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

# 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 (*==*).

# 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 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.

- *
*add_element/2*

- *
*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*

# DATA TYPES¶

set(Element)

A GB set.

set()

*set()*is equivalent to

*set(term())*.

iter(Element)

A GB set iterator.

iter()

*iter()*is equivalent to

*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*. 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:

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

del_element(Element, Set1) -> Set2

Types:

Set1 = Set2 =

**set**(Element)
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

subtract(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 =

**set**(Element)
Returns only the elements of

*Set1*which are not also elements of*Set2*.empty() -> Set

new() -> Set

Types:

Set =

**gb_sets: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*may 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(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 =

**set**(Element)
Returns the intersection of

*Set1*and*Set2*.intersection(SetList) -> Set

Types:

SetList = [
Set =

**set**(Element), ...]**set**(Element)
Returns the intersection of the non-empty list of sets.

is_disjoint(Set1, Set2) -> boolean()

Types:

Set1 = Set2 =

**set**(Element)
Returns

*true*if*Set1*and*Set2*are disjoint (have no elements in common), and*false*otherwise.is_empty(Set) -> boolean()

Types:

Set =

**gb_sets:set()**
Returns

*true*if*Set*is an empty set, and*false*otherwise.is_member(Element, Set) -> boolean()

is_element(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 =
Iter =

**set**(Element)**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.largest(Set) -> Element

Types:

Set =

**set**(Element)
Returns the largest element in

*Set*. Assumes that*Set*is nonempty.next(Iter1) -> {Element, Iter2} | none

Types:

Iter1 = Iter2 =

**iter**(Element)
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) -> set(Element)

Returns a set containing only the element

*Element*.size(Set) -> integer() >= 0

Types:

Set =

**gb_sets: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 nonempty.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 nonempty.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 nonempty.to_list(Set) -> List

Types:

Set =
List = [Element]

**set**(Element)
Returns the elements of

*Set*as a list.union(Set1, Set2) -> Set3

Types:

Set1 = Set2 = Set3 =

**set**(Element)
Returns the merged (union) set of

*Set1*and*Set2*.union(SetList) -> Set

Types:

SetList = [
Set =

**set**(Element), ...]**set**(Element)
Returns the merged (union) set of the list of sets.

# SEE ALSO¶

**gb_trees(3erl)**,

**ordsets(3erl)**,

**sets(3erl)**

stdlib 2.2 | Ericsson AB |