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[alg.set.operations]
# 26 Algorithms library [[algorithms]](./#algorithms)
## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#alg.set.operations)
### 26.8.7 Set operations on sorted structures [alg.set.operations]
#### [26.8.7.1](#general) General [[alg.set.operations.general]](alg.set.operations.general)
[1](#general-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10265)
Subclause [alg.set.operations] defines all the basic set operations on sorted structures[.](#general-1.sentence-1)
They also work with multisets ([[multiset]](multiset "23.4.7 Class template multiset"))
containing multiple copies of equivalent elements[.](#general-1.sentence-2)
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[.](#general-1.sentence-3)
#### [26.8.7.2](#includes) includes [[includes]](includes)
[🔗](#lib: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);
template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
class Proj1 = identity, class Proj2 = identity,
[indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<I1, Proj1>,
projected<I2, Proj2>> Comp = ranges::less>
constexpr bool ranges::includes(I1 first1, S1 last1, I2 first2, S2 last2, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, class Proj1 = identity,
class Proj2 = identity,
[indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<iterator_t<R1>, Proj1>,
projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
constexpr bool ranges::includes(R1&& r1, R2&& r2, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
class Proj1 = identity, class Proj2 = identity,
[indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<I1, Proj1>, projected<I2, Proj2>> Comp =
ranges::less>
bool ranges::includes(Ep&& exec, I1 first1, S1 last1, I2 first2, S2 last2,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
class Proj1 = identity, class Proj2 = identity,
[indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<iterator_t<R1>, Proj1>,
projected<iterator_t<R2>, Proj2>> Comp = ranges::less>
bool ranges::includes(Ep&& exec, R1&& r1, R2&& r2,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
`
[1](#includes-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10325)
Let comp be less{},proj1 be identity{}, andproj2 be identity{},
for the overloads with no parameters by those names[.](#includes-1.sentence-1)
[2](#includes-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10331)
*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#includes-2.sentence-1)
[3](#includes-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10336)
*Returns*: true if and only if [first2, last2) is a subsequence of [first1, last1)[.](#includes-3.sentence-1)
[*Note [1](#includes-note-1)*:
A sequence S is a subsequence of another sequence T if S can be obtained
from T by removing some, all, or none of T's elements and keeping the
remaining elements in the same order[.](#includes-3.sentence-2)
— *end note*]
[4](#includes-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10346)
*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#includes-4.sentence-1)
#### [26.8.7.3](#set.union) set_union [[set.union]](set.union)
[🔗](#lib: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);
template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
[weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
constexpr ranges::set_union_result<I1, I2, O>
ranges::set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O,
class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
constexpr ranges::set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
ranges::set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") O, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<O> OutS, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
ranges::set_union_result<I1, I2, O>
ranges::set_union(Ep&& exec, I1 first1, S1 last1,
I2 first2, S2 last2, O result, OutS result_last,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
[sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") OutR, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
ranges::set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>,
borrowed_iterator_t<OutR>>
ranges::set_union(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
`
[1](#set.union-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10416)
Let:
- [(1.1)](#set.union-1.1)
comp be less{},
and proj1 and proj2 be identity{} for the overloads with no parameters by those names;
- [(1.2)](#set.union-1.2)
M be last1 - first1 plus the number of elements in [first2, last2)
that are not present in [first1, last1);
- [(1.3)](#set.union-1.3)
result_last be result + M for the overloads with no parameter result_last or result_r;
- [(1.4)](#set.union-1.4)
N be min(M, result_last - result)[.](#set.union-1.sentence-1)
[2](#set.union-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10433)
*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#set.union-2.sentence-1)
The resulting range does not overlap with either of the original ranges[.](#set.union-2.sentence-2)
[3](#set.union-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10439)
*Effects*: Constructs a sorted union of N elements from the two ranges;
that is, the set of elements that are present in one or both of the ranges[.](#set.union-3.sentence-1)
[4](#set.union-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10444)
*Returns*:
- [(4.1)](#set.union-4.1)
result_last for the overloads in namespace std[.](#set.union-4.1.sentence-1)
- [(4.2)](#set.union-4.2)
{last1, last2, result + N} for the overloads in namespace ranges,
if N is equal to M[.](#set.union-4.2.sentence-1)
- [(4.3)](#set.union-4.3)
Otherwise, {j1, j2, result_last} for the overloads in namespace ranges,
where the iterators j1 and j2 point to positions past the last copied or skipped elements
in [first1, last1) and [first2, last2), respectively[.](#set.union-4.3.sentence-1)
[5](#set.union-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10462)
*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#set.union-5.sentence-1)
[6](#set.union-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10467)
*Remarks*: Stable ([[algorithm.stable]](algorithm.stable "16.4.6.8 Requirements for stable algorithms"))[.](#set.union-6.sentence-1)
If [first1, last1) contains m elements
that are equivalent to each other and
[first2, last2) contains n elements
that are equivalent to them,
then all m elements from the first range
