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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

       gb_set()

              A GB set.

       iter()

              A GB set iterator.

EXPORTS

       add(Element, Set1) -> Set2

       add_element(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.

SEE ALSO

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