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cppdraft/lower/bound.md

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+[lower.bound]
+
+# 26 Algorithms library [[algorithms]](./#algorithms)
+
+## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#lower.bound)
+
+### 26.8.4 Binary search [[alg.binary.search]](alg.binary.search#lower.bound)
+
+#### 26.8.4.2 lower_bound [lower.bound]
+
+[🔗](#lib:lower_bound)
+
+`template<class ForwardIterator, class T = iterator_traits<ForwardIterator>::value_type>
+  constexpr ForwardIterator
+    lower_bound(ForwardIterator first, ForwardIterator last,
+                const T& value);
+
+template<class ForwardIterator, class T = iterator_traits<ForwardIterator>::value_type,
+         class Compare>
+  constexpr ForwardIterator
+    lower_bound(ForwardIterator first, ForwardIterator last,
+                const T& value, Compare comp);
+
+template<[forward_iterator](iterator.concept.forward#concept:forward_iterator "24.3.4.11 Concept forward_­iterator [iterator.concept.forward]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I> S, class Proj = identity,
+         class T = projected_value_t<I, Proj>,
+         [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<const T*, projected<I, Proj>> Comp = ranges::less>
+  constexpr I ranges::lower_bound(I first, S last, const T& value, Comp comp = {},
+                                  Proj proj = {});
+template<[forward_range](range.refinements#concept:forward_range "25.4.6 Other range refinements [range.refinements]") R, class Proj = identity,
+         class T = projected_value_t<iterator_t<R>, Proj>,
+         [indirect_strict_weak_order](indirectcallable.indirectinvocable#concept:indirect_strict_weak_order "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<const T*, projected<iterator_t<R>, Proj>> Comp =
+           ranges::less>
+  constexpr borrowed_iterator_t<R>
+    ranges::lower_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
+`
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9436)
+
+Let comp be less{} andproj be identity{} for overloads with no parameters by those names[.](#1.sentence-1)
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9441)
+
+*Preconditions*: The elements e of [first, last)
+are partitioned with respect to the expression  
+
+bool(invoke(comp, invoke(proj, e), value))[.](#2.sentence-2)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9447)
+
+*Returns*: The furthermost iterator i in the range [first, last]
+such that for every iterator j in the range [first, i),bool(invoke(comp, invoke(proj, *j), value)) is true[.](#3.sentence-1)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9453)
+
+*Complexity*: At most log2(last - first)+O(1) comparisons and projections[.](#4.sentence-1)