are copied to the output range, in order, and
then the final max(n−m,0) elements from the second range
are copied to the output range, in order[.](#set.union-6.sentence-2)
#### [26.8.7.4](#set.intersection) set_intersection [[set.intersection]](set.intersection)
[🔗](#lib: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);
template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
[weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
constexpr ranges::set_intersection_result<I1, I2, O>
ranges::set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O,
class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
constexpr ranges::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
ranges::set_intersection(R1&& r1, R2&& r2, O result,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") O, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<O> OutS, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
ranges::set_intersection_result<I1, I2, O>
ranges::set_intersection(Ep&& exec, I1 first1, S1 last1,
I2 first2, S2 last2, O result, OutS result_last,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
[sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") OutR, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
ranges::set_intersection_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>,
borrowed_iterator_t<OutR>>
ranges::set_intersection(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
`
[1](#set.intersection-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10546)
Let:
- [(1.1)](#set.intersection-1.1)
comp be less{},
and proj1 and proj2 be identity{} for the overloads with no parameters by those names;
- [(1.2)](#set.intersection-1.2)
M be the number of elements in [first1, last1)
that are present in [first2, last2);
- [(1.3)](#set.intersection-1.3)
result_last be result + M for the overloads with no parameter result_last or result_r;
- [(1.4)](#set.intersection-1.4)
N be min(M, result_last - result)[.](#set.intersection-1.sentence-1)
[2](#set.intersection-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10563)
*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#set.intersection-2.sentence-1)
The resulting range does not overlap with either of the original ranges[.](#set.intersection-2.sentence-2)
[3](#set.intersection-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10569)
*Effects*: Constructs a sorted intersection of N elements from the two ranges;
that is, the set of elements that are present in both of the ranges[.](#set.intersection-3.sentence-1)
[4](#set.intersection-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10574)
*Returns*:
- [(4.1)](#set.intersection-4.1)
result_last for the overloads in namespace std[.](#set.intersection-4.1.sentence-1)
- [(4.2)](#set.intersection-4.2)
{last1, last2, result + N} for the overloads in namespace ranges,
if N is equal to M[.](#set.intersection-4.2.sentence-1)
- [(4.3)](#set.intersection-4.3)
Otherwise, {j1, j2, result_last} for the overloads in namespace ranges,
where the iterators j1 and j2 point to positions past the last copied or skipped elements
in [first1, last1) and [first2, last2), respectively[.](#set.intersection-4.3.sentence-1)
[5](#set.intersection-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10592)
*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#set.intersection-5.sentence-1)
[6](#set.intersection-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10597)
*Remarks*: Stable ([[algorithm.stable]](algorithm.stable "16.4.6.8 Requirements for stable algorithms"))[.](#set.intersection-6.sentence-1)
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
are copied from the first range to the output range, in order[.](#set.intersection-6.sentence-2)
#### [26.8.7.5](#set.difference) set_difference [[set.difference]](set.difference)
[🔗](#lib:set_difference)
`template<class InputIterator1, class InputIterator2,
class OutputIterator>
constexpr OutputIterator
set_difference(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
class ForwardIterator>
ForwardIterator
set_difference(ExecutionPolicy&& exec,
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
ForwardIterator result);
template<class InputIterator1, class InputIterator2,
class OutputIterator, class Compare>
constexpr OutputIterator
set_difference(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
class ForwardIterator, class Compare>
ForwardIterator
set_difference(ExecutionPolicy&& exec,
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
ForwardIterator result, Compare comp);
template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
[weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
constexpr ranges::set_difference_result<I1, O>
ranges::set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O,
class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
constexpr ranges::set_difference_result<borrowed_iterator_t<R1>, O>
ranges::set_difference(R1&& r1, R2&& r2, O result,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") O, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<O> OutS, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
ranges::set_difference_result<I1, O>
ranges::set_difference(Ep&& exec, I1 first1, S1 last1,
I2 first2, S2 last2, O result, OutS result_last,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
[sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") OutR, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
ranges::set_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<OutR>>
ranges::set_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
`
[1](#set.difference-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10673)
Let:
- [(1.1)](#set.difference-1.1)
comp be less{},
and proj1 and proj2 be identity{} for the overloads with no parameters by those names;
- [(1.2)](#set.difference-1.2)
M be the number of elements in [first1, last1)
that are not present in [first2, last2);
- [(1.3)](#set.difference-1.3)
result_last be result + M for the overloads with no parameter result_last or result_r;
- [(1.4)](#set.difference-1.4)
N be min(M, result_last - result)[.](#set.difference-1.sentence-1)
[2](#set.difference-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10690)
*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#set.difference-2.sentence-1)
The resulting range does not overlap with either of the original ranges[.](#set.difference-2.sentence-2)
