28 Algorithms library [algorithms]

28.1 General [algorithms.general]

This Clause describes components that C++ programs may use to perform algorithmic operations on containers (Clause [containers]) and other sequences.

The following subclauses describe components for non-modifying sequence operations, modifying sequence operations, sorting and related operations, and algorithms from the ISO C library, as summarized in Table 95 .

Table 95 — Algorithms library summary

Subclause		Header(s)
[alg.nonmodifying]	Non-modifying sequence operations
[alg.modifying.operations]	Mutating sequence operations	<algorithm>
[alg.sorting]	Sorting and related operations
[alg.c.library]	C library algorithms	<cstdlib>

28.2 Header <algorithm> synopsis [algorithm.syn]

#include <initializer_list>

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

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

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

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

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

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

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

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

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

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

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

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

  template<class ForwardIterator1, class ForwardIterator2>
    bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                        ForwardIterator2 first2, ForwardIterator2 last2);

  template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                        ForwardIterator2 first2, ForwardIterator2 last2,
                        BinaryPredicate pred);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

28.3 Algorithms requirements [algorithms.requirements]

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.

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.

Throughout this Clause, the names of template parameters are used to express type requirements.

(3.1)
If an algorithm's template parameter is named InputIterator, InputIterator1, or InputIterator2, the template argument shall satisfy the requirements of an input iterator ([input.iterators]).
(3.2)
If an algorithm's template parameter is named OutputIterator, OutputIterator1, or OutputIterator2, the template argument shall satisfy the requirements of an output iterator ([output.iterators]).
(3.3)
If an algorithm's template parameter is named ForwardIterator, ForwardIterator1, or ForwardIterator2, the template argument shall satisfy the requirements of a forward iterator ([forward.iterators]).
(3.4)
If an algorithm's template parameter is named BidirectionalIterator, BidirectionalIterator1, or BidirectionalIterator2, the template argument shall satisfy the requirements of a bidirectional iterator ([bidirectional.iterators]).
(3.5)
If an algorithm's template parameter is named RandomAccessIterator, RandomAccessIterator1, or RandomAccessIterator2, the template argument shall satisfy the requirements of a random-access iterator ([random.access.iterators]).

If an algorithm's Effects: section says that a value pointed to by any iterator passed as an argument is modified, then that algorithm has an additional type requirement: The type of that argument shall satisfy the requirements of a mutable iterator ([iterator.requirements]).

[ Note

This requirement does not affect arguments that are named OutputIterator, OutputIterator1, or OutputIterator2, because output iterators must always be mutable.

— end note

]

Both in-place and copying versions are provided for certain algorithms.262

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).

The Predicate parameter is used whenever an algorithm expects a function object ([function.objects]) that, when applied to the result of dereferencing the corresponding iterator, returns a value testable as true.

In other words, if an algorithm takes Predicate pred as its argument and first as its iterator argument, it should work correctly in the construct pred(*first) contextually converted to bool (Clause [conv]).

The function object pred shall not apply any non-constant function through the dereferenced iterator.

The BinaryPredicate parameter is used whenever an algorithm expects a function object that when applied to the result of dereferencing two corresponding iterators or to dereferencing an iterator and type T when T is part of the signature returns a value testable as true.

In other words, if an algorithm takes BinaryPredicate binary_pred as its argument and first1 and first2 as its iterator arguments, it should work correctly in the construct binary_pred(*first1, *first2) contextually converted to bool (Clause [conv]).

BinaryPredicate always takes the first iterator's value_type as its first argument, that is, in those cases when T value is part of the signature, it should work correctly in the construct binary_pred(*first1, value) contextually converted to bool (Clause [conv]).

binary_pred shall not apply any non-constant function through the dereferenced iterators.

[ 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

]

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.

In the description of the algorithms operators + and - are used for some of the iterator categories for which they do not have to be defined.

In these cases the semantics of a+n is the same as that of

X tmp = a;
advance(tmp, n);
return tmp;

and that of b-a is the same as of

return distance(a, b);

262)

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.

28.4 Parallel algorithms [algorithms.parallel]

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

28.4.1 Terms and definitions [algorithms.parallel.defns]

A parallel algorithm is a function template listed in this International Standard with a template parameter named ExecutionPolicy.

Parallel algorithms access objects indirectly accessible via their arguments by invoking the following functions:

(2.1)
All operations of the categories of the iterators that the algorithm is instantiated with.
(2.2)
Operations on those sequence elements that are required by its specification.
(2.3)
User-provided function objects to be applied during the execution of the algorithm, if required by the specification.
(2.4)
Operations on those function objects required by the specification.

[ Note
:
See [algorithms.general].
— 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

]

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

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.

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

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.

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

]

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

]

The invocations of element access functions in parallel algorithms invoked with an execution policy object of type execution::parallel_policy are permitted to execute in either the invoking thread of execution or in a thread of execution implicitly created by the library to support parallel algorithm execution.

If the threads of execution created by thread ([thread.thread.class]) provide concurrent forward progress guarantees ([intro.progress]), then a thread of execution implicitly created by the library will provide parallel forward progress guarantees; otherwise, the provided forward progress guarantee is implementation-defined.

Any such invocations executing in the same thread of execution are indeterminately sequenced with respect to each other.

[ Note

It is the caller's responsibility to ensure that the invocation does not introduce data races or deadlocks.

— end note

]

[ Example

int a[] = {0,1};
std::vector<int> v;
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int i) {
  v.push_back(i*2+1); // incorrect: data race
});

The program above has a data race because of the unsynchronized access to the container v.

— end example

]

[ Example

std::atomic<int> x{0};
int a[] = {1,2};
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int) {
  x.fetch_add(1, std::memory_order_relaxed);
  // spin wait for another iteration to change the value of x
  while (x.load(std::memory_order_relaxed) == 1) { } // incorrect: assumes execution order
});

The above example depends on the order of execution of the iterations, and will not terminate if both iterations are executed sequentially on the same thread of execution.

— end example

]

[ Example

int x = 0;
std::mutex m;
int a[] = {1,2};
std::for_each(std::execution::par, std::begin(a), std::end(a), [&](int) {
  std::lock_guard<mutex> guard(m);
  ++x;
});

The above example synchronizes access to object x ensuring that it is incremented correctly.

— end example

]

The invocations of element access functions in parallel algorithms invoked with an execution policy of type execution::parallel_unsequenced_policy are permitted to execute in an unordered fashion in unspecified threads of execution, and unsequenced with respect to one another within each thread of execution.

These threads of execution are either the invoking thread of execution or threads of execution implicitly created by the library; the latter will provide weakly parallel forward progress guarantees.

[ Note

This means that multiple function object invocations may be interleaved on a single thread of execution, which overrides the usual guarantee from [intro.execution] that function executions do not interleave with one another.

— end note

]

Since execution::parallel_unsequenced_policy allows the execution of element access functions to be interleaved on a single thread of execution, blocking synchronization, including the use of mutexes, risks deadlock.

Thus, the synchronization with execution::parallel_unsequenced_policy is restricted as follows: A standard library function is vectorization-unsafe if it is specified to synchronize with another function invocation, or another function invocation is specified to synchronize with it, and if it is not a memory allocation or deallocation function.

Vectorization-unsafe standard library functions may not be invoked by user code called from execution::parallel_unsequenced_policy algorithms.

[ Note

Implementations must ensure that internal synchronization inside standard library functions does not prevent forward progress when those functions are executed by threads of execution with weakly parallel forward progress guarantees.

— end note

]

[ Example

int x = 0;
std::mutex m;
int a[] = {1,2};
std::for_each(std::execution::par_unseq, std::begin(a), std::end(a), [&](int) {
  std::lock_guard<mutex> guard(m); // incorrect: lock_guard constructor calls m.lock()
  ++x;
});

The above program may result in two consecutive calls to m.lock() on the same thread of execution (which may deadlock), because the applications of the function object are not guaranteed to run on different threads of execution.

