Standard library header <algorithm>

This header is part of the algorithm library.

Functions

Non-modifying sequence operations
all_ofany_ofnone_of (C++11)(C++11)(C++11)	checks if a predicate is true for all, any or none of the elements in a range (function template)
for_each	applies a function to a range of elements (function template)
for_each_n (C++17)	applies a function object to the first n elements of a sequence (function template)
countcount_if	returns the number of elements satisfying specific criteria (function template)
mismatch	finds the first position where two ranges differ (function template)
findfind_iffind_if_not (C++11)	finds the first element satisfying specific criteria (function template)
find_end	finds the last sequence of elements in a certain range (function template)
find_first_of	searches for any one of a set of elements (function template)
adjacent_find	finds the first two adjacent items that are equal (or satisfy a given predicate) (function template)
search	searches for a range of elements (function template)
search_n	searches a range for a number of consecutive copies of an element (function template)
Modifying sequence operations
copycopy_if (C++11)	copies a range of elements to a new location (function template)
copy_n (C++11)	copies a number of elements to a new location (function template)
copy_backward	copies a range of elements in backwards order (function template)
move (C++11)	moves a range of elements to a new location (function template)
move_backward (C++11)	moves a range of elements to a new location in backwards order (function template)
fill	copy-assigns the given value to every element in a range (function template)
fill_n	copy-assigns the given value to N elements in a range (function template)
transform	applies a function to a range of elements (function template)
generate	assigns the results of successive function calls to every element in a range (function template)
generate_n	assigns the results of successive function calls to N elements in a range (function template)
removeremove_if	removes elements satisfying specific criteria (function template)
remove_copyremove_copy_if	copies a range of elements omitting those that satisfy specific criteria (function template)
replacereplace_if	replaces all values satisfying specific criteria with another value (function template)
replace_copyreplace_copy_if	copies a range, replacing elements satisfying specific criteria with another value (function template)
swap	swaps the values of two objects (function template)
swap_ranges	swaps two ranges of elements (function template)
iter_swap	swaps the elements pointed to by two iterators (function template)
reverse	reverses the order of elements in a range (function template)
reverse_copy	creates a copy of a range that is reversed (function template)
rotate	rotates the order of elements in a range (function template)
rotate_copy	copies and rotate a range of elements (function template)
shift_leftshift_right (C++20)	shifts elements in a range (function template)
random_shuffleshuffle (until C++17)(C++11)	randomly re-orders elements in a range (function template)
sample (C++17)	selects n random elements from a sequence (function template)
unique	removes consecutive duplicate elements in a range (function template)
unique_copy	creates a copy of some range of elements that contains no consecutive duplicates (function template)
Partitioning operations
is_partitioned (C++11)	determines if the range is partitioned by the given predicate (function template)
partition	divides a range of elements into two groups (function template)
partition_copy (C++11)	copies a range dividing the elements into two groups (function template)
stable_partition	divides elements into two groups while preserving their relative order (function template)
partition_point (C++11)	locates the partition point of a partitioned range (function template)
Sorting operations
is_sorted (C++11)	checks whether a range is sorted into ascending order (function template)
is_sorted_until (C++11)	finds the largest sorted subrange (function template)
sort	sorts a range into ascending order (function template)
partial_sort	sorts the first N elements of a range (function template)
partial_sort_copy	copies and partially sorts a range of elements (function template)
stable_sort	sorts a range of elements while preserving order between equal elements (function template)
nth_element	partially sorts the given range making sure that it is partitioned by the given element (function template)
Binary search operations (on sorted ranges)
lower_bound	returns an iterator to the first element not less than the given value (function template)
upper_bound	returns an iterator to the first element greater than a certain value (function template)
binary_search	determines if an element exists in a certain range (function template)
equal_range	returns range of elements matching a specific key (function template)
Other operations on sorted ranges
merge	merges two sorted ranges (function template)
inplace_merge	merges two ordered ranges in-place (function template)
Set operations (on sorted ranges)
includes	returns true if one set is a subset of another (function template)
set_difference	computes the difference between two sets (function template)
set_intersection	computes the intersection of two sets (function template)
set_symmetric_difference	computes the symmetric difference between two sets (function template)
set_union	computes the union of two sets (function template)
Heap operations
is_heap (C++11)	checks if the given range is a max heap (function template)
is_heap_until (C++11)	finds the largest subrange that is a max heap (function template)
make_heap	creates a max heap out of a range of elements (function template)
push_heap	adds an element to a max heap (function template)
pop_heap	removes the largest element from a max heap (function template)
sort_heap	turns a max heap into a range of elements sorted in ascending order (function template)
Minimum/maximum operations
max	returns the greater of the given values (function template)
max_element	returns the largest element in a range (function template)
min	returns the smaller of the given values (function template)
min_element	returns the smallest element in a range (function template)
minmax (C++11)	returns the smaller and larger of two elements (function template)
minmax_element (C++11)	returns the smallest and the largest elements in a range (function template)
clamp (C++17)	clamps a value between a pair of boundary values (function template)
Comparison operations
equal	determines if two sets of elements are the same (function template)
lexicographical_compare	returns true if one range is lexicographically less than another (function template)
compare_3way (C++20)	compares two values using three-way comparison (function template)
lexicographical_compare_3way (C++20)	compares two ranges using three-way comparison (function template)
Permutation operations
is_permutation (C++11)	determines if a sequence is a permutation of another sequence (function template)
next_permutation	generates the next greater lexicographic permutation of a range of elements (function template)
prev_permutation	generates the next smaller lexicographic permutation of a range of elements (function template)

Niebloids

Defined in namespace `std::ranges`
Non-modifying sequence operations
all_ofany_ofnone_of	checks if a predicate is true for all, any or none of the elements in a range (niebloid)
for_each	applies a function to a range of elements (niebloid)
countcount_if	returns the number of elements satisfying specific criteria (niebloid)
mismatch	finds the first position where two ranges differ (niebloid)
findfind_iffind_if_not	finds the first element satisfying specific criteria (niebloid)
find_end	finds the last sequence of elements in a certain range (niebloid)
find_first_of	searches for any one of a set of elements (niebloid)
adjacent_find	finds the first two adjacent items that are equal (or satisfy a given predicate) (niebloid)
search	searches for a range of elements (niebloid)
search_n	searches for a number consecutive copies of an element in a range (niebloid)
Modifying sequence operations
copycopy_if	copies a range of elements to a new location (niebloid)
copy_n	copies a number of elements to a new location (niebloid)
copy_backward	copies a range of elements in backwards order (niebloid)
move	moves a range of elements to a new location (niebloid)
move_backward	moves a range of elements to a new location in backwards order (niebloid)
fill	assigns a range of elements a certain value (niebloid)
fill_n	assigns a value to a number of elements (niebloid)
transform	applies a function to a range of elements (niebloid)
generate	saves the result of a function in a range (niebloid)
generate_n	saves the result of N applications of a function (niebloid)
removeremove_if	removes elements satisfying specific criteria (niebloid)
remove_copyremove_copy_if	copies a range of elements omitting those that satisfy specific criteria (niebloid)
replacereplace_if	replaces all values satisfying specific criteria with another value (niebloid)
replace_copyreplace_copy_if	copies a range, replacing elements satisfying specific criteria with another value (niebloid)
swap_ranges	swaps two ranges of elements (niebloid)
reverse	reverses the order of elements in a range (niebloid)
reverse_copy	creates a copy of a range that is reversed (niebloid)
rotate	rotates the order of elements in a range (niebloid)
rotate_copy	copies and rotate a range of elements (niebloid)
shuffle	randomly re-orders elements in a range (niebloid)
unique	removes consecutive duplicate elements in a range (niebloid)
unique_copy	creates a copy of some range of elements that contains no consecutive duplicates (niebloid)
Partitioning operations
is_partitioned	determines if the range is partitioned by the given predicate (niebloid)
partition	divides a range of elements into two groups (niebloid)
partition_copy	copies a range dividing the elements into two groups (niebloid)
stable_partition	divides elements into two groups while preserving their relative order (niebloid)
partition_point	locates the partition point of a partitioned range (niebloid)
Sorting operations
is_sorted	checks whether a range is sorted into ascending order (niebloid)
is_sorted_until	finds the largest sorted subrange (niebloid)
sort	sorts a range into ascending order (niebloid)
partial_sort	sorts the first N elements of a range (niebloid)
partial_sort_copy	copies and partially sorts a range of elements (niebloid)
stable_sort	sorts a range of elements while preserving order between equal elements (niebloid)
nth_element	partially sorts the given range making sure that it is partitioned by the given element (niebloid)
Binary search operations (on sorted ranges)
lower_bound	returns an iterator to the first element not less than the given value (niebloid)
upper_bound	returns an iterator to the first element greater than a certain value (niebloid)
binary_search	determines if an element exists in a certain range (niebloid)
equal_range	returns range of elements matching a specific key (niebloid)
Other operations on sorted ranges
merge	merges two sorted ranges (niebloid)
inplace_merge	merges two ordered ranges in-place (niebloid)
Set operations (on sorted ranges)
includes	returns true if one set is a subset of another (niebloid)
set_difference	computes the difference between two sets (niebloid)
set_intersection	computes the intersection of two sets (niebloid)
set_symmetric_difference	computes the symmetric difference between two sets (niebloid)
set_union	computes the union of two sets (niebloid)
Heap operations
is_heap	checks if the given range is a max heap (niebloid)
is_heap_until	finds the largest subrange that is a max heap (niebloid)
make_heap	creates a max heap out of a range of elements (niebloid)
push_heap	adds an element to a max heap (niebloid)
pop_heap	removes the largest element from a max heap (niebloid)
sort_heap	turns a max heap into a range of elements sorted in ascending order (niebloid)
Minimum/maximum operations
max	returns the greater of the given values (niebloid)
max_element	returns the largest element in a range (niebloid)
min	returns the smaller of the given values (niebloid)
min_element	returns the smallest element in a range (niebloid)
minmax	returns the smaller and larger of two elements (niebloid)
minmax_element	returns the smallest and the largest elements in a range (niebloid)
Comparison operations
equal	determines if two sets of elements are the same (niebloid)
lexicographical_compare	returns true if one range is lexicographically less than another (niebloid)
Permutation operations
is_permutation	determines if a sequence is a permutation of another sequence (niebloid)
next_permutation	generates the next greater lexicographic permutation of a range of elements (niebloid)
prev_permutation	generates the next smaller lexicographic permutation of a range of elements (niebloid)

