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# lower_bound

### Synopsis

    template<
          typename Sequence
        , typename T
        , typename Pred = less<_1,_2>
        >
    struct lower_bound
    {
        typedef unspecified type;
    };

### Description

Returns the first position in the sorted `Sequence` where `T` could be inserted without violating the ordering.

### Header

    #include <boost/mpl/lower_bound.hpp>

### Parameters

Parameter | Requirement | Description
--- | --- | ---
`Sequence` | Forward Sequence | A sorted sequence to search in.
`T` | Any type | A type to search a position for.
`Pred` | Binary Lambda Expression | A search criteria.

### Expression semantics

For any sorted Forward Sequence `s`, binary Lambda Expression `pred`, and arbitrary type `x`:

    typedef lower_bound< s,x,pred >::type i;

Return type: | Forward Iterator.
Semantics: | `i` is the furthermost iterator in [`begin<s>::type`, `end<s>::type`) such that, for every iterator `j` in [`begin<s>::type`, `i`),
    apply< pred, deref<j>::type, x >::type::value == true

### Complexity

The number of comparisons is logarithmic: at most log2( `size<s>::value` ) + 1. If `s` is a Random Access Sequence then the number of steps through the range is also logarithmic; otherwise, the number of steps is proportional to `size<s>::value`.

### Example

    typedef vector_c<int,1,2,3,3,3,5,8> numbers;
    typedef lower_bound< numbers, int_<3> >::type iter;

    BOOST_MPL_ASSERT_RELATION(
          (distance< begin<numbers>::type,iter >::value), ==, 2
        );

    BOOST_MPL_ASSERT_RELATION( deref<iter>::type::value, ==, 3 );

### See also

Querying Algorithms, upper_bound, find, find_if, min_element