— end example

]

[ Note

The semantics of the execution::parallel_policy or the execution::parallel_unsequenced_policy invocation allow the implementation to fall back to sequential execution if the system cannot parallelize an algorithm invocation due to lack of resources.

— end note

]

If an invocation of a parallel algorithm uses threads of execution implicitly created by the library, then the invoking thread of execution will either

(6.1)
temporarily block with forward progress guarantee delegation ([intro.progress]) on the completion of these library-managed threads of execution, or
(6.2)
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

]

The semantics of parallel algorithms invoked with an execution policy object of implementation-defined type are implementation-defined.

28.4.4 Parallel algorithm exceptions [algorithms.parallel.exceptions]

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.

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.

28.4.5 ExecutionPolicy algorithm overloads [algorithms.parallel.overloads]

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

]

Unless otherwise specified, the semantics of ExecutionPolicy algorithm overloads are identical to their overloads without.

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

O ()

notation, the complexity of the algorithm shall be

O (expr)

Parallel algorithms shall not participate in overload resolution unless is_execution_policy_v<decay_t<ExecutionPolicy>> is true.

28.5 Non-modifying sequence operations [alg.nonmodifying]

28.5.1 All of [alg.all_of]

🔗

template <class InputIterator, class Predicate>
  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);

Returns: true if [first, last) is empty or if pred(*i) is true for every iterator i in the range [first, last), and false otherwise.

Complexity: At most last - first applications of the predicate.

28.5.2 Any of [alg.any_of]

🔗

template <class InputIterator, class Predicate>
  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);

Returns: false if [first, last) is empty or if there is no iterator i in the range [first, last) such that pred(*i) is true, and true otherwise.

Complexity: At most last - first applications of the predicate.

28.5.3 None of [alg.none_of]

🔗

template <class InputIterator, class Predicate>
  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);

Returns: true if [first, last) is empty or if pred(*i) is false for every iterator i in the range [first, last), and false otherwise.

Complexity: At most last - first applications of the predicate.

28.5.4 For each [alg.foreach]

🔗

template<class InputIterator, class Function>
  Function for_each(InputIterator first, InputIterator last, Function f);

Requires: Function shall meet the requirements of MoveConstructible (Table 23).

[ Note

Function need not meet the requirements of CopyConstructible (Table 24).

— end note

]

Effects: Applies f to the result of dereferencing every iterator in the range [first, last), starting from first and proceeding to last - 1.

[ Note

If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.

— end note

]

Returns: f.

Complexity: Applies f exactly last - first times.

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);

Requires: Function shall meet the requirements of CopyConstructible.

Effects: Applies f to the result of dereferencing every iterator in the range [first, last).

[ Note

If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.

— end note

]

Complexity: Applies f exactly last - first times.

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.

[ Note

Does not return a copy of its Function parameter, since parallelization may not permit efficient state accumulation.

— end note

]

🔗

template<class InputIterator, class Size, class Function>
  InputIterator for_each_n(InputIterator first, Size n, Function f);

Requires: Function shall meet the requirements of MoveConstructible

[ Note

Function need not meet the requirements of CopyConstructible.

— end note

]

Requires: n >= 0.

Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n) in order.

[ Note

If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.

— end note

]

Returns: first + n.

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);

Requires: Function shall meet the requirements of CopyConstructible.

Requires: n >= 0.

Effects: Applies f to the result of dereferencing every iterator in the range [first, first + n).

[ Note

If the type of first satisfies the requirements of a mutable iterator, f may apply non-constant functions through the dereferenced iterator.

— end note

]

Returns: first + n.

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.

28.5.5 Find [alg.find]

🔗

template<class InputIterator, class T>
  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>
  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>
  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);

Returns: The first iterator i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false, pred(*i) == false.

Returns last if no such iterator is found.

Complexity: At most last - first applications of the corresponding predicate.

28.5.6 Find end [alg.find.end]

🔗

template<class ForwardIterator1, class ForwardIterator2>
  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>
  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);

Effects: Finds a subsequence of equal values in a sequence.

Returns: The last iterator i in the range [first1, last1 - (last2 - first2)) such that for every non-negative integer n < (last2 - first2), the following corresponding conditions hold: *(i + n) == *(first2 + n), pred(*(i + n), *(first2 + n)) != false.

Returns last1 if [first2, last2) is empty or if no such iterator is found.

Complexity: At most (last2 - first2) * (last1 - first1 - (last2 - first2) + 1) applications of the corresponding predicate.

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

🔗

template<class InputIterator, class ForwardIterator>
  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>
  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);

Effects: Finds an element that matches one of a set of values.

Returns: The first iterator i in the range [first1, last1) such that for some iterator j in the range [first2, last2) the following conditions hold: *i == *j, pred(*i,*j) != false.

Returns last1 if [first2, last2) is empty or if no such iterator is found.

Complexity: At most (last1-first1) * (last2-first2) applications of the corresponding predicate.

28.5.8 Adjacent find [alg.adjacent.find]

🔗

template<class ForwardIterator>
  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>
  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);

Returns: The first iterator i such that both i and i + 1 are in the range [first, last) for which the following corresponding conditions hold: *i == *(i + 1), pred(*i, *(i + 1)) != false.

Returns last if no such iterator is found.

Complexity: For the overloads with no ExecutionPolicy, exactly min((i - first) + 1, (last - first) - 1) applications of the corresponding predicate, where i is adjacent_find's return value.

For the overloads with an ExecutionPolicy,

O (last - first)

applications of the corresponding predicate.

28.5.9 Count [alg.count]

🔗

template<class InputIterator, class T>
  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>
  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);

Effects: Returns the number of iterators i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false.

Complexity: Exactly last - first applications of the corresponding predicate.

28.5.10 Mismatch [mismatch]

🔗

template<class InputIterator1, class InputIterator2>
  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>
  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>
  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>
  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);

Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.

Returns: A pair of iterators first1 + n and first2 + n, where n is the smallest integer such that, respectively,

(2.1)
!(*(first1 + n) == *(first2 + n)) or
(2.2)
pred(*(first1 + n), *(first2 + n)) == false,

or min(last1 - first1, last2 - first2) if no such integer exists.

Complexity: At most min(last1 - first1, last2 - first2) applications of the corresponding predicate.

28.5.11 Equal [alg.equal]

🔗

template<class InputIterator1, class InputIterator2>
  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>
  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>
  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>
  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);

Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.

Returns: If last1 - first1 != last2 - first2, return false.

Otherwise return true if for every iterator i in the range [first1, last1) the following corresponding conditions hold: *i == *(first2 + (i - first1)), pred(*i, *(first2 + (i - first1))) != false.

Otherwise, returns false.

Complexity:

(3.1)
For the overloads with no ExecutionPolicy,
- (3.1.1)
  if InputIterator1 and InputIterator2 meet the requirements of random access iterators ([random.access.iterators]) and last1 - first1 != last2 - first2, then no applications of the corresponding predicate; otherwise,
- (3.1.2)
  at most $min (last1 - first1, last2 - first2)$ applications of the corresponding predicate.
(3.2)
For the overloads with no ExecutionPolicy,
- (3.2.1)
  if ForwardIterator1 and ForwardIterator2 meet the requirements of random access iterators and last1 - first1 != last2 - first2, then no applications of the corresponding predicate; otherwise,
- (3.2.2)
  $O (min (last1 - first1, last2 - first2))$ applications of the corresponding predicate.

