[section:lower_bound lower_bound]

[heading Prototype]

``
template<class ForwardRange, class Value>
typename range_iterator<ForwardRange>::type
lower_bound(ForwardRange& rng, Value val);

template<
    range_return_value re,
    class ForwardRange,
    class Value
    >
typename range_return<ForwardRange, re>::type
lower_bound(ForwardRange& rng, Value val);
``

[heading Description]

The versions of `lower_bound` that return an iterator, returns the first iterator in the range `rng` such that:
without predicate - `*i < value` is `false`,
with predicate - `pred(*i, value)` is `false`.

`end(rng)` is returned if no such iterator exists.

The versions of `lower_bound` that return a `range_return`, defines `found` in the same manner as the returned iterator described above.

[heading Definition]

Defined in the header file `boost/range/algorithm/lower_bound.hpp`

[heading Requirements]

[*For the non-predicate versions:]

* `ForwardRange` is a model of the __forward_range__ Concept.
* `Value` is a model of the `LessThanComparableConcept`.
* The ordering of objects of type `Value` is a [*/strict weak ordering/], as defined in the `LessThanComparableConcept` requirements.
* `ForwardRange`'s value type is the same type as `Value`.

[*For the predicate versions:]

* `ForwardRange` is a model of the __forward_range__ Concept.
* `BinaryPredicate` is a model of the `StrictWeakOrderingConcept`.
* `ForwardRange`'s value type is the same type as `Value`.
* `ForwardRange`'s value type is convertible to both of `BinaryPredicate`'s argument types.

[heading Precondition:]

[*For the non-predicate versions:]

`rng` is sorted in ascending order according to `operator<`.

[*For the predicate versions:]

`rng` is sorted in ascending order according to `pred`.

[heading Complexity]

For ranges that model the __random_access_range__ concept the complexity is `O(log N)`, where `N` is `distance(rng)`.

For all other range types the complexity is `O(N)`.


[endsect]