  • (13.2)
    {last, result + N}, for the algorithms in namespace ranges.
14
#
Complexity: Exactly last - first applications of the corresponding predicate and any projection.
15
#
Remarks: Stable ([algorithm.stable]).

25.7.9 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); template<permutable I, sentinel_­for<I> S, class Proj = identity, indirect_­equivalence_­relation<projected<I, Proj>> C = ranges::equal_to> constexpr subrange<I> ranges::unique(I first, S last, C comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­equivalence_­relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to> requires permutable<iterator_t<R>> constexpr borrowed_subrange_t<R> ranges::unique(R&& r, C comp = {}, Proj proj = {});
1
#
Let pred be equal_­to{} for the overloads with no parameter pred, and let E be
  • (1.1)
    bool(pred(*(i - 1), *i)) for the overloads in namespace std;
  • (1.2)
    bool(invoke(comp, invoke(proj, *(i - 1)), invoke(proj, *i))) for the overloads in namespace ranges.
2
#
Preconditions: For the overloads in namepace std, pred is an equivalence relation and the type of *first meets the Cpp17MoveAssignable requirements (Table 30).
3
#
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 E is true.
4
#
Returns: Let j be the end of the resulting range.
Returns:
  • (4.1)
    j for the overloads in namespace std.
  • (4.2)
    {j, last} for the overloads in namespace ranges.
5
#
Complexity: For nonempty ranges, exactly (last - first) - 1 applications of the corresponding predicate and no more than twice as many applications of any projection.
🔗
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); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O, class Proj = identity, indirect_­equivalence_­relation<projected<I, Proj>> C = ranges::equal_to> requires indirectly_­copyable<I, O> && (forward_­iterator<I> || (input_­iterator<O> && same_­as<iter_value_t<I>, iter_value_t<O>>) || indirectly_­copyable_­storable<I, O>) constexpr ranges::unique_copy_result<I, O> ranges::unique_copy(I first, S last, O result, C comp = {}, Proj proj = {}); template<input_­range R, weakly_­incrementable O, class Proj = identity, indirect_­equivalence_­relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to> requires indirectly_­copyable<iterator_t<R>, O> && (forward_­iterator<iterator_t<R>> || (input_­iterator<O> && same_as<range_value_t<R>, iter_value_t<O>>) || indirectly_­copyable_­storable<iterator_t<R>, O>) constexpr ranges::unique_copy_result<borrowed_iterator_t<R>, O> ranges::unique_copy(R&& r, O result, C comp = {}, Proj proj = {});
6
#
Let pred be equal_­to{} for the overloads in namespace std with no parameter pred, and let E be
  • (6.1)
    bool(pred(*i, *(i - 1))) for the overloads in namespace std;
  • (6.2)
    bool(invoke(comp, invoke(proj, *i), invoke(proj, *(i - 1)))) for the overloads in namespace ranges.
7
#
Mandates: *first is writable ([iterator.requirements.general]) to result.
8
#
Preconditions:
  • (8.1)
    The ranges [first, last) and [result, result+(last-first)) do not overlap.
  • (8.2)
    For the overloads in namespace std:
    • (8.2.1)
      The comparison function is an equivalence relation.
    • (8.2.2)
      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 meets the Cpp17CopyAssignable (Table 31) requirements. Otherwise, T meets both the Cpp17CopyConstructible (Table 29) and Cpp17CopyAssignable requirements.
      [ Note
      : For the overloads with an ExecutionPolicy, there may be a performance cost if the value type of ForwardIterator1 does not meet both the Cpp17CopyConstructible and Cpp17CopyAssignable requirements. — end note
       ]
9
#
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 E holds.
10
#
Returns:
  • (10.1)
    result + N for the overloads in namespace std.
  • (10.2)
    {last, result + N} for the overloads in namespace ranges.
11
#
Complexity: Exactly last - first - 1 applications of the corresponding predicate and no more than twice as many applications of any projection.

25.7.10 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); template<bidirectional_­iterator I, sentinel_­for<I> S> requires permutable<I> constexpr I ranges::reverse(I first, S last); template<bidirectional_­range R> requires permutable<iterator_t<R>> constexpr borrowed_iterator_t<R> ranges::reverse(R&& r);
1
#
Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).
2
#
Effects: For each non-negative integer i < (last - first) / 2, applies std​::​iter_­swap, or ranges​::​​iter_­swap for the overloads in namespace ranges, to all pairs of iterators first + i, (last - i) - 1.
3
#
Returns: last for the overloads in namespace ranges.
4
#
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); template<bidirectional_­iterator I, sentinel_­for<I> S, weakly_­incrementable O> requires indirectly_­copyable<I, O> constexpr ranges::reverse_copy_result<I, O> ranges::reverse_copy(I first, S last, O result); template<bidirectional_­range R, weakly_­incrementable O> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::reverse_copy_result<borrowed_iterator_t<R>, O> ranges::reverse_copy(R&& r, O result);
5
#
Let N be last - first.
6
#
Preconditions: The ranges [first, last) and [result, result + N) do not overlap.
7
#
Effects: Copies the range [first, last) to the range [result, result + N) such that for every non-negative integer i < N the following assignment takes place: *(result + N - 1 - i) = *(first + i).
8
#
Returns:
  • (8.1)
    result + N for the overloads in namespace std.
  • (8.2)
    {last, result + N} for the overloads in namespace ranges.
9
#
Complexity: Exactly N assignments.

25.7.11 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); template<permutable I, sentinel_­for<I> S> constexpr subrange<I> ranges::rotate(I first, I middle, S last);
1
#
Preconditions: [first, middle) and [middle, last) are valid ranges.
For the overloads in namespace std, ForwardIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) 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).
[ Note
:
This is a left rotate.
— end note
 ]
3
#
Returns:
  • (3.1)
    first + (last - middle) for the overloads in namespace std.
  • (3.2)
    {first + (last - middle), last} for the overload in namespace ranges.
4
#
Complexity: At most last - first swaps.
🔗
template<forward_­range R> requires permutable<iterator_t<R>> constexpr borrowed_subrange_t<R> ranges::rotate(R&& r, iterator_t<R> middle);
5
#
Effects: Equivalent to: return ranges​::​rotate(ranges​::​begin(r), middle, ranges​::​end(r));
🔗
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); template<forward_­iterator I, sentinel_­for<I> S, weakly_­incrementable O> requires indirectly_­copyable<I, O> constexpr ranges::rotate_copy_result<I, O> ranges::rotate_copy(I first, I middle, S last, O result);
6
#
Let N be last - first.
7
#
Preconditions: [first, middle) and [middle, last) are valid ranges.
The ranges [first, last) and [result, result + N) do not overlap.
8
#
Effects: Copies the range [first, last) to the range [result, result + N) such that for each non-negative integer the following assignment takes place: *(result + i) = *(first + (i + (middle - first)) % N).
9
#
Returns:
  • (9.1)
    result + N for the overloads in namespace std.
  • (9.2)
    {last, result + N} for the overload in namespace ranges.
10
#
Complexity: Exactly N assignments.
🔗
template<forward_­range R, weakly_­incrementable O> requires indirectly_­copyable<iterator_t<R>, O> constexpr ranges::rotate_copy_result<borrowed_iterator_t<R>, O> ranges::rotate_copy(R&& r, iterator_t<R> middle, O result);
11
#
Effects: Equivalent to: 
return ranges::rotate_copy(ranges::begin(r), middle, ranges::end(r), result);

25.7.12 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); template<input_iterator I, sentinel_for<I> S, weakly_­incrementable O, class Gen> requires (forward_iterator<I> || random_access_iterator<O>) && indirectly_­copyable<I, O> && uniform_random_bit_generator<remove_reference_t<Gen>> O ranges::sample(I first, S last, O out, iter_difference_t<I> n, Gen&& g); template<input_­range R, weakly_­incrementable O, class Gen> requires (forward_range<R> || random_access_iterator<O>) && indirectly_­copyable<iterator_t<R>, O> && uniform_random_bit_generator<remove_reference_t<Gen>> O ranges::sample(R&& r, O out, range_difference_t<R> n, Gen&& g);
1
#
Mandates: For the overload in namespace std, Distance is an integer type and *first is writable ([iterator.requirements.general]) to out.
2
#
Preconditions: out is not in the range [first, last).
For the overload in namespace std:
3
#
Effects: Copies 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
 ]
4
#
Returns: The end of the resulting sample range.
5
#
Complexity: .
6
#
Remarks:
  • (6.1)
    For the overload in namespace std, stable if and only if PopulationIterator meets the Cpp17ForwardIterator requirements. For the first overload in namespace ranges, stable if and only if I models forward_­iterator.
  • (6.2)
    To the extent that the implementation of this function makes use of random numbers, the object g serves as the implementation's source of randomness.

