gb_sets(3)

NAME
gb_sets - Sets represented by 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.

The data representing a set as used by this module is to be regarded as opaque by other modules. In abstract terms, the representation is a composite type of existing Erlang terms. See note on data types. Any code assuming knowledge of the format is running on thin ice.

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

See the Compatibility Section in the sets(3) module for information about the compatibility of the different implementations of sets in the Standard Library.

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

del_element(Element, Set1) -> Set2
delete_any(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.

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.

difference(Set1, Set2) -> Set3
subtract(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(none())

    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.

filtermap(Fun, Set1) -> Set2

    Types:
        Fun = fun((Element1) -> boolean() | {true, Element2})
        Set1 = set(Element1)
        Set2 = set(Element1 | Element2)

    Filters and maps elements in Set1 using function Fun.

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()
is_member(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_equal(Set1, Set2) -> boolean()

    Types:
        Set1 = Set2 = set()

    Returns true if Set1 and Set2 are equal, that is when every element of one set is also a member of the respective other set, otherwise false.

is_set(Term) -> boolean()

    Types:
        Term = term()

    Returns true if Term appears to be a set, otherwise false. This function will return true for any term that coincides with the representation of a gb_set, while not really being a gb_set, thus it might return false positive results. See also note on data types.

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.

    Equivalent to iterator(Set, ordered).

iterator(Set, Order) -> Iter

    Types:
        Set = set(Element)
        Iter = iter(Element)
        Order = ordered | reversed

    Returns an iterator that can be used for traversing the entries of Set in either ordered or reversed direction; 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:
        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 iterator starts with the first element greater than or equal to Element.

    Equivalent to iterator_from(Element, Set, ordered).

iterator_from(Element, Set, Order) -> Iter

    Types:
        Set = set(Element)
        Iter = iter(Element)
        Order = ordered | reversed

    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/2 is that the iterator starts with the first element next to or equal to Element.

larger(Element1, Set) -> none | {found, Element2}

    Types:
        Element1 = Element2 = Element
        Set = set(Element)

    Returns {found, Element2}, where Element2 is the least element strictly greater than Element1.

    Returns none if no such element exists.

largest(Set) -> Element

    Types:
        Set = set(Element)

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

map(Fun, Set1) -> Set2

    Types:
        Fun = fun((Element1) -> Element2)
        Set1 = set(Element1)
        Set2 = set(Element2)

    Maps elements in Set1 using mapping function Fun.

new() -> Set

    Types:
        Set = set(none())

    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.

smaller(Element1, Set) -> none | {found, Element2}

    Types:
        Element1 = Element2 = Element
        Set = set(Element)

    Returns {found, Element2}, where Element2 is the greatest element strictly less than Element1.

    Returns none if no such element exists.

smallest(Set) -> Element

    Types:
        Set = set(Element)

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

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)