# 25 Algorithms library [algorithms]

## 25.1 General [algorithms.general]

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

The following subclauses describe components for non-modifying sequence operation, modifying sequence operations, sorting and related operations, and algorithms from the ISO C library, as summarized in Table [tab:algorithms.summary].

Table 112 — Algorithms library summary
 Subclause Header(s) [alg.nonmodifying] Non-modifying sequence operations [alg.modifying.operations] Mutating sequence operations [alg.sorting] Sorting and related operations [alg.c.library] C library algorithms

#include <initializer_list>

namespace std {

// [alg.nonmodifying], non-modifying sequence operations:
template <class InputIterator, class Predicate>
bool all_of(InputIterator first, InputIterator last, Predicate pred);
template <class InputIterator, class Predicate>
bool any_of(InputIterator first, InputIterator last, Predicate pred);
template <class InputIterator, class Predicate>
bool none_of(InputIterator first, InputIterator last, Predicate pred);

template<class InputIterator, class Function>
Function for_each(InputIterator first, InputIterator last, Function f);
template<class InputIterator, class T>
InputIterator find(InputIterator first, InputIterator last,
const T& value);
template<class InputIterator, class Predicate>
InputIterator find_if(InputIterator first, InputIterator last,
Predicate pred);
template<class InputIterator, class Predicate>
InputIterator find_if_not(InputIterator first, InputIterator last,
Predicate pred);
template<class ForwardIterator1, class ForwardIterator2>
ForwardIterator1
find_end(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
template<class ForwardIterator1, class ForwardIterator2,
class BinaryPredicate>
ForwardIterator1
find_end(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
BinaryPredicate pred);

template<class InputIterator, class ForwardIterator>
InputIterator
find_first_of(InputIterator first1, InputIterator last1,
ForwardIterator first2, ForwardIterator last2);
template<class InputIterator, class ForwardIterator,
class BinaryPredicate>
InputIterator
find_first_of(InputIterator first1, InputIterator last1,
ForwardIterator first2, ForwardIterator last2,
BinaryPredicate pred);

template<class ForwardIterator>
ForwardIterator last);
template<class ForwardIterator, class BinaryPredicate>
ForwardIterator last,
BinaryPredicate pred);

template<class InputIterator, class T>
typename iterator_traits<InputIterator>::difference_type
count(InputIterator first, InputIterator last, const T& value);
template<class InputIterator, class Predicate>
typename iterator_traits<InputIterator>::difference_type
count_if(InputIterator first, InputIterator last, Predicate pred);

template<class InputIterator1, class InputIterator2>
pair<InputIterator1, InputIterator2>
mismatch(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2);
template
<class InputIterator1, class InputIterator2, class BinaryPredicate>
pair<InputIterator1, InputIterator2>
mismatch(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, BinaryPredicate pred);

template<class InputIterator1, class InputIterator2>
pair<InputIterator1, InputIterator2>
mismatch(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2);

template
<class InputIterator1, class InputIterator2, class BinaryPredicate>
pair<InputIterator1, InputIterator2>
mismatch(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
BinaryPredicate pred);

template<class InputIterator1, class InputIterator2>
bool equal(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2);
template
<class InputIterator1, class InputIterator2, class BinaryPredicate>
bool equal(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, BinaryPredicate pred);

template<class InputIterator1, class InputIterator2>
bool equal(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2);

template
<class InputIterator1, class InputIterator2, class BinaryPredicate>
bool equal(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
BinaryPredicate pred);

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

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

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

template<class ForwardIterator1, class ForwardIterator2>
ForwardIterator1 search(
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
template<class ForwardIterator1, class ForwardIterator2,
class BinaryPredicate>
ForwardIterator1 search(
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
BinaryPredicate pred);
template<class ForwardIterator, class Size, class T>
ForwardIterator search_n(ForwardIterator first, ForwardIterator last,
Size count, const T& value);
template
<class ForwardIterator, class Size, class T, class BinaryPredicate>
ForwardIterator search_n(ForwardIterator first, ForwardIterator last,
Size count, const T& value,
BinaryPredicate pred);

// [alg.modifying.operations], modifying sequence operations:
// [alg.copy], copy:
template<class InputIterator, class OutputIterator>
OutputIterator copy(InputIterator first, InputIterator last,
OutputIterator result);
template<class InputIterator, class Size, class OutputIterator>
OutputIterator copy_n(InputIterator first, Size n,
OutputIterator result);
template<class InputIterator, class OutputIterator, class Predicate>
OutputIterator copy_if(InputIterator first, InputIterator last,
OutputIterator result, Predicate pred);
template<class BidirectionalIterator1, class BidirectionalIterator2>
BidirectionalIterator2 copy_backward(
BidirectionalIterator1 first, BidirectionalIterator1 last,
BidirectionalIterator2 result);

// [alg.move], move:
template<class InputIterator, class OutputIterator>
OutputIterator move(InputIterator first, InputIterator last,
OutputIterator result);
template<class BidirectionalIterator1, class BidirectionalIterator2>
BidirectionalIterator2 move_backward(
BidirectionalIterator1 first, BidirectionalIterator1 last,
BidirectionalIterator2 result);

