Version 5.0 The LEDA User Manual

list S.intersection sorted(const rat segment& q)
list S.intersection(const rat line& l)
list S.intersection sorted(const rat line& l)
void S.del(const rat segment& s)
as above, but the returned segments are ordered
as they are intersected by q if one travels from
q.source( ) to q.target( ).
returns all items ∈ S with s ∩ l ≠ ∅.
Precondition: l is orthogonal to the segments in
S.
as above, but the returned segments are ordered
as they are intersected by l if one travels along
l in direction l.direction( ).
deletes the item with segment s from S.
void S.del item(seg item it) removes item it from S.
Precondition: it is an item in S.
void S.change inf(seg 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 rat segment set.
bool S.empty( ) returns true iff S is empty.
int S.size( ) returns the size of S.
4. Implementation
Segment sets are implemented by dynamic segment trees based on BB[α] trees ([90, 57])
trees. Operations key, inf, change inf, empty, and size take time O(1), insert, lookup, del,
and del item take time O(log 2 n) and an intersection operation takes time O(k + log 2 n),
where k is the size of the returned list. Here n is the current size of the set. The space
requirement is O(n log n).