Synopsis

#include <initializer_list>
 
namespace std {
  // non-modifying sequence operations:
  // all of:
  template<class InputIt, class Pred>
    constexpr bool all_of(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    bool all_of(ExecutionPolicy&& exec,
                ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr bool all_of(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool all_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // any of:
  template<class InputIt, class Pred>
    constexpr bool any_of(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    bool any_of(ExecutionPolicy&& exec,
                ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr bool any_of(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool any_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // none of:
  template<class InputIt, class Pred>
    constexpr bool none_of(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    bool none_of(ExecutionPolicy&& exec,
                 ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr bool none_of(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool none_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // for each:
  template<class InputIt, class Function>
    constexpr Function for_each(InputIt first, InputIt last, Function f);
  template<class ExecutionPolicy, class ForwardIt, class Function>
    void for_each(ExecutionPolicy&& exec,
                  ForwardIt first, ForwardIt last, Function f);
 
  namespace ranges {
    template<class I, class F>
    struct for_each_result {
      [[no_unique_address]] I in;
      [[no_unique_address]] F fun;
 
      template<class I2, class F2>
        requires ConvertibleTo<const I&, I2> && ConvertibleTo<const F&, F2>
        operator for_each_result<I2, F2>() const & {
          return {in, fun};
        }
 
      template<class I2, class F2>
        requires ConvertibleTo<I, I2> && ConvertibleTo<F, F2>
        operator for_each_result<I2, F2>() && {
          return {std::move(in), std::move(fun)};
        }
    };
 
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryInvocable<projected<I, Proj>> Fun>
      constexpr for_each_result<I, Fun>
        for_each(I first, S last, Fun f, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryInvocable<projected<iterator_t<R>, Proj>> Fun>
      constexpr for_each_result<safe_iterator_t<R>, Fun>
        for_each(R&& r, Fun f, Proj proj = {});
  }
 
  template<class InputIt, class Size, class Function>
    constexpr InputIt for_each_n(InputIt first, Size n, Function f);
  template<class ExecutionPolicy, class ForwardIt, class Size, class Function>
    ForwardIt for_each_n(ExecutionPolicy&& exec,
                         ForwardIt first, Size n, Function f);
 
  // find:
  template<class InputIt, class T>
    constexpr InputIt find(InputIt first, InputIt last,
                           const T& value);
  template<class ExecutionPolicy, class ForwardIt, class T>
    ForwardIt find(ExecutionPolicy&& exec,
                   ForwardIt first, ForwardIt last, const T& value);
  template<class InputIt, class Pred>
    constexpr InputIt find_if(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    ForwardIt find_if(ExecutionPolicy&& exec,
                      ForwardIt first, ForwardIt last, Pred pred);
  template<class InputIt, class Pred>
    constexpr InputIt find_if_not(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    ForwardIt find_if_not(ExecutionPolicy&& exec,
                          ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class T, class Proj = identity>
      requires IndirectRelation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr I find(I first, S last, const T& value, Proj proj = {});
    template<InputRange R, class T, class Proj = identity>
      requires IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
      constexpr safe_iterator_t<R>
        find(R&& r, const T& value, Proj proj = {});
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr I find_if(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        find_if(R&& r, Pred pred, Proj proj = {});
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr I find_if_not(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        find_if_not(R&& r, Pred pred, Proj proj = {});
  }
 
  // find end:
  template<class ForwardIt1, class ForwardIt2>
    constexpr ForwardIt1
      find_end(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ForwardIt1, class ForwardIt2, class BinaryPred>
    constexpr ForwardIt1
      find_end(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
               BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt1
      find_end(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1,
           class ForwardIt2, class BinaryPred>
    ForwardIt1
      find_end(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
               BinaryPred pred);
 
  namespace ranges {
    template<ForwardIterator I1, Sentinel<I1> S1, ForwardIterator I2, Sentinel<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<I1, I2, Pred, Proj1, Proj2>
      constexpr subrange<I1>
        find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<ForwardRange R1, ForwardRange R2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr safe_subrange_t<R1>
        find_end(R1&& r1, R2&& r2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // find first:
  template<class InputIt, class ForwardIt>
    constexpr InputIt
      find_first_of(InputIt first1, InputIt last1, ForwardIt first2, ForwardIt last2);
  template<class InputIt, class ForwardIt, class BinaryPred>
    constexpr InputIt
      find_first_of(InputIt first1, InputIt last1, ForwardIt first2, ForwardIt last2,
                    BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt1
      find_first_of(ExecutionPolicy&& exec,
                    ForwardIt1 first1, ForwardIt1 last1,
                    ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    ForwardIt1
      find_first_of(ExecutionPolicy&& exec,
                    ForwardIt1 first1, ForwardIt1 last1,
                    ForwardIt2 first2, ForwardIt2 last2,
                    BinaryPred pred);
 
  namespace ranges {
    template<InputIterator I1, Sentinel<I1> S1, ForwardIterator I2, Sentinel<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectRelation<projected<I1, Proj1>,
                              projected<I2, Proj2>> Pred = ranges::equal_to>
      constexpr I1 find_first_of(I1 first1, S1 last1, I2 first2, S2 last2,
                                 Pred pred = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, ForwardRange R2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectRelation<projected<iterator_t<R1>, Proj1>,
                              projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to>
      constexpr safe_iterator_t<R1>
        find_first_of(R1&& r1, R2&& r2,
                      Pred pred = {},
                      Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // adjacent find:
  template<class ForwardIt>
    constexpr ForwardIt
      adjacent_find(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class BinaryPred>
    constexpr ForwardIt
      adjacent_find(ForwardIt first, ForwardIt last, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt
      adjacent_find(ExecutionPolicy&& exec,
                    ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class BinaryPred>
    ForwardIt
      adjacent_find(ExecutionPolicy&& exec,
                    ForwardIt first, ForwardIt last, BinaryPred pred);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectRelation<projected<I, Proj>> Pred = ranges::equal_to>
      constexpr I adjacent_find(I first, S last, Pred pred = {},
                                Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectRelation<projected<iterator_t<R>, Proj>> Pred = ranges::equal_to>
      constexpr safe_iterator_t<R>
        adjacent_find(R&& r, Pred pred = {}, Proj proj = {});
  }
 
  // count:
  template<class InputIt, class T>
    constexpr typename iterator_traits<InputIt>::difference_type
      count(InputIt first, InputIt last, const T& value);
  template<class ExecutionPolicy, class ForwardIt, class T>
    typename iterator_traits<ForwardIt>::difference_type
      count(ExecutionPolicy&& exec,
            ForwardIt first, ForwardIt last, const T& value);
  template<class InputIt, class Pred>
    constexpr typename iterator_traits<InputIt>::difference_type
      count_if(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    typename iterator_traits<ForwardIt>::difference_type
      count_if(ExecutionPolicy&& exec,
               ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class T, class Proj = identity>
      requires IndirectRelation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr iter_difference_t<I>
        count(I first, S last, const T& value, Proj proj = {});
    template<InputRange R, class T, class Proj = identity>
      requires IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
      constexpr iter_difference_t<iterator_t<R>>
        count(R&& r, const T& value, Proj proj = {});
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr iter_difference_t<I>
        count_if(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr iter_difference_t<iterator_t<R>>
        count_if(R&& r, Pred pred, Proj proj = {});
  }
 
