next up previous contents index
Next: Sets of Parallel Segments Up: Advanced Data Types for Previous: Point Location in Triangulations   Contents   Index


Sets of Intervals ( interval_set )

Definition

An instance S of the parameterized data type interval_set<I> is a collection of items ( is$ \_$item ). Every item in S contains a closed interval of the double numbers as key and an information from data type I , called the information type of S . The number of items in S is called the size of S . An interval set of size zero is said to be empty. We use < x, y, i > to denote the item with interval [x, y] and information i ; x (y ) is called the left (right) boundary of the item. For each interval [x, y] there is at most one item < x, y, i > $ \in$ S .

#include < LEDA/geo/interval_set.h >

Creation

interval_set< I> S creates an instance S of type interval_set<I> and initializes S to the empty set.

Operations

double S.left(is_item it) returns the left boundary of item it .
Precondition it is an item in S.

double S.right(is_item it) returns the right boundary of item it .
Precondition it is an item in S.

const I& S.inf(is_item it) returns the information of item it .
Precondition it is an item in S.

is_item S.insert(double x, double y, const I& i)
    associates the information i with interval [x, y] . If there is an item < x, y, j > in S then j is replaced by i , else a new item < x, y, i > is added to S . In both cases the item is returned.

is_item S.lookup(double x, double y)
    returns the item with interval [x, y] (nil if no such item exists in S).

list< is_item> const S.intersection(double a, double b)
    returns all items < x, y, i >   $ \in$  S with [x, y] $ \cap$ [a, b]! = $ \emptyset$ .

void S.del(double x, double y) deletes the item with interval [x, y] from S.

void S.del_item(is_item it) removes item it from S.
Precondition it is an item in S.

void S.change_inf(is_item it, const I& i)
    makes i the information of item it .
Precondition it is an item in S.

void S.clear() makes S the empty interval_set.

bool S.empty() returns true iff S is empty.

int S.size() returns the size of S.

Implementation

Interval sets are implemented by two-dimensional range trees [90,57]. Operations insert, lookup, del_item and del take time O(log2n) , intersection takes time O(k + log2n) , where k is the size of the returned list. Operations left, right, inf, empty, and size take time O(1) , and clear O(n log n) . Here n is always the current size of the interval set. The space requirement is O(n log n) .


next up previous contents index
Next: Sets of Parallel Segments Up: Advanced Data Types for Previous: Point Location in Triangulations   Contents   Index
Christian Uhrig 2017-04-07