// [alg.swap], swap:
template<class ForwardIterator1, class ForwardIterator2>
ForwardIterator2 swap_ranges(ForwardIterator1 first1,
ForwardIterator1 last1, ForwardIterator2 first2);
template<class ForwardIterator1, class ForwardIterator2>
void iter_swap(ForwardIterator1 a, ForwardIterator2 b);

template<class InputIterator, class OutputIterator, class UnaryOperation>
OutputIterator transform(InputIterator first, InputIterator last,
OutputIterator result, UnaryOperation op);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class BinaryOperation>
OutputIterator transform(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, OutputIterator result,
BinaryOperation binary_op);

template<class ForwardIterator, class T>
void replace(ForwardIterator first, ForwardIterator last,
const T& old_value, const T& new_value);
template<class ForwardIterator, class Predicate, class T>
void replace_if(ForwardIterator first, ForwardIterator last,
Predicate pred, const T& new_value);
template<class InputIterator, class OutputIterator, class T>
OutputIterator replace_copy(InputIterator first, InputIterator last,
OutputIterator result,
const T& old_value, const T& new_value);
template<class InputIterator, class OutputIterator, class Predicate, class T>
OutputIterator replace_copy_if(InputIterator first, InputIterator last,
OutputIterator result,
Predicate pred, const T& new_value);

template<class ForwardIterator, class T>
void fill(ForwardIterator first, ForwardIterator last, const T& value);
template<class OutputIterator, class Size, class T>
OutputIterator fill_n(OutputIterator first, Size n, const T& value);

template<class ForwardIterator, class Generator>
void generate(ForwardIterator first, ForwardIterator last,
Generator gen);
template<class OutputIterator, class Size, class Generator>
OutputIterator generate_n(OutputIterator first, Size n, Generator gen);

template<class ForwardIterator, class T>
ForwardIterator remove(ForwardIterator first, ForwardIterator last,
const T& value);
template<class ForwardIterator, class Predicate>
ForwardIterator remove_if(ForwardIterator first, ForwardIterator last,
Predicate pred);
template<class InputIterator, class OutputIterator, class T>
OutputIterator remove_copy(InputIterator first, InputIterator last,
OutputIterator result, const T& value);
template<class InputIterator, class OutputIterator, class Predicate>
OutputIterator remove_copy_if(InputIterator first, InputIterator last,
OutputIterator result, Predicate pred);

template<class ForwardIterator>
ForwardIterator unique(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class BinaryPredicate>
ForwardIterator unique(ForwardIterator first, ForwardIterator last,
BinaryPredicate pred);
template<class InputIterator, class OutputIterator>
OutputIterator unique_copy(InputIterator first, InputIterator last,
OutputIterator result);
template<class InputIterator, class OutputIterator, class BinaryPredicate>
OutputIterator unique_copy(InputIterator first, InputIterator last,
OutputIterator result, BinaryPredicate pred);

template<class BidirectionalIterator>
void reverse(BidirectionalIterator first, BidirectionalIterator last);
template<class BidirectionalIterator, class OutputIterator>
OutputIterator reverse_copy(BidirectionalIterator first,
BidirectionalIterator last,
OutputIterator result);

template<class ForwardIterator>
ForwardIterator rotate(ForwardIterator first, ForwardIterator middle,
ForwardIterator last);
template<class ForwardIterator, class OutputIterator>
OutputIterator rotate_copy(
ForwardIterator first, ForwardIterator middle,
ForwardIterator last, OutputIterator result);

// [depr.alg.random.shuffle], random_shuffle (deprecated):
template<class RandomAccessIterator>
void random_shuffle(RandomAccessIterator first,
RandomAccessIterator last);
template<class RandomAccessIterator, class RandomNumberGenerator>
void random_shuffle(RandomAccessIterator first,
RandomAccessIterator last,
RandomNumberGenerator&& rng);

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

// [alg.partitions], partitions:
template <class InputIterator, class Predicate>
bool is_partitioned(InputIterator first, InputIterator last, Predicate pred);

template<class ForwardIterator, class Predicate>
ForwardIterator partition(ForwardIterator first,
ForwardIterator last,
Predicate pred);
template<class BidirectionalIterator, class Predicate>
BidirectionalIterator stable_partition(BidirectionalIterator first,
BidirectionalIterator last,
Predicate pred);
template <class InputIterator, class OutputIterator1,
class OutputIterator2, class Predicate>
pair<OutputIterator1, OutputIterator2>
partition_copy(InputIterator first, InputIterator last,
OutputIterator1 out_true, OutputIterator2 out_false,
Predicate pred);
template<class ForwardIterator, class Predicate>
ForwardIterator partition_point(ForwardIterator first,
ForwardIterator last,
Predicate pred);

// [alg.sorting], sorting and related operations:
// [alg.sort], sorting:
template<class RandomAccessIterator>
void sort(RandomAccessIterator first, RandomAccessIterator last);
template<class RandomAccessIterator, class Compare>
void sort(RandomAccessIterator first, RandomAccessIterator last,
Compare comp);

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

template<class RandomAccessIterator>
void partial_sort(RandomAccessIterator first,
RandomAccessIterator middle,
RandomAccessIterator last);
template<class RandomAccessIterator, class Compare>
void partial_sort(RandomAccessIterator first,
RandomAccessIterator middle,
RandomAccessIterator last, Compare comp);
template<class InputIterator, class RandomAccessIterator>
RandomAccessIterator partial_sort_copy(
InputIterator first, InputIterator last,
RandomAccessIterator result_first,
RandomAccessIterator result_last);
template<class InputIterator, class RandomAccessIterator, class Compare>
RandomAccessIterator partial_sort_copy(
InputIterator first, InputIterator last,
RandomAccessIterator result_first,
RandomAccessIterator result_last,
Compare comp);
template<class ForwardIterator>
bool is_sorted(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class Compare>
bool is_sorted(ForwardIterator first, ForwardIterator last,
Compare comp);
template<class ForwardIterator>
ForwardIterator is_sorted_until(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class Compare>
ForwardIterator is_sorted_until(ForwardIterator first, ForwardIterator last,
Compare comp);

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

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

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

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

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

// [alg.merge], merge:
template<class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator merge(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class Compare>
OutputIterator merge(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);

template<class BidirectionalIterator>
void inplace_merge(BidirectionalIterator first,
BidirectionalIterator middle,
BidirectionalIterator last);
template<class BidirectionalIterator, class Compare>
void inplace_merge(BidirectionalIterator first,
BidirectionalIterator middle,
BidirectionalIterator last, Compare comp);