  // mismatch:
  template<class InputIt1, class InputIt2>
    constexpr pair<InputIt1, InputIt2>
      mismatch(InputIt1 first1, InputIt1 last1, InputIt2 first2);
  template<class InputIt1, class InputIt2, class BinaryPred>
    constexpr pair<InputIt1, InputIt2>
      mismatch(InputIt1 first1, InputIt1 last1, InputIt2 first2, BinaryPred pred);
  template<class InputIt1, class InputIt2>
    constexpr pair<InputIt1, InputIt2>
      mismatch(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2);
  template<class InputIt1, class InputIt2, class BinaryPred>
    constexpr pair<InputIt1, InputIt2>
      mismatch(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
               BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    pair<ForwardIt1, ForwardIt2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class BinaryPred>
    pair<ForwardIt1, ForwardIt2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    pair<ForwardIt1, ForwardIt2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    pair<ForwardIt1, ForwardIt2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
               BinaryPred pred);
 
  namespace ranges {
    template<class I1, class I2>
    struct mismatch_result {
      [[no_unique_address]] I1 in1;
      [[no_unique_address]] I2 in2;
 
      template<class II1, class II2>
        requires ConvertibleTo<const I1&, II1> && ConvertibleTo<const I2&, II2>
        operator mismatch_result<II1, II2>() const & {
          return {in1, in2};
        }
 
      template<class II1, class II2>
        requires ConvertibleTo<I1, II1> && ConvertibleTo<I2, II2>
        operator mismatch_result<II1, II2>() && {
          return {std::move(in1), std::move(in2)};
        }
    };
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectRelation<projected<I1, Proj1>,
                              projected<I2, Proj2>> Pred = ranges::equal_to>
      constexpr mismatch_result<I1, I2>
        mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectRelation<projected<iterator_t<R1>, Proj1>,
                              projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to>
      constexpr mismatch_result<safe_iterator_t<R1>, safe_iterator_t<R2>>
        mismatch(R1&& r1, R2&& r2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // equal:
  template<class InputIt1, class InputIt2>
    constexpr bool equal(InputIt1 first1, InputIt1 last1, InputIt2 first2);
  template<class InputIt1, class InputIt2, class BinaryPred>
    constexpr bool equal(InputIt1 first1, InputIt1 last1, InputIt2 first2,
                         BinaryPred pred);
  template<class InputIt1, class InputIt2>
    constexpr bool equal(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2);
  template<class InputIt1, class InputIt2, class BinaryPred>
    constexpr bool equal(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                         BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    bool equal(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    bool equal(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    bool equal(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    bool equal(ExecutionPolicy&& exec,
               ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
               BinaryPred pred);
 
  namespace ranges {
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<I1, I2, Pred, Proj1, Proj2>
      constexpr bool equal(I1 first1, S1 last1, I2 first2, S2 last2,
                           Pred pred = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr bool equal(R1&& r1, R2&& r2, Pred pred = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // is permutation:
  template<class ForwardIt1, class ForwardIt2>
    constexpr bool is_permutation(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2);
  template<class ForwardIt1, class ForwardIt2, class BinaryPred>
    constexpr bool is_permutation(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2,
                                  BinaryPred pred);
  template<class ForwardIt1, class ForwardIt2>
    constexpr bool is_permutation(ForwardIt1 first1, ForwardIt1 last1,
                                  ForwardIt2 first2, ForwardIt2 last2);
  template<class ForwardIt1, class ForwardIt2, class BinaryPred>
    constexpr bool is_permutation(ForwardIt1 first1, ForwardIt1 last1,
                                  ForwardIt2 first2, ForwardIt2 last2,
                                  BinaryPred pred);
 
  namespace ranges {
    template<ForwardIterator I1, Sentinel<I1> S1, ForwardIterator I2,
             Sentinel<I2> S2, class Pred = ranges::equal_to, class Proj1 = identity,
             class Proj2 = identity>
      requires IndirectlyComparable<I1, I2, Pred, Proj1, Proj2>
      constexpr bool is_permutation(I1 first1, S1 last1, I2 first2, S2 last2,
                                    Pred pred = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});
    template<ForwardRange R1, ForwardRange R2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr bool is_permutation(R1&& r1, R2&& r2, Pred pred = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // search:
  template<class ForwardIt1, class ForwardIt2>
    constexpr ForwardIt1
      search(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ForwardIt1, class ForwardIt2, class BinaryPred>
    constexpr ForwardIt1
      search(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
             BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt1
      search(ExecutionPolicy&& exec,
             ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    ForwardIt1
      search(ExecutionPolicy&& exec,
             ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
             BinaryPred pred);
 
  namespace ranges {
    template<ForwardIterator I1, Sentinel<I1> S1, ForwardIterator I2,
             Sentinel<I2> S2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<I1, I2, Pred, Proj1, Proj2>
      constexpr subrange<I1>
        search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
               Proj1 proj1 = {}, Proj2 proj2 = {});
    template<ForwardRange R1, ForwardRange R2, class Pred = ranges::equal_to,
             class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyComparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
      constexpr safe_subrange_t<R1>
        search(R1&& r1, R2&& r2, Pred pred = {},
               Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class ForwardIt, class Size, class T>
    constexpr ForwardIt
      search_n(ForwardIt first, ForwardIt last, Size count, const T& value);
  template<class ForwardIt, class Size, class T, class BinaryPred>
    constexpr ForwardIt
      search_n(ForwardIt first, ForwardIt last,
               Size count, const T& value, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt, class Size, class T>
    ForwardIt
      search_n(ExecutionPolicy&& exec,
               ForwardIt first, ForwardIt last, Size count, const T& value);
  template<class ExecutionPolicy, class ForwardIt, class Size, class T, class BinaryPred>
    ForwardIt
      search_n(ExecutionPolicy&& exec,
               ForwardIt first, ForwardIt last,
               Size count, const T& value, BinaryPred pred);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class T,
             class Pred = ranges::equal_to, class Proj = identity>
      requires IndirectlyComparable<I, const T*, Pred, Proj>
      constexpr subrange<I>
        search_n(I first, S last, iter_difference_t<I> count,
                 const T& value, Pred pred = {}, Proj proj = {});
    template<ForwardRange R, class T, class Pred = ranges::equal_to,
             class Proj = identity>
      requires IndirectlyComparable<iterator_t<R>, const T*, Pred, Proj>
      constexpr safe_subrange_t<R>
        search_n(R&& r, iter_difference_t<iterator_t<R>> count,
                 const T& value, Pred pred = {}, Proj proj = {});
  }
 
  template<class ForwardIt, class Searcher>
    constexpr ForwardIt
      search(ForwardIt first, ForwardIt last, const Searcher& searcher);
 
  // mutating sequence operations:
  // copy:
  template<class InputIt, class OutputIt>
    constexpr OutputIt copy(InputIt first, InputIt last, OutputIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2 copy(ExecutionPolicy&& exec,
                    ForwardIt1 first, ForwardIt1 last, ForwardIt2 result);
 
  namespace ranges {
    template<class I, class O>
    struct copy_result {
      [[no_unique_address]] I in;
      [[no_unique_address]] O out;
 
      template<class I2, class O2>
        requires ConvertibleTo<const I&, I2> && ConvertibleTo<const O&, O2>
        operator copy_result<I2, O2>() const & {
          return {in, out};
        }
 
      template<class I2, class O2>
        requires ConvertibleTo<I, I2> && ConvertibleTo<O, O2>
        operator copy_result<I2, O2>() && {
          return {std::move(in), std::move(out)};
        }
    };
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O>
      requires IndirectlyCopyable<I, O>
      constexpr copy_result<I, O>
        copy(I first, S last, O result);
    template<InputRange R, WeaklyIncrementable O>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr copy_result<safe_iterator_t<R>, O>
        copy(R&& r, O result);
  }
 
  template<class InputIt, class Size, class OutputIt>
    constexpr OutputIt copy_n(InputIt first, Size n, OutputIt result);
  template<class ExecutionPolicy, class ForwardIt1, class Size, class ForwardIt2>
    ForwardIt2 copy_n(ExecutionPolicy&& exec,
                      ForwardIt1 first, Size n, ForwardIt2 result);
 
  namespace ranges {
    template<class I, class O>
    using copy_n_result = copy_result<I, O>;
 
    template<InputIterator I, WeaklyIncrementable O>
      requires IndirectlyCopyable<I, O>
      constexpr copy_n_result<I, O>
        copy_n(I first, iter_difference_t<I> n, O result);
  }
 
  template<class InputIt, class OutputIt, class Pred>
    constexpr OutputIt copy_if(InputIt first, InputIt last, OutputIt result, Pred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Pred>
    ForwardIt2 copy_if(ExecutionPolicy&& exec,
                       ForwardIt1 first, ForwardIt1 last, ForwardIt2 result, Pred pred);
 
  namespace ranges {
    template<class I, class O>
    using copy_if_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires IndirectlyCopyable<I, O>
      constexpr copy_if_result<I, O>
        copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<InputRange R, WeaklyIncrementable O, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr copy_if_result<safe_iterator_t<R>, O>
        copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }
 
  template<class BidirectionalIt1, class BidirectionalIt2>
    constexpr BidirectionalIt2
      copy_backward(BidirectionalIt1 first, BidirectionalIt1 last,
                    BidirectionalIt2 result);
 
  namespace ranges {
    template<class I1, class I2>
    using copy_backward_result = copy_result<I1, I2>;
 
    template<BidirectionalIterator I1, Sentinel<I1> S1, BidirectionalIterator I2>
      requires IndirectlyCopyable<I1, I2>
      constexpr copy_backward_result<I1, I2>
        copy_backward(I1 first, S1 last, I2 result);
    template<BidirectionalRange R, BidirectionalIterator I>
      requires IndirectlyCopyable<iterator_t<R>, I>
      constexpr copy_backward_result<safe_iterator_t<R>, I>
        copy_backward(R&& r, I result);
  }
 
