gb_sets - General balanced trees.
Please see following description for synopsis
gb_sets(3) Erlang Module Definition gb_sets(3)
NAME
gb_sets - General balanced trees.
DESCRIPTION
This module provides ordered sets using Prof. Arne Andersson's General
Balanced Trees. Ordered sets can be much more efficient than using
ordered lists, for larger sets, but depends on the application.
This module considers two elements as different if and only if they do
not compare equal (==).
COMPLEXITY NOTE
The complexity on set operations is bounded by either O(|S|) or O(|T| *
log(|S|)), where S is the largest given set, depending on which is
fastest for any particular function call. For operating on sets of
almost equal size, this implementation is about 3 times slower than
using ordered-list sets directly. For sets of very different sizes,
however, this solution can be arbitrarily much faster; in practical
cases, often 10-100 times. This implementation is particularly suited
for accumulating elements a few at a time, building up a large set (>
100-200 elements), and repeatedly testing for membership in the current
set.
As with normal tree structures, lookup (membership testing), insertion,
and deletion have logarithmic complexity.
COMPATIBILITY
The following functions in this module also exist and provides the same
functionality in the sets(3) and ordsets(3) modules. That is, by only
changing the module name for each call, you can try out different set
representations.
* add_element/2
* del_element/2
* filter/2
* fold/3
* from_list/1
* intersection/1
* intersection/2
* is_element/2
* is_empty/1
* is_set/1
* is_subset/2
* new/0
* size/1
* subtract/2
* to_list/1
* union/1
* union/2
DATA TYPES
set(Element)
A general balanced set.
set() = set(term())
iter(Element)
A general balanced set iterator.
iter() = iter(term())
EXPORTS
add(Element, Set1) -> Set2
add_element(Element, Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Returns a new set formed from Set1 with Element inserted. If
Element is already an element in Set1, nothing is changed.
balance(Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Rebalances the tree representation of Set1. Notice that this is
rarely necessary, but can be motivated when a large number of
elements have been deleted from the tree without further inser-
tions. Rebalancing can then be forced to minimise lookup times,
as deletion does not rebalance the tree.
del_element(Element, Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Returns a new set formed from Set1 with Element removed. If Ele-
ment is not an element in Set1, nothing is changed.
delete(Element, Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Returns a new set formed from Set1 with Element removed. Assumes
that Element is present in Set1.
delete_any(Element, Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Returns a new set formed from Set1 with Element removed. If Ele-
ment is not an element in Set1, nothing is changed.
difference(Set1, Set2) -> Set3
Types:
Set1 = Set2 = Set3 = set(Element)
Returns only the elements of Set1 that are not also elements of
Set2.
empty() -> Set
Types:
Set = set()
Returns a new empty set.
filter(Pred, Set1) -> Set2
Types:
Pred = fun((Element) -> boolean())
Set1 = Set2 = set(Element)
Filters elements in Set1 using predicate function Pred.
fold(Function, Acc0, Set) -> Acc1
Types:
Function = fun((Element, AccIn) -> AccOut)
Acc0 = Acc1 = AccIn = AccOut = Acc
Set = set(Element)
Folds Function over every element in Set returning the final
value of the accumulator.
from_list(List) -> Set
Types:
List = [Element]
Set = set(Element)
Returns a set of the elements in List, where List can be
unordered and contain duplicates.
from_ordset(List) -> Set
Types:
List = [Element]
Set = set(Element)
Turns an ordered-set list List into a set. The list must not
contain duplicates.
insert(Element, Set1) -> Set2
Types:
Set1 = Set2 = set(Element)
Returns a new set formed from Set1 with Element inserted.
Assumes that Element is not present in Set1.
intersection(SetList) -> Set
Types:
SetList = [set(Element), ...]
Set = set(Element)
Returns the intersection of the non-empty list of sets.
intersection(Set1, Set2) -> Set3
Types:
Set1 = Set2 = Set3 = set(Element)
Returns the intersection of Set1 and Set2.
is_disjoint(Set1, Set2) -> boolean()
Types:
Set1 = Set2 = set(Element)
Returns true if Set1 and Set2 are disjoint (have no elements in
common), otherwise false.
is_element(Element, Set) -> boolean()
Types:
Set = set(Element)
Returns true if Element is an element of Set, otherwise false.
is_empty(Set) -> boolean()
Types:
Set = set()
Returns true if Set is an empty set, otherwise false.
is_member(Element, Set) -> boolean()
Types:
Set = set(Element)
Returns true if Element is an element of Set, otherwise false.
is_set(Term) -> boolean()
Types:
Term = term()
Returns true if Term appears to be a set, otherwise false.
is_subset(Set1, Set2) -> boolean()
Types:
Set1 = Set2 = set(Element)
Returns true when every element of Set1 is also a member of
Set2, otherwise false.
iterator(Set) -> Iter
Types:
Set = set(Element)
Iter = iter(Element)
Returns an iterator that can be used for traversing the entries
of Set; see next/1. The implementation of this is very effi-
cient; traversing the whole set using next/1 is only slightly
slower than getting the list of all elements using to_list/1 and
traversing that. The main advantage of the iterator approach is
that it does not require the complete list of all elements to be
built in memory at one time.
iterator_from(Element, Set) -> Iter
Types:
Set = set(Element)
Iter = iter(Element)
Returns an iterator that can be used for traversing the entries
of Set; see next/1. The difference as compared to the iterator
returned by iterator/1 is that the first element greater than or
equal to Element is returned.
largest(Set) -> Element
Types:
Set = set(Element)
Returns the largest element in Set. Assumes that Set is not
empty.
new() -> Set
Types:
Set = set()
Returns a new empty set.
next(Iter1) -> {Element, Iter2} | none
Types:
Iter1 = Iter2 = iter(Element)
Returns {Element, Iter2}, where Element is the smallest element
referred to by iterator Iter1, and Iter2 is the new iterator to
be used for traversing the remaining elements, or the atom none
if no elements remain.
singleton(Element) -> set(Element)
Returns a set containing only element Element.
size(Set) -> integer() >= 0
Types:
Set = set()
Returns the number of elements in Set.
smallest(Set) -> Element
Types:
Set = set(Element)
Returns the smallest element in Set. Assumes that Set is not
empty.
subtract(Set1, Set2) -> Set3
Types:
Set1 = Set2 = Set3 = set(Element)
Returns only the elements of Set1 that are not also elements of
Set2.
take_largest(Set1) -> {Element, Set2}
Types:
Set1 = Set2 = set(Element)
Returns {Element, Set2}, where Element is the largest element in
Set1, and Set2 is this set with Element deleted. Assumes that
Set1 is not empty.
take_smallest(Set1) -> {Element, Set2}
Types:
Set1 = Set2 = set(Element)
Returns {Element, Set2}, where Element is the smallest element
in Set1, and Set2 is this set with Element deleted. Assumes that
Set1 is not empty.
to_list(Set) -> List
Types:
Set = set(Element)
List = [Element]
Returns the elements of Set as a list.
union(SetList) -> Set
Types:
SetList = [set(Element), ...]
Set = set(Element)
Returns the merged (union) set of the list of sets.
union(Set1, Set2) -> Set3
Types:
Set1 = Set2 = Set3 = set(Element)
Returns the merged (union) set of Set1 and Set2.
SEE ALSO
gb_trees(3), ordsets(3), sets(3)
Ericsson AB stdlib 3.17 gb_sets(3)