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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:

                 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

              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.

       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.

       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 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 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(3erl), ordsets(3erl), sets(3erl)