[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)