Version 5.0 The LEDA User Manual

void D.del(const K& k) deletes the item with key k from the set (null
operation, if no such item exists).
void
D.del item(pp dic item it)
removes item it from the set.
Precondition: it is an item in the set.
pp dic item D.change inf(pp dic item it, const I& i)
makes i the information of item it. This may
create a new item; the item in
the new set is returned.
Precondition: it is an item in the set.
void D.clear( ) makes D the empty dictionary.
3.2 Access operations
const K&
D.key(pp dic item it) returns the key of item it.
Precondition: it ∈ D.
const I& D.inf(pp dic item it) returns the information of item it.
Precondition: it ∈ D.
pp dic item D.lookup(const K& k)
pp dic item D.locate succ(const K& k)
pp dic item D.locate pred(const K& k)
int D.size( ) returns the size of D.
returns the item with key k (nil if no such item
exists in D).
returns the item x in D so that key(x) =
min{key(y)| y ∈ D ∧ key(y) ≥ k}.
returns the item x in D so that key(x) =
max{key(y)| y ∈ D ∧ key(y) ≤ k}.
bool D.empty( ) returns true if D is empty, false otherwise.
4. Implementation
Partially persistent dictionaries are implemented by leaf oriented partially persistent redblack
trees. Operations insert, del, del item and lookup take expected time O(log n), the
expected time for key, inf, empty, size and change inf is O(1), and clear takes expected
time O(n). Here n is the number of items in the version of the dictionary to which the
operation is applied. The expected space requirement is O(1) for each update operation.