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##### lower_bound

###### 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);

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

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

###### 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.

###### Definition

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

###### 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.

###### 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`.

###### 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)`.