25.7.13 Shuffle [alg.random.shuffle]

🔗
template<class RandomAccessIterator, class UniformRandomBitGenerator> void shuffle(RandomAccessIterator first, RandomAccessIterator last, UniformRandomBitGenerator&& g); template<random_­access_­iterator I, sentinel_­for<I> S, class Gen> requires permutable<I> && uniform_­random_­bit_­generator<remove_reference_t<Gen>> I ranges::shuffle(I first, S last, Gen&& g); template<random_­access_­range R, class Gen> requires permutable<iterator_t<R>> && uniform_­random_­bit_­generator<remove_reference_t<Gen>> borrowed_iterator_t<R> ranges::shuffle(R&& r, Gen&& g);
1
#
Preconditions: For the overload in namespace std:
2
#
Effects: Permutes the elements in the range [first, last) such that each possible permutation of those elements has equal probability of appearance.
3
#
Returns: last for the overloads in namespace ranges.
4
#
Complexity: Exactly (last - first) - 1 swaps.
5
#
Remarks: To the extent that the implementation of this function makes use of random numbers, the object referenced by g shall serve as the implementation's source of randomness.

25.7.14 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
#
Preconditions: n >= 0 is true.
The type of *first meets 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 < last - first, otherwise first.
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
#
Preconditions: n >= 0 is true.
The type of *first meets the Cpp17MoveAssignable requirements.
ForwardIterator meets 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 meets 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 < last - first, otherwise last.
8
#
Complexity: At most (last - first) - n assignments or swaps.

25.8 Sorting and related operations [alg.sorting]

1
#
The operations in [alg.sorting] defined directly in namespace std 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]) that meets the requirements for a template parameter named BinaryPredicate ([algorithms.requirements]).
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.
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 comp and proj for a comparator and projection comp and proj 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, 
bool(invoke(comp, invoke(proj, *(i + n)), invoke(proj, *i)))
is 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).

25.8.1 Sorting [alg.sort]

25.8.1.1 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::sort(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::sort(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Sorts the elements in the range [first, last) with respect to comp and proj.
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: Let N be last - first.
comparisons and projections.

25.8.1.2 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> I ranges::stable_sort(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> borrowed_iterator_t<R> ranges::stable_sort(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Sorts the elements in the range [first, last) with respect to comp and proj.
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: Let N be last - first.
If enough extra memory is available, comparisons.
Otherwise, at most comparisons.
In either case, twice as many projections as the number of comparisons.
6
#
Remarks: Stable ([algorithm.stable]).

25.8.1.3 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: [first, middle) and [middle, last) are valid ranges.
For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Places the first middle - first elements from the range [first, last) as sorted with respect to comp and proj into the range [first, middle).
The rest of the elements in the range [middle, last) are placed in an unspecified order.
4
#
Returns: last for the overload in namespace ranges.
5
#
Complexity: Approximately (last - first) * log(middle - first) comparisons, and twice as many projections.
🔗
template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::partial_sort(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});
6
#
Effects: Equivalent to: 
return ranges::partial_sort(ranges::begin(r), middle, ranges::end(r), comp, proj);

25.8.1.4 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); template<input_­iterator I1, sentinel_­for<I1> S1, random_­access_­iterator I2, sentinel_­for<I2> S2, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires indirectly_­copyable<I1, I2> && sortable<I2, Comp, Proj2> && indirect_­strict_­weak_­order<Comp, projected<I1, Proj1>, projected<I2, Proj2>> constexpr ranges::partial_sort_copy_result<I1, I2> ranges::partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, random_­access_­range R2, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires indirectly_­copyable<iterator_t<R1>, iterator_t<R2>> && sortable<iterator_t<R2>, Comp, Proj2> && indirect_­strict_­weak_­order<Comp, projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>> constexpr ranges::partial_sort_copy_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>> ranges::partial_sort_copy(R1&& r, R2&& result_r, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let N be .
Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.
2
#
Mandates: For the overloads in namespace std, the expression *first is writable ([iterator.requirements.general]) to result_­first.
3
#
Preconditions: For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), the type of *result_­first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
4
#
Preconditions: For iterators a1 and b1 in [first, last), and iterators x2 and y2 in [result_­first, result_­last), after evaluating the assignment *y2 = *b1, let E be the value of 
bool(invoke(comp, invoke(proj1, *a1), invoke(proj2, *y2))).
Then, after evaluating the assignment *x2 = *a1, E is equal to 
bool(invoke(comp, invoke(proj2, *x2), invoke(proj2, *y2))).
[ Note
: Writing a value from the input range into the output range does not affect how it is ordered by comp and proj1 or proj2. — end note
 ]
5
#
Effects: Places the first N elements as sorted with respect to comp and proj2 into the range [result_­first, result_­first + N).
6
#
Returns:
  • (6.1)
    result_­first + N for the overloads in namespace std.
  • (6.2)
    {last, result_­first + N} for the overloads in namespace ranges.
7
#
Complexity: Approximately (last - first) * log N comparisons, and twice as many projections.

25.8.1.5 is_­sorted [is.sorted]

🔗
template<class ForwardIterator> constexpr bool is_sorted(ForwardIterator first, ForwardIterator last);
1
#
Effects: Equivalent to: return is_­sorted_­until(first, last) == last;
🔗
template<class ExecutionPolicy, class ForwardIterator> bool is_sorted(ExecutionPolicy&& exec, ForwardIterator first, ForwardIterator last);
2
#
Effects: Equivalent to: 
return 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
#
Effects: Equivalent to: return 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
#
Effects: Equivalent to: 
return is_sorted_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last;
🔗
template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::is_sorted(I first, S last, Comp comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr bool ranges::is_sorted(R&& r, Comp comp = {}, Proj proj = {});
5
#
Effects: Equivalent to: return ranges​::​is_­sorted_­until(first, last, comp, proj) == 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); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::is_sorted_until(I first, S last, Comp comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});
6
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
7
#
Returns: The last iterator i in [first, last] for which the range [first, i) is sorted with respect to comp and proj.
8
#
Complexity: Linear.

25.8.2 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: [first, nth) and [nth, last) are valid ranges.
For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]), and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
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 with respect to comp and proj, 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: bool(invoke(comp, invoke(proj, *j), invoke(proj, *i))) is false.
4
#
Returns: last for the overload in namespace ranges.
5
#
Complexity: For the overloads with no ExecutionPolicy, linear on average.
For the overloads with an ExecutionPolicy, applications of the predicate, and swaps, where .
🔗
template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});
6
#
Effects: Equivalent to: 
return ranges::nth_element(ranges::begin(r), nth, ranges::end(r), comp, proj);

25.8.3 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 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.

25.8.3.1 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); template<forward_­iterator I, sentinel_­for<I> S, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<I, Proj>> Comp = ranges::less> constexpr I ranges::lower_bound(I first, S last, const T& value, Comp comp = {}, Proj proj = {}); template<forward_­range R, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::lower_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
2
#
Preconditions: The elements e of [first, last) are partitioned with respect to the expression bool(invoke(comp, invoke(proj, e), value)).
3
#
Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i), bool(invoke(comp, invoke(proj, *j), value)) is true.
4
#
Complexity: At most comparisons and projections.

25.8.3.2 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); template<forward_­iterator I, sentinel_­for<I> S, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<I, Proj>> Comp = ranges::less> constexpr I ranges::upper_bound(I first, S last, const T& value, Comp comp = {}, Proj proj = {}); template<forward_­range R, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::upper_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
2
#
Preconditions: The elements e of [first, last) are partitioned with respect to the expression !bool(invoke(comp, value, invoke(proj, e))).
3
#
Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i), !bool(invoke(comp, value, invoke(proj, *j))) is true.
4
#
Complexity: At most comparisons and projections.

25.8.3.3 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); template<forward_­iterator I, sentinel_­for<I> S, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<I, Proj>> Comp = ranges::less> constexpr subrange<I> ranges::equal_range(I first, S last, const T& value, Comp comp = {}, Proj proj = {}); template<forward_­range R, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_subrange_t<R> ranges::equal_range(R&& r, const T& value, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
2
#
Preconditions: The elements e of [first, last) are partitioned with respect to the expressions bool(invoke(comp, invoke(proj, e), value)) and !bool(invoke(comp, value, invoke(proj, e))).
Also, for all elements e of [first, last), bool(comp(e, value)) implies !bool(comp(​value, e)) for the overloads in namespace std.
3
#
Returns:
  • (3.1)
    For the overloads in namespace std: 
    {lower_bound(first, last, value, comp),
 upper_bound(first, last, value, comp)}
  • (3.2)
    For the overloads in namespace ranges: 
    {ranges::lower_bound(first, last, value, comp, proj),
 ranges::upper_bound(first, last, value, comp, proj)}
4
#
Complexity: At most comparisons and projections.

25.8.3.4 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); template<forward_­iterator I, sentinel_­for<I> S, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::binary_search(I first, S last, const T& value, Comp comp = {}, Proj proj = {}); template<forward_­range R, class T, class Proj = identity, indirect_­strict_­weak_­order<const T*, projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr bool ranges::binary_search(R&& r, const T& value, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
2
#
Preconditions: The elements e of [first, last) are partitioned with respect to the expressions bool(invoke(comp, invoke(proj, e), value)) and !bool(invoke(comp, value, invoke(proj, e))).
Also, for all elements e of [first, last), bool(comp(e, value)) implies !bool(comp(​value, e)) for the overloads in namespace std.
3
#
Returns: true if and only if for some iterator i in the range [first, last), !bool(invoke(comp, invoke(proj, *i), value)) && !bool(invoke(comp, value, invoke(proj, *i))) is true.
4
#
Complexity: At most comparisons and projections.