  // move:
  template<class InputIt, class OutputIt>
    constexpr OutputIt move(InputIt first, InputIt last, OutputIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2 move(ExecutionPolicy&& exec,
                    ForwardIt1 first, ForwardIt1 last, ForwardIt2 result);
 
  namespace ranges {
    template<class I, class O>
    using move_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O>
      requires IndirectlyMovable<I, O>
      constexpr move_result<I, O>
        move(I first, S last, O result);
    template<InputRange R, WeaklyIncrementable O>
      requires IndirectlyMovable<iterator_t<R>, O>
      constexpr move_result<safe_iterator_t<R>, O>
        move(R&& r, O result);
  }
 
  template<class BidirectionalIt1, class BidirectionalIt2>
    constexpr BidirectionalIt2
      move_backward(BidirectionalIt1 first, BidirectionalIt1 last,
                    BidirectionalIt2 result);
 
  namespace ranges {
    template<class I1, class I2>
    using move_backward_result = copy_result<I1, I2>;
 
    template<BidirectionalIterator I1, Sentinel<I1> S1, BidirectionalIterator I2>
      requires IndirectlyMovable<I1, I2>
      constexpr move_backward_result<I1, I2>
        move_backward(I1 first, S1 last, I2 result);
    template<BidirectionalRange R, BidirectionalIterator I>
      requires IndirectlyMovable<iterator_t<R>, I>
      constexpr move_backward_result<safe_iterator_t<R>, I>
        move_backward(R&& r, I result);
  }
 
  // swap:
  template<class ForwardIt1, class ForwardIt2>
    constexpr ForwardIt2 swap_ranges(ForwardIt1 first1, ForwardIt1 last1,
                                     ForwardIt2 first2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2 swap_ranges(ExecutionPolicy&& exec,
                           ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2);
 
  namespace ranges {
    template<class I1, class I2>
    using swap_ranges_result = mismatch_result<I1, I2>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2>
      requires IndirectlySwappable<I1, I2>
      constexpr swap_ranges_result<I1, I2>
        swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2);
    template<InputRange R1, InputRange R2>
      requires IndirectlySwappable<iterator_t<R1>, iterator_t<R2>>
      constexpr swap_ranges_result<safe_iterator_t<R1>, safe_iterator_t<R2>>
        swap_ranges(R1&& r1, R2&& r2);
  }
 
  template<class ForwardIt1, class ForwardIt2>
    constexpr void iter_swap(ForwardIt1 a, ForwardIt2 b);
 
  // transform:
  template<class InputIt, class OutputIt, class UnaryOperation>
    constexpr OutputIt
      transform(InputIt first1, InputIt last1, OutputIt result, UnaryOperation op);
  template<class InputIt1, class InputIt2, class OutputIt, class BinaryOperation>
    constexpr OutputIt
      transform(InputIt1 first1, InputIt1 last1, InputIt2 first2, OutputIt result,
                BinaryOperation binary_op);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class UnaryOperation>
    ForwardIt2
      transform(ExecutionPolicy&& exec,
                ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 result, UnaryOperation op);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class BinaryOperation>
    ForwardIt
      transform(ExecutionPolicy&& exec,
                ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt result,
                BinaryOperation binary_op);
 
  namespace ranges {
    template<class I, class O>
    using unary_transform_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O,
             CopyConstructible F, class Proj = identity>
      requires Writable<O, indirect_result_t<F&, projected<I, Proj>>>
      constexpr unary_transform_result<I, O>
        transform(I first1, S last1, O result, F op, Proj proj = {});
    template<InputRange R, WeaklyIncrementable O, CopyConstructible F,
             class Proj = identity>
      requires Writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
      constexpr unary_transform_result<safe_iterator_t<R>, O>
        transform(R&& r, O result, F op, Proj proj = {});
 
    template<class I1, class I2, class O>
    struct binary_transform_result {
      [[no_unique_address]] I1 in1;
      [[no_unique_address]] I2 in2;
      [[no_unique_address]] O  out;
 
      template<class II1, class II2, class OO>
        requires ConvertibleTo<const I1&, II1> &&
          ConvertibleTo<const I2&, II2> && ConvertibleTo<const O&, OO>
        operator binary_transform_result<II1, II2, OO>() const & {
          return {in1, in2, out};
        }
 
      template<class II1, class II2, class OO>
        requires ConvertibleTo<I1, II1> &&
          ConvertibleTo<I2, II2> && ConvertibleTo<O, OO>
        operator binary_transform_result<II1, II2, OO>() && {
          return {std::move(in1), std::move(in2), std::move(out)};
        }
    };
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, CopyConstructible F, class Proj1 = identity,
             class Proj2 = identity>
      requires Writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                             projected<I2, Proj2>>>
      constexpr binary_transform_result<I1, I2, O>
        transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             CopyConstructible F, class Proj1 = identity, class Proj2 = identity>
      requires Writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                             projected<iterator_t<R2>, Proj2>>>
      constexpr binary_transform_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        transform(R1&& r1, R2&& r2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // replace:
  template<class ForwardIt, class T>
    constexpr void replace(ForwardIt first, ForwardIt last,
                           const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIt, class T>
    void replace(ExecutionPolicy&& exec,
                 ForwardIt first, ForwardIt last,
                 const T& old_value, const T& new_value);
  template<class ForwardIt, class Pred, class T>
    constexpr void replace_if(ForwardIt first, ForwardIt last,
                              Pred pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIt, class Pred, class T>
    void replace_if(ExecutionPolicy&& exec,
                    ForwardIt first, ForwardIt last,
                    Pred pred, const T& new_value);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class T1, class T2, class Proj = identity>
      requires Writable<I, const T2&> &&
               IndirectRelation<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr I
        replace(I first, S last, const T1& old_value, const T2& new_value, Proj proj = {});
    template<InputRange R, class T1, class T2, class Proj = identity>
      requires Writable<iterator_t<R>, const T2&> &&
               IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>,
                 const T1*>
      constexpr safe_iterator_t<R>
        replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {});
    template<InputIterator I, Sentinel<I> S, class T, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires Writable<I, const T&>
      constexpr I replace_if(I first, S last,
                             Pred pred, const T& new_value, Proj proj = {});
    template<InputRange R, class T, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires Writable<iterator_t<R>, const T&>
      constexpr safe_iterator_t<R>
        replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});
  }
 
  template<class InputIt, class OutputIt, class T>
    constexpr OutputIt replace_copy(InputIt first, InputIt last, OutputIt result,
                                    const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T>
    ForwardIt2 replace_copy(ExecutionPolicy&& exec,
                            ForwardIt1 first, ForwardIt1 last, ForwardIt2 result,
                            const T& old_value, const T& new_value);
  template<class InputIt, class OutputIt, class Pred, class T>
    constexpr OutputIt replace_copy_if(InputIt first, InputIt last, OutputIt result,
                                       Pred pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Pred, class T>
    ForwardIt2 replace_copy_if(ExecutionPolicy&& exec,
                               ForwardIt1 first, ForwardIt1 last, ForwardIt2 result,
                               Pred pred, const T& new_value);
 
  namespace ranges {
    template<class I, class O>
    using replace_copy_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, class T1, class T2,
             OutputIterator<const T2&> O, class Proj = identity>
      requires IndirectlyCopyable<I, O> &&
               IndirectRelation<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr replace_copy_result<I, O>
        replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});
    template<InputRange R, class T1, class T2, OutputIterator<const T2&> O,
             class Proj = identity>
      requires IndirectlyCopyable<iterator_t<R>, O> &&
               IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>,
                 const T1*>
      constexpr replace_copy_result<safe_iterator_t<R>, O>
        replace_copy(R&& r, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});
 
    template<class I, class O>
    using replace_copy_if_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, class T, OutputIterator<const T&> O,
             class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires IndirectlyCopyable<I, O>
      constexpr replace_copy_if_result<I, O>
        replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                        Proj proj = {});
    template<InputRange R, class T, OutputIterator<const T&> O, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr replace_copy_if_result<safe_iterator_t<R>, O>
        replace_copy_if(R&& r, O result, Pred pred, const T& new_value,
                        Proj proj = {});
  }
 
  // fill:
  template<class ForwardIt, class T>
    constexpr void fill(ForwardIt first, ForwardIt last, const T& value);
  template<class ExecutionPolicy, class ForwardIt, class T>
    void fill(ExecutionPolicy&& exec,
              ForwardIt first, ForwardIt last, const T& value);
  template<class OutputIt, class Size, class T>
    constexpr OutputIt fill_n(OutputIt first, Size n, const T& value);
  template<class ExecutionPolicy, class ForwardIt, class Size, class T>
    ForwardIt fill_n(ExecutionPolicy&& exec,
                     ForwardIt first, Size n, const T& value);
 
  namespace ranges {
    template<class T, OutputIterator<const T&> O, Sentinel<O> S>
      constexpr O fill(O first, S last, const T& value);
    template<class T, OutputRange<const T&> R>
      constexpr safe_iterator_t<R> fill(R&& r, const T& value);
    template<class T, OutputIterator<const T&> O>
      constexpr O fill_n(O first, iter_difference_t<O> n, const T& value);
  }
 
