## table of contents

- bookworm 1:25.2.3+dfsg-1
- testing 1:25.2.3+dfsg-1
- unstable 1:25.2.3+dfsg-1
- experimental 1:26.0.2+dfsg-1

gb_sets(3erl) | Erlang Module Definition | gb_sets(3erl) |

# 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(3erl)* and *ordsets(3erl)*
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:

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:

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 insertions.
Rebalancing can then be forced to minimise lookup times, as deletion does
not rebalance the tree.

del_element(Element, Set1) -> Set2

Types:

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

delete(Element, Set1) -> Set2

Types:

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

delete_any(Element, Set1) -> Set2

Types:

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

difference(Set1, Set2) -> Set3

Types:

Returns only the elements of *Set1* that are not also
elements of *Set2*.

empty() -> Set

Types:

Returns a new empty set.

filter(Pred, Set1) -> Set2

Types:

Set1 = Set2 = set(Element)

Filters elements in *Set1* using predicate function
*Pred*.

fold(Function, Acc0, Set) -> Acc1

Types:

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:

Set = set(Element)

Returns a set of the elements in *List*, where *List*
can be unordered and contain duplicates.

from_ordset(List) -> Set

Types:

Set = set(Element)

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

insert(Element, Set1) -> Set2

Types:

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

intersection(SetList) -> Set

Types:

Set = set(Element)

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

intersection(Set1, Set2) -> Set3

Types:

Returns the intersection of *Set1* and *Set2*.

is_disjoint(Set1, Set2) -> boolean()

Types:

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

is_element(Element, Set) -> boolean()

Types:

Returns *true* if *Element* is an element of *Set*,
otherwise *false*.

is_empty(Set) -> boolean()

Types:

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

is_member(Element, Set) -> boolean()

Types:

Returns *true* if *Element* is an element of *Set*,
otherwise *false*.

is_set(Term) -> boolean()

Types:

Returns *true* if *Term* appears to be a set, otherwise
*false*.

is_subset(Set1, Set2) -> boolean()

Types:

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

iterator(Set) -> Iter

Types:

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 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.

iterator_from(Element, Set) -> Iter

Types:

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:

Returns the largest element in *Set*. Assumes that *Set*
is not empty.

new() -> Set

Types:

Returns a new empty set.

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

Types:

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:

Returns the number of elements in *Set*.

smallest(Set) -> Element

Types:

Returns the smallest element in *Set*. Assumes that
*Set* is not empty.

subtract(Set1, Set2) -> Set3

Types:

Returns only the elements of *Set1* that are not also
elements of *Set2*.

take_largest(Set1) -> {Element, Set2}

Types:

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:

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:

List = [Element]

Returns the elements of *Set* as a list.

union(SetList) -> Set

Types:

Set = set(Element)

Returns the merged (union) set of the list of sets.

union(Set1, Set2) -> Set3

Types:

Returns the merged (union) set of *Set1* and *Set2*.

# SEE ALSO¶

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

stdlib 3.17.2 | Ericsson AB |