25.8.4 Partitions [alg.partitions]

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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); template<input_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr bool ranges::is_partitioned(I first, S last, Pred pred, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr bool ranges::is_partitioned(R&& r, Pred pred, Proj proj = {});
1
#
Let proj be identity{} for the overloads with no parameter named proj.
2
#
Returns: true if and only if the elements e of [first, last) are partitioned with respect to the expression bool(invoke(pred, invoke(proj, e))).
3
#
Complexity: Linear.
At most last - first applications of pred and proj.
🔗
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); template<permutable I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr subrange<I> ranges::partition(I first, S last, Pred pred, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires permutable<iterator_t<R>> constexpr borrowed_subrange_t<R> ranges::partition(R&& r, Pred pred, Proj proj = {});
4
#
Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(​pred, invoke(proj, x))).
5
#
Preconditions: For the overloads in namespace std, ForwardIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).
6
#
Effects: Places all the elements e in [first, last) that satisfy E(e) before all the elements that do not.
7
#
Returns: Let i be an iterator such that is true for every iterator j in [first, i) and false for every iterator j in [i, last).
Returns:
  • (7.1)
    i for the overloads in namespace std.
  • (7.2)
    {i, last} for the overloads in namespace ranges.
8
#
Complexity: Let :
  • (8.1)
    For the overload with no ExecutionPolicy, exactly N applications of the predicate and projection. At most swaps if the type of first meets the Cpp17BidirectionalIterator requirements for the overloads in namespace std or models bidirectional_­iterator for the overloads in namespace ranges, and at most N swaps otherwise.
  • (8.2)
    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); template<bidirectional_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires permutable<I> subrange<I> ranges::stable_partition(I first, S last, Pred pred, Proj proj = {}); template<bidirectional_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires permutable<iterator_t<R>> borrowed_subrange_t<R> ranges::stable_partition(R&& r, Pred pred, Proj proj = {});
9
#
Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(​pred, invoke(proj, x))).
10
#
Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
11
#
Effects: Places all the elements e in [first, last) that satisfy E(e) before all the elements that do not.
The relative order of the elements in both groups is preserved.
12
#
Returns: Let i be an iterator such that for every iterator j in [first, i), is true, and for every iterator j in the range [i, last), is false.
Returns:
  • (12.1)
    i for the overloads in namespace std.
  • (12.2)
    {i, last} for the overloads in namespace ranges.
13
#
Complexity: Let N = last - first:
  • (13.1)
    For the overloads with no ExecutionPolicy, at most swaps, but only swaps if there is enough extra memory. Exactly N applications of the predicate and projection.
  • (13.2)
    For the overload with an ExecutionPolicy, swaps and applications of the predicate.
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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); template<input_­iterator I, sentinel_­for<I> S, weakly_­incrementable O1, weakly_­incrementable O2, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> requires indirectly_­copyable<I, O1> && indirectly_­copyable<I, O2> constexpr ranges::partition_copy_result<I, O1, O2> ranges::partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred, Proj proj = {}); template<input_­range R, weakly_­incrementable O1, weakly_­incrementable O2, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> requires indirectly_­copyable<iterator_t<R>, O1> && indirectly_­copyable<iterator_t<R>, O2> constexpr ranges::partition_copy_result<borrowed_iterator_t<R>, O1, O2> ranges::partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});
14
#
Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(​pred, invoke(proj, x))).
15
#
Mandates: For the overloads in namespace std, the expression *first is writable ([iterator.requirements.general]) to out_­true and out_­false.
16
#
Preconditions: The input range and output ranges do not overlap.
[ Note
:
For the overload with an ExecutionPolicy, there may be a performance cost if first's value type does not meet the Cpp17CopyConstructible requirements.
— end note
 ]
17
#
Effects: For each iterator i in [first, last), copies *i to the output range beginning with out_­true if is true, or to the output range beginning with out_­false otherwise.
18
#
Returns: Let o1 be the end of the output range beginning at out_­true, and o2 the end of the output range beginning at out_­false.
Returns
  • (18.1)
    {o1, o2} for the overloads in namespace std.
  • (18.2)
    {last, o1, o2} for the overloads in namespace ranges.
19
#
Complexity: Exactly last - first applications of pred and proj.
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template<class ForwardIterator, class Predicate> constexpr ForwardIterator partition_point(ForwardIterator first, ForwardIterator last, Predicate pred); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­unary_­predicate<projected<I, Proj>> Pred> constexpr I ranges::partition_point(I first, S last, Pred pred, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­unary_­predicate<projected<iterator_t<R>, Proj>> Pred> constexpr borrowed_iterator_t<R> ranges::partition_point(R&& r, Pred pred, Proj proj = {});
20
#
Let proj be identity{} for the overloads with no parameter named proj and let E(x) be bool(invoke(​pred, invoke(proj, x))).
21
#
Preconditions: The elements e of [first, last) are partitioned with respect to E(e).
22
#
Returns: An iterator mid such that is true for all iterators i in [first, mid), and false for all iterators i in [mid, last).
23
#
Complexity: applications of pred and proj.

25.8.5 Merge [alg.merge]

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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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<I1, I2, O, Comp, Proj1, Proj2> constexpr ranges::merge_result<I1, I2, O> ranges::merge(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2> constexpr ranges::merge_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O> ranges::merge(R1&& r1, R2&& r2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let N be (last1 - first1) + (last2 - first2).
Let comp be less{}, proj1 be identity{}, and proj2 be identity{}, for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
The resulting range does not overlap with either of the original ranges.
3
#
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 + N.
If an element a precedes b in an input range, a is copied into the output range before b.
If e1 is an element of [first1, last1) and e2 of [first2, last2), e2 is copied into the output range before e1 if and only if bool(invoke(comp, invoke(proj2, e2), invoke(proj1, e1))) is true.
4
#
Returns:
  • (4.1)
    result_­last for the overloads in namespace std.
  • (4.2)
    {last1, last2, result_­last} for the overloads in namespace ranges.
5
#
Complexity:
  • (5.1)
    For the overloads with no ExecutionPolicy, at most comparisons and applications of each projection.
  • (5.2)
    For the overloads with an ExecutionPolicy, comparisons.
6
#
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); template<bidirectional_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> I ranges::inplace_merge(I first, I middle, S last, Comp comp = {}, Proj proj = {});
7
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
8
#
Preconditions: [first, middle) and [middle, last) are valid ranges sorted with respect to comp and proj.
For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
9
#
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 is sorted with respect to comp and proj.
10
#
Returns: last for the overload in namespace ranges.
11
#
Complexity: Let :
  • (11.1)
    For the overloads with no ExecutionPolicy, and if enough additional memory is available, exactly comparisons.
  • (11.2)
    Otherwise, comparisons.
In either case, twice as many projections as comparisons.
12
#
Remarks: Stable.
🔗
template<bidirectional_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> borrowed_iterator_t<R> ranges::inplace_merge(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});
13
#
Effects: Equivalent to: 
return ranges::inplace_merge(ranges::begin(r), middle, ranges::end(r), comp, proj);

25.8.6 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.

25.8.6.1 includes [includes]

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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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, class Proj1 = identity, class Proj2 = identity, indirect_­strict_­weak_­order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less> constexpr bool ranges::includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, class Proj1 = identity, class Proj2 = identity, indirect_­strict_­weak_­order<projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>> Comp = ranges::less> constexpr bool ranges::includes(R1&& r1, R2&& r2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let comp be less{}, proj1 be identity{}, and proj2 be identity{}, for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
3
#
Returns: true if and only if [first2, last2) is a subsequence of [first1, last1).
[ Note
:
A sequence S is a subsequence of another sequence T if S can be obtained from T by removing some, all, or none of T's elements and keeping the remaining elements in the same order.
— end note
 ]
4
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.

25.8.6.2 set_­union [set.union]

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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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<I1, I2, O, Comp, Proj1, Proj2> constexpr ranges::set_union_result<I1, I2, O> ranges::set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2> constexpr ranges::set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O> ranges::set_union(R1&& r1, R2&& r2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
The resulting range does not overlap with either of the original ranges.
3
#
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.
4
#
Returns: Let result_­last be the end of the constructed range.
Returns
  • (4.1)
    result_­last for the overloads in namespace std.
  • (4.2)
    {last1, last2, result_­last} for the overloads in namespace ranges.
5
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.
6
#
Remarks: Stable ([algorithm.stable]).
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 are copied to the output range, in order, and then the final elements from the second range are copied to the output range, in order.