  // generate:
  template<class ForwardIt, class Generator>
    constexpr void generate(ForwardIt first, ForwardIt last, Generator gen);
  template<class ExecutionPolicy, class ForwardIt, class Generator>
    void generate(ExecutionPolicy&& exec,
                  ForwardIt first, ForwardIt last, Generator gen);
  template<class OutputIt, class Size, class Generator>
    constexpr OutputIt generate_n(OutputIt first, Size n, Generator gen);
  template<class ExecutionPolicy, class ForwardIt, class Size, class Generator>
    ForwardIt generate_n(ExecutionPolicy&& exec,
                         ForwardIt first, Size n, Generator gen);
 
  namespace ranges {
    template<Iterator O, Sentinel<O> S, CopyConstructible F>
      requires Invocable<F&> && Writable<O, invoke_result_t<F&>>
      constexpr O generate(O first, S last, F gen);
    template<class R, CopyConstructible F>
      requires Invocable<F&> && OutputRange<R, invoke_result_t<F&>>
      constexpr safe_iterator_t<R> generate(R&& r, F gen);
    template<Iterator O, CopyConstructible F>
      requires Invocable<F&> && Writable<O, invoke_result_t<F&>>
      constexpr O generate_n(O first, iter_difference_t<O> n, F gen);
  }
 
  // remove:
  template<class ForwardIt, class T>
    constexpr ForwardIt remove(ForwardIt first, ForwardIt last, const T& value);
  template<class ExecutionPolicy, class ForwardIt, class T>
    ForwardIt remove(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last, const T& value);
  template<class ForwardIt, class Pred>
    constexpr ForwardIt remove_if(ForwardIt first, ForwardIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    ForwardIt remove_if(ExecutionPolicy&& exec,
                        ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<Permutable I, Sentinel<I> S, class T, class Proj = identity>
      requires IndirectRelation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr I remove(I first, S last, const T& value, Proj proj = {});
    template<ForwardRange R, class T, class Proj = identity>
      requires Permutable<iterator_t<R>> &&
               IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
      constexpr safe_iterator_t<R>
        remove(R&& r, const T& value, Proj proj = {});
    template<Permutable I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr I remove_if(I first, S last, Pred pred, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires Permutable<iterator_t<R>>
      constexpr safe_iterator_t<R>
        remove_if(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class InputIt, class OutputIt, class T>
    constexpr OutputIt
      remove_copy(InputIt first, InputIt last, OutputIt result, const T& value);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T>
    ForwardIt2
      remove_copy(ExecutionPolicy&& exec,
                  ForwardIt1 first, ForwardIt1 last, ForwardIt2 result, const T& value);
  template<class InputIt, class OutputIt, class Pred>
    constexpr OutputIt
      remove_copy_if(InputIt first, InputIt last, OutputIt result, Pred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class Pred>
    ForwardIt2
      remove_copy_if(ExecutionPolicy&& exec,
                     ForwardIt1 first, ForwardIt1 last, ForwardIt2 result, Pred pred);
 
  namespace ranges {
    template<class I, class O>
    using remove_copy_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O, class T,
             class Proj = identity>
      requires IndirectlyCopyable<I, O> &&
               IndirectRelation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr remove_copy_result<I, O>
        remove_copy(I first, S last, O result, const T& value, Proj proj = {});
    template<InputRange R, WeaklyIncrementable O, class T, class Proj = identity>
      requires IndirectlyCopyable<iterator_t<R>, O> &&
               IndirectRelation<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
      constexpr remove_copy_result<safe_iterator_t<R>, O>
        remove_copy(R&& r, O result, const T& value, Proj proj = {});
 
    template<class I, class O>
    using remove_copy_if_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O,
             class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires IndirectlyCopyable<I, O>
      constexpr remove_copy_if_result<I, O>
        remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<InputRange R, WeaklyIncrementable O, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr remove_copy_if_result<safe_iterator_t<R>, O>
        remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }
 
  // unique:
  template<class ForwardIt>
    constexpr ForwardIt unique(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class BinaryPred>
    constexpr ForwardIt unique(ForwardIt first, ForwardIt last, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt unique(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class BinaryPred>
    ForwardIt unique(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last, BinaryPred pred);
 
  namespace ranges {
    template<Permutable I, Sentinel<I> S, class Proj = identity,
             IndirectRelation<projected<I, Proj>> C = ranges::equal_to>
      constexpr I unique(I first, S last, C comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectRelation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires Permutable<iterator_t<R>>
      constexpr safe_iterator_t<R>
        unique(R&& r, C comp = {}, Proj proj = {});
  }
 
  template<class InputIt, class OutputIt>
    constexpr OutputIt
      unique_copy(InputIt first, InputIt last, OutputIt result);
  template<class InputIt, class OutputIt, class BinaryPred>
    constexpr OutputIt
      unique_copy(InputIt first, InputIt last, OutputIt result, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2
      unique_copy(ExecutionPolicy&& exec,
                  ForwardIt1 first, ForwardIt1 last, ForwardIt2 result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryPred>
    ForwardIt2
      unique_copy(ExecutionPolicy&& exec,
                  ForwardIt1 first, ForwardIt1 last, ForwardIt2 result, BinaryPred pred);
 
  namespace ranges {
    template<class I, class O>
    using unique_copy_result = copy_result<I, O>;
 
    template<InputIterator I, Sentinel<I> S, WeaklyIncrementable O,
             class Proj = identity,
             IndirectRelation<projected<I, Proj>> C = ranges::equal_to>
      requires IndirectlyCopyable<I, O> &&
               (ForwardIterator<I> ||
                (InputIterator<O> && Same<iter_value_t<I>, iter_value_t<O>>) ||
                IndirectlyCopyableStorable<I, O>)
      constexpr unique_copy_result<I, O>
        unique_copy(I first, S last, O result, C comp = {}, Proj proj = {});
    template<InputRange R, WeaklyIncrementable O, class Proj = identity,
             IndirectRelation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires IndirectlyCopyable<iterator_t<R>, O> &&
               (ForwardIterator<iterator_t<R>> ||
                (InputIterator<O> && Same<iter_value_t<iterator_t<R>>, iter_value_t<O>>) ||
                IndirectlyCopyableStorable<iterator_t<R>, O>)
      constexpr unique_copy_result<safe_iterator_t<R>, O>
        unique_copy(R&& r, O result, C comp = {}, Proj proj = {});
  }
 
  // reverse:
  template<class BidirectionalIt>
    constexpr void reverse(BidirectionalIt first, BidirectionalIt last);
  template<class ExecutionPolicy, class BidirectionalIt>
    void reverse(ExecutionPolicy&& exec,
                 BidirectionalIt first, BidirectionalIt last);
 
  namespace ranges {
    template<BidirectionalIterator I, Sentinel<I> S>
      requires Permutable<I>
      constexpr I reverse(I first, S last);
    template<BidirectionalRange R>
      requires Permutable<iterator_t<R>>
      constexpr safe_iterator_t<R> reverse(R&& r);
  }
 
  template<class BidirectionalIt, class OutputIt>
    constexpr OutputIt
      reverse_copy(BidirectionalIt first, BidirectionalIt last, OutputIt result);
  template<class ExecutionPolicy, class BidirectionalIt, class ForwardIt>
    ForwardIt
      reverse_copy(ExecutionPolicy&& exec,
                   BidirectionalIt first, BidirectionalIt last, ForwardIt result);
 
  namespace ranges {
    template<class I, class O>
    using reverse_copy_result = copy_result<I, O>;
 
    template<BidirectionalIterator I, Sentinel<I> S, WeaklyIncrementable O>
      requires IndirectlyCopyable<I, O>
      constexpr reverse_copy_result<I, O>
        reverse_copy(I first, S last, O result);
    template<BidirectionalRange R, WeaklyIncrementable O>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr reverse_copy_result<safe_iterator_t<R>, O>
        reverse_copy(R&& r, O result);
  }
 
  // rotate:
  template<class ForwardIt>
    constexpr ForwardIt rotate(ForwardIt first, ForwardIt middle, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt rotate(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt middle, ForwardIt last);
 
  namespace ranges {
    template<Permutable I, Sentinel<I> S>
      constexpr subrange<I> rotate(I first, I middle, S last);
    template<ForwardRange R>
      requires Permutable<iterator_t<R>>
      constexpr safe_subrange_t<R> rotate(R&& r, iterator_t<R> middle);
  }
 
  template<class ForwardIt, class OutputIt>
    constexpr OutputIt
      rotate_copy(ForwardIt first, ForwardIt middle, ForwardIt last, OutputIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    ForwardIt2
      rotate_copy(ExecutionPolicy&& exec,
                  ForwardIt1 first, ForwardIt1 middle, ForwardIt1 last, ForwardIt2 result);
 
  namespace ranges {
    template<class I, class O>
    using rotate_copy_result = copy_result<I, O>;
 
    template<ForwardIterator I, Sentinel<I> S, WeaklyIncrementable O>
      requires IndirectlyCopyable<I, O>
      constexpr rotate_copy_result<I, O>
        rotate_copy(I first, I middle, S last, O result);
    template<ForwardRange R, WeaklyIncrementable O>
      requires IndirectlyCopyable<iterator_t<R>, O>
      constexpr rotate_copy_result<safe_iterator_t<R>, O>
        rotate_copy(R&& r, iterator_t<R> middle, O result);
  }
 
  // sample:
  template<class PopulationIt, class SampleIt,
           class Distance, class UniformRndBitGen>
    SampleIt sample(PopulationIt first, PopulationIt last, SampleIt out, Distance n,
                    UniformRndBitGen&& g);
 