// [alg.set.operations], set operations:
template<class InputIterator1, class InputIterator2>
bool includes(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2);
template<class InputIterator1, class InputIterator2, class Compare>
bool includes(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2, Compare comp);

template<class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_union(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class Compare>
OutputIterator set_union(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);

template<class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_intersection(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class Compare>
OutputIterator set_intersection(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);

template<class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_difference(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class Compare>
OutputIterator set_difference(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);

template<class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_symmetric_difference(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class InputIterator1, class InputIterator2, class OutputIterator,
class Compare>
OutputIterator set_symmetric_difference(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);

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

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

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

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

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

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

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

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

template<class ForwardIterator>
ForwardIterator min_element(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class Compare>
ForwardIterator min_element(ForwardIterator first, ForwardIterator last,
Compare comp);
template<class ForwardIterator>
ForwardIterator max_element(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class Compare>
ForwardIterator max_element(ForwardIterator first, ForwardIterator last,
Compare comp);
template<class ForwardIterator>
pair<ForwardIterator, ForwardIterator>
minmax_element(ForwardIterator first, ForwardIterator last);
template<class ForwardIterator, class Compare>
pair<ForwardIterator, ForwardIterator>
minmax_element(ForwardIterator first, ForwardIterator last, Compare comp);

template<class InputIterator1, class InputIterator2>
bool lexicographical_compare(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2);
template<class InputIterator1, class InputIterator2, class Compare>
bool lexicographical_compare(
InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
Compare comp);

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


All of the algorithms are separated from the particular implementations of data structures and are parameterized by iterator types. Because of this, they can work with program-defined data structures, as long as these data structures have iterator types satisfying the assumptions on the algorithms.

For purposes of determining the existence of data races, algorithms shall not modify objects referenced through an iterator argument unless the specification requires such modification.

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

• If an algorithm's template parameter is named InputIterator, InputIterator1, or InputIterator2, the template argument shall satisfy the requirements of an input iterator ([input.iterators]).

• If an algorithm's template parameter is named OutputIterator, OutputIterator1, or OutputIterator2, the template argument shall satisfy the requirements of an output iterator ([output.iterators]).

• If an algorithm's template parameter is named ForwardIterator, ForwardIterator1, or ForwardIterator2, the template argument shall satisfy the requirements of a forward iterator ([forward.iterators]).

• If an algorithm's template parameter is named BidirectionalIterator, BidirectionalIterator1, or BidirectionalIterator2, the template argument shall satisfy the requirements of a bidirectional iterator ([bidirectional.iterators]).

• If an algorithm's template parameter is named RandomAccessIterator, RandomAccessIterator1, or RandomAccessIterator2, the template argument shall satisfy the requirements of a random-access iterator ([random.access.iterators]).

If an algorithm's Effects section says that a value pointed to by any iterator passed as an argument is modified, then that algorithm has an additional type requirement: The type of that argument shall satisfy the requirements of a mutable iterator ([iterator.requirements]). [ Note: This requirement does not affect arguments that are named OutputIterator, OutputIterator1, or OutputIterator2, because output iterators must always be mutable.  — end note ]

Both in-place and copying versions are provided for certain algorithms.269 When such a version is provided for algorithm it is called algorithm_copy. Algorithms that take predicates end with the suffix _if (which follows the suffix _copy).

The Predicate parameter is used whenever an algorithm expects a function object ([function.objects]) that, when applied to the result of dereferencing the corresponding iterator, returns a value testable as true. In other words, if an algorithm takes Predicate pred as its argument and first as its iterator argument, it should work correctly in the construct pred(*first) contextually converted to bool (Clause [conv]). The function object pred shall not apply any non-constant function through the dereferenced iterator.

The BinaryPredicate parameter is used whenever an algorithm expects a function object that when applied to the result of dereferencing two corresponding iterators or to dereferencing an iterator and type T when T is part of the signature returns a value testable as true. In other words, if an algorithm takes BinaryPredicate binary_pred as its argument and first1 and first2 as its iterator arguments, it should work correctly in the construct binary_pred(*first1, *first2) contextually converted to bool (Clause [conv]). BinaryPredicate always takes the first iterator's value_type as its first argument, that is, in those cases when T value is part of the signature, it should work correctly in the construct binary_pred(*first1, value) contextually converted to bool (Clause [conv]). binary_pred shall not apply any non-constant function through the dereferenced iterators.

Note: Unless otherwise specified, algorithms that take function objects as arguments are permitted to copy those function objects freely. Programmers for whom object identity is important should consider using a wrapper class that points to a noncopied implementation object such as reference_wrapper<T> ([refwrap]), or some equivalent solution.  — end note ]

When the description of an algorithm gives an expression such as *first == value for a condition, the expression shall evaluate to either true or false in boolean contexts.

In the description of the algorithms operators + and - are used for some of the iterator categories for which they do not have to be defined. In these cases the semantics of a+n is the same as that of

X tmp = a;
return tmp;


and that of b-a is the same as of

return distance(a, b);


The decision whether to include a copying version was usually based on complexity considerations. When the cost of doing the operation dominates the cost of copy, the copying version is not included. For example, sort_copy is not included because the cost of sorting is much more significant, and users might as well do copy followed by sort.

## 25.2 Non-modifying sequence operations [alg.nonmodifying]

### 25.2.1 All of [alg.all_of]

 template <class InputIterator, class Predicate> bool all_of(InputIterator first, InputIterator last, Predicate pred); 

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

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

### 25.2.2 Any of [alg.any_of]

 template <class InputIterator, class Predicate> bool any_of(InputIterator first, InputIterator last, Predicate pred); 

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

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

### 25.2.3 None of [alg.none_of]

 template <class InputIterator, class Predicate> bool none_of(InputIterator first, InputIterator last, Predicate pred); 

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

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

### 25.2.4 For each [alg.foreach]

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

Requires: Function shall meet the requirements of MoveConstructible (Table [moveconstructible]). [ Note: Function need not meet the requirements of CopyConstructible (Table [copyconstructible]).  — end note ]

Effects: Applies f to the result of dereferencing every iterator in the range [first,last), starting from first and proceeding to last - 1. [ Note: If the type of first satisfies the requirements of a mutable iterator, f may apply nonconstant functions through the dereferenced iterator. — end note ]

Returns: std::move(f).