25.8.6.3 set_­intersection [set.intersection]

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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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<I1, I2, O, Comp, Proj1, Proj2> constexpr ranges::set_intersection_result<I1, I2, O> ranges::set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2> constexpr ranges::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O> ranges::set_intersection(R1&& r1, R2&& r2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
The resulting range does not overlap with either of the original ranges.
3
#
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.
4
#
Returns: Let result_­last be the end of the constructed range.
Returns
  • (4.1)
    result_­last for the overloads in namespace std.
  • (4.2)
    {last1, last2, result_­last} for the overloads in namespace ranges.
5
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.
6
#
Remarks: Stable ([algorithm.stable]).
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 are copied from the first range to the output range, in order.

25.8.6.4 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<I1, I2, O, Comp, Proj1, Proj2> constexpr ranges::set_difference_result<I1, O> ranges::set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2> constexpr ranges::set_difference_result<borrowed_iterator_t<R1>, O> ranges::set_difference(R1&& r1, R2&& r2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
The resulting range does not overlap with either of the original ranges.
3
#
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.
4
#
Returns: Let result_­last be the end of the constructed range.
Returns
  • (4.1)
    result_­last for the overloads in namespace std.
  • (4.2)
    {last1, result_­last} for the overloads in namespace ranges.
5
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.
6
#
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) is copied to the output range, in order.

25.8.6.5 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<I1, I2, O, Comp, Proj1, Proj2> constexpr ranges::set_symmetric_difference_result<I1, I2, O> ranges::set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, weakly_­incrementable O, class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity> requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2> constexpr ranges::set_symmetric_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O> ranges::set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Let comp be less{}, and proj1 and proj2 be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The ranges [first1, last1) and [first2, last2) are sorted with respect to comp and proj1 or proj2, respectively.
The resulting range does not overlap with either of the original ranges.
3
#
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.
4
#
Returns: Let result_­last be the end of the constructed range.
Returns
  • (4.1)
    result_­last for the overloads in namespace std.
  • (4.2)
    {last1, last2, result_­last} for the overloads in namespace ranges.
5
#
Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection.
6
#
Remarks: Stable ([algorithm.stable]).
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 .
In either case, the elements are copied in order.

25.8.7 Heap operations [alg.heap.operations]

1
#
A random access range [a, b) is a heap with respect to comp and proj for a comparator and projection comp and proj if its elements are organized such that:
  • (1.1)
    With N = b - a, for all i, , bool(invoke(comp, invoke(proj, a[]), invoke(​proj, 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.

25.8.7.1 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::push_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::push_heap(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The range [first, last - 1) is a valid heap with respect to comp and proj.
For the overloads in namespace std, the type of *first meets the Cpp17MoveConstructible requirements (Table 28) and the Cpp17MoveAssignable requirements (Table 30).
3
#
Effects: Places the value in the location last - 1 into the resulting heap [first, last).
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: At most comparisons and twice as many projections.

25.8.7.2 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::pop_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::pop_heap(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The range [first, last) is a valid non-empty heap with respect to comp and proj.
For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Swaps the value in the location first with the value in the location last - 1 and makes [first, last - 1) into a heap with respect to comp and proj.
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: At most comparisons and twice as many projections.

25.8.7.3 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::make_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::make_heap(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: For the overloads in namespace std, the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Constructs a heap with respect to comp and proj out of the range [first, last).
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: At most comparisons and twice as many projections.

25.8.7.4 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr I ranges::sort_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr borrowed_iterator_t<R> ranges::sort_heap(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
2
#
Preconditions: The range [first, last) is a valid heap with respect to comp and proj.
For the overloads in namespace std, RandomAccessIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]) and the type of *first meets the Cpp17MoveConstructible (Table 28) and Cpp17MoveAssignable (Table 30) requirements.
3
#
Effects: Sorts elements in the heap [first, last) with respect to comp and proj.
4
#
Returns: last for the overloads in namespace ranges.
5
#
Complexity: At most comparisons, where , and twice as many projections.

25.8.7.5 is_­heap [is.heap]

🔗
template<class RandomAccessIterator> constexpr bool is_heap(RandomAccessIterator first, RandomAccessIterator last);
1
#
Effects: Equivalent to: return is_­heap_­until(first, last) == last;
🔗
template<class ExecutionPolicy, class RandomAccessIterator> bool is_heap(ExecutionPolicy&& exec, RandomAccessIterator first, RandomAccessIterator last);
2
#
Effects: Equivalent to: 
return 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
#
Effects: Equivalent to: return 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
#
Effects: Equivalent to: 
return is_heap_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last;
🔗
template<random_­access_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr bool ranges::is_heap(R&& r, Comp comp = {}, Proj proj = {});
5
#
Effects: Equivalent to: return ranges​::​is_­heap_­until(first, last, comp, proj) == 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); template<random_­access_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::is_heap_until(I first, S last, Comp comp = {}, Proj proj = {}); template<random_­access_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::is_heap_until(R&& r, Comp comp = {}, Proj proj = {});
6
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
7
#
Returns: The last iterator i in [first, last] for which the range [first, i) is a heap with respect to comp and proj.
8
#
Complexity: Linear.

25.8.8 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); template<class T, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr const T& ranges::min(const T& a, const T& b, Comp comp = {}, Proj proj = {});
1
#
Preconditions: For the first form, T meets the Cpp17LessThanComparable requirements (Table 26).
2
#
Returns: The smaller value.
3
#
Remarks: Returns the first argument when the arguments are equivalent.
An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
4
#
Complexity: Exactly one comparison and two applications of the projection, if any.
🔗
template<class T> constexpr T min(initializer_list<T> r); template<class T, class Compare> constexpr T min(initializer_list<T> r, Compare comp); template<copyable T, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr T ranges::min(initializer_list<T> r, Comp comp = {}, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> requires indirectly_­copyable_storable<iterator_t<R>, range_value_t<R>*> constexpr range_value_t<R> ranges::min(R&& r, Comp comp = {}, Proj proj = {});
5
#
Preconditions: ranges​::​distance(r) > 0.
For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements.
For the first form, T meets the Cpp17LessThanComparable requirements (Table 26).
6
#
Returns: The smallest value in the input range.
7
#
Remarks: Returns a copy of the leftmost element when several elements are equivalent to the smallest.
An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
8
#
Complexity: Exactly ranges​::​distance(r) - 1 comparisons and twice as many applications of the projection, if any.
🔗
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, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr const T& ranges::max(const T& a, const T& b, Comp comp = {}, Proj proj = {});
9
#
Preconditions: For the first form, T meets the Cpp17LessThanComparable requirements (Table 26).
10
#
Returns: The larger value.
11
#
Remarks: Returns the first argument when the arguments are equivalent.
An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
12
#
Complexity: Exactly one comparison and two applications of the projection, if any.
🔗
template<class T> constexpr T max(initializer_list<T> r); template<class T, class Compare> constexpr T max(initializer_list<T> r, Compare comp); template<copyable T, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr T ranges::max(initializer_list<T> r, Comp comp = {}, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> requires indirectly_­copyable_­storable<iterator_t<R>, range_value_t<R>*> constexpr range_value_t<R> ranges::max(R&& r, Comp comp = {}, Proj proj = {});
13
#
Preconditions: ranges​::​distance(r) > 0.
For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements.
For the first form, T meets the Cpp17LessThanComparable requirements (Table 26).
14
#
Returns: The largest value in the input range.
15
#
Remarks: Returns a copy of the leftmost element when several elements are equivalent to the largest.
An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
16
#
Complexity: Exactly ranges​::​distance(r) - 1 comparisons and twice as many applications of the projection, if any.
🔗
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, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr ranges::minmax_result<const T&> ranges::minmax(const T& a, const T& b, Comp comp = {}, Proj proj = {});
17
#
Preconditions: For the first form, T meets the Cpp17LessThanComparable requirements (Table 26).
18
#
Returns: {b, a} if b is smaller than a, and {a, b} otherwise.
19
#
Remarks: An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
20
#
Complexity: Exactly one comparison and two applications of the projection, if any.
🔗
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<copyable T, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr ranges::minmax_result<T> ranges::minmax(initializer_list<T> r, Comp comp = {}, Proj proj = {}); template<input_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> requires indirectly_­copyable_­storable<iterator_t<R>, range_value_t<R>*> constexpr ranges::minmax_result<range_value_t<R>> ranges::minmax(R&& r, Comp comp = {}, Proj proj = {});
21
#
Preconditions: ranges​::​distance(r) > 0.
For the overloads in namespace std, T meets the Cpp17CopyConstructible requirements.
For the first form, type T meets the Cpp17LessThanComparable requirements (Table 26).
22
#
Returns: Let X be the return type.
Returns X{x, y}, where x is a copy of the leftmost element with the smallest value and y a copy of the rightmost element with the largest value in the input range.
23
#
Remarks: An invocation may explicitly specify an argument for the template parameter T of the overloads in namespace std.
24
#
Complexity: At most applications of the corresponding predicate and twice as many applications of the projection, if any.
🔗
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); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::min_element(I first, S last, Comp comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::min_element(R&& r, Comp comp = {}, Proj proj = {});
25
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
26
#
Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last), 
bool(invoke(comp, invoke(proj, *j), invoke(proj, *i)))
is false.
Returns last if first == last.
27
#
Complexity: Exactly comparisons and twice as many projections.
🔗
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); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr I ranges::max_element(I first, S last, Comp comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr borrowed_iterator_t<R> ranges::max_element(R&& r, Comp comp = {}, Proj proj = {});
28
#
Let comp be less{} and proj be identity{} for the overloads with no parameters by those names.
29
#
Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last), 
bool(invoke(comp, invoke(proj, *i), invoke(proj, *j)))
is false.
Returns last if first == last.
30
#
Complexity: Exactly comparisons and twice as many projections.
🔗
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); template<forward_­iterator I, sentinel_­for<I> S, class Proj = identity, indirect_­strict_­weak_­order<projected<I, Proj>> Comp = ranges::less> constexpr ranges::minmax_result<I> ranges::minmax_element(I first, S last, Comp comp = {}, Proj proj = {}); template<forward_­range R, class Proj = identity, indirect_­strict_­weak_­order<projected<iterator_t<R>, Proj>> Comp = ranges::less> constexpr ranges::minmax_result<borrowed_iterator_t<R>> ranges::minmax_element(R&& r, Comp comp = {}, Proj proj = {});
31
#
Returns: {first, first} if [first, last) is empty, otherwise {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 iterator234 in [first, last) such that no iterator in the range refers to a larger element.
32
#
Complexity: Let N be last - first.
At most comparisons and twice as many applications of the projection, if any.
234)
This behavior intentionally differs from max_­element.
⮥