  // shuffle:
  template<class RandomAccessIt, class UniformRndBitGen>
    void shuffle(RandomAccessIt first, RandomAccessIt last, UniformRndBitGen&& g);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Gen>
      requires Permutable<I> &&
               UniformRandomBitGenerator<remove_reference_t<Gen>> &&
               ConvertibleTo<invoke_result_t<Gen&>, iter_difference_t<I>>
      I shuffle(I first, S last, Gen&& g);
    template<RandomAccessRange R, class Gen>
      requires Permutable<iterator_t<R>> &&
               UniformRandomBitGenerator<remove_reference_t<Gen>> &&
               ConvertibleTo<invoke_result_t<Gen&>, iter_difference_t<iterator_t<R>>>
      safe_iterator_t<R> shuffle(R&& r, Gen&& g);
  }
 
  // shift:
  template<class ForwardIt>
    constexpr ForwardIt
      shift_left(ForwardIt first, ForwardIt last,
                 typename iterator_traits<ForwardIt>::difference_type n);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt
      shift_left(ExecutionPolicy&& exec,
                 ForwardIt first, ForwardIt last,
                 typename iterator_traits<ForwardIt>::difference_type n);
  template<class ForwardIt>
    constexpr ForwardIt
      shift_right(ForwardIt first, ForwardIt last,
                  typename iterator_traits<ForwardIt>::difference_type n);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt
      shift_right(ExecutionPolicy&& exec,
                  ForwardIt first, ForwardIt last,
                  typename iterator_traits<ForwardIt>::difference_type n);
 
  // sorting and related operations:
  // sorting:
  template<class RandomAccessIt>
    constexpr void sort(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void sort(RandomAccessIt first, RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    void sort(ExecutionPolicy&& exec,
              RandomAccessIt first, RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    void sort(ExecutionPolicy&& exec,
              RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        sort(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        sort(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    void stable_sort(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    void stable_sort(RandomAccessIt first, RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    void stable_sort(ExecutionPolicy&& exec,
                     RandomAccessIt first, RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    void stable_sort(ExecutionPolicy&& exec,
                     RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      I stable_sort(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      safe_iterator_t<R>
        stable_sort(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr void partial_sort(RandomAccessIt first, RandomAccessIt middle,
                                RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void partial_sort(RandomAccessIt first, RandomAccessIt middle,
                                RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    void partial_sort(ExecutionPolicy&& exec,
                      RandomAccessIt first, RandomAccessIt middle, RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    void partial_sort(ExecutionPolicy&& exec,
                      RandomAccessIt first, RandomAccessIt middle, RandomAccessIt last,
                      Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        partial_sort(R&& r, iterator_t<R> middle, Comp comp = {},
                     Proj proj = {});
  }
 
  template<class InputIt, class RandomAccessIt>
    constexpr RandomAccessIt
      partial_sort_copy(InputIt first, InputIt last,
                        RandomAccessIt result_first, RandomAccessIt result_last);
  template<class InputIt, class RandomAccessIt, class Compare>
    constexpr RandomAccessIt
      partial_sort_copy(InputIt first, InputIt last,
                        RandomAccessIt result_first, RandomAccessIt result_last,
                        Compare comp);
  template<class ExecutionPolicy, class ForwardIt, class RandomAccessIt>
    RandomAccessIt
      partial_sort_copy(ExecutionPolicy&& exec, 
                        ForwardIt first, ForwardIt last,
                        RandomAccessIt result_first, RandomAccessIt result_last);
  template<class ExecutionPolicy, class ForwardIt, class RandomAccessIt, class Compare>
    RandomAccessIt
      partial_sort_copy(ExecutionPolicy&& exec, 
                        ForwardIt first, ForwardIt last,
                        RandomAccessIt result_first, RandomAccessIt result_last,
                        Compare comp);
 
  namespace ranges {
    template<InputIterator I1, Sentinel<I1> S1, RandomAccessIterator I2, Sentinel<I2> S2,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyCopyable<I1, I2> && Sortable<I2, Comp, Proj2> &&
               IndirectStrictWeakOrder<Comp, projected<I1, Proj1>, projected<I2, Proj2>>
      constexpr I2
        partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last,
                          Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, RandomAccessRange R2, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires IndirectlyCopyable<iterator_t<R1>, iterator_t<R2>> &&
               Sortable<iterator_t<R2>, Comp, Proj2> &&
               IndirectStrictWeakOrder<Comp, projected<iterator_t<R1>, Proj1>,
                                       projected<iterator_t<R2>, Proj2>>
      constexpr safe_iterator_t<R2>
        partial_sort_copy(R1&& r, R2&& result_r, Comp comp = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class ForwardIt>
    constexpr bool is_sorted(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class Compare>
    constexpr bool is_sorted(ForwardIt first, ForwardIt last, Compare comp);
  template<class ExecutionPolicy, class ForwardIt>
    bool is_sorted(ExecutionPolicy&& exec,
                   ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class Compare>
    bool is_sorted(ExecutionPolicy&& exec,
                   ForwardIt first, ForwardIt last, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr bool is_sorted(I first, S last, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr bool is_sorted(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt>
    constexpr ForwardIt
      is_sorted_until(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class Compare>
    constexpr ForwardIt
      is_sorted_until(ForwardIt first, ForwardIt last, Compare comp);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt
      is_sorted_until(ExecutionPolicy&& exec,
                      ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class Compare>
    ForwardIt
      is_sorted_until(ExecutionPolicy&& exec,
                      ForwardIt first, ForwardIt last, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr I is_sorted_until(I first, S last, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr safe_iterator_t<R>
        is_sorted_until(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  // Nth element:
  template<class RandomAccessIt>
    constexpr void nth_element(RandomAccessIt first, RandomAccessIt nth,
                               RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void nth_element(RandomAccessIt first, RandomAccessIt nth,
                               RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    void nth_element(ExecutionPolicy&& exec,
                     RandomAccessIt first, RandomAccessIt nth,
                     RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    void nth_element(ExecutionPolicy&& exec,
                     RandomAccessIt first, RandomAccessIt nth,
                     RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});
  }
 
  // binary search:
  template<class ForwardIt, class T>
    constexpr ForwardIt
      lower_bound(ForwardIt first, ForwardIt last, const T& value);
  template<class ForwardIt, class T, class Compare>
    constexpr ForwardIt
      lower_bound(ForwardIt first, ForwardIt last, const T& value, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr I lower_bound(I first, S last, const T& value, Comp comp = {},
                              Proj proj = {});
    template<ForwardRange R, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr safe_iterator_t<R>
        lower_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt, class T>
    constexpr ForwardIt
      upper_bound(ForwardIt first, ForwardIt last, const T& value);
  template<class ForwardIt, class T, class Compare>
    constexpr ForwardIt
      upper_bound(ForwardIt first, ForwardIt last, const T& value, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr I upper_bound(I first, S last,
                              const T& value, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr safe_iterator_t<R>
        upper_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt, class T>
    constexpr pair<ForwardIt, ForwardIt>
      equal_range(ForwardIt first, ForwardIt last, const T& value);
  template<class ForwardIt, class T, class Compare>
    constexpr pair<ForwardIt, ForwardIt>
      equal_range(ForwardIt first, ForwardIt last, const T& value, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr subrange<I>
        equal_range(I first, S last, const T& value, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr safe_subrange_t<R>
        equal_range(R&& r, const T& value, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt, class T>
    constexpr bool
      binary_search(ForwardIt first, ForwardIt last, const T& value);
  template<class ForwardIt, class T, class Compare>
    constexpr bool
      binary_search(ForwardIt first, ForwardIt last, const T& value, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<I, Proj>> Comp = ranges::less>
      constexpr bool binary_search(I first, S last, const T& value, Comp comp = {},
                                   Proj proj = {});
    template<ForwardRange R, class T, class Proj = identity,
             IndirectStrictWeakOrder<const T*, projected<iterator_t<R>, Proj>> Comp =
               ranges::less>
      constexpr bool binary_search(R&& r, const T& value, Comp comp = {},
                                   Proj proj = {});
  }
 
  // partitions:
  template<class InputIt, class Pred>
    constexpr bool is_partitioned(InputIt first, InputIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    bool is_partitioned(ExecutionPolicy&& exec,
                        ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<InputIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr bool is_partitioned(I first, S last, Pred pred, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool is_partitioned(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class ForwardIt, class Pred>
    constexpr ForwardIt partition(ForwardIt first, ForwardIt last, Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class Pred>
    ForwardIt partition(ExecutionPolicy&& exec,
                        ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<Permutable I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr I
        partition(I first, S last, Pred pred, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires Permutable<iterator_t<R>>
      constexpr safe_iterator_t<R>
        partition(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class BidirectionalIt, class Pred>
    BidirectionalIt stable_partition(BidirectionalIt first, BidirectionalIt last,
                                     Pred pred);
  template<class ExecutionPolicy, class BidirectionalIt, class Pred>
    BidirectionalIt stable_partition(ExecutionPolicy&& exec,
                                     BidirectionalIt first, BidirectionalIt last,
                                     Pred pred);
 
  namespace ranges {
    template<BidirectionalIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires Permutable<I>
      I stable_partition(I first, S last, Pred pred, Proj proj = {});
    template<BidirectionalRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires Permutable<iterator_t<R>>
      safe_iterator_t<R> stable_partition(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class InputIt, class OutputIt1, class OutputIt2, class Pred>
    constexpr pair<OutputIt1, OutputIt2>
      partition_copy(InputIt first, InputIt last, OutputIt1 out_true, OutputIt2 out_false,
                     Pred pred);
  template<class ExecutionPolicy, class ForwardIt, class ForwardIt1,
           class ForwardIt2, class Pred>
    pair<ForwardIt1, ForwardIt2>
      partition_copy(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last,
                     ForwardIt1 out_true, ForwardIt2 out_false,
                     Pred pred);
 
