Provided by: erlang-manpages_16.b.3-dfsg-1ubuntu2_all NAME

```       gb_sets - General Balanced Trees

```

DESCRIPTION

```       An  implementation  of  ordered  sets using Prof. Arne Andersson's General Balanced Trees.
This 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
(==).

```

COMPLEXITYNOTE

```       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  between  10  and  100
times.  This  implementation  is  particularly suited for accumulating elements a few at a
time, building up a large set (more than 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

```       All of the following functions in this module also exist and do the same thing in the sets
and  ordsets modules. That is, by only changing the module name for each call, you can try
out different set representations.

* del_element/2

* filter/2

* fold/3

* from_list/1

* intersection/1

* intersection/2

* is_element/2

* is_set/1

* is_subset/2

* new/0

* size/1

* subtract/2

* to_list/1

* union/1

* union/2

```

DATATYPES

```       gb_set()

A GB set.

iter()

A GB set iterator.

```

EXPORTS

```       add(Element, Set1) -> Set2

Types:

Element = term()
Set1 = Set2 = gb_set()

Returns a new gb_set formed from Set1 with Element inserted. If Element is  already
an element in Set1, nothing is changed.

balance(Set1) -> Set2

Types:

Set1 = Set2 = gb_set()

Rebalances the tree representation of Set1. Note that this is rarely necessary, but
may be motivated when a large number of elements have been deleted  from  the  tree
without  further  insertions. Rebalancing could then be forced in order to minimise
lookup times, since deletion only does not rebalance the tree.

delete(Element, Set1) -> Set2

Types:

Element = term()
Set1 = Set2 = gb_set()

Returns a new gb_set formed from Set1 with Element removed. Assumes that Element is
present in Set1.

delete_any(Element, Set1) -> Set2

del_element(Element, Set1) -> Set2

Types:

Element = term()
Set1 = Set2 = gb_set()

Returns  a  new  gb_set formed from Set1 with Element removed. If Element is not an
element in Set1, nothing is changed.

difference(Set1, Set2) -> Set3

subtract(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 = gb_set()

Returns only the elements of Set1 which are not also elements of Set2.

empty() -> Set

new() -> Set

Types:

Set = gb_set()

Returns a new empty gb_set.

filter(Pred, Set1) -> Set2

Types:

Pred = fun((E :: term()) -> boolean())
Set1 = Set2 = gb_set()

Filters elements in Set1 using predicate function Pred.

fold(Function, Acc0, Set) -> Acc1

Types:

Function = fun((E :: term(), AccIn) -> AccOut)
Acc0 = Acc1 = AccIn = AccOut = term()
Set = gb_set()

Folds Function over  every  element  in  Set  returning  the  final  value  of  the
accumulator.

from_list(List) -> Set

Types:

List = [term()]
Set = gb_set()

Returns  a  gb_set of the elements in List, where List may be unordered and contain
duplicates.

from_ordset(List) -> Set

Types:

List = [term()]
Set = gb_set()

Turns an ordered-set list List into a gb_set. The list must not contain duplicates.

insert(Element, Set1) -> Set2

Types:

Element = term()
Set1 = Set2 = gb_set()

Returns a new gb_set formed from Set1 with Element inserted. Assumes  that  Element
is not present in Set1.

intersection(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 = gb_set()

Returns the intersection of Set1 and Set2.

intersection(SetList) -> Set

Types:

SetList = [gb_set(), ...]
Set = gb_set()

Returns the intersection of the non-empty list of gb_sets.

is_disjoint(Set1, Set2) -> boolean()

Types:

Set1 = Set2 = gb_set()

Returns  true if Set1 and Set2 are disjoint (have no elements in common), and false
otherwise.

is_empty(Set) -> boolean()

Types:

Set = gb_set()

Returns true if Set is an empty set, and false otherwise.

is_member(Element, Set) -> boolean()

is_element(Element, Set) -> boolean()

Types:

Element = term()
Set = gb_set()

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 gb_set, otherwise false.

is_subset(Set1, Set2) -> boolean()

Types:

Set1 = Set2 = gb_set()

Returns true when every element of Set1 is also a member of Set2, otherwise false.

iterator(Set) -> Iter

Types:

Set = gb_set()
Iter = iter()

Returns an iterator that can be used for traversing the entries of Set; see next/1.
The implementation of this is very efficient; 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.

largest(Set) -> term()

Types:

Set = gb_set()

Returns the largest element in Set. Assumes that Set is nonempty.

next(Iter1) -> {Element, Iter2} | none

Types:

Iter1 = Iter2 = iter()
Element = term()

Returns {Element, Iter2} where Element is the smallest element referred to  by  the
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) -> gb_set()

Types:

Element = term()

Returns a gb_set containing only the element Element.

size(Set) -> integer() >= 0

Types:

Set = gb_set()

Returns the number of elements in Set.

smallest(Set) -> term()

Types:

Set = gb_set()

Returns the smallest element in Set. Assumes that Set is nonempty.

take_largest(Set1) -> {Element, Set2}

Types:

Set1 = Set2 = gb_set()
Element = term()

Returns {Element, Set2}, where Element is the largest element in Set1, and Set2  is
this set with Element deleted. Assumes that Set1 is nonempty.

take_smallest(Set1) -> {Element, Set2}

Types:

Set1 = Set2 = gb_set()
Element = term()

Returns {Element, Set2}, where Element is the smallest element in Set1, and Set2 is
this set with Element deleted. Assumes that Set1 is nonempty.

to_list(Set) -> List

Types:

Set = gb_set()
List = [term()]

Returns the elements of Set as a list.

union(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 = gb_set()

Returns the merged (union) gb_set of Set1 and Set2.

union(SetList) -> Set

Types:

SetList = [gb_set(), ...]
Set = gb_set()

Returns the merged (union) gb_set of the list of gb_sets.

```

SEEALSO

```       gb_trees(3erl), ordsets(3erl), sets(3erl)
```