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[upper.bound]
# 26 Algorithms library [[algorithms]](./#algorithms)
## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#upper.bound)
### 26.8.4 Binary search [[alg.binary.search]](alg.binary.search#upper.bound)
#### 26.8.4.3 upper_bound [upper.bound]
[🔗](#lib:upper_bound)
`template<class ForwardIterator, class T = iterator_traits<ForwardIterator>::value_type>
constexpr ForwardIterator
upper_bound(ForwardIterator first, ForwardIterator last,
const T& value);
template<class ForwardIterator, class T = iterator_traits<ForwardIterator>::value_type,
class Compare>
constexpr ForwardIterator
upper_bound(ForwardIterator first, ForwardIterator last,
const T& value, Compare comp);
template<[forward_iterator](iterator.concept.forward#concept:forward_iterator "24.3.4.11Concept forward_­iterator[iterator.concept.forward]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7Concept 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 "24.3.6.3Indirect callables[indirectcallable.indirectinvocable]")<const T*, projected<I, Proj>> Comp = ranges::less>
constexpr I ranges::upper_bound(I first, S last, const T& value, Comp comp = {}, Proj proj = {});
template<[forward_range](range.refinements#concept:forward_range "25.4.6Other 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 "24.3.6.3Indirect callables[indirectcallable.indirectinvocable]")<const T*, projected<iterator_t<R>, Proj>> Comp =
ranges::less>
constexpr borrowed_iterator_t<R>
ranges::upper_bound(R&& r, const T& value, Comp comp = {}, Proj proj = {});
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9486)
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#L9491)
*Preconditions*: The elements e of [first, last)
are partitioned with respect to the expression
!bool(invoke(comp, value, invoke(proj, e)))[.](#2.sentence-2)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9497)
*Returns*: The furthermost iterator i in the range [first, last]
such that for every iterator j in the range [first, i),!bool(invoke(comp, value, invoke(proj, *j))) is true[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L9503)
*Complexity*: At most log2(last - first)+O(1) comparisons and projections[.](#4.sentence-1)