Complexity: Applies f exactly last - first times.

Remarks: If f returns a result, the result is ignored.

### 25.2.5 Find [alg.find]

 template<class InputIterator, class T> InputIterator find(InputIterator first, InputIterator last, const T& value); template<class InputIterator, class Predicate> InputIterator find_if(InputIterator first, InputIterator last, Predicate pred); template<class InputIterator, class Predicate> InputIterator find_if_not(InputIterator first, InputIterator last, Predicate pred); 

Returns: The first iterator i in the range [first,last) for which the following corresponding conditions hold: *i == value, pred(*i) != false, pred(*i) == false. Returns last if no such iterator is found.

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

### 25.2.6 Find end [alg.find.end]

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

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

Returns: The last iterator i in the range [first1,last1 - (last2 - first2)) such that for every non-negative integer n < (last2 - first2), the following corresponding conditions hold: *(i + n) == *(first2 + n), pred(*(i + n), *(first2 + n)) != false. Returns last1 if [first2,last2) is empty or if no such iterator is found.

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

### 25.2.7 Find first [alg.find.first.of]

 template<class InputIterator, class ForwardIterator> InputIterator find_first_of(InputIterator first1, InputIterator last1, ForwardIterator first2, ForwardIterator last2); template<class InputIterator, class ForwardIterator, class BinaryPredicate> InputIterator find_first_of(InputIterator first1, InputIterator last1, ForwardIterator first2, ForwardIterator last2, BinaryPredicate pred); 

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

Returns: The first iterator i in the range [first1,last1) such that for some iterator j in the range [first2,last2) the following conditions hold: *i == *j, pred(*i,*j) != false. Returns last1 if [first2,last2) is empty or if no such iterator is found.

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

 template<class ForwardIterator> ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class BinaryPredicate> ForwardIterator adjacent_find(ForwardIterator first, ForwardIterator last, BinaryPredicate pred); 

Returns: The first iterator i such that both i and i + 1 are in the range [first,last) for which the following corresponding conditions hold: *i == *(i + 1), pred(*i, *(i + 1)) != false. Returns last if no such iterator is found.

Complexity: For a nonempty range, exactly min((i - first) + 1, (last - first) - 1) applications of the corresponding predicate, where i is adjacent_find's return value.

### 25.2.9 Count [alg.count]

 template<class InputIterator, class T> typename iterator_traits<InputIterator>::difference_type count(InputIterator first, InputIterator last, const T& value); template<class InputIterator, class Predicate> typename iterator_traits<InputIterator>::difference_type count_if(InputIterator first, InputIterator last, Predicate pred); 

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

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

### 25.2.10 Mismatch [mismatch]

 template<class InputIterator1, class InputIterator2> pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, BinaryPredicate pred); template<class InputIterator1, class InputIterator2> pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template <class InputIterator1, class InputIterator2, class BinaryPredicate> pair<InputIterator1, InputIterator2> mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, BinaryPredicate pred); 

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

Returns: A pair of iterators i and j such that j == first2 + (i - first1) and i is the first iterator in the range [first1,last1) for which the following corresponding conditions hold:

• j is in the range [first2, last2).

• !(*i == *(first2 + (i - first1)))

• pred(*i, *(first2 + (i - first1))) == false

Returns the pair first1 + min(last1 - first1, last2 - first2) and first2 + min(last1 - first1, last2 - first2) if such an iterator i is not found.

Complexity: At most last1 - first1 applications of the corresponding predicate.

### 25.2.11 Equal [alg.equal]

 template<class InputIterator1, class InputIterator2> bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, BinaryPredicate pred); template<class InputIterator1, class InputIterator2> bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class InputIterator1, class InputIterator2, class BinaryPredicate> bool equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, BinaryPredicate pred); 

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

Returns: If last1 - first1 != last2 - first2, return false. Otherwise return true if for every iterator i in the range [first1,last1) the following corresponding conditions hold: *i == *(first2 + (i - first1)), pred(*i, *(first2 + (i - first1))) != false. Otherwise, returns false.

Complexity: No applications of the corresponding predicate if InputIterator1 and InputIterator2 meet the requirements of random access iterators and last1 - first1 != last2 - first2. Otherwise, at most min(last1 - first1, last2 - first2) applications of the corresponding predicate.

### 25.2.12 Is permutation [alg.is_permutation]

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

Requires: ForwardIterator1 and ForwardIterator2 shall have the same value type. The comparison function shall be an equivalence relation.

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

Returns: If last1 - first1 != last2 - first2, return false. Otherwise return true if there exists a permutation of the elements in the range [first2,first2 + (last1 - first1)), beginning with ForwardIterator2 begin, such that equal(first1, last1, begin) returns true or equal(first1, last1, begin, pred) returns true; otherwise, returns false.

Complexity: No applications of the corresponding predicate if ForwardIterator1 and ForwardIterator2 meet the requirements of random access iterators and last1 - first1 != last2 - first2. Otherwise, exactly distance(first1, last1) applications of the corresponding predicate if equal(first1, last1, first2, last2) would return true if pred was not given in the argument list or equal(first1, last1, first2, last2, pred) would return true if pred was given in the argument list; otherwise, at worst Ο(N2), where N has the value distance(first1, last1).

### 25.2.13 Search [alg.search]

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

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

Returns: The first iterator i in the range [first1,last1 - (last2-first2)) such that for every non-negative integer n less than last2 - first2 the following corresponding conditions hold: *(i + n) == *(first2 + n), pred(*(i + n), *(first2 + n)) != false. Returns first1 if [first2,last2) is empty, otherwise returns last1 if no such iterator is found.

