23 Algorithms library [algorithms]

23.7 Sorting and related operations [alg.sorting]

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

23.7.1 Sorting [alg.sort]

23.7.1.1 sort [sort]

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

23.7.1.2 stable_­sort [stable.sort]

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

23.7.1.3 partial_­sort [partial.sort]

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

23.7.1.4 partial_­sort_­copy [partial.sort.copy]

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

23.7.1.5 is_­sorted [is.sorted]

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

23.7.2 Nth element [alg.nth.element]

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

23.7.3 Binary search [alg.binary.search]

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

23.7.3.1 lower_­bound [lower.bound]

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

23.7.3.2 upper_­bound [upper.bound]

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

23.7.3.3 equal_­range [equal.range]

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

23.7.3.4 binary_­search [binary.search]

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

23.7.4 Partitions [alg.partitions]

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

23.7.5 Merge [alg.merge]

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

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

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

23.7.6.1 includes [includes]

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

23.7.6.2 set_­union [set.union]

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

23.7.6.3 set_­intersection [set.intersection]

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

23.7.6.4 set_­difference [set.difference]

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

23.7.6.5 set_­symmetric_­difference [set.symmetric.difference]

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

23.7.7 Heap operations [alg.heap.operations]

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

23.7.7.1 push_­heap [push.heap]

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

23.7.7.2 pop_­heap [pop.heap]

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

23.7.7.3 make_­heap [make.heap]

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

23.7.7.4 sort_­heap [sort.heap]

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

23.7.7.5 is_­heap [is.heap]

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

23.7.8 Minimum and maximum [alg.min.max]

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

23.7.9 Bounded value [alg.clamp]

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

23.7.10 Lexicographical comparison [alg.lex.comparison]

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

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

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

23.7.12 Permutation generators [alg.permutation.generators]

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