28.5.12 Is permutation [alg.is_permutation]

🔗

template<class ForwardIterator1, class ForwardIterator2>
  bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                      ForwardIterator2 first2);
template<class ForwardIterator1, class ForwardIterator2,
                 class BinaryPredicate>
  bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                      ForwardIterator2 first2, BinaryPredicate pred);
template<class ForwardIterator1, class ForwardIterator2>
  bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                      ForwardIterator2 first2, ForwardIterator2 last2);
template<class ForwardIterator1, class ForwardIterator2,
                 class BinaryPredicate>
  bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                      ForwardIterator2 first2, ForwardIterator2 last2,
                      BinaryPredicate pred);

Requires: ForwardIterator1 and ForwardIterator2 shall have the same value type.

The comparison function shall be an equivalence relation.

Remarks: If last2 was not given in the argument list, it denotes first2 + (last1 - first1) below.

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.

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

O (N^{2})

, where N has the value last1 - first1.

28.5.13 Search [alg.search]

🔗

template<class ForwardIterator1, class ForwardIterator2>
  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>
  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);

Effects: Finds a subsequence of equal values in a sequence.

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.

Complexity: At most (last1 - first1) * (last2 - first2) applications of the corresponding predicate.

🔗

template<class ForwardIterator, class Size, class T>
  ForwardIterator
    search_n(ForwardIterator first, ForwardIterator last, Size count,
             const T& value);

template<class ForwardIterator, class Size, class T,
         class BinaryPredicate>
  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,
             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,
             ForwardIterator first, ForwardIterator last,
             Size count, const T& value,
             BinaryPredicate pred);

Requires: The type Size shall be convertible to integral type ([conv.integral], [class.conv]).

Effects: Finds a subsequence of equal values in a sequence.

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.

Complexity: At most last - first applications of the corresponding predicate.

🔗

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

Effects: Equivalent to: return searcher(first, last).first;

Remarks: Searcher need not meet the CopyConstructible requirements.

28.6 Mutating sequence operations [alg.modifying.operations]

28.6.1 Copy [alg.copy]

🔗

template<class InputIterator, class OutputIterator>
  OutputIterator copy(InputIterator first, InputIterator last,
                      OutputIterator result);

Requires: result shall not be in the range [first, last).

Effects: Copies elements in the range [first, last) into the range [result, result + (last - first)) starting from first and proceeding to last.

For each non-negative integer n < (last - first), performs *(result + n) = *(first + n).

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

🔗

template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
  ForwardIterator2 copy(ExecutionPolicy&& policy,
                        ForwardIterator1 first, ForwardIterator1 last,
                        ForwardIterator2 result);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

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).

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

🔗

template<class InputIterator, class Size, class OutputIterator>
  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);

Effects: For each non-negative integer

i < n

, performs *(result + i) = *(first + i).

Returns: result + n.

Complexity: Exactly n assignments.

🔗

template<class InputIterator, class OutputIterator, class Predicate>
  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);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

[ Note

For the overload with an ExecutionPolicy, there may be a performance cost if iterator_traits<ForwardIterator1>::value_type is not MoveConstructible (Table 23).

— end note

]

Effects: Copies all of the elements referred to by the iterator i in the range [first, last) for which pred(*i) is true.

Returns: The end of the resulting range.

Complexity: Exactly last - first applications of the corresponding predicate.

Remarks: Stable ([algorithm.stable]).

🔗

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

Requires: result shall not be in the range (first, last].

Effects: Copies elements in the range [first, last) into the range [result - (last-first), result) starting from last - 1 and proceeding to first.263

For each positive integer n <= (last - first), performs *(result - n) = *(last - n).

Returns: result - (last - first).

Complexity: Exactly last - first assignments.

263)

copy_backward should be used instead of copy when last is in the range [result - (last - first), result).

28.6.2 Move [alg.move]

🔗

template<class InputIterator, class OutputIterator>
  OutputIterator move(InputIterator first, InputIterator last, OutputIterator result);

Requires: result shall not be in the range [first, last).

Effects: Moves elements in the range [first, last) into the range [result, result + (last - first)) starting from first and proceeding to last.

For each non-negative integer n < (last-first), performs *(result + n) = std::move(*(first + n)).

Returns: result + (last - first).

Complexity: Exactly last - first move assignments.

🔗

template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2>
  ForwardIterator2 move(ExecutionPolicy&& policy,
                        ForwardIterator1 first, ForwardIterator1 last,
                        ForwardIterator2 result);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

Effects: Moves elements in the range [first, last) into the range [result, result + (last - first)).

For each non-negative integer n < (last - first), performs *(result + n) = std::move(*(first + n)).

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

🔗

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

Requires: result shall not be in the range (first, last].

Effects: Moves elements in the range [first, last) into the range [result - (last-first), result) starting from last - 1 and proceeding to first.264

For each positive integer n <= (last - first), performs *(result - n) = std::move(*(last - n)).

Returns: result - (last - first).

Complexity: Exactly last - first assignments.

264)

move_backward should be used instead of move when last is in the range [result - (last - first), result).

28.6.3 Swap [alg.swap]

🔗

template<class ForwardIterator1, class ForwardIterator2>
  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);

Requires: The two ranges [first1, last1) and [first2, first2 + (last1 - first1)) shall not overlap.

*(first1 + n) shall be swappable with ([swappable.requirements]) *(first2 + n).

Effects: For each non-negative integer n < (last1 - first1) performs: swap(*(first1 + n), *(first2 + n)).

Returns: first2 + (last1 - first1).

Complexity: Exactly last1 - first1 swaps.

🔗

template<class ForwardIterator1, class ForwardIterator2>
  void iter_swap(ForwardIterator1 a, ForwardIterator2 b);

Requires: a and b shall be dereferenceable.

*a shall be swappable with ([swappable.requirements]) *b.

Effects: As if by swap(*a, *b).

28.6.4 Transform [alg.transform]

🔗

template<class InputIterator, class OutputIterator,
         class UnaryOperation>
  OutputIterator
    transform(InputIterator first, InputIterator last,
              OutputIterator result, UnaryOperation op);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
         class UnaryOperation>
  ForwardIterator2
    transform(ExecutionPolicy&& exec,
              ForwardIterator1 first, ForwardIterator1 last,
              ForwardIterator2 result, UnaryOperation op);

template<class InputIterator1, class InputIterator2,
         class OutputIterator, class BinaryOperation>
  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);

Requires: op and binary_op shall not invalidate iterators or subranges, or modify elements in the ranges

(1.1)
[first1, last1],
(1.2)
[first2, first2 + (last1 - first1)], and
(1.3)
[result, result + (last1 - first1)].265

Effects: Assigns through every iterator i in the range [result, result + (last1 - first1)) a new corresponding value equal to op(*(first1 + (i - result))) or binary_op(*(first1 + (i - result)), *(first2 + (i - result))).

Returns: result + (last1 - first1).

Complexity: Exactly last1 - first1 applications of op or binary_op.

This requirement also applies to the overload with an ExecutionPolicy .

Remarks: result may be equal to first in case of unary transform, or to first1 or first2 in case of binary transform.

265)

The use of fully closed ranges is intentional.

28.6.5 Replace [alg.replace]

🔗

template<class ForwardIterator, class T>
  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>
  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);

Requires: The expression *first = new_value shall be valid.

Effects: Substitutes elements referred by the iterator i in the range [first, last) with new_value, when the following corresponding conditions hold: *i == old_value, pred(*i) != false.

Complexity: Exactly last - first applications of the corresponding predicate.

🔗

template<class InputIterator, class OutputIterator, class T>
  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>
  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);

Requires: The results of the expressions *first and new_value shall be writable ([iterator.requirements.general]) to the result output iterator.

The ranges [first, last) and [result, result + (last - first)) shall not overlap.