25.8.9 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); template<class T, class Proj = identity, indirect_­strict_­weak_­order<projected<const T*, Proj>> Comp = ranges::less> constexpr const T& ranges::clamp(const T& v, const T& lo, const T& hi, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} for the overloads with no parameter comp, and let proj be identity{} for the overloads with no parameter proj.
2
#
Preconditions: bool(comp(proj(hi), proj(lo))) is false.
For the first form, type T meets the Cpp17LessThanComparable requirements (Table 26).
3
#
Returns: lo if bool(comp(proj(v), proj(lo))) is true, hi if bool(comp(proj(hi), proj(v))) is true, otherwise v.
4
#
[ Note
:
If NaN is avoided, T can be a floating-point type.
— end note
 ]
5
#
Complexity: At most two comparisons and three applications of the projection.

25.8.10 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); template<input_­iterator I1, sentinel_­for<I1> S1, input_­iterator I2, sentinel_­for<I2> S2, class Proj1 = identity, class Proj2 = identity, indirect_­strict_­weak_­order<projected<I1, Proj1>, projected<I2, Proj2>> Comp = ranges::less> constexpr bool ranges::lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {}); template<input_­range R1, input_­range R2, class Proj1 = identity, class Proj2 = identity, indirect_­strict_­weak_­order<projected<iterator_t<R1>, Proj1>, projected<iterator_t<R2>, Proj2>> Comp = ranges::less> constexpr bool ranges::lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
1
#
Returns: true if and only 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).
2
#
Complexity: At most applications of the corresponding comparison and each projection, if any.
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 proper 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
:
ranges​::​lexicographical_­compare(I1, S1, I2, S2, Comp, Proj1, Proj2) could be implemented as: 
for ( ; first1 != last1 && first2 != last2 ; ++first1, (void) ++first2) {
  if (invoke(comp, invoke(proj1, *first1), invoke(proj2, *first2))) return true;
  if (invoke(comp, invoke(proj2, *first2), invoke(proj1, *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
 ]

25.8.11 Three-way comparison algorithms [alg.three.way]

🔗
template<class InputIterator1, class InputIterator2, class Cmp> constexpr auto lexicographical_compare_three_way(InputIterator1 b1, InputIterator1 e1, InputIterator2 b2, InputIterator2 e2, Cmp comp) -> decltype(comp(*b1, *b2));
1
#
Mandates: decltype(comp(*b1, *b2)) is a comparison category type.
2
#
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_three_way(InputIterator1 b1, InputIterator1 e1, InputIterator2 b2, InputIterator2 e2);
3
#
Effects: Equivalent to: 
return lexicographical_compare_three_way(b1, e1, b2, e2, compare_three_way());

25.8.12 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); template<bidirectional_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr ranges::next_permutation_result<I> ranges::next_permutation(I first, S last, Comp comp = {}, Proj proj = {}); template<bidirectional_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr ranges::next_permutation_result<borrowed_iterator_t<R>> ranges::next_permutation(R&& r, Comp comp = {}, Proj proj = {});
1
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
2
#
Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).
3
#
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 comp and proj.
If no such permutation exists, transforms the sequence into the first permutation; that is, the ascendingly-sorted one.
4
#
Returns: Let B be true if a next permutation was found and otherwise false.
Returns:
  • (4.1)
    B for the overloads in namespace std.
  • (4.2)
    { last, B } for the overloads in namespace ranges.
5
#
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); template<bidirectional_­iterator I, sentinel_­for<I> S, class Comp = ranges::less, class Proj = identity> requires sortable<I, Comp, Proj> constexpr ranges::prev_permutation_result<I> ranges::prev_permutation(I first, S last, Comp comp = {}, Proj proj = {}); template<bidirectional_­range R, class Comp = ranges::less, class Proj = identity> requires sortable<iterator_t<R>, Comp, Proj> constexpr ranges::prev_permutation_result<borrowed_iterator_t<R>> ranges::prev_permutation(R&& r, Comp comp = {}, Proj proj = {});
6
#
Let comp be less{} and proj be identity{} for overloads with no parameters by those names.
7
#
Preconditions: For the overloads in namespace std, BidirectionalIterator meets the Cpp17ValueSwappable requirements ([swappable.requirements]).
8
#
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 comp and proj.
If no such permutation exists, transforms the sequence into the last permutation; that is, the descendingly-sorted one.
9
#
Returns: Let B be true if a previous permutation was found and otherwise false.
Returns:
  • (9.1)
    B for the overloads in namespace std.
  • (9.2)
    { last, B } for the overloads in namespace ranges.
10
#
Complexity: At most (last - first) / 2 swaps.

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

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

  // [reduce], reduce
  template<class InputIterator>
    constexpr typename iterator_traits<InputIterator>::value_type
      reduce(InputIterator first, InputIterator last);
  template<class InputIterator, class T>
    constexpr T reduce(InputIterator first, InputIterator last, T init);
  template<class InputIterator, class T, class BinaryOperation>
    constexpr 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>
    constexpr T inner_product(InputIterator1 first1, InputIterator1 last1,
                              InputIterator2 first2, T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    constexpr 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>
    constexpr T transform_reduce(InputIterator1 first1, InputIterator1 last1,
                                 InputIterator2 first2, T init);
  template<class InputIterator1, class InputIterator2, class T,
           class BinaryOperation1, class BinaryOperation2>
    constexpr 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>
    constexpr 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>
    constexpr OutputIterator
      partial_sum(InputIterator first, InputIterator last,
                  OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    constexpr OutputIterator
      partial_sum(InputIterator first, InputIterator last,
                  OutputIterator result, BinaryOperation binary_op);

  // [exclusive.scan], exclusive scan
  template<class InputIterator, class OutputIterator, class T>
    constexpr OutputIterator
      exclusive_scan(InputIterator first, InputIterator last,
                     OutputIterator result, T init);
  template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
    constexpr 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>
    constexpr OutputIterator
      inclusive_scan(InputIterator first, InputIterator last,
                     OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    constexpr OutputIterator
      inclusive_scan(InputIterator first, InputIterator last,
                     OutputIterator result, BinaryOperation binary_op);
  template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
    constexpr 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>
    constexpr 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>
    constexpr 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>
    constexpr 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>
    constexpr OutputIterator
      adjacent_difference(InputIterator first, InputIterator last,
                          OutputIterator result);
  template<class InputIterator, class OutputIterator, class BinaryOperation>
    constexpr 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>
    constexpr 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);

  // [numeric.ops.midpoint], midpoint
  template<class T>
    constexpr T midpoint(T a, T b) noexcept;
  template<class T>
    constexpr T* midpoint(T* a, T* b);
}

25.10 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
 ]

25.10.1 Definitions [numerics.defns]

1
#
Define GENERALIZED_­NONCOMMUTATIVE_­SUM(op, a1, ..., aN) as follows:
  • (1.1)
    a1 when N is 1, otherwise
  • (1.2)
    op(GENERALIZED_­NONCOMMUTATIVE_­SUM(op, a1, ..., aK),
    op(GENERALIZED_­NONCOMMUTATIVE_­SUM(op, aM, ..., aN)) for any K where .
2
#
Define GENERALIZED_­SUM(op, a1, ..., aN) as GENERALIZED_­NONCOMMUTATIVE_­SUM(op, b1, ..., bN), where b1, ..., bN may be any permutation of a1, ..., aN.

