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cppdraft/alg/nth/element.md

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+[alg.nth.element]
+
+# 26 Algorithms library [[algorithms]](./#algorithms)
+
+## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#alg.nth.element)
+
+### 26.8.3 Nth element [alg.nth.element]
+
+[🔗](#lib: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);
+
+template<[random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I> S, class Comp = ranges::less,
+         class Proj = identity>
+  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<I, Comp, Proj>
+  constexpr I
+    ranges::nth_element(I first, I nth, S last, Comp comp = {}, Proj proj = {});
+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]") I, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I> S,
+         class Comp = ranges::less, class Proj = identity>
+  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<I, Comp, Proj>
+  I ranges::nth_element(Ep&& exec, I first, I nth, S last, Comp comp = {}, Proj proj = {});
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9320)
+
+Let comp be less{} and proj be identity{} for the overloads with no parameters by those names[.](#1.sentence-1)
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9325)
+
+*Preconditions*: [first, nth) and [nth, last) are valid ranges[.](#2.sentence-1)
+
+For the overloads in namespace std,RandomAccessIterator meets
+the [*Cpp17ValueSwappable*](swappable.requirements#:Cpp17ValueSwappable "16.4.4.3 Swappable requirements [swappable.requirements]") requirements ([[swappable.requirements]](swappable.requirements "16.4.4.3 Swappable requirements")), and
+the type of *first meets
+the [*Cpp17MoveConstructible*](utility.arg.requirements#:Cpp17MoveConstructible "16.4.4.2 Template argument requirements [utility.arg.requirements]") (Table [31](utility.arg.requirements#tab:cpp17.moveconstructible "Table 31: Cpp17MoveConstructible requirements")) and[*Cpp17MoveAssignable*](utility.arg.requirements#:Cpp17MoveAssignable "16.4.4.2 Template argument requirements [utility.arg.requirements]") (Table [33](utility.arg.requirements#tab:cpp17.moveassignable "Table 33: Cpp17MoveAssignable requirements")) requirements[.](#2.sentence-2)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9335)
+
+*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 with respect to comp and proj,
+unless nth == last[.](#3.sentence-1)
+
+Also for every iterator i in the range [first, nth)
+and every iterator j in the range [nth, last)
+it holds that:bool(invoke(comp, invoke(proj, *j), invoke(proj, *i))) is false[.](#3.sentence-2)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9346)
+
+*Returns*: last for the overload in namespace ranges[.](#4.sentence-1)
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9350)
+
+*Complexity*: For the non-parallel algorithm overloads, linear on average[.](#5.sentence-1)
+
+For the parallel algorithm overloads, O(N) applications of
+the predicate, and O(NlogN) swaps, where N=last - first[.](#5.sentence-2)
+
+[🔗](#itemdecl:2)
+
+`template<[random_access_range](range.refinements#concept:random_access_range "25.4.6 Other range refinements [range.refinements]") R, class Comp = ranges::less, class Proj = identity>
+  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<iterator_t<R>, Comp, Proj>
+  constexpr borrowed_iterator_t<R>
+    ranges::nth_element(R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});
+`
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9365)
+
+*Effects*: Equivalent to:return ranges::nth_element(ranges::begin(r), nth, ranges::end(r), comp, proj);
+
+[🔗](#itemdecl:3)
+
+`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]") R, class Comp = ranges::less,
+         class Proj = identity>
+  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<iterator_t<R>, Comp, Proj>
+  borrowed_iterator_t<R>
+    ranges::nth_element(Ep&& exec, R&& r, iterator_t<R> nth, Comp comp = {}, Proj proj = {});
+`
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9382)
+
+*Effects*: Equivalent to:return ranges::nth_element(std::forward<Ep>(exec), ranges::begin(r), nth, ranges::end(r),
+ comp, proj);