Effects: Assigns to every iterator i in the range [result, result + (last - first)) either new_value or *(first + (i - result)) depending on whether the following corresponding conditions hold:

*(first + (i - result)) == old_value
pred(*(first + (i - result))) != false

Returns: result + (last - first).

Complexity: Exactly last - first applications of the corresponding predicate.

28.6.6 Fill [alg.fill]

🔗

template<class ForwardIterator, class T>
  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>
  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);

Requires: The expression value shall be writable ([iterator.requirements.general]) to the output iterator.

The type Size shall be convertible to an integral type ([conv.integral], [class.conv]).

Effects: The fill algorithms assign value through all the iterators in the range [first, last).

The fill_n algorithms assign value through all the iterators in the range [first, first + n) if n is positive, otherwise they do nothing.

Returns: fill_n returns first + n for non-negative values of n and first for negative values.

Complexity: Exactly last - first, n, or 0 assignments, respectively.

28.6.7 Generate [alg.generate]

🔗

template<class ForwardIterator, class Generator>
  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>
  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);

Requires: gen takes no arguments, Size shall be convertible to an integral type ([conv.integral], [class.conv]).

Effects: The generate algorithms invoke the function object gen and assign the return value of gen through all the iterators in the range [first, last).

The generate_n algorithms invoke the function object gen and assign the return value of gen through all the iterators in the range [first, first + n) if n is positive, otherwise they do nothing.

Returns: generate_n returns first + n for non-negative values of n and first for negative values.

Complexity: Exactly last - first, n, or 0 invocations of gen and assignments, respectively.

28.6.8 Remove [alg.remove]

🔗

template<class ForwardIterator, class T>
  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>
  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);

Requires: The type of *first shall satisfy the MoveAssignable requirements (Table 25).

Effects: Eliminates all the elements referred to by iterator i in the range [first, last) for which the following corresponding conditions hold: *i == value, pred(*i) != false.

Returns: The end of the resulting range.

Remarks: Stable ([algorithm.stable]).

Complexity: Exactly last - first applications of the corresponding predicate.

[ 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>
  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>
  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);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

The expression *result = *first shall be valid.

[ Note

For the overloads with an ExecutionPolicy, there may be a performance cost if iterator_traits<ForwardIterator1>::value_type is not MoveConstructible (Table 23).

— end note

]

Effects: Copies all the elements referred to by the iterator i in the range [first, last) for which the following corresponding conditions do not hold: *i == value, pred(*i) != false.

Returns: The end of the resulting range.

Complexity: Exactly last - first applications of the corresponding predicate.

Remarks: Stable ([algorithm.stable]).

28.6.9 Unique [alg.unique]

🔗

template<class ForwardIterator>
  ForwardIterator unique(ForwardIterator first, ForwardIterator last);
template<class ExecutionPolicy, class ForwardIterator>
  ForwardIterator unique(ExecutionPolicy&& exec,
                         ForwardIterator first, ForwardIterator last);

template<class ForwardIterator, class BinaryPredicate>
  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);

Requires: The comparison function shall be an equivalence relation.

The type of *first shall satisfy the MoveAssignable requirements (Table 25).

Effects: For a nonempty range, eliminates all but the first element from every consecutive group of equivalent elements referred to by the iterator i in the range [first + 1, last) for which the following conditions hold: *(i - 1) == *i or pred(*(i - 1), *i) != false.

Returns: The end of the resulting range.

Complexity: For nonempty ranges, exactly (last - first) - 1 applications of the corresponding predicate.

🔗

template<class InputIterator, class OutputIterator>
  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>
  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);

Requires:

(5.1)
The comparison function shall be an equivalence relation.
(5.2)
The ranges [first, last) and [result, result+(last-first)) shall not overlap.
(5.3)
The expression *result = *first shall be valid.
(5.4)
For the overloads with no ExecutionPolicy, let T be the value type of InputIterator.

If InputIterator meets the forward iterator requirements, then there are no additional requirements for T.

Otherwise, if OutputIterator meets the forward iterator requirements and its value type is the same as T, then T shall be CopyAssignable (Table 26).

Otherwise, T shall be both CopyConstructible (Table 24) and CopyAssignable.

[ Note
:
For the overloads with an ExecutionPolicy, there may be a performance cost if the value type of ForwardIterator1 is not both CopyConstructible and CopyAssignable.
— end note
]

Effects: Copies only the first element from every consecutive group of equal elements referred to by the iterator i in the range [first, last) for which the following corresponding conditions hold: *i == *(i - 1) or pred(*i, *(i - 1)) != false.

Returns: The end of the resulting range.

Complexity: For nonempty ranges, exactly last - first - 1 applications of the corresponding predicate.

28.6.10 Reverse [alg.reverse]

🔗

template<class BidirectionalIterator>
  void reverse(BidirectionalIterator first, BidirectionalIterator last);
template<class ExecutionPolicy, class BidirectionalIterator>
  void reverse(ExecutionPolicy&& exec,
               BidirectionalIterator first, BidirectionalIterator last);

Requires: *first shall be swappable ([swappable.requirements]).

Effects: For each non-negative integer i < (last - first) / 2, applies iter_swap to all pairs of iterators first + i, (last - i) - 1.

Requires: BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

Complexity: Exactly (last - first)/2 swaps.

🔗

template<class BidirectionalIterator, class OutputIterator>
  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);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

Effects: Copies the range [first, last) to the range [result, result + (last - first)) such that for every non-negative integer i < (last - first) the following assignment takes place: *(result + (last - first) - 1 - i) = *(first + i).

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

28.6.11 Rotate [alg.rotate]

🔗

template<class ForwardIterator>
  ForwardIterator
    rotate(ForwardIterator first, ForwardIterator middle, ForwardIterator last);
template<class ExecutionPolicy, class ForwardIterator>
  ForwardIterator
    rotate(ExecutionPolicy&& exec,
           ForwardIterator first, ForwardIterator middle, ForwardIterator last);

Requires: [first, middle) and [middle, last) shall be valid ranges.

ForwardIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and the requirements of MoveAssignable (Table 25).

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).

Returns: first + (last - middle).

Remarks: This is a left rotate.

Complexity: At most last - first swaps.

🔗

template<class ForwardIterator, class OutputIterator>
  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);

Requires: The ranges [first, last) and [result, result + (last - first)) shall not overlap.

Effects: Copies the range [first, last) to the range [result, result + (last - first)) such that for each non-negative integer i < (last - first) the following assignment takes place: *(result + i) = *(first + (i + (middle - first)) % (last - first)).

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

28.6.12 Sample [alg.random.sample]

🔗

template<class PopulationIterator, class SampleIterator,
         class Distance, class UniformRandomBitGenerator>
  SampleIterator sample(PopulationIterator first, PopulationIterator last,
                        SampleIterator out, Distance n,
                        UniformRandomBitGenerator&& g);

Requires:

(1.1)
PopulationIterator shall satisfy the requirements of an input iterator ([input.iterators]).
(1.2)
SampleIterator shall satisfy the requirements of an output iterator ([output.iterators]).
(1.3)
SampleIterator shall satisfy the additional requirements of a random access iterator ([random.access.iterators]) unless PopulationIterator satisfies the additional requirements of a forward iterator ([forward.iterators]).
(1.4)
PopulationIterator's value type shall be writable ([iterator.requirements.general]) to out.
(1.5)
Distance shall be an integer type.
(1.6)
remove_reference_t<UniformRandomBitGenerator> shall meet the requirements of a uniform random bit generator type ([rand.req.urng]) whose return type is convertible to Distance.
(1.7)
out shall not be in the range [first, last).

Effects: Copies min(last - first, n) elements (the sample) from [first, last) (the population) to out such that each possible sample has equal probability of appearance.

[ Note

Algorithms that obtain such effects include selection sampling and reservoir sampling.