[3](#set.difference-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10696)
*Effects*: Copies N elements of the range [first1, last1)
which are not present in the range [first2, last2)
to the range [result, result + N)[.](#set.difference-3.sentence-1)
The elements in the constructed range are sorted[.](#set.difference-3.sentence-2)
[4](#set.difference-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10703)
*Returns*:
- [(4.1)](#set.difference-4.1)
result_last for the overloads in namespace std[.](#set.difference-4.1.sentence-1)
- [(4.2)](#set.difference-4.2)
{last1, result + N} for the overloads in namespace ranges,
if N is equal to M[.](#set.difference-4.2.sentence-1)
- [(4.3)](#set.difference-4.3)
Otherwise, {j1, result_last} for the overloads in namespace ranges,
where the iterator j1 points to positions past the last copied or skipped elements
in [first1, last1) and [first2, last2), respectively[.](#set.difference-4.3.sentence-1)
[5](#set.difference-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10721)
*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#set.difference-5.sentence-1)
[6](#set.difference-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10726)
*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)
are copied to the output range, in order[.](#set.difference-6.sentence-1)
#### [26.8.7.6](#set.symmetric.difference) set_symmetric_difference [[set.symmetric.difference]](set.symmetric.difference)
[🔗](#lib:set_symmetric_difference)
`template<class InputIterator1, class InputIterator2,
class OutputIterator>
constexpr OutputIterator
set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
class ForwardIterator>
ForwardIterator
set_symmetric_difference(ExecutionPolicy&& exec,
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
ForwardIterator result);
template<class InputIterator1, class InputIterator2,
class OutputIterator, class Compare>
constexpr OutputIterator
set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
InputIterator2 first2, InputIterator2 last2,
OutputIterator result, Compare comp);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
class ForwardIterator, class Compare>
ForwardIterator
set_symmetric_difference(ExecutionPolicy&& exec,
ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
ForwardIterator result, Compare comp);
template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
[weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
constexpr ranges::set_symmetric_difference_result<I1, I2, O>
ranges::set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
Comp comp = {}, Proj1 proj1 = {},
Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O,
class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
constexpr ranges::set_symmetric_difference_result<borrowed_iterator_t<R1>,
borrowed_iterator_t<R2>, O>
ranges::set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") O, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<O> OutS, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
ranges::set_symmetric_difference_result<I1, I2, O>
ranges::set_symmetric_difference(Ep&& exec, I1 first1, S1 last1,
I2 first2, S2 last2, O result, OutS result_last,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
[sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") OutR, class Comp = ranges::less,
class Proj1 = identity, class Proj2 = identity>
requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
ranges::set_symmetric_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>,
borrowed_iterator_t<OutR>>
ranges::set_symmetric_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r,
Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
`
[1](#set.symmetric.difference-1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10804)
Let:
- [(1.1)](#set.symmetric.difference-1.1)
comp be less{},
and proj1 and proj2 be identity{} for the overloads with no parameters by those names;
- [(1.2)](#set.symmetric.difference-1.2)
K be the number of elements in [first1, last1) that are not present in [first2, last2)[.](#set.symmetric.difference-1.2.sentence-1)
- [(1.3)](#set.symmetric.difference-1.3)
M be the number of elements in [first2, last2) that are not present in [first1, last1)[.](#set.symmetric.difference-1.3.sentence-1)
- [(1.4)](#set.symmetric.difference-1.4)
result_last be result + M + K for the overloads with no parameter result_last or result_r;
- [(1.5)](#set.symmetric.difference-1.5)
N be min(K+M, result_last - result)[.](#set.symmetric.difference-1.5.sentence-1)
[2](#set.symmetric.difference-2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10822)
*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#set.symmetric.difference-2.sentence-1)
The resulting range does not overlap with either of the original ranges[.](#set.symmetric.difference-2.sentence-2)
[3](#set.symmetric.difference-3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10828)
*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 [result, result + N)[.](#set.symmetric.difference-3.sentence-1)
The elements in the constructed range are sorted[.](#set.symmetric.difference-3.sentence-2)
[4](#set.symmetric.difference-4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10837)
*Returns*:
- [(4.1)](#set.symmetric.difference-4.1)
result_last for the overloads in namespace std[.](#set.symmetric.difference-4.1.sentence-1)
- [(4.2)](#set.symmetric.difference-4.2)
{last1, last2, result + N} for the overloads in namespace ranges,
if N is equal to M+K[.](#set.symmetric.difference-4.2.sentence-1)
- [(4.3)](#set.symmetric.difference-4.3)
Otherwise, {j1, j2, result_last} for the overloads in namespace ranges,
where the iterators j1 and j2 point to positions past the last copied or skipped elements
in [first1, last1) and [first2, last2), respectively[.](#set.symmetric.difference-4.3.sentence-1)
[5](#set.symmetric.difference-5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10855)
*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#set.symmetric.difference-5.sentence-1)
[6](#set.symmetric.difference-6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10860)
*Remarks*: Stable ([[algorithm.stable]](algorithm.stable "16.4.6.8 Requirements for stable algorithms"))[.](#set.symmetric.difference-6.sentence-1)
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[.](#set.symmetric.difference-6.sentence-2)
In either case, the elements are copied in order[.](#set.symmetric.difference-6.sentence-3)
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