25.10.2 Accumulate [accumulate]

🔗
template<class InputIterator, class T> constexpr T accumulate(InputIterator first, InputIterator last, T init); template<class InputIterator, class T, class BinaryOperation> constexpr T accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);
1
#
Preconditions: T meets the Cpp17CopyConstructible (Table 29) and Cpp17CopyAssignable (Table 31) requirements.
In the range [first, last], binary_­op neither modifies elements nor invalidates iterators or subranges.235
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.236
235)
The use of fully closed ranges is intentional.
⮥
236)
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.
⮥

25.10.3 Reduce [reduce]

🔗
template<class InputIterator> constexpr 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> constexpr 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> constexpr 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
#
Mandates: All of
  • (5.1)
    binary_­op(init, *first),
  • (5.2)
    binary_­op(*first, init),
  • (5.3)
    binary_­op(init, init), and
  • (5.4)
    binary_­op(*first, *first)
are convertible to T.
6
#
Preconditions:
  • (6.1)
    T meets the Cpp17MoveConstructible (Table 28) requirements.
  • (6.2)
    binary_­op neither invalidates iterators or subranges, nor modifies elements in the range [first, last].
7
#
Returns: GENERALIZED_­SUM(binary_­op, init, *i, ...) for every i in [first, last).
8
#
Complexity: applications of binary_­op.
9
#
[ 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
 ]

25.10.4 Inner product [inner.product]

🔗
template<class InputIterator1, class InputIterator2, class T> constexpr T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init); template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> constexpr T inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);
1
#
Preconditions: T meets the Cpp17CopyConstructible (Table 29) and Cpp17CopyAssignable (Table 31) requirements.
In the ranges [first1, last1] and [first2, first2 + (last1 - first1)] binary_­op1 and binary_­op2 neither modifies elements nor invalidates iterators or subranges.237
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.
237)
The use of fully closed ranges is intentional.
⮥

25.10.5 Transform reduce [transform.reduce]

🔗
template<class InputIterator1, class InputIterator2, class T> constexpr 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> constexpr 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
#
Mandates: All of
  • (3.1)
    binary_­op1(init, init),
  • (3.2)
    binary_­op1(init, binary_­op2(*first1, *first2)),
  • (3.3)
    binary_­op1(binary_­op2(*first1, *first2), init), and
  • (3.4)
    binary_­op1(binary_­op2(*first1, *first2), binary_­op2(*first1, *first2))
are convertible to T.
4
#
Preconditions:
  • (4.1)
    T meets the Cpp17MoveConstructible (Table 28) requirements.
  • (4.2)
    Neither binary_­op1 nor binary_­op2 invalidates subranges, nor modifies elements in the ranges [first1, last1] and [first2, first2 + (last1 - first1)].
5
#
Returns: 
GENERALIZED_SUM(binary_op1, init, binary_op2(*i, *(first2 + (i - first1))), ...)
for every iterator i in [first1, last1).
6
#
Complexity: applications each of binary_­op1 and binary_­op2.
🔗
template<class InputIterator, class T, class BinaryOperation, class UnaryOperation> constexpr 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);
7
#
Mandates: All of
  • (7.1)
    binary_­op(init, init),
  • (7.2)
    binary_­op(init, unary_­op(*first)),
  • (7.3)
    binary_­op(unary_­op(*first), init), and
  • (7.4)
    binary_­op(unary_­op(*first), unary_­op(*first))
are convertible to T.
8
#
Preconditions:
  • (8.1)
    T meets the Cpp17MoveConstructible (Table 28) requirements.
  • (8.2)
    Neither unary_­op nor binary_­op invalidates subranges, nor modifies elements in the range [first, last].
9
#
Returns: 
GENERALIZED_SUM(binary_op, init, unary_op(*i), ...)
for every iterator i in [first, last).
10
#
Complexity: applications each of unary_­op and binary_­op.
11
#
[ Note
:
transform_­reduce does not apply unary_­op to init.
— end note
 ]

25.10.6 Partial sum [partial.sum]

🔗
template<class InputIterator, class OutputIterator> constexpr OutputIterator partial_sum(InputIterator first, InputIterator last, OutputIterator result); template<class InputIterator, class OutputIterator, class BinaryOperation> constexpr OutputIterator partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);
1
#
Mandates: InputIterator's value type is constructible from *first.
The result of the expression std​::​move(acc) + *i or binary_­op(std​::​move(acc), *i) is implicitly convertible to InputIterator's value type.
acc is writable ([iterator.requirements.general]) to result.
2
#
Preconditions: In the ranges [first, last] and [result, result + (last - first)] binary_­op neither modifies elements nor invalidates iterators or subranges.238
3
#
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)).
4
#
Returns: result + (last - first).
5
#
Complexity: Exactly (last - first) - 1 applications of the binary operation.
6
#
Remarks: result may be equal to first.
238)
The use of fully closed ranges is intentional.
⮥

25.10.7 Exclusive scan [exclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class T> constexpr 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> constexpr 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
#
Mandates: All of
  • (3.1)
    binary_­op(init, init),
  • (3.2)
    binary_­op(init, *first), and
  • (3.3)
    binary_­op(*first, *first)
are convertible to T.
4
#
Preconditions:
  • (4.1)
    T meets the Cpp17MoveConstructible (Table 28) requirements.
  • (4.2)
    binary_­op neither invalidates iterators or subranges, nor modifies elements in the ranges [first, last] or [result, result + (last - first)].
5
#
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))
6
#
Returns: The end of the resulting range beginning at result.
7
#
Complexity: applications of binary_­op.
8
#
Remarks: result may be equal to first.
9
#
[ 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
 ]

25.10.8 Inclusive scan [inclusive.scan]

🔗
template<class InputIterator, class OutputIterator> constexpr 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> constexpr 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> constexpr 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
#
Let U be the value type of decltype(first).
4
#
Mandates: If init is provided, all of
  • (4.1)
    binary_­op(init, init),
  • (4.2)
    binary_­op(init, *first), and
  • (4.3)
    binary_­op(*first, *first)
are convertible to T; otherwise, binary_­op(*first, *first) is convertible to U.
5
#
Preconditions:
  • (5.1)
    If init is provided, T meets the Cpp17MoveConstructible (Table 28) requirements; otherwise, U meets the Cpp17MoveConstructible requirements.
  • (5.2)
    binary_­op neither invalidates iterators or subranges, nor modifies elements in the ranges [first, last] or [result, result + (last - first)].
6
#
Effects: For each integer K in [0, last - first) assigns through result + K the value of
  • (6.1)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op, init, *(first + 0), *(first + 1), ..., *(first + K))
    if init is provided, or
  • (6.2)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op, *(first + 0), *(first + 1), ..., *(first + K))
    otherwise.
7
#
Returns: The end of the resulting range beginning at result.
8
#
Complexity: applications of binary_­op.
9
#
Remarks: result may be equal to first.
10
#
[ 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
 ]

25.10.9 Transform exclusive scan [transform.exclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class T, class BinaryOperation, class UnaryOperation> constexpr 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
#
Mandates: All of
  • (1.1)
    binary_­op(init, init),
  • (1.2)
    binary_­op(init, unary_­op(*first)), and
  • (1.3)
    binary_­op(unary_­op(*first), unary_­op(*first))
are convertible to T.
2
#
Preconditions:
  • (2.1)
    T meets the Cpp17MoveConstructible (Table 28) requirements.
  • (2.2)
    Neither unary_­op nor binary_­op invalidates iterators or subranges, nor modifies elements in the ranges [first, last] or [result, result + (last - first)].
3
#
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)))
4
#
Returns: The end of the resulting range beginning at result.
5
#
Complexity: applications each of unary_­op and binary_­op.
6
#
Remarks: result may be equal to first.
7
#
[ 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
 ]

25.10.10 Transform inclusive scan [transform.inclusive.scan]

🔗
template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation> constexpr 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> constexpr 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
#
Let U be the value type of decltype(first).
2
#
Mandates: If init is provided, all of
  • (2.1)
    binary_­op(init, init),
  • (2.2)
    binary_­op(init, unary_­op(*first)), and
  • (2.3)
    binary_­op(unary_­op(*first), unary_­op(*first))
are convertible to T; otherwise, binary_­op(unary_­op(*first), unary_­op(*first)) is convertible to U.
3
#
Preconditions:
  • (3.1)
    If init is provided, T meets the Cpp17MoveConstructible (Table 28) requirements; otherwise, U meets the Cpp17MoveConstructible requirements.
  • (3.2)
    Neither unary_­op nor binary_­op invalidates iterators or subranges, nor modifies 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,
        unary_­op(*(first + 0)), unary_­op(*(first + 1)), ..., unary_­op(*(first + K)))
    if init is provided, or
  • (4.2)
    GENERALIZED_­NONCOMMUTATIVE_­SUM(
        binary_­op,
        unary_­op(*(first + 0)), unary_­op(*(first + 1)), ..., unary_­op(*(first + K)))
    otherwise.
5
#
Returns: The end of the resulting range beginning at result.
6
#
Complexity: applications each of unary_­op and binary_­op.
7
#
Remarks: result may be equal to first.
8
#
[ 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
 ]

25.10.11 Adjacent difference [adjacent.difference]

🔗
template<class InputIterator, class OutputIterator> constexpr 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> constexpr 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
#
Mandates:
  • (2.1)
    For the overloads with no ExecutionPolicy, T is constructible from *first. acc (defined below) is writable ([iterator.requirements.general]) to the result output iterator. The result of the expression binary_­op(val, std​::​move(acc)) is writable to result.
  • (2.2)
    For the overloads with an ExecutionPolicy, the result of the expressions binary_­op(*first, *first) and *first are writable to result.
3
#
Preconditions:
  • (3.1)
    For the overloads with no ExecutionPolicy, T meets the Cpp17MoveAssignable (Table 30) requirements.
  • (3.2)
    For all overloads, in the ranges [first, last] and [result, result + (last - first)], binary_­op neither modifies elements nor invalidate iterators or subranges.239
4
#
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.
5
#
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))).
6
#
Returns: result + (last - first).
7
#
Complexity: Exactly (last - first) - 1 applications of the binary operation.
8
#
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.
239)
The use of fully closed ranges is intentional.
⮥

25.10.12 Iota [numeric.iota]

🔗
template<class ForwardIterator, class T> constexpr void iota(ForwardIterator first, ForwardIterator last, T value);
1
#
Mandates: T is convertible to ForwardIterator's value type.
The expression ++val, where val has type T, is 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.