— end note

]

Returns: The end of the resulting sample range.

Complexity:

O (last - first)

Remarks:

(5.1)
Stable if and only if PopulationIterator satisfies the requirements of a forward iterator.
(5.2)
To the extent that the implementation of this function makes use of random numbers, the object g shall serve as the implementation's source of randomness.

28.6.13 Shuffle [alg.random.shuffle]

🔗

template<class RandomAccessIterator, class UniformRandomBitGenerator>
  void shuffle(RandomAccessIterator first,
               RandomAccessIterator last,
               UniformRandomBitGenerator&& g);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type remove_reference_t<UniformRandomBitGenerator> shall meet the requirements of a uniform random bit generator ([rand.req.urng]) type whose return type is convertible to iterator_traits<RandomAccessIterator>::difference_type.

Effects: Permutes the elements in the range [first, last) such that each possible permutation of those elements has equal probability of appearance.

Complexity: Exactly (last - first) - 1 swaps.

Remarks: To the extent that the implementation of this function makes use of random numbers, the object g shall serve as the implementation's source of randomness.

28.7 Sorting and related operations [alg.sorting]

All the operations in [alg.sorting] have two versions: one that takes a function object of type Compare and one that uses an operator<.

Compare is a function object type ([function.objects]).

The return value of the function call operation applied to an object of type Compare, when contextually converted to bool (Clause [conv]), yields true if the first argument of the call is less than the second, and false otherwise.

Compare comp is used throughout for algorithms assuming an ordering relation.

It is assumed that comp will not apply any non-constant function through the dereferenced iterator.

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.

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
(4.5)
The induced relation is a strict total ordering.

— end note

]

A sequence is sorted with respect to a comparator comp if for every iterator i pointing to the sequence and every non-negative integer n such that i + n is a valid iterator pointing to an element of the sequence, comp(*(i + n), *i) == false.

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.

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).

28.7.1 Sorting [alg.sort]

28.7.1.1 sort [sort]

🔗

template<class RandomAccessIterator>
  void sort(RandomAccessIterator first, RandomAccessIterator last);
template<class ExecutionPolicy, class RandomAccessIterator>
  void sort(ExecutionPolicy&& exec,
            RandomAccessIterator first, RandomAccessIterator last);

template<class RandomAccessIterator, class Compare>
  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);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Sorts the elements in the range [first, last).

Complexity:

O (N log N)

comparisons, where

N = last - first

28.7.1.2 stable_sort [stable.sort]

🔗

template<class RandomAccessIterator>
  void stable_sort(RandomAccessIterator first, RandomAccessIterator last);
template<class ExecutionPolicy, class RandomAccessIterator>
  void stable_sort(ExecutionPolicy&& exec,
                   RandomAccessIterator first, RandomAccessIterator last);

template<class RandomAccessIterator, class Compare>
  void stable_sort(RandomAccessIterator first, RandomAccessIterator last,
                   Compare comp);
template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
  void stable_sort(ExecutionPolicy&& exec,
                   RandomAccessIterator first, RandomAccessIterator last,
                   Compare comp);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Sorts the elements in the range [first, last).

Complexity: At most

N log^{2} (N)

comparisons, where

N = last - first

, but only

N log N

comparisons if there is enough extra memory.

Remarks: Stable ([algorithm.stable]).

28.7.1.3 partial_sort [partial.sort]

🔗

template<class RandomAccessIterator>
  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>
  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);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Places the first middle - first sorted elements from the range [first, last) into the range [first, middle).

The rest of the elements in the range [middle, last) are placed in an unspecified order.

Complexity: Approximately (last - first) * log(middle - first) comparisons.

28.7.1.4 partial_sort_copy [partial.sort.copy]

🔗

template<class InputIterator, class RandomAccessIterator>
  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>
  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);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *result_first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Places the first min(last - first, result_last - result_first) sorted elements into the range [result_first, result_first + min(last - first, result_last - result_first)).

Returns: The smaller of: result_last or result_first + (last - first).

Complexity: Approximately (last - first) * log(min(last - first, result_last - result_first)) comparisons.

28.7.1.5 is_sorted [is.sorted]

🔗

template<class ForwardIterator>
  bool is_sorted(ForwardIterator first, ForwardIterator last);

Returns: is_sorted_until(first, last) == last

🔗

template<class ExecutionPolicy, class ForwardIterator>
  bool is_sorted(ExecutionPolicy&& exec,
                 ForwardIterator first, ForwardIterator last);

Returns: is_sorted_until(std::forward<ExecutionPolicy>(exec), first, last) == last

🔗

template<class ForwardIterator, class Compare>
  bool is_sorted(ForwardIterator first, ForwardIterator last,
                 Compare comp);

Returns: is_sorted_until(first, last, comp) == last

🔗

template<class ExecutionPolicy, class ForwardIterator, class Compare>
  bool is_sorted(ExecutionPolicy&& exec,
                 ForwardIterator first, ForwardIterator last,
                 Compare comp);

Returns:

is_sorted_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last

🔗

template<class ForwardIterator>
  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>
  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);

Returns: If (last - first) < 2, returns last.

Otherwise, returns the last iterator i in [first, last] for which the range [first, i) is sorted.

Complexity: Linear.

28.7.2 Nth element [alg.nth.element]

🔗

template<class RandomAccessIterator>
  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>
  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);

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: After nth_element the element in the position pointed to by nth is the element that would be in that position if the whole range were sorted, unless nth == last.

Also for every iterator i in the range [first, nth) and every iterator j in the range [nth, last) it holds that: !(*j < *i) or comp(*j, *i) == false.

Complexity: For the overloads with no ExecutionPolicy, linear on average.

For the overloads with an ExecutionPolicy,

O (N)

applications of the predicate, and

O (N log N)

swaps, where

N = last - first

28.7.3 Binary search [alg.binary.search]

All of the algorithms in this section are versions of binary search and assume that the sequence being searched is partitioned with respect to an expression formed by binding the search key to an argument of the implied or explicit comparison function.

They work on non-random access iterators minimizing the number of comparisons, which will be logarithmic for all types of iterators.

They are especially appropriate for random access iterators, because these algorithms do a logarithmic number of steps through the data structure.

For non-random access iterators they execute a linear number of steps.

28.7.3.1 lower_bound [lower.bound]

🔗

template<class ForwardIterator, class T>
  ForwardIterator
    lower_bound(ForwardIterator first, ForwardIterator last,
                const T& value);

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

Requires: The elements e of [first, last) shall be partitioned with respect to the expression e < value or comp(e, value).

Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i) the following corresponding conditions hold: *j < value or comp(*j, value) != false.

Complexity: At most

log_{2} (last - first) + O (1)

comparisons.

28.7.3.2 upper_bound [upper.bound]

🔗

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

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

Requires: The elements e of [first, last) shall be partitioned with respect to the expression !(value < e) or !comp(value, e).

Returns: The furthermost iterator i in the range [first, last] such that for every iterator j in the range [first, i) the following corresponding conditions hold: !(value < *j) or comp(value, *j) == false.

Complexity: At most

log_{2} (last - first) + O (1)

comparisons.

28.7.3.3 equal_range [equal.range]

🔗

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

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

Requires: The elements e of [first, last) shall be partitioned with respect to the expressions e < value and !(value < e) or comp(e, value) and !comp(value, e).

Also, for all elements e of [first, last), e < value shall imply !(value < e) or comp(e, value) shall imply !comp(value, e).

Returns:

make_pair(lower_bound(first, last, value),
          upper_bound(first, last, value))

make_pair(lower_bound(first, last, value, comp),
          upper_bound(first, last, value, comp))

Complexity: At most

2 * log_{2} (last - first) + O (1)

comparisons.

