Binary search algorithms

Functions
template<typename ForwardIterator, typename Type>
ForwardIterator	std::lower_bound (ForwardIterator first, ForwardIterator last, const Type &__val)
	Finds the first position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare>
ForwardIterator	std::lower_bound (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
	Finds the first position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type>
ForwardIterator	std::upper_bound (ForwardIterator first, ForwardIterator last, const Type &__val)
	Finds the last position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare>
ForwardIterator	std::upper_bound (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
	Finds the last position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type>
pair< ForwardIterator, ForwardIterator >	std::equal_range (ForwardIterator first, ForwardIterator last, const Type &__val)
	Finds the largest subrange in which val could be inserted at any place in it without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare>
pair< ForwardIterator, ForwardIterator >	std::equal_range (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
	Finds the largest subrange in which val could be inserted at any place in it without changing the ordering.
template<typename ForwardIterator, typename Type>
bool	std::binary_search (ForwardIterator first, ForwardIterator last, const Type &__val)
	Determines whether an element exists in a range.
template<typename ForwardIterator, typename Type, typename Compare>
bool	std::binary_search (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
	Determines whether an element exists in a range.

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Detailed Description

These algorithms are variations of a classic binary search. They all assume that the sequence being searched is already sorted.

The number of comparisons will be logarithmic (and as few as possible). The number of steps through the sequence will be logarithmic for random-access iterators (e.g., pointers), and linear otherwise.

The LWG has passed Defect Report 270, which notes: The proposed resolution reinterprets binary search. Instead of thinking about searching for a value in a sorted range, we view that as an important special case of a more general algorithm: searching for the partition point in a partitioned range. We also add a guarantee that the old wording did not: we ensure that the upper bound is no earlier than the lower bound, that the pair returned by equal_range is a valid range, and that the first part of that pair is the lower bound.

The actual effect of the first sentence is that a comparison functor passed by the user doesn't necessarily need to induce a strict weak ordering relation. Rather, it partitions the range.

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Function Documentation

template<typename ForwardIterator, typename Type, typename Compare> bool std::binary_search (  ForwardIterator  first, ForwardIterator  last, const Type &  __val, Compare  comp )

Determines whether an element exists in a range. Parameters: first  An iterator. last  Another iterator. val  The search term. comp  A functor to use for comparisons. Returns: True if val (or its equivelent) is in [first,last ]. Note that this does not actually return an iterator to val. For that, use std::find or a container's specialized find member functions. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 3938 of file stl_algo.h. References std::lower_bound().

template<typename ForwardIterator, typename Type> bool std::binary_search (  ForwardIterator  first, ForwardIterator  last, const Type &  __val )

Determines whether an element exists in a range. Parameters: first  An iterator. last  Another iterator. val  The search term. Returns: True if val (or its equivelent) is in [first,last ]. Note that this does not actually return an iterator to val. For that, use std::find or a container's specialized find member functions. Definition at line 3906 of file stl_algo.h. References std::lower_bound().

template<typename ForwardIterator, typename Type, typename Compare> pair<ForwardIterator, ForwardIterator> std::equal_range (  ForwardIterator  first, ForwardIterator  last, const Type &  __val, Compare  comp )

Finds the largest subrange in which val could be inserted at any place in it without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. comp  A functor to use for comparisons. Returns: An pair of iterators defining the subrange. This is equivalent to std::make_pair(lower_bound(first, last, val, comp), upper_bound(first, last, val, comp)) but does not actually call those functions. Definition at line 3848 of file stl_algo.h. References std::distance(), std::lower_bound(), and std::upper_bound().

template<typename ForwardIterator, typename Type> pair<ForwardIterator, ForwardIterator> std::equal_range (  ForwardIterator  first, ForwardIterator  last, const Type &  __val )

Finds the largest subrange in which val could be inserted at any place in it without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. Returns: An pair of iterators defining the subrange. This is equivalent to std::make_pair(lower_bound(first, last, val), upper_bound(first, last, val)) but does not actually call those functions. Definition at line 3786 of file stl_algo.h. References std::distance(), std::lower_bound(), and std::upper_bound().

template<typename ForwardIterator, typename Type, typename Compare> ForwardIterator std::lower_bound (  ForwardIterator  first, ForwardIterator  last, const Type &  __val, Compare  comp )

Finds the first position in which val could be inserted without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. comp  A functor to use for comparisons. Returns: An iterator pointing to the first element "not less than" val, or end() if every element is less than val. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 2662 of file stl_algo.h. References std::distance().

template<typename ForwardIterator, typename Type> ForwardIterator std::lower_bound (  ForwardIterator  first, ForwardIterator  last, const Type &  __val )

Finds the first position in which val could be inserted without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. Returns: An iterator pointing to the first element "not less than" val, or end() if every element is less than val. Definition at line 2607 of file stl_algo.h. References std::distance(). Referenced by std::binary_search(), std::equal_range(), and std::map< Key, Type, Compare, Allocator >::operator[]().

template<typename ForwardIterator, typename Type, typename Compare> ForwardIterator std::upper_bound (  ForwardIterator  first, ForwardIterator  last, const Type &  __val, Compare  comp )

Finds the last position in which val could be inserted without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. comp  A functor to use for comparisons. Returns: An iterator pointing to the first element greater than val, or end() if no elements are greater than val. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 2761 of file stl_algo.h. References std::distance().

template<typename ForwardIterator, typename Type> ForwardIterator std::upper_bound (  ForwardIterator  first, ForwardIterator  last, const Type &  __val )

Finds the last position in which val could be inserted without changing the ordering. Parameters: first  An iterator. last  Another iterator. val  The search term. Returns: An iterator pointing to the first element greater than val, or end() if no elements are greater than val. Definition at line 2709 of file stl_algo.h. References std::distance(). Referenced by std::equal_range().

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