  namespace ranges {
    template<class I, class O1, class O2>
    struct partition_copy_result {
      [[no_unique_address]] I  in;
      [[no_unique_address]] O1 out1;
      [[no_unique_address]] O2 out2;
 
      template<class II, class OO1, class OO2>
        requires ConvertibleTo<const I&, II> &&
          ConvertibleTo<const O1&, OO1> && ConvertibleTo<const O2&, OO2>
        operator partition_copy_result<II, OO1, OO2>() const & {
          return {in, out1, out2};
        }
 
      template<class II, class OO1, class OO2>
        requires ConvertibleTo<I, II> &&
          ConvertibleTo<O1, OO1> && ConvertibleTo<O2, OO2>
        operator partition_copy_result<II, OO1, OO2>() && {
          return {std::move(in), std::move(out1), std::move(out2)};
        }
    };
 
    template<InputIterator I, Sentinel<I> S,
             WeaklyIncrementable O1, WeaklyIncrementable O2,
             class Proj = identity, IndirectUnaryPredicate<projected<I, Proj>> Pred>
      requires IndirectlyCopyable<I, O1> && IndirectlyCopyable<I, O2>
      constexpr partition_copy_result<I, O1, O2>
        partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                       Proj proj = {});
    template<InputRange R, WeaklyIncrementable O1, WeaklyIncrementable O2,
             class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      requires IndirectlyCopyable<iterator_t<R>, O1> &&
               IndirectlyCopyable<iterator_t<R>, O2>
      constexpr partition_copy_result<safe_iterator_t<R>, O1, O2>
        partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});
  }
 
  template<class ForwardIt, class Pred>
    constexpr ForwardIt
      partition_point(ForwardIt first, ForwardIt last, Pred pred);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectUnaryPredicate<projected<I, Proj>> Pred>
      constexpr I partition_point(I first, S last, Pred pred, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectUnaryPredicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        partition_point(R&& r, Pred pred, Proj proj = {});
  }
 
  // merge:
  template<class InputIt1, class InputIt2, class OutputIt>
    constexpr OutputIt
      merge(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
            OutputIt result);
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
    constexpr OutputIt
      merge(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
            OutputIt result, Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class ForwardIt>
    ForwardIt
      merge(ExecutionPolicy&& exec,
            ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
            ForwardIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class Compare>
    ForwardIt
      merge(ExecutionPolicy&& exec,
            ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
            ForwardIt result, Compare comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using merge_result = binary_transform_result<I1, I2, O>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, class Comp = ranges::less, class Proj1 = identity,
             class Proj2 = identity>
      requires Mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr merge_result<I1, I2, O>
        merge(I1 first1, S1 last1, I2 first2, S2 last2, O result,
              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr merge_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        merge(R1&& r1, R2&& r2, O result,
              Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class BidirectionalIt>
    void inplace_merge(BidirectionalIt first,
                       BidirectionalIt middle,
                       BidirectionalIt last);
  template<class BidirectionalIt, class Compare>
    void inplace_merge(BidirectionalIt first,
                       BidirectionalIt middle,
                       BidirectionalIt last, Compare comp);
  template<class ExecutionPolicy, class BidirectionalIt>
    void inplace_merge(ExecutionPolicy&& exec,
                       BidirectionalIt first,
                       BidirectionalIt middle,
                       BidirectionalIt last);
  template<class ExecutionPolicy, class BidirectionalIt, class Compare>
    void inplace_merge(ExecutionPolicy&& exec,
                       BidirectionalIt first,
                       BidirectionalIt middle,
                       BidirectionalIt last, Compare comp);
 
  namespace ranges {
    template<BidirectionalIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      I inplace_merge(I first, I middle, S last, Comp comp = {}, Proj proj = {});
    template<BidirectionalRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      safe_iterator_t<R>
        inplace_merge(R&& r, iterator_t<R> middle, Comp comp = {},
                      Proj proj = {});
  }
 
  // set operations:
  template<class InputIt1, class InputIt2>
    constexpr bool includes(InputIt1 first1, InputIt1 last1,
                            InputIt2 first2, InputIt2 last2);
  template<class InputIt1, class InputIt2, class Compare>
    constexpr bool includes(InputIt1 first1, InputIt1 last1,
                            InputIt2 first2, InputIt2 last2,
                            Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    bool includes(ExecutionPolicy&& exec,
                  ForwardIt1 first1, ForwardIt1 last1,
                  ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class Compare>
    bool includes(ExecutionPolicy&& exec,
                  ForwardIt1 first1, ForwardIt1 last1,
                  ForwardIt2 first2, ForwardIt2 last2,
                  Compare comp);
 
  namespace ranges {
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectStrictWeakOrder<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
               ranges::less>
      constexpr bool includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, class Proj1 = identity,
             class Proj2 = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R1>, Proj1>,
                                     projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
      constexpr bool includes(R1&& r1, R2&& r2, Comp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIt1, class InputIt2, class OutputIt>
    constexpr OutputIt
      set_union(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                OutputIt result);
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
    constexpr OutputIt
                set_union(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                OutputIt result, Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt>
    ForwardIt
      set_union(ExecutionPolicy&& exec,
                ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
                ForwardIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class Compare>
    ForwardIt
      set_union(ExecutionPolicy&& exec,
                ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2,
                ForwardIt result, Compare comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_union_result = binary_transform_result<I1, I2, O>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_union_result<I1, I2, O>
        set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_union_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIt1, class InputIt2, class OutputIt>
    constexpr OutputIt
      set_intersection(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                       OutputIt result);
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
    constexpr OutputIt
      set_intersection(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                       OutputIt result, Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt>
    ForwardIt
      set_intersection(ExecutionPolicy&& exec,
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2, ForwardIt2 last2,
                       ForwardIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class Compare>
    ForwardIt
      set_intersection(ExecutionPolicy&& exec,
                       ForwardIt1 first1, ForwardIt1 last1,
                       ForwardIt2 first2, ForwardIt2 last2,
                       ForwardIt result, Compare comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_intersection_result = binary_transform_result<I1, I2, O>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_intersection_result<I1, I2, O>
        set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                         Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_intersection_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_intersection(R1&& r1, R2&& r2, O result,
                         Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIt1, class InputIt2, class OutputIt>
    constexpr OutputIt
      set_difference(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                     OutputIt result);
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
    constexpr OutputIt
      set_difference(InputIt1 first1, InputIt1 last1, InputIt2 first2, InputIt2 last2,
                     OutputIt result, Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt>
    ForwardIt
      set_difference(ExecutionPolicy&& exec,
                     ForwardIt1 first1, ForwardIt1 last1,
                     ForwardIt2 first2, ForwardIt2 last2,
                     ForwardIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class Compare>
    ForwardIt
      set_difference(ExecutionPolicy&& exec,
                     ForwardIt1 first1, ForwardIt1 last1,
                     ForwardIt2 first2, ForwardIt2 last2,
                     ForwardIt result, Compare comp);
 
  namespace ranges {
    template<class I, class O>
    using set_difference_result = copy_result<I, O>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_difference_result<I1, O>
        set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                       Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr set_difference_result<safe_iterator_t<R1>, O>
        set_difference(R1&& r1, R2&& r2, O result,
                       Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIt1, class InputIt2, class OutputIt>
    constexpr OutputIt
      set_symmetric_difference(InputIt1 first1, InputIt1 last1,
                               InputIt2 first2, InputIt2 last2,
                               OutputIt result);
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
    constexpr OutputIt
      set_symmetric_difference(InputIt1 first1, InputIt1 last1,
                               InputIt2 first2, InputIt2 last2,
                               OutputIt result, Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt>
    ForwardIt
      set_symmetric_difference(ExecutionPolicy&& exec,
                               ForwardIt1 first1, ForwardIt1 last1,
                               ForwardIt2 first2, ForwardIt2 last2,
                               ForwardIt result);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class ForwardIt, class Compare>
    ForwardIt
      set_symmetric_difference(ExecutionPolicy&& exec,
                               ForwardIt1 first1, ForwardIt1 last1,
                               ForwardIt2 first2, ForwardIt2 last2,
                               ForwardIt result, Compare comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_symmetric_difference_result = binary_transform_result<I1, I2, O>;
 