28.7.3.4 binary_search [binary.search]

🔗

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

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

Requires: The elements e of [first, last) are partitioned with respect to the expressions e < value and !(value < e) or comp(e, value) and !comp(value, e).

Also, for all elements e of [first, last), e < value implies !(value < e) or comp(e, value) implies !comp(value, e).

Returns: true if there is an iterator i in the range [first, last) that satisfies the corresponding conditions: !(*i < value) && !(value < *i) or comp(*i, value) == false && comp(value, *i) == false.

Complexity: At most

log_{2} (last - first) + O (1)

comparisons.

28.7.4 Partitions [alg.partitions]

🔗

template <class InputIterator, class Predicate>
  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);

Requires: For the overload with no ExecutionPolicy, InputIterator's value type shall be convertible to Predicate's argument type.

For the overload with an ExecutionPolicy, ForwardIterator's value type shall be convertible to Predicate's argument type.

Returns: true if [first, last) is empty or if [first, last) is partitioned by pred, i.e. if all elements that satisfy pred appear before those that do not.

Complexity: Linear.

At most last - first applications of pred.

🔗

template<class ForwardIterator, class Predicate>
  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);

Requires: ForwardIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

Effects: Places all the elements in the range [first, last) that satisfy pred before all the elements that do not satisfy it.

Returns: An iterator i such that for every iterator j in the range [first, i) pred(*j) != false, and for every iterator k in the range [i, last), pred(*k) == false.

Complexity: Let

N = last - first

(7.1)
For the overload with no ExecutionPolicy, exactly N applications of the predicate.

At most $N / 2$ swaps if ForwardIterator meets the BidirectionalIterator requirements and at most N swaps otherwise.
(7.2)
For the overload with an ExecutionPolicy, $O (N log N)$ swaps and $O (N)$ 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);

Requires: BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Places all the elements in the range [first, last) that satisfy pred before all the elements that do not satisfy it.

Returns: An iterator i such that for every iterator j in the range [first, i), pred(*j) != false, and for every iterator k in the range [i, last), pred(*k) == false.

The relative order of the elements in both groups is preserved.

Complexity: Let N = last - first:

(11.1)
For the overload with no ExecutionPolicy, at most $N log N$ swaps, but only $O (N)$ swaps if there is enough extra memory.

Exactly N applications of the predicate.
(11.2)
For the overload with an ExecutionPolicy, $O (N log N)$ swaps and $O (N)$ applications of the predicate.

🔗

template <class InputIterator, class OutputIterator1,
          class OutputIterator2, class Predicate>
  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);

Requires:

(12.1)
For the overload with no ExecutionPolicy, InputIterator's value type shall be CopyAssignable (Table 26), and shall be writable ([iterator.requirements.general]) to the out_true and out_false OutputIterators, and shall be convertible to Predicate's argument type.
(12.2)
For the overload with an ExecutionPolicy, ForwardIterator's value type shall be CopyAssignable, and shall be writable to the out_true and out_false ForwardIterators, and shall be convertible to Predicate's argument type.

[ Note
:
There may be a performance cost if ForwardIterator's value type is not CopyConstructible.
— end note
]
(12.3)
For both overloads, the input range shall not overlap with either of the output ranges.

Effects: For each iterator i in [first, last), copies *i to the output range beginning with out_true if pred(*i) is true, or to the output range beginning with out_false otherwise.

Returns: A pair p such that p.first is the end of the output range beginning at out_true and p.second is the end of the output range beginning at out_false.

Complexity: Exactly last - first applications of pred.

🔗

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

Requires: ForwardIterator's value type shall be convertible to Predicate's argument type.

[first, last) shall be partitioned by pred, i.e. all elements that satisfy pred shall appear before those that do not.

Returns: An iterator mid such that all_of(first, mid, pred) and none_of(mid, last, pred) are both true.

Complexity:

O (log (last - first))

applications of pred.

28.7.5 Merge [alg.merge]

🔗

template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  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>
  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);

Requires: The ranges [first1, last1) and [first2, last2) shall be sorted with respect to operator< or comp.

The resulting range shall not overlap with either of the original ranges.

Effects: Copies all the elements of the two ranges [first1, last1) and [first2, last2) into the range [result, result_last), where result_last is result + (last1 - first1) + (last2 - first2), such that the resulting range satisfies is_sorted(result, result_last) or is_sorted(result, result_last, comp), respectively.

Returns: result + (last1 - first1) + (last2 - first2).

Complexity: Let

N = (last1 - first1) + (last2 - first2)

(4.1)
For the overloads with no ExecutionPolicy, at most $N - 1$ comparisons.
(4.2)
For the overloads with an ExecutionPolicy, $O (N)$ comparisons.

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);

Requires: The ranges [first, middle) and [middle, last) shall be sorted with respect to operator< or comp.

BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Merges two sorted consecutive ranges [first, middle) and [middle, last), putting the result of the merge into the range [first, last).

The resulting range will be in non-decreasing order; that is, for every iterator i in [first, last) other than first, the condition *i < *(i - 1) or, respectively, comp(*i, *(i - 1)) will be false.

Complexity: Let

N = last - first

(8.1)
For the overloads with no ExecutionPolicy, if enough additional memory is available, exactly $N - 1$ comparisons.
(8.2)
For the overloads with no ExecutionPolicy if no additional memory is available, $O (N log N)$ comparisons.
(8.3)
For the overloads with an ExecutionPolicy, $O (N log N)$ comparisons.

Remarks: Stable ([algorithm.stable]).

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

This section 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.

28.7.6.1 includes [includes]

🔗

template<class InputIterator1, class InputIterator2>
  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>
  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);

Returns: true if [first2, last2) is empty or if every element in the range [first2, last2) is contained in the range [first1, last1).

Returns false otherwise.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

28.7.6.2 set_union [set.union]

🔗

template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  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>
  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);

Requires: The resulting range shall not overlap with either of the original ranges.

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.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then all m elements from the first range shall be copied to the output range, in order, and then

max (n - m, 0)

elements from the second range shall be copied to the output range, in order.

28.7.6.3 set_intersection [set.intersection]

🔗

template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  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>
  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);

Requires: The resulting range shall not overlap with either of the original ranges.

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.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, the first

min (m, n)

elements shall be copied from the first range to the output range, in order.

28.7.6.4 set_difference [set.difference]

🔗

template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  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>
  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);

Requires: The resulting range shall not overlap with either of the original ranges.

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.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

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

max (m - n, 0)

elements from [first1, last1) shall be copied to the output range.

28.7.6.5 set_symmetric_difference [set.symmetric.difference]

🔗

template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  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>
  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);

Requires: The resulting range shall not overlap with either of the original ranges.

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.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Remarks: If [first1, last1) contains m elements that are equivalent to each other and [first2, last2) contains n elements that are equivalent to them, then

| m - n |

of those elements shall be copied to the output range: the last

m - n

of these elements from [first1, last1) if

m > n

, and the last

n - m

of these elements from [first2, last2) if

m < n

28.7.7 Heap operations [alg.heap.operations]

A heap is a particular organization of elements in a range between two random access iterators [a, b) such that:

(1.1)
With N = b - a, for all i, $0 < i < N$ , comp(a[ $⌊ \frac{i - 1}{2} ⌋$ ], a[i]) is false.
(1.2)
*a may be removed by pop_heap(), or a new element added by push_heap(), in $O (log N)$ time.

These properties make heaps useful as priority queues.

make_heap() converts a range into a heap and sort_heap() turns a heap into a sorted sequence.

28.7.7.1 push_heap [push.heap]

🔗

template<class RandomAccessIterator>
  void push_heap(RandomAccessIterator first, RandomAccessIterator last);

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

Requires: The range [first, last - 1) shall be a valid heap.