25.10.13 Greatest common divisor [numeric.ops.gcd]

🔗
template<class M, class N> constexpr common_type_t<M,N> gcd(M m, N n);
1
#
Mandates: M and N both are integer types and not cv bool.
2
#
Preconditions: |m| and |n| are representable as a value of common_­type_­t<M, N>.
[ Note
:
These requirements ensure, for example, that is representable as a value of type M.
— end note
 ]
3
#
Returns: Zero when m and n are both zero.
Otherwise, returns the greatest common divisor of |m| and |n|.
4
#
Throws: Nothing.

25.10.14 Least common multiple [numeric.ops.lcm]

🔗
template<class M, class N> constexpr common_type_t<M,N> lcm(M m, N n);
1
#
Mandates: M and N both are integer types and not cv bool.
2
#
Preconditions: |m| and |n| are representable as a value of common_­type_­t<M, N>.
The least common multiple of |m| and |n| is representable as a value of type common_­type_­t<M,N>.
3
#
Returns: Zero when either m or n is zero.
Otherwise, returns the least common multiple of |m| and |n|.
4
#
Throws: Nothing.

25.10.15 Midpoint [numeric.ops.midpoint]

🔗
template<class T> constexpr T midpoint(T a, T b) noexcept;
1
#
Constraints: T is an arithmetic type other than bool.
2
#
Returns: Half the sum of a and b.
If T is an integer type and the sum is odd, the result is rounded towards a.
3
#
Remarks: No overflow occurs.
If T is a floating-point type, at most one inexact operation occurs.
🔗
template<class T> constexpr T* midpoint(T* a, T* b);
4
#
Constraints: T is an object type.
5
#
Mandates: T is a complete type.
6
#
Preconditions: a and b point to, respectively, elements i and j of the same array object x.
[ Note
:
As specified in [basic.compound], an object that is not an array element is considered to belong to a single-element array for this purpose and a pointer past the last element of an array of n elements is considered to be equivalent to a pointer to a hypothetical array element n for this purpose.
— end note
 ]
7
#
Returns: A pointer to array element of x, where the result of the division is truncated towards zero.

25.11 Specialized <memory> algorithms [specialized.algorithms]

1
#
The contents specified in this subclause [specialized.algorithms] are declared in the header <memory> ([memory.syn]).
2
#
Unless otherwise specified, if an exception is thrown in the following algorithms, objects constructed by a placement new-expression are destroyed in an unspecified order before allowing the exception to propagate.
3
#
[ Note
:
When invoked on ranges of potentially-overlapping subobjects ([intro.object]), the algorithms specified in this subclause [specialized.algorithms] result in undefined behavior.
— end note
 ]
4
#
Some algorithms specified in this clause make use of the exposition-only function voidify: 
template<class T>
  constexpr void* voidify(T& obj) noexcept {
    return const_cast<void*>(static_cast<const volatile void*>(addressof(obj)));
  }

25.11.1 Special memory concepts [special.mem.concepts]

1
#
Some algorithms in this subclause are constrained with the following exposition-only concepts:
🔗
template<class I> concept no-throw-input-iterator = // exposition only input_iterator<I> && is_lvalue_reference_v<iter_reference_t<I>> && same_as<remove_cvref_t<iter_reference_t<I>>, iter_value_t<I>>;
2
#
A type I models no-throw-input-iterator only if no exceptions are thrown from increment, copy construction, move construction, copy assignment, move assignment, or indirection through valid iterators.
3
#
[ Note
:
This concept allows some input_­iterator ([iterator.concept.input]) operations to throw exceptions.
— end note
 ]
🔗
template<class S, class I> concept no-throw-sentinel = sentinel_for<S, I>; // exposition only
4
#
Types S and I model no-throw-sentinel only if no exceptions are thrown from copy construction, move construction, copy assignment, move assignment, or comparisons between valid values of type I and S.
5
#
[ Note
:
This concept allows some sentinel_­for ([iterator.concept.sentinel]) operations to throw exceptions.
— end note
 ]
🔗
template<class R> concept no-throw-input-range = // exposition only range<R> && no-throw-input-iterator<iterator_t<R>> && no-throw-sentinel<sentinel_t<R>, iterator_t<R>>;
6
#
A type R models no-throw-input-range only if no exceptions are thrown from calls to ranges​::​begin and ranges​::​end on an object of type R.
🔗
template<class I> concept no-throw-forward-iterator = // exposition only no-throw-input-iterator<I> && forward_iterator<I> && no-throw-sentinel<I, I>;
7
#
[ Note
:
This concept allows some forward_­iterator ([iterator.concept.forward]) operations to throw exceptions.
— end note
 ]
🔗
template<class R> concept no-throw-forward-range = // exposition only no-throw-input-range<R> && no-throw-forward-iterator<iterator_t<R>>;

25.11.2 uninitialized_­default_­construct [uninitialized.construct.default]

🔗
template<class NoThrowForwardIterator> void uninitialized_default_construct(NoThrowForwardIterator first, NoThrowForwardIterator last);
1
#
Effects: Equivalent to: 
for (; first != last; ++first)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type;
🔗
namespace ranges { template<no-throw-forward-iterator I, no-throw-sentinel<I> S> requires default_initializable<iter_value_t<I>> I uninitialized_default_construct(I first, S last); template<no-throw-forward-range R> requires default_initializable<range_value_t<R>> borrowed_iterator_t<R> uninitialized_default_construct(R&& r); }
2
#
Effects: Equivalent to: 
for (; first != last; ++first)
  ::new (voidify(*first)) remove_reference_t<iter_reference_t<I>>;
return first;
🔗
template<class NoThrowForwardIterator, class Size> NoThrowForwardIterator uninitialized_default_construct_n(NoThrowForwardIterator first, Size n);
3
#
Effects: Equivalent to: 
for (; n > 0; (void)++first, --n)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type;
return first;
🔗
namespace ranges { template<no-throw-forward-iterator I> requires default_initializable<iter_value_t<I>> I uninitialized_default_construct_n(I first, iter_difference_t<I> n); }
4
#
Effects: Equivalent to: 
return uninitialized_default_construct(counted_iterator(first, n),
                                       default_sentinel).base();

25.11.3 uninitialized_­value_­construct [uninitialized.construct.value]

🔗
template<class NoThrowForwardIterator> void uninitialized_value_construct(NoThrowForwardIterator first, NoThrowForwardIterator last);
1
#
Effects: Equivalent to: 
for (; first != last; ++first)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type();
🔗
namespace ranges { template<no-throw-forward-iterator I, no-throw-sentinel<I> S> requires default_initializable<iter_value_t<I>> I uninitialized_value_construct(I first, S last); template<no-throw-forward-range R> requires default_initializable<range_value_t<R>> borrowed_iterator_t<R> uninitialized_value_construct(R&& r); }
2
#
Effects: Equivalent to: 
for (; first != last; ++first)
  ::new (voidify(*first)) remove_reference_t<iter_reference_t<I>>();
return first;
🔗
template<class NoThrowForwardIterator, class Size> NoThrowForwardIterator uninitialized_value_construct_n(NoThrowForwardIterator first, Size n);
3
#
Effects: Equivalent to: 
for (; n > 0; (void)++first, --n)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type();
return first;
🔗
namespace ranges { template<no-throw-forward-iterator I> requires default_initializable<iter_value_t<I>> I uninitialized_value_construct_n(I first, iter_difference_t<I> n); }
4
#
Effects: Equivalent to: 
return uninitialized_value_construct(counted_iterator(first, n),
                                     default_sentinel).base();

25.11.4 uninitialized_­copy [uninitialized.copy]