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             WeaklyIncrementable O, class Comp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<I1, I2, O, Comp, Proj1, Proj2>
      constexpr set_symmetric_difference_result<I1, I2, O>
        set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                 Comp comp = {}, Proj1 proj1 = {},
                                 Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, WeaklyIncrementable O,
             class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires Mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
      constexpr
        set_symmetric_difference_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // heap operations:
  template<class RandomAccessIt>
    constexpr void push_heap(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void push_heap(RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        push_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        push_heap(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr void pop_heap(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void pop_heap(RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        pop_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        pop_heap(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr void make_heap(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void make_heap(RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        make_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        make_heap(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr void sort_heap(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr void sort_heap(RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr I
        sort_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Comp = ranges::less, class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr safe_iterator_t<R>
        sort_heap(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr bool is_heap(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr bool is_heap(RandomAccessIt first, RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    bool is_heap(ExecutionPolicy&& exec,
                 RandomAccessIt first, RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    bool is_heap(ExecutionPolicy&& exec,
                 RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr bool is_heap(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr bool is_heap(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIt>
    constexpr RandomAccessIt
      is_heap_until(RandomAccessIt first, RandomAccessIt last);
  template<class RandomAccessIt, class Compare>
    constexpr RandomAccessIt
      is_heap_until(RandomAccessIt first, RandomAccessIt last, Compare comp);
  template<class ExecutionPolicy, class RandomAccessIt>
    RandomAccessIt
      is_heap_until(ExecutionPolicy&& exec,
                    RandomAccessIt first, RandomAccessIt last);
  template<class ExecutionPolicy, class RandomAccessIt, class Compare>
    RandomAccessIt
      is_heap_until(ExecutionPolicy&& exec,
                    RandomAccessIt first, RandomAccessIt last, Compare comp);
 
  namespace ranges {
    template<RandomAccessIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr I is_heap_until(I first, S last, Comp comp = {}, Proj proj = {});
    template<RandomAccessRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr safe_iterator_t<R>
        is_heap_until(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  // minimum and maximum:
  template<class T> constexpr const T& min(const T& a, const T& b);
  template<class T, class Compare>
    constexpr const T& min(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr T min(initializer_list<T> t);
  template<class T, class Compare>
    constexpr T min(initializer_list<T> t, Compare comp);
 
  namespace ranges {
    template<class T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr const T& min(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<Copyable T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr T min(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires IndirectlyCopyableStorable<iterator_t<R>, iter_value_t<iterator_t<R>>*>
      constexpr iter_value_t<iterator_t<R>>
        min(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class T> constexpr const T& max(const T& a, const T& b);
  template<class T, class Compare>
    constexpr const T& max(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr T max(initializer_list<T> t);
  template<class T, class Compare>
    constexpr T max(initializer_list<T> t, Compare comp);
 
  namespace ranges {
    template<class T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr const T& max(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<Copyable T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr T max(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires IndirectlyCopyableStorable<iterator_t<R>, iter_value_t<iterator_t<R>>*>
      constexpr iter_value_t<iterator_t<R>>
        max(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class T> constexpr pair<const T&, const T&> minmax(const T& a, const T& b);
  template<class T, class Compare>
    constexpr pair<const T&, const T&> minmax(const T& a, const T& b, Compare comp);
  template<class T>
    constexpr pair<T, T> minmax(initializer_list<T> t);
  template<class T, class Compare>
    constexpr pair<T, T> minmax(initializer_list<T> t, Compare comp);
 
  namespace ranges {
    template<class T>
    struct minmax_result {
      [[no_unique_address]] T min;
      [[no_unique_address]] T max;
 
      template<class T2>
        requires ConvertibleTo<const T&, T2>
        operator minmax_result<T2>() const & {
          return {min, max};
        }
 
      template<class T2>
        requires ConvertibleTo<T, T2>
        operator minmax_result<T2>() && {
          return {std::move(min), std::move(max)};
        }
    };
 
    template<class T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr minmax_result<const T&>
        minmax(const T& a, const T& b, Comp comp = {}, Proj proj = {});
    template<Copyable T, class Proj = identity,
             IndirectStrictWeakOrder<projected<const T*, Proj>> Comp = ranges::less>
      constexpr minmax_result<T>
        minmax(initializer_list<T> r, Comp comp = {}, Proj proj = {});
    template<InputRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      requires IndirectlyCopyableStorable<iterator_t<R>, iter_value_t<iterator_t<R>>*>
      constexpr minmax_result<iter_value_t<iterator_t<R>>>
        minmax(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt>
    constexpr ForwardIt min_element(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class Compare>
    constexpr ForwardIt min_element(ForwardIt first, ForwardIt last,
                                          Compare comp);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt min_element(ExecutionPolicy&& exec,
                          ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class Compare>
    ForwardIt min_element(ExecutionPolicy&& exec,
                          ForwardIt first, ForwardIt last, Compare comp);
 
  namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr I min_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr safe_iterator_t<R>
        min_element(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt>
    constexpr ForwardIt max_element(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class Compare>
    constexpr ForwardIt max_element(ForwardIt first, ForwardIt last, Compare comp);
  template<class ExecutionPolicy, class ForwardIt>
    ForwardIt max_element(ExecutionPolicy&& exec,
                          ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class Compare>
    ForwardIt max_element(ExecutionPolicy&& exec,
                          ForwardIt first, ForwardIt last, Compare comp);
 
 namespace ranges {
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr I max_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr safe_iterator_t<R>
        max_element(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIt>
    constexpr pair<ForwardIt, ForwardIt>
      minmax_element(ForwardIt first, ForwardIt last);
  template<class ForwardIt, class Compare>
    constexpr pair<ForwardIt, ForwardIt>
      minmax_element(ForwardIt first, ForwardIt last, Compare comp);
  template<class ExecutionPolicy, class ForwardIt>
    pair<ForwardIt, ForwardIt>
      minmax_element(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last);
  template<class ExecutionPolicy, class ForwardIt, class Compare>
    pair<ForwardIt, ForwardIt>
      minmax_element(ExecutionPolicy&& exec,
                     ForwardIt first, ForwardIt last, Compare comp);
 
  namespace ranges {
    template<class I>
    using minmax_element_result = minmax_result<I>;
 
    template<ForwardIterator I, Sentinel<I> S, class Proj = identity,
             IndirectStrictWeakOrder<projected<I, Proj>> Comp = ranges::less>
      constexpr minmax_element_result<I>
        minmax_element(I first, S last, Comp comp = {}, Proj proj = {});
    template<ForwardRange R, class Proj = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R>, Proj>> Comp = ranges::less>
      constexpr minmax_element_result<safe_iterator_t<R>>
        minmax_element(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  // 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);
 
  // lexicographical comparison:
  template<class InputIt1, class InputIt2>
    constexpr bool
      lexicographical_compare(InputIt1 first1, InputIt1 last1,
                              InputIt2 first2, InputIt2 last2);
  template<class InputIt1, class InputIt2, class Compare>
    constexpr bool
      lexicographical_compare(InputIt1 first1, InputIt1 last1,
                              InputIt2 first2, InputIt2 last2,
                              Compare comp);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2>
    bool
      lexicographical_compare(ExecutionPolicy&& exec,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2);
  template<class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
           class Compare>
    bool
      lexicographical_compare(ExecutionPolicy&& exec,
                              ForwardIt1 first1, ForwardIt1 last1,
                              ForwardIt2 first2, ForwardIt2 last2,
                              Compare comp);
 
  namespace ranges {
    template<InputIterator I1, Sentinel<I1> S1, InputIterator I2, Sentinel<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             IndirectStrictWeakOrder<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
               ranges::less>
      constexpr bool
        lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
                                Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<InputRange R1, InputRange R2, class Proj1 = identity,
             class Proj2 = identity,
             IndirectStrictWeakOrder<projected<iterator_t<R1>, Proj1>,
                                     projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
      constexpr bool
        lexicographical_compare(R1&& r1, R2&& r2, Comp comp = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // three-way comparison algorithms:
  template<class T, class U>
    constexpr auto compare_3way(const T& a, const U& b);
  template<class InputIt1, class InputIt2, class Cmp>
    constexpr auto
      lexicographical_compare_3way(InputIt1 b1, InputIt1 e1, InputIt2 b2, InputIt2 e2,
                                   Cmp comp)
        -> common_comparison_category_t<decltype(comp(*b1, *b2)), strong_ordering>;
  template<class InputIt1, class InputIt2>
    constexpr auto
      lexicographical_compare_3way(InputIt1 b1, InputIt1 e1, InputIt2 b2, InputIt2 e2);
 
  // permutations:
  template<class BidirectionalIt>
    constexpr bool next_permutation(BidirectionalIt first, BidirectionalIt last);
  template<class BidirectionalIt, class Compare>
    constexpr bool next_permutation(BidirectionalIt first, BidirectionalIt last,
                                    Compare comp);
 
  namespace ranges {
    template<BidirectionalIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr bool
        next_permutation(I first, S last, Comp comp = {}, Proj proj = {});
    template<BidirectionalRange R, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr bool
        next_permutation(R&& r, Comp comp = {}, Proj proj = {});
  }
 
  template<class BidirectionalIt>
    constexpr bool prev_permutation(BidirectionalIt first, BidirectionalIt last);
  template<class BidirectionalIt, class Compare>
    constexpr bool prev_permutation(BidirectionalIt first, BidirectionalIt last,
                                    Compare comp);
 
  namespace ranges {
    template<BidirectionalIterator I, Sentinel<I> S, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<I, Comp, Proj>
      constexpr bool
        prev_permutation(I first, S last, Comp comp = {}, Proj proj = {});
    template<BidirectionalRange R, class Comp = ranges::less,
             class Proj = identity>
      requires Sortable<iterator_t<R>, Comp, Proj>
      constexpr bool
        prev_permutation(R&& r, Comp comp = {}, Proj proj = {});
  }
}

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications

Standard library header <algorithm>

Functions

Non-modifying sequence operations

Modifying sequence operations

Partitioning operations

Sorting operations

Binary search operations (on sorted ranges)

Other operations on sorted ranges

Set operations (on sorted ranges)

Heap operations

Minimum/maximum operations

Comparison operations

Permutation operations

Niebloids

Non-modifying sequence operations

Modifying sequence operations

Partitioning operations

Sorting operations

Binary search operations (on sorted ranges)

Other operations on sorted ranges

Set operations (on sorted ranges)

Heap operations

Minimum/maximum operations

Comparison operations

Permutation operations

Synopsis