The type of *first shall satisfy the MoveConstructible requirements (Table 23) and the MoveAssignable requirements (Table 25).

Effects: Places the value in the location last - 1 into the resulting heap [first, last).

Complexity: At most

log (last - first)

comparisons.

28.7.7.2 pop_heap [pop.heap]

🔗

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

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

Requires: The range [first, last) shall be a valid non-empty heap.

RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Swaps the value in the location first with the value in the location last - 1 and makes [first, last - 1) into a heap.

Complexity: At most

2 log (last - first)

comparisons.

28.7.7.3 make_heap [make.heap]

🔗

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

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

Requires: The type of *first shall satisfy the MoveConstructible requirements (Table 23) and the MoveAssignable requirements (Table 25).

Effects: Constructs a heap out of the range [first, last).

Complexity: At most

3 (last - first)

comparisons.

28.7.7.4 sort_heap [sort.heap]

🔗

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

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

Requires: The range [first, last) shall be a valid heap.

RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

The type of *first shall satisfy the requirements of MoveConstructible (Table 23) and of MoveAssignable (Table 25).

Effects: Sorts elements in the heap [first, last).

Complexity: At most

N log N

comparisons, where

N = last - first

28.7.7.5 is_heap [is.heap]

🔗

template<class RandomAccessIterator>
  bool is_heap(RandomAccessIterator first, RandomAccessIterator last);

Returns: is_heap_until(first, last) == last

🔗

template<class ExecutionPolicy, class RandomAccessIterator>
  bool is_heap(ExecutionPolicy&& exec,
               RandomAccessIterator first, RandomAccessIterator last);

Returns: is_heap_until(std::forward<ExecutionPolicy>(exec), first, last) == last

🔗

template<class RandomAccessIterator, class Compare>
  bool is_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Returns: is_heap_until(first, last, comp) == last

🔗

template<class ExecutionPolicy, class RandomAccessIterator, class Compare>
  bool is_heap(ExecutionPolicy&& exec,
               RandomAccessIterator first, RandomAccessIterator last, Compare comp);

Returns:

is_heap_until(std::forward<ExecutionPolicy>(exec), first, last, comp) == last

🔗

template<class RandomAccessIterator>
  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>
  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);

Returns: If (last - first) < 2, returns last.

Otherwise, returns the last iterator i in [first, last] for which the range [first, i) is a heap.

Complexity: Linear.

28.7.8 Minimum and maximum [alg.min.max]

🔗

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

Requires: For the first form, type T shall be LessThanComparable (Table 21).

Returns: The smaller value.

Remarks: Returns the first argument when the arguments are equivalent.

Complexity: Exactly one comparison.

🔗

template<class T>
  constexpr T min(initializer_list<T> t);
template<class T, class Compare>
  constexpr T min(initializer_list<T> t, Compare comp);

Requires: T shall be CopyConstructible and t.size() > 0.

For the first form, type T shall be LessThanComparable.

Returns: The smallest value in the initializer_list.

Remarks: Returns a copy of the leftmost argument when several arguments are equivalent to the smallest.

Complexity: Exactly t.size() - 1 comparisons.

🔗

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

Requires: For the first form, type T shall be LessThanComparable (Table 21).

Returns: The larger value.

Remarks: Returns the first argument when the arguments are equivalent.

Complexity: Exactly one comparison.

🔗

template<class T>
  constexpr T max(initializer_list<T> t);
template<class T, class Compare>
  constexpr T max(initializer_list<T> t, Compare comp);

Requires: T shall be CopyConstructible and t.size() > 0.

For the first form, type T shall be LessThanComparable.

Returns: The largest value in the initializer_list.

Remarks: Returns a copy of the leftmost argument when several arguments are equivalent to the largest.

Complexity: Exactly t.size() - 1 comparisons.

🔗

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

Requires: For the first form, type T shall be LessThanComparable (Table 21).

Returns: pair<const T&, const T&>(b, a) if b is smaller than a, and pair<const T&, const T&>(a, b) otherwise.

Remarks: Returns pair<const T&, const T&>(a, b) when the arguments are equivalent.

Complexity: Exactly one comparison.

🔗

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

Requires: T shall be CopyConstructible and t.size() > 0.

For the first form, type T shall be LessThanComparable.

Returns: pair<T, T>(x, y), where x has the smallest and y has the largest value in the initializer list.

Remarks: x is a copy of the leftmost argument when several arguments are equivalent to the smallest.

y is a copy of the rightmost argument when several arguments are equivalent to the largest.

Complexity: At most

(3 / 2) t.size()

applications of the corresponding predicate.

🔗

template<class ForwardIterator>
  constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last);

template<class ExecutionPolicy, class ForwardIterator>
  ForwardIterator min_element(ExecutionPolicy&& exec,
                              ForwardIterator first, ForwardIterator last);

template<class ForwardIterator, class Compare>
  constexpr ForwardIterator min_element(ForwardIterator first, ForwardIterator last,
                                        Compare comp);
template<class ExecutionPolicy, class ForwardIterator, class Compare>
  ForwardIterator min_element(ExecutionPolicy&& exec,
                              ForwardIterator first, ForwardIterator last,
                              Compare comp);

Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last) the following corresponding conditions hold: !(*j < *i) or comp(*j, *i) == false.

Returns last if first == last.

Complexity: Exactly

max (last - first - 1, 0)

applications of the corresponding comparisons.

🔗

template<class ForwardIterator>
  constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last);
template<class ExecutionPolicy, class ForwardIterator>
  ForwardIterator max_element(ExecutionPolicy&& exec,
                              ForwardIterator first, ForwardIterator last);

template<class ForwardIterator, class Compare>
  constexpr ForwardIterator max_element(ForwardIterator first, ForwardIterator last,
                                        Compare comp);
template<class ExecutionPolicy, class ForwardIterator, class Compare>
  ForwardIterator max_element(ExecutionPolicy&& exec,
                              ForwardIterator first, ForwardIterator last,
                              Compare comp);

Returns: The first iterator i in the range [first, last) such that for every iterator j in the range [first, last) the following corresponding conditions hold: !(*i < *j) or comp(*i, *j) == false.

Returns last if first == last.

Complexity: Exactly

max (last - first - 1, 0)

applications of the corresponding comparisons.

🔗

template<class ForwardIterator>
  constexpr pair<ForwardIterator, ForwardIterator>
    minmax_element(ForwardIterator first, ForwardIterator last);
template<class ExecutionPolicy, class ForwardIterator>
  pair<ForwardIterator, ForwardIterator>
    minmax_element(ExecutionPolicy&& exec,
                   ForwardIterator first, ForwardIterator last);

template<class ForwardIterator, class Compare>
  constexpr pair<ForwardIterator, ForwardIterator>
    minmax_element(ForwardIterator first, ForwardIterator last, Compare comp);
template<class ExecutionPolicy, class ForwardIterator, class Compare>
  pair<ForwardIterator, ForwardIterator>
    minmax_element(ExecutionPolicy&& exec,
                   ForwardIterator first, ForwardIterator last, Compare comp);

Returns: make_pair(first, first) if [first, last) is empty, otherwise make_pair(m, M), where m is the first iterator in [first, last) such that no iterator in the range refers to a smaller element, and where M is the last iterator266 in [first, last) such that no iterator in the range refers to a larger element.

Complexity: At most

max (⌊ \frac{3}{2} (N - 1) ⌋, 0)

applications of the corresponding predicate, where N is last - first.

266)

This behavior intentionally differs from max_element().

28.7.9 Bounded value [alg.clamp]

🔗

template<class T>
  constexpr const T& clamp(const T& v, const T& lo, const T& hi);
template<class T, class Compare>
  constexpr const T& clamp(const T& v, const T& lo, const T& hi, Compare comp);

Requires: The value of lo shall be no greater than hi.