🔗
template<class InputIterator, class NoThrowForwardIterator> NoThrowForwardIterator uninitialized_copy(InputIterator first, InputIterator last, NoThrowForwardIterator result);
1
#
Preconditions: does not overlap with [first, last).
2
#
Effects: Equivalent to: 
for (; first != last; ++result, (void) ++first)
  ::new (voidify(*result))
    typename iterator_traits<NoThrowForwardIterator>::value_type(*first);
3
#
Returns: result.
🔗
namespace ranges { template<input_iterator I, sentinel_for<I> S1, no-throw-forward-iterator O, no-throw-sentinel<O> S2> requires constructible_from<iter_value_t<O>, iter_reference_t<I>> uninitialized_copy_result<I, O> uninitialized_copy(I ifirst, S1 ilast, O ofirst, S2 olast); template<input_­range IR, no-throw-forward-range OR> requires constructible_from<range_value_t<OR>, range_reference_t<IR>> uninitialized_copy_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>> uninitialized_copy(IR&& in_range, OR&& out_range); }
4
#
Preconditions: [ofirst, olast) does not overlap with [ifirst, ilast).
5
#
Effects: Equivalent to: 
for (; ifirst != ilast && ofirst != olast; ++ofirst, (void)++ifirst) {
  ::new (voidify(*ofirst)) remove_reference_t<iter_reference_t<O>>(*ifirst);
}
return {std::move(ifirst), ofirst};
🔗
template<class InputIterator, class Size, class NoThrowForwardIterator> NoThrowForwardIterator uninitialized_copy_n(InputIterator first, Size n, NoThrowForwardIterator result);
6
#
Preconditions: does not overlap with .
7
#
Effects: Equivalent to: 
for ( ; n > 0; ++result, (void) ++first, --n) {
  ::new (voidify(*result))
    typename iterator_traits<NoThrowForwardIterator>::value_type(*first);
}
8
#
Returns: result.
🔗
namespace ranges { template<input_iterator I, no-throw-forward-iterator O, no-throw-sentinel<O> S> requires constructible_from<iter_value_t<O>, iter_reference_t<I>> uninitialized_copy_n_result<I, O> uninitialized_copy_n(I ifirst, iter_difference_t<I> n, O ofirst, S olast); }
9
#
Preconditions: [ofirst, olast) does not overlap with .
10
#
Effects: Equivalent to: 
auto t = uninitialized_copy(counted_iterator(ifirst, n),
                            default_sentinel, ofirst, olast);
return {std::move(t.in).base(), t.out};

25.11.5 uninitialized_­move [uninitialized.move]

🔗
template<class InputIterator, class NoThrowForwardIterator> NoThrowForwardIterator uninitialized_move(InputIterator first, InputIterator last, NoThrowForwardIterator result);
1
#
Preconditions: does not overlap with [first, last).
2
#
Effects: Equivalent to: 
for (; first != last; (void)++result, ++first)
  ::new (voidify(*result))
    typename iterator_traits<NoThrowForwardIterator>::value_type(std::move(*first));
return result;
🔗
namespace ranges { template<input_iterator I, sentinel_for<I> S1, no-throw-forward-iterator O, no-throw-sentinel<O> S2> requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>> uninitialized_move_result<I, O> uninitialized_move(I ifirst, S1 ilast, O ofirst, S2 olast); template<input_­range IR, no-throw-forward-range OR> requires constructible_from<range_value_t<OR>, range_rvalue_reference_t<IR>> uninitialized_move_result<borrowed_iterator_t<IR>, borrowed_iterator_t<OR>> uninitialized_move(IR&& in_range, OR&& out_range); }
3
#
Preconditions: [ofirst, olast) does not overlap with [ifirst, ilast).
4
#
Effects: Equivalent to: 
for (; ifirst != ilast && ofirst != olast; ++ofirst, (void)++ifirst) {
  ::new (voidify(*ofirst))
    remove_reference_t<iter_reference_t<O>>(ranges::iter_move(ifirst));
}
return {std::move(ifirst), ofirst};
5
#
[ Note
:
If an exception is thrown, some objects in the range [first, last) are left in a valid, but unspecified state.
— end note
 ]
🔗
template<class InputIterator, class Size, class NoThrowForwardIterator> pair<InputIterator, NoThrowForwardIterator> uninitialized_move_n(InputIterator first, Size n, NoThrowForwardIterator result);
6
#
Preconditions: does not overlap with .
7
#
Effects: Equivalent to: 
for (; n > 0; ++result, (void) ++first, --n)
  ::new (voidify(*result))
    typename iterator_traits<NoThrowForwardIterator>::value_type(std::move(*first));
return {first, result};
🔗
namespace ranges { template<input_iterator I, no-throw-forward-iterator O, no-throw-sentinel<O> S> requires constructible_from<iter_value_t<O>, iter_rvalue_reference_t<I>> uninitialized_move_n_result<I, O> uninitialized_move_n(I ifirst, iter_difference_t<I> n, O ofirst, S olast); }
8
#
Preconditions: [ofirst, olast) does not overlap with .
9
#
Effects: Equivalent to: 
auto t = uninitialized_move(counted_iterator(ifirst, n),
                            default_sentinel, ofirst, olast);
return {std::move(t.in).base(), t.out};
10
#
[ Note
:
If an exception is thrown, some objects in the range are left in a valid but unspecified state.
— end note
 ]

25.11.6 uninitialized_­fill [uninitialized.fill]

🔗
template<class NoThrowForwardIterator, class T> void uninitialized_fill(NoThrowForwardIterator first, NoThrowForwardIterator last, const T& x);
1
#
Effects: Equivalent to: 
for (; first != last; ++first)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type(x);
🔗
namespace ranges { template<no-throw-forward-iterator I, no-throw-sentinel<I> S, class T> requires constructible_from<iter_value_t<I>, const T&> I uninitialized_fill(I first, S last, const T& x); template<no-throw-forward-range R, class T> requires constructible_from<range_value_t<R>, const T&> borrowed_iterator_t<R> uninitialized_fill(R&& r, const T& x); }
Effects: Equivalent to: 
for (; first != last; ++first) {
  ::new (voidify(*first)) remove_reference_t<iter_reference_t<I>>(x);
}
return first;
🔗
template<class NoThrowForwardIterator, class Size, class T> NoThrowForwardIterator uninitialized_fill_n(NoThrowForwardIterator first, Size n, const T& x);
2
#
Effects: Equivalent to: 
for (; n--; ++first)
  ::new (voidify(*first))
    typename iterator_traits<NoThrowForwardIterator>::value_type(x);
return first;
🔗
namespace ranges { template<no-throw-forward-iterator I, class T> requires constructible_from<iter_value_t<I>, const T&> I uninitialized_fill_n(I first, iter_difference_t<I> n, const T& x); }
3
#
Effects: Equivalent to: 
return uninitialized_fill(counted_iterator(first, n), default_sentinel, x).base();

25.11.7 construct_­at [specialized.construct]

🔗
template<class T, class... Args> constexpr T* construct_at(T* location, Args&&... args); namespace ranges { template<class T, class... Args> constexpr T* construct_at(T* location, Args&&... args); }
1
#
Constraints: The expression ​::​new (declval<void*>()) T(declval<Args>()...) is well-formed when treated as an unevaluated operand.
2
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Effects: Equivalent to: 
return ::new (voidify(*location)) T(std::forward<Args>(args)...);

25.11.8 destroy [specialized.destroy]

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template<class T> constexpr void destroy_at(T* location); namespace ranges { template<destructible T> constexpr void destroy_at(T* location) noexcept; }
1
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Effects:
  • (1.1)
    If T is an array type, equivalent to destroy(begin(*location), end(*location)).
  • (1.2)
    Otherwise, equivalent to location->~T().
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template<class NoThrowForwardIterator> constexpr void destroy(NoThrowForwardIterator first, NoThrowForwardIterator last);
2
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Effects: Equivalent to: 
for (; first != last; ++first)
  destroy_at(addressof(*first));
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namespace ranges { template<no-throw-input-iterator I, no-throw-sentinel<I> S> requires destructible<iter_value_t<I>> constexpr I destroy(I first, S last) noexcept; template<no-throw-input-range R> requires destructible<range_value_t<R>> constexpr borrowed_iterator_t<R> destroy(R&& r) noexcept; }
3
#
Effects: Equivalent to: 
for (; first != last; ++first)
  destroy_at(addressof(*first));
return first;
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template<class NoThrowForwardIterator, class Size> constexpr NoThrowForwardIterator destroy_n(NoThrowForwardIterator first, Size n);
4
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Effects: Equivalent to: 
for (; n > 0; (void)++first, --n)
  destroy_at(addressof(*first));
return first;
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namespace ranges { template<no-throw-input-iterator I> requires destructible<iter_value_t<I>> constexpr I destroy_n(I first, iter_difference_t<I> n) noexcept; }
5
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Effects: Equivalent to: 
return destroy(counted_iterator(first, n), default_sentinel).base();

25.12 C library algorithms [alg.c.library]

1
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[ Note
:
The header <cstdlib> ([cstdlib.syn]) declares the functions described in this subclause.
— end note
 ]
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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
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Effects: These functions have the semantics specified in the C standard library.
3
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Preconditions: The objects in the array pointed to by base are of trivial type.
4
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Throws: Any exception thrown by compar ([res.on.exception.handling]).
See also: ISO C 7.22.5.