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

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

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

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

Returns: The first iterator i in the range [first,last-count) such that for every non-negative integer n less than count the following corresponding conditions hold: *(i + n) == value, pred(*(i + n),value) != false. Returns last if no such iterator is found.

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

## 25.3 Mutating sequence operations [alg.modifying.operations]

### 25.3.1 Copy [alg.copy]

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

Effects: Copies elements in the range [first,last) into the range [result,result + (last - first)) starting from first and proceeding to last. For each non-negative integer n < (last - first), performs *(result + n) = *(first + n).

Returns: result + (last - first).

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

Complexity: Exactly last - first assignments.

 template<class InputIterator, class Size, class OutputIterator> OutputIterator copy_n(InputIterator first, Size n, OutputIterator result); 

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

Returns: result + n.

Complexity: Exactly n assignments.

 template<class InputIterator, class OutputIterator, class Predicate> OutputIterator copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred); 

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

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

Returns: The end of the resulting range.

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

Remarks: Stable ([algorithm.stable]).

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

Effects: Copies elements in the range [first,last) into the range [result - (last-first),result) starting from last - 1 and proceeding to first.270 For each positive integer n <= (last - first), performs *(result - n) = *(last - n).

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

Returns: result - (last - first).

Complexity: Exactly last - first assignments.

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

### 25.3.2 Move [alg.move]

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

Effects: Moves elements in the range [first,last) into the range [result,result + (last - first)) starting from first and proceeding to last. For each non-negative integer n < (last-first), performs *(result + n) = std::move(*(first + n)).

Returns: result + (last - first).

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

Complexity: Exactly last - first move assignments.

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

Effects: Moves elements in the range [first,last) into the range [result - (last-first),result) starting from last - 1 and proceeding to first.271 For each positive integer n <= (last - first), performs *(result - n) = std::move(*(last - n)).

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

Returns: result - (last - first).

Complexity: Exactly last - first assignments.

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

### 25.3.3 swap [alg.swap]

 template<class ForwardIterator1, class ForwardIterator2> ForwardIterator2 swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2); 

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

Requires: The two ranges [first1,last1) and [first2,first2 + (last1 - first1)) shall not overlap. *(first1 + n) shall be swappable with ([swappable.requirements]) *(first2 + n).

Returns: first2 + (last1 - first1).

Complexity: Exactly last1 - first1 swaps.

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

Effects: swap(*a, *b).

Requires: a and b shall be dereferenceable. *a shall be swappable with ([swappable.requirements]) *b.

### 25.3.4 Transform [alg.transform]

 template<class InputIterator, class OutputIterator, class UnaryOperation> OutputIterator transform(InputIterator first, InputIterator last, OutputIterator result, UnaryOperation op); template<class InputIterator1, class InputIterator2, class OutputIterator, class BinaryOperation> OutputIterator transform(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, OutputIterator result, BinaryOperation binary_op); 

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

Requires: op and binary_op shall not invalidate iterators or subranges, or modify elements in the ranges [first1,last1], [first2,first2 + (last1 - first1)], and [result,result + (last1 - first1)].272

Returns: result + (last1 - first1).

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

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

The use of fully closed ranges is intentional.

### 25.3.5 Replace [alg.replace]

 template<class ForwardIterator, class T> void replace(ForwardIterator first, ForwardIterator last, const T& old_value, const T& new_value); template<class ForwardIterator, class Predicate, class T> void replace_if(ForwardIterator first, ForwardIterator last, Predicate pred, const T& new_value); 

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

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

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

 template<class InputIterator, class OutputIterator, class T> OutputIterator replace_copy(InputIterator first, InputIterator last, OutputIterator result, const T& old_value, const T& new_value); template<class InputIterator, class OutputIterator, class Predicate, class T> OutputIterator replace_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred, const T& new_value); 

Requires: The results of the expressions *first and new_value shall be writable to the result output iterator. The ranges [first,last) and [result,result + (last - first)) shall not overlap.

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

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


Returns: result + (last - first).

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

### 25.3.6 Fill [alg.fill]

 template<class ForwardIterator, class T> void fill(ForwardIterator first, ForwardIterator last, const T& value); template<class OutputIterator, class Size, class T> OutputIterator fill_n(OutputIterator first, Size n, const T& value); 

Requires: The expression value shall be writable to the output iterator. The type Size shall be convertible to an integral type ([conv.integral], [class.conv]).

Effects: The first algorithm assigns value through all the iterators in the range [first,last). The second algorithm assigns value through all the iterators in the range [first,first + n) if n is positive, otherwise it does nothing.

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

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

### 25.3.7 Generate [alg.generate]

 template<class ForwardIterator, class Generator> void generate(ForwardIterator first, ForwardIterator last, Generator gen); template<class OutputIterator, class Size, class Generator> OutputIterator generate_n(OutputIterator first, Size n, Generator gen); 

Effects: The first algorithm invokes the function object gen and assigns the return value of gen through all the iterators in the range [first,last). The second algorithm invokes the function object gen and assigns the return value of gen through all the iterators in the range [first,first + n) if n is positive, otherwise it does nothing.

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

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

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

### 25.3.8 Remove [alg.remove]

 template<class ForwardIterator, class T> ForwardIterator remove(ForwardIterator first, ForwardIterator last, const T& value); template<class ForwardIterator, class Predicate> ForwardIterator remove_if(ForwardIterator first, ForwardIterator last, Predicate pred); 

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

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

Returns: The end of the resulting range.

Remarks: Stable ([algorithm.stable]).

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

Note: each element in the range [ret,last), where ret is the returned value, has a valid but unspecified state, because the algorithms can eliminate elements by moving from elements that were originally in that range.

 template<class InputIterator, class OutputIterator, class T> OutputIterator remove_copy(InputIterator first, InputIterator last, OutputIterator result, const T& value); template<class InputIterator, class OutputIterator, class Predicate> OutputIterator remove_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred); 

Requires: The ranges [first,last) and [result,result + (last - first)) shall not overlap. The expression *result = *first shall be valid.