For the first form, type T shall be LessThanComparable (Table 21).

Returns: lo if v is less than lo, hi if hi is less than v, otherwise v.

[ Note

If NaN is avoided, T can be a floating-point type.

— end note

]

Complexity: At most two comparisons.

28.7.10 Lexicographical comparison [alg.lex.comparison]

🔗

template<class InputIterator1, class InputIterator2>
  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>
  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);

Returns: true if the sequence of elements defined by the range [first1, last1) is lexicographically less than the sequence of elements defined by the range [first2, last2) and false otherwise.

Complexity: At most

2 min (last1 - first1, last2 - first2)

applications of the corresponding comparison.

Remarks: If two sequences have the same number of elements and their corresponding elements (if any) are equivalent, then neither sequence is lexicographically less than the other.

If one sequence is a prefix of the other, then the shorter sequence is lexicographically less than the longer sequence.

Otherwise, the lexicographical comparison of the sequences yields the same result as the comparison of the first corresponding pair of elements that are not equivalent.

[ Example

The following sample implementation satisfies these requirements:

for ( ; first1 != last1 && first2 != last2 ; ++first1, (void) ++first2) {
  if (*first1 < *first2) return true;
  if (*first2 < *first1) return false;
}
return first1 == last1 && first2 != last2;

— end example

]

[ Note

An empty sequence is lexicographically less than any non-empty sequence, but not less than any empty sequence.

— end note

]

28.7.11 Permutation generators [alg.permutation.generators]

🔗

template<class BidirectionalIterator>
  bool next_permutation(BidirectionalIterator first,
                        BidirectionalIterator last);

template<class BidirectionalIterator, class Compare>
  bool next_permutation(BidirectionalIterator first,
                        BidirectionalIterator last, Compare comp);

Requires: BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

Effects: Takes a sequence defined by the range [first, last) and transforms it into the next permutation.

The next permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp.

Returns: true if such a permutation exists.

Otherwise, it transforms the sequence into the smallest permutation, that is, the ascendingly sorted one, and returns false.

Complexity: At most (last - first) / 2 swaps.

🔗

template<class BidirectionalIterator>
  bool prev_permutation(BidirectionalIterator first,
                        BidirectionalIterator last);

template<class BidirectionalIterator, class Compare>
  bool prev_permutation(BidirectionalIterator first,
                        BidirectionalIterator last, Compare comp);

Requires: BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]).

Effects: Takes a sequence defined by the range [first, last) and transforms it into the previous permutation.

The previous permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp.

Returns: true if such a permutation exists.

Otherwise, it transforms the sequence into the largest permutation, that is, the descendingly sorted one, and returns false.

Complexity: At most (last - first) / 2 swaps.

28.8 C library algorithms [alg.c.library]

[ Note

The header <cstdlib> ([cstdlib.syn]) declares the functions described in this subclause.

— end note

]

🔗

void* bsearch(const void* key, const void* base, size_t nmemb, size_t size,
              c-compare-pred* compar);
void* bsearch(const void* key, const void* base, size_t nmemb, size_t size,
              compare-pred* compar);
void qsort(void* base, size_t nmemb, size_t size, c-compare-pred* compar);
void qsort(void* base, size_t nmemb, size_t size, compare-pred* compar);

Effects: These functions have the semantics specified in the C standard library.

Remarks: The behavior is undefined unless the objects in the array pointed to by base are of trivial type.

Throws: Any exception thrown by compar() ([res.on.exception.handling]).

28 Algorithms library [algorithms]

28.1 General [algorithms.general]

28.2 Header <algorithm> synopsis [algorithm.syn]

28.3 Algorithms requirements [algorithms.requirements]

28.4 Parallel algorithms [algorithms.parallel]

28.4.1 Terms and definitions [algorithms.parallel.defns]

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

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

28.4.4 Parallel algorithm exceptions [algorithms.parallel.exceptions]

28.4.5 ExecutionPolicy algorithm overloads [algorithms.parallel.overloads]

28.5 Non-modifying sequence operations [alg.nonmodifying]

28.5.1 All of [alg.all_of]

28.5.2 Any of [alg.any_of]

28.5.3 None of [alg.none_of]

28.5.4 For each [alg.foreach]

28.5.5 Find [alg.find]

28.5.6 Find end [alg.find.end]

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

28.5.8 Adjacent find [alg.adjacent.find]

28.5.9 Count [alg.count]

28.5.10 Mismatch [mismatch]

28.5.11 Equal [alg.equal]

28.5.12 Is permutation [alg.is_permutation]

28.5.13 Search [alg.search]

28.6 Mutating sequence operations [alg.modifying.operations]

28.6.1 Copy [alg.copy]

28.6.2 Move [alg.move]

28.6.3 Swap [alg.swap]

28.6.4 Transform [alg.transform]

28.6.5 Replace [alg.replace]

28.6.6 Fill [alg.fill]

28.6.7 Generate [alg.generate]

28.6.8 Remove [alg.remove]

28.6.9 Unique [alg.unique]

28.6.10 Reverse [alg.reverse]

28.6.11 Rotate [alg.rotate]

28.6.12 Sample [alg.random.sample]

28.6.13 Shuffle [alg.random.shuffle]

28.7 Sorting and related operations [alg.sorting]

28.7.1 Sorting [alg.sort]

28.7.1.1 sort [sort]

28.7.1.2 stable_­sort [stable.sort]

28.7.1.3 partial_­sort [partial.sort]

28.7.1.4 partial_­sort_­copy [partial.sort.copy]

28.7.1.5 is_­sorted [is.sorted]

28.7.2 Nth element [alg.nth.element]

28.7.3 Binary search [alg.binary.search]

28.7.3.1 lower_­bound [lower.bound]

28.7.3.2 upper_­bound [upper.bound]

28.7.3.3 equal_­range [equal.range]

28.7.3.4 binary_­search [binary.search]

28.7.4 Partitions [alg.partitions]

28.7.5 Merge [alg.merge]

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

28.7.6.1 includes [includes]

28.7.6.2 set_­union [set.union]

28.7.6.3 set_­intersection [set.intersection]

28.7.6.4 set_­difference [set.difference]

28.7.6.5 set_­symmetric_­difference [set.symmetric.difference]

28.7.7 Heap operations [alg.heap.operations]

28.7.7.1 push_­heap [push.heap]

28.7.7.2 pop_­heap [pop.heap]

28.7.7.3 make_­heap [make.heap]

28.7.7.4 sort_­heap [sort.heap]

28.7.7.5 is_­heap [is.heap]

28.7.8 Minimum and maximum [alg.min.max]

28.7.9 Bounded value [alg.clamp]

28.7.10 Lexicographical comparison [alg.lex.comparison]

28.7.11 Permutation generators [alg.permutation.generators]

28.8 C library algorithms [alg.c.library]

28.7.1.2 stable_sort [stable.sort]

28.7.1.3 partial_sort [partial.sort]

28.7.1.4 partial_sort_copy [partial.sort.copy]

28.7.1.5 is_sorted [is.sorted]

28.7.3.1 lower_bound [lower.bound]

28.7.3.2 upper_bound [upper.bound]

28.7.3.3 equal_range [equal.range]

28.7.3.4 binary_search [binary.search]

28.7.6.2 set_union [set.union]

28.7.6.3 set_intersection [set.intersection]

28.7.6.4 set_difference [set.difference]

28.7.6.5 set_symmetric_difference [set.symmetric.difference]

28.7.7.1 push_heap [push.heap]

28.7.7.2 pop_heap [pop.heap]

28.7.7.3 make_heap [make.heap]

28.7.7.4 sort_heap [sort.heap]

28.7.7.5 is_heap [is.heap]