CGAL::Interval_skip_list<Interval>

Definition

The class Interval_skip_list<Interval> is a dynamic datastructure that allows to find all members of a set of intervals that overlap a point.

#include <CGAL/Interval_skip_list.h>

Types

typedef Interval::Value
	Value;	the type of inf and sup of the interval.

Interval_skip_list<Interval>::const_iterator
	An iterator over all intervals.

Creation

Interval_skip_list<Interval> isl;
	Default constructor.
template < class InputIterator >
Interval_skip_list<Interval> isl ( InputIterator first, InputIterator last);
	Constructor that inserts the iterator range [first, last) in the interval skip list. Precondition: The value_type of first and last is Interval.

Operations

template < class InputIterator >
int	isl.insert ( InputIterator first, InputIterator last)
		Inserts the iterator range [first, last) in the interval skip list, and returns the number of inserted intervals. Precondition: The value_type of first and last is Interval.
void	isl.insert ( Interval i)
		inserts interval i in the interval skip list.
bool	isl.remove ( Interval i)
		removes interval i from the interval skip list. Returns true iff removal was succesful.
bool	isl.is_contained ( Value v)
		Returns true iff there is an interval that contains v.
template < class OutputIterator >
OutputIterator	isl.find_intervals ( Value v, OutputIterator out)
		Writes the intervals i with i.inf() $$ v $$ i.sup to the output iterator out. Precondition: The value_type of out is Interval.
void	isl.clear ()	Removes all intervals from the interval skip list.
const_iterator	isl.begin ()	Returns an iterator over all intervals.
const_iterator	isl.end ()	Returns the past the end iterator.

I/O

ostream&	ostream& os << isl
		Inserts the interval skip list isl into the stream os. Precondition: The output operator must be defined for Interval.

Implementation

The insertion and deletion of a segment in the interval skip list takes expected time $$O(log$$² n), if the segment endpoints are chosen from a continuous distribution. A stabbing query takes expected time $$O(log$$n), and finding all intervals that contain a point takes expected time $$O(log$$n + k), where $$k is the number of intervals.

The implementation is based on the code developed by Eric N. Hansen, which can be found at http://www-pub.cise.ufl.edu/~hanson/IS-lists/. Attention, this code has memory leaks.