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

Returns: The end of the resulting range.

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

Remarks: Stable ([algorithm.stable]).

### 25.3.9 Unique [alg.unique]

 template<class ForwardIterator> ForwardIterator unique(ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class BinaryPredicate> ForwardIterator unique(ForwardIterator first, ForwardIterator last, BinaryPredicate pred); 

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

Requires: The comparison function shall be an equivalence relation. The type of *first shall satisfy the MoveAssignable requirements (Table [moveassignable]).

Returns: The end of the resulting range.

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

 template<class InputIterator, class OutputIterator> OutputIterator unique_copy(InputIterator first, InputIterator last, OutputIterator result); template<class InputIterator, class OutputIterator, class BinaryPredicate> OutputIterator unique_copy(InputIterator first, InputIterator last, OutputIterator result, BinaryPredicate pred); 

Requires: The comparison function shall be an equivalence relation. The ranges [first,last) and [result,result+(last-first)) shall not overlap. The expression *result = *first shall be valid. If neither InputIterator nor OutputIterator meets the requirements of forward iterator then the value type of InputIterator shall be CopyConstructible (Table [copyconstructible]) and CopyAssignable (Table [copyassignable]). Otherwise CopyConstructible is not required.

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

Returns: The end of the resulting range.

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

### 25.3.10 Reverse [alg.reverse]

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

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

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

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

 template<class BidirectionalIterator, class OutputIterator> OutputIterator reverse_copy(BidirectionalIterator first, BidirectionalIterator last, OutputIterator result); 

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

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

Returns: result + (last - first).

Complexity: Exactly last - first assignments.

### 25.3.11 Rotate [alg.rotate]

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

Effects: For each non-negative integer i < (last - first), places the element from the position first + i into position first + (i + (last - middle)) % (last - first).

Returns: first + (last - middle).

Remarks: This is a left rotate.

Requires: [first,middle) and [middle,last) shall be valid ranges. ForwardIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and the requirements of MoveAssignable (Table [moveassignable]).

Complexity: At most last - first swaps.

 template<class ForwardIterator, class OutputIterator> OutputIterator rotate_copy(ForwardIterator first, ForwardIterator middle, ForwardIterator last, OutputIterator result); 

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

Returns: result + (last - first).

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

Complexity: Exactly last - first assignments.

### 25.3.12 Shuffle [alg.random.shuffle]

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

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

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type UniformRandomNumberGenerator shall meet the requirements of a uniform random number generator ([rand.req.urng]) type whose return type is convertible to iterator_traits<RandomAccessIterator>::difference_type.

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

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

### 25.3.13 Partitions [alg.partitions]

 template <class InputIterator, class Predicate> bool is_partitioned(InputIterator first, InputIterator last, Predicate pred); 

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

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

Complexity: Linear. At most last - first applications of pred.

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

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

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

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

Complexity: If ForwardIterator meets the requirements for a BidirectionalIterator, at most (last - first) / 2 swaps are done; otherwise at most last - first swaps are done. Exactly last - first applications of the predicate are done.

 template<class BidirectionalIterator, class Predicate> BidirectionalIterator stable_partition(BidirectionalIterator first, BidirectionalIterator last, Predicate pred); 

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

Returns: An iterator i such that for every iterator j in the range [first,i), pred(*j) != false, and for every iterator k in the range [i,last), pred(*k) == false. The relative order of the elements in both groups is preserved.

Requires: BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: At most (last - first) * log(last - first) swaps, but only linear number of swaps if there is enough extra memory. Exactly last - first applications of the predicate.

 template <class InputIterator, class OutputIterator1, class OutputIterator2, class Predicate> pair<OutputIterator1, OutputIterator2> partition_copy(InputIterator first, InputIterator last, OutputIterator1 out_true, OutputIterator2 out_false, Predicate pred); 

Requires: InputIterator's value type shall be CopyAssignable, and shall be writable to the out_true and out_false OutputIterators, and shall be convertible to Predicate's argument type. The input range shall not overlap with either of the output ranges.

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

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

Complexity: Exactly last - first applications of pred.

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

Requires: ForwardIterator's value type shall be convertible to Predicate's argument type. [first,last) shall be partitioned by pred, i.e. all elements that satisfy pred shall appear before those that do not.

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

Complexity: Ο(log(last - first)) applications of pred.

## 25.4 Sorting and related operations [alg.sorting]

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

Compare is a function object type ([function.objects]). The return value of the function call operation applied to an object of type Compare, when contextually converted to bool (Clause [conv]), yields true if the first argument of the call is less than the second, and false otherwise. Compare comp is used throughout for algorithms assuming an ordering relation. It is assumed that comp will not apply any non-constant function through the dereferenced iterator.

For all algorithms that take Compare, there is a version that uses operator< instead. That is, comp(*i, *j) != false defaults to *i < *j != false. For algorithms other than those described in [alg.binary.search] to work correctly, comp has to induce a strict weak ordering on the values.

The term strict refers to the requirement of an irreflexive relation (!comp(x, x) for all x), and the term weak to requirements that are not as strong as those for a total ordering, but stronger than those for a partial ordering. If we define equiv(a, b) as !comp(a, b) && !comp(b, a), then the requirements are that comp and equiv both be transitive relations:

• comp(a, b) && comp(b, c) implies comp(a, c)

• equiv(a, b) && equiv(b, c) implies equiv(a, c)Note: Under these conditions, it can be shown that

• equiv is an equivalence relation

• comp induces a well-defined relation on the equivalence classes determined by equiv

• The induced relation is a strict total ordering.  — end note ]

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

A sequence [start,finish) is partitioned with respect to an expression f(e) if there exists an integer n such that for all 0 <= i < distance(start, finish), f(*(start + i)) is true if and only if i < n.

