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### is_sorted

The header file `<boost/algorithm/cxx11/is_sorted.hpp>` contains functions for determining if a sequence is ordered.

##### is_sorted

The function `is_sorted(sequence)` determines whether or not a sequence is completely sorted according so some criteria. If no comparison predicate is specified, then std::less_equal is used (i.e, the test is to see if the sequence is non-decreasing)

    namespace boost { namespace algorithm {
    	template <typename Iterator, typename Pred>
    	bool is_sorted ( Iterator first, Iterator last, Pred p );

    	template <typename Iterator>
    	bool is_sorted ( Iterator first, Iterator last );

    	template <typename Range, typename Pred>
    	bool is_sorted ( const Range &r, Pred p );

    	template <typename Range>
    	bool is_sorted ( const Range &r );
    }}

Iterator requirements: The `is_sorted` functions will work on all kinds of iterators (except output iterators).

##### is_sorted_until

If `distance(first, last) < 2`, then `is_sorted ( first, last )` returns `last`. Otherwise, it returns the last iterator i in [first,last] for which the range [first,i) is sorted.

In short, it returns the element in the sequence that is "out of order". If the entire sequence is sorted (according to the predicate), then it will return `last`.

    namespace boost { namespace algorithm {
    	template <typename ForwardIterator, typename Pred>
    	FI is_sorted_until ( ForwardIterator first, ForwardIterator last, Pred p );

    	template <typename ForwardIterator>
    	ForwardIterator is_sorted_until ( ForwardIterator first, ForwardIterator last );

    	template <typename Range, typename Pred>
    	typename boost::range_iterator<const R>::type is_sorted_until ( const Range &r, Pred p );

    	template <typename Range>
    	typename boost::range_iterator<const R>::type is_sorted_until ( const Range &r );
    }}

Iterator requirements: The `is_sorted_until` functions will work on forward iterators or better. Since they have to return a place in the input sequence, input iterators will not suffice.

Complexity: `is_sorted_until` will make at most N-1 calls to the predicate (given a sequence of length N).

Examples:

Given the sequence `{ 1, 2, 3, 4, 5, 3 }`, `is_sorted_until ( beg, end, std::less<int>())` would return an iterator pointing at the second `3`.

Given the sequence `{ 1, 2, 3, 4, 5, 9 }`, `is_sorted_until ( beg, end, std::less<int>())` would return `end`.

There are also a set of "wrapper functions" for is_ordered which make it easy to see if an entire sequence is ordered. These functions return a boolean indicating success or failure rather than an iterator to where the out of order items were found.

To test if a sequence is increasing (each element at least as large as the preceeding one):

    namespace boost { namespace algorithm {
    	template <typename Iterator>
    	bool is_increasing ( Iterator first, Iterator last );

    	template <typename R>
    	bool is_increasing ( const R &range );
    }}

To test if a sequence is decreasing (each element no larger than the preceeding one):

    namespace boost { namespace algorithm {
    	template <typename Iterator>
    	bool is_decreasing ( Iterator first, Iterator last );

    	template <typename R>
    	bool is_decreasing ( const R &range );
    }}

To test if a sequence is strictly increasing (each element larger than the preceeding one):

    namespace boost { namespace algorithm {
    	template <typename Iterator>
    	bool is_strictly_increasing ( Iterator first, Iterator last );

    	template <typename R>
    	bool is_strictly_increasing ( const R &range );
    }}

To test if a sequence is strictly decreasing (each element smaller than the preceeding one):

    namespace boost { namespace algorithm {
    	template <typename Iterator>
    	bool is_strictly_decreasing ( Iterator first, Iterator last );

    	template <typename R>
    	bool is_strictly_decreasing ( const R &range );
    }}

Complexity: Each of these calls is just a thin wrapper over `is_sorted`, so they have the same complexity as `is_sorted`.

##### Notes

- The routines `is_sorted` and `is_sorted_until` are part of the C++11 standard. When compiled using a C++11 implementation, the implementation from the standard library will be used.
- `is_sorted` and `is_sorted_until` both return true for empty ranges and ranges of length one.