In the descriptions of the functions that deal with ordering relationships we frequently use a notion of equivalence to describe concepts such as stability. The equivalence to which we refer is not necessarily an operator==, but an equivalence relation induced by the strict weak ordering. That is, two elements a and b are considered equivalent if and only if !(a < b) && !(b < a).

### 25.4.1 Sorting [alg.sort]

#### 25.4.1.1sort[sort]

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

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

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: Ο(Nlog(N)) (where N == last - first) comparisons.

#### 25.4.1.2stable_sort[stable.sort]

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

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

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: It does at most N log2(N) (where N == last - first) comparisons; if enough extra memory is available, it is N log(N).

Remarks: Stable ([algorithm.stable]).

#### 25.4.1.3partial_sort[partial.sort]

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

Effects: Places the first middle - first sorted elements from the range [first,last) into the range [first,middle). The rest of the elements in the range [middle,last) are placed in an unspecified order.

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: It takes approximately (last - first) * log(middle - first) comparisons.

#### 25.4.1.4partial_sort_copy[partial.sort.copy]

 template<class InputIterator, class RandomAccessIterator> RandomAccessIterator partial_sort_copy(InputIterator first, InputIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last); template<class InputIterator, class RandomAccessIterator, class Compare> RandomAccessIterator partial_sort_copy(InputIterator first, InputIterator last, RandomAccessIterator result_first, RandomAccessIterator result_last, Compare comp); 

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

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

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *result_first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

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

#### 25.4.1.5is_sorted[is.sorted]

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

Returns: is_sorted_until(first, last) == last

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

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

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

Returns: If distance(first, last) < 2, returns last. Otherwise, returns the last iterator i in [first,last] for which the range [first,i) is sorted.

Complexity: Linear.

### 25.4.2 Nth element [alg.nth.element]

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

After nth_element the element in the position pointed to by nth is the element that would be in that position if the whole range were sorted, unless nth == last. Also for every iterator i in the range [first,nth) and every iterator j in the range [nth,last) it holds that: !(*j < *i) or comp(*j, *i) == false.

Requires: RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: Linear on average.

### 25.4.3 Binary search [alg.binary.search]

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

#### 25.4.3.1lower_bound[lower.bound]

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

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

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

Complexity: At most log2(last - first) + Ο(1) comparisons.

#### 25.4.3.2upper_bound[upper.bound]

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

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

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

Complexity: At most log2(last - first) + Ο(1) comparisons.

#### 25.4.3.3equal_range[equal.range]

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

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

Returns:

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


or

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


Complexity: At most 2 * log2(last - first) + Ο(1) comparisons.

#### 25.4.3.4binary_search[binary.search]

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

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

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

Complexity: At most log2(last - first) + Ο(1) comparisons.

### 25.4.4 Merge [alg.merge]

 template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator merge(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator merge(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); 

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

Requires: The ranges [first1,last1) and [first2,last2) shall be sorted with respect to operator< or comp. The resulting range shall not overlap with either of the original ranges.

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

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

Remarks: Stable ([algorithm.stable]).

 template<class BidirectionalIterator> void inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last); template<class BidirectionalIterator, class Compare> void inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last, Compare comp); 

Effects: Merges two sorted consecutive ranges [first,middle) and [middle,last), putting the result of the merge into the range [first,last). The resulting range will be in non-decreasing order; that is, for every iterator i in [first,last) other than first, the condition *i < *(i - 1) or, respectively, comp(*i, *(i - 1)) will be false.

Requires: The ranges [first,middle) and [middle,last) shall be sorted with respect to operator< or comp. BidirectionalIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: When enough additional memory is available, (last - first) - 1 comparisons. If no additional memory is available, an algorithm with complexity N log(N) (where N is equal to last - first) may be used.

Remarks: Stable ([algorithm.stable]).

### 25.4.5 Set operations on sorted structures [alg.set.operations]

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

#### 25.4.5.1includes[includes]

 template<class InputIterator1, class InputIterator2> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); 

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

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

#### 25.4.5.2set_union[set.union]

 template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); 

Effects: Constructs a sorted union of the elements from the two ranges; that is, the set of elements that are present in one or both of the ranges.

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

Returns: The end of the constructed range.

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

Remarks: If [first1,last1) contains m elements that are equivalent to each other and [first2,last2) contains n elements that are equivalent to them, then all m elements from the first range shall be copied to the output range, in order, and then max(n - m, 0) elements from the second range shall be copied to the output range, in order.

#### 25.4.5.3set_intersection[set.intersection]

 template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); 

Effects: Constructs a sorted intersection of the elements from the two ranges; that is, the set of elements that are present in both of the ranges.

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

Returns: The end of the constructed range.

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

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

#### 25.4.5.4set_difference[set.difference]

 template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); 

Effects: Copies the elements of the range [first1,last1) which are not present in the range [first2,last2) to the range beginning at result. The elements in the constructed range are sorted.

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

Returns: The end of the constructed range.

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

Remarks: If [first1,last1) contains m elements that are equivalent to each other and [first2,last2) contains n elements that are equivalent to them, the last max(m - n, 0) elements from [first1,last1) shall be copied to the output range.

#### 25.4.5.5set_symmetric_difference[set.symmetric.difference]

 template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); 

Effects: Copies the elements of the range [first1,last1) that are not present in the range [first2,last2), and the elements of the range [first2,last2) that are not present in the range [first1,last1) to the range beginning at result. The elements in the constructed range are sorted.

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

Returns: The end of the constructed range.

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

Remarks: If [first1,last1) contains m elements that are equivalent to each other and [first2,last2) contains n elements that are equivalent to them, then |m - n| of those elements shall be copied to the output range: the last m - n of these elements from [first1,last1) if m > n, and the last n - m of these elements from [first2,last2) if m < n.

### 25.4.6 Heap operations [alg.heap.operations]

A heap is a particular organization of elements in a range between two random access iterators [a,b). Its two key properties are:

• There is no element greater than *a in the range and

• *a may be removed by pop_heap(), or a new element added by push_heap(), in O(log(N)) time.

These properties make heaps useful as priority queues.

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

#### 25.4.6.1push_heap[push.heap]

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

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

Requires: The range [first,last - 1) shall be a valid heap. The type of *first shall satisfy the MoveConstructible requirements (Table [moveconstructible]) and the MoveAssignable requirements (Table [moveassignable]).

Complexity: At most log(last - first) comparisons.

#### 25.4.6.2pop_heap[pop.heap]

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

Requires: The range [first,last) shall be a valid non-empty heap. RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

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

Complexity: At most 2 * log(last - first) comparisons.

#### 25.4.6.3make_heap[make.heap]

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

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

Requires: The type of *first shall satisfy the MoveConstructible requirements (Table [moveconstructible]) and the MoveAssignable requirements (Table [moveassignable]).

Complexity: At most 3 * (last - first) comparisons.

#### 25.4.6.4sort_heap[sort.heap]

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

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

Requires: The range [first,last) shall be a valid heap. RandomAccessIterator shall satisfy the requirements of ValueSwappable ([swappable.requirements]). The type of *first shall satisfy the requirements of MoveConstructible (Table [moveconstructible]) and of MoveAssignable (Table [moveassignable]).

Complexity: At most N log(N) comparisons (where N == last - first).

#### 25.4.6.5is_heap[is.heap]

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

Returns: is_heap_until(first, last) == last

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

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

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

Returns: If distance(first, last) < 2, returns last. Otherwise, returns the last iterator i in [first,last] for which the range [first,i) is a heap.

Complexity: Linear.

### 25.4.7 Minimum and maximum [alg.min.max]

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

Requires: Type T is LessThanComparable (Table [lessthancomparable]).

Returns: The smaller value.

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

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

Requires: T is LessThanComparable and CopyConstructible and t.size() > 0.

Returns: The smallest value in the initializer_list.

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

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

Requires: Type T is LessThanComparable (Table [lessthancomparable]).

Returns: The larger value.

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

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

Requires: T is LessThanComparable and CopyConstructible and t.size() > 0.

Returns: The largest value in the initializer_list.

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

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

Requires: Type T shall be LessThanComparable (Table [lessthancomparable]).

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

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

Complexity: Exactly one comparison.

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

Requires: T is LessThanComparable and CopyConstructible and t.size() > 0.

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

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

Complexity: At most (3/2) * t.size() applications of the corresponding predicate.

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

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

Complexity: Exactly max((last - first) - 1, 0) applications of the corresponding comparisons.

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

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

Complexity: Exactly max((last - first) - 1, 0) applications of the corresponding comparisons.

 template<class ForwardIterator> pair<ForwardIterator, ForwardIterator> minmax_element(ForwardIterator first, ForwardIterator last); template<class ForwardIterator, class Compare> pair<ForwardIterator, ForwardIterator> minmax_element(ForwardIterator first, ForwardIterator last, Compare comp); 

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

Complexity: At most applications of the corresponding predicate, where N is distance(first, last).

### 25.4.8 Lexicographical comparison [alg.lex.comparison]

 template<class InputIterator1, class InputIterator2> bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> bool lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); 

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

Complexity: At most 2*min((last1 - first1), (last2 - first2)) applications of the corresponding comparison.

Remarks: If two sequences have the same number of elements and their corresponding elements are equivalent, then neither sequence is lexicographically less than the other. If one sequence is a prefix of the other, then the shorter sequence is lexicographically less than the longer sequence. Otherwise, the lexicographical comparison of the sequences yields the same result as the comparison of the first corresponding pair of elements that are not equivalent.

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


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

### 25.4.9 Permutation generators [alg.permutation.generators]

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

Effects: Takes a sequence defined by the range [first,last) and transforms it into the next permutation. The next permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp. If such a permutation exists, it returns true. Otherwise, it transforms the sequence into the smallest permutation, that is, the ascendingly sorted one, and returns false.

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

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

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

Effects: Takes a sequence defined by the range [first,last) and transforms it into the previous permutation. The previous permutation is found by assuming that the set of all permutations is lexicographically sorted with respect to operator< or comp.

Returns: true if such a permutation exists. Otherwise, it transforms the sequence into the largest permutation, that is, the descendingly sorted one, and returns false.

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

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

## 25.5 C library algorithms [alg.c.library]

Table [tab:algorithms.hdr.cstdlib] describes some of the contents of the header <cstdlib>.

Table 113 — Header <cstdlib> synopsis
 Type Name(s) Type: size_t Functions: bsearch qsort

The contents are the same as the Standard C library header <stdlib.h> with the following exceptions:

The function signature:

bsearch(const void *, const void *, size_t, size_t,
int (*)(const void *, const void *));


is replaced by the two declarations:

extern "C" void* bsearch(const void* key, const void* base,
size_t nmemb, size_t size,
int (*compar)(const void*, const void*));
extern "C++" void* bsearch(const void* key, const void* base,
size_t nmemb, size_t size,
int (*compar)(const void*, const void*));


both of which have the same behavior as the original declaration.

The function signature:

qsort(void *, size_t, size_t,
int (*)(const void *, const void *));


is replaced by the two declarations:

extern "C" void qsort(void* base, size_t nmemb, size_t size,
int (*compar)(const void*, const void*));
extern "C++" void qsort(void* base, size_t nmemb, size_t size,
int (*compar)(const void*, const void*));


both of which have the same behavior as the original declaration. The behavior is undefined unless the objects in the array pointed to by base are of trivial type.

Note: Because the function argument compar() may throw an exception, bsearch() and qsort() are allowed to propagate the exception ([res.on.exception.handling]).  — end note ]