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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 thesetsandordsetsmodules. 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)->Set2add_element(Element,Set1)->Set2Types: Element = term() Set1 = Set2 = gb_set() Returns a new gb_set formed fromSet1withElementinserted. IfElementis already an element inSet1, nothing is changed.balance(Set1)->Set2Types: Set1 = Set2 = gb_set() Rebalances the tree representation ofSet1. 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)->Set2Types: Element = term() Set1 = Set2 = gb_set() Returns a new gb_set formed fromSet1withElementremoved. Assumes thatElementis present inSet1.delete_any(Element,Set1)->Set2del_element(Element,Set1)->Set2Types: Element = term() Set1 = Set2 = gb_set() Returns a new gb_set formed fromSet1withElementremoved. IfElementis not an element inSet1, nothing is changed.difference(Set1,Set2)->Set3subtract(Set1,Set2)->Set3Types: Set1 = Set2 = Set3 = gb_set() Returns only the elements ofSet1which are not also elements ofSet2.empty()->Setnew()->SetTypes: Set = gb_set() Returns a new empty gb_set.filter(Pred,Set1)->Set2Types: Pred = fun((E :: term()) -> boolean()) Set1 = Set2 = gb_set() Filters elements inSet1using predicate functionPred.fold(Function,Acc0,Set)->Acc1Types: Function = fun((E :: term(), AccIn) -> AccOut) Acc0 = Acc1 = AccIn = AccOut = term() Set = gb_set() FoldsFunctionover every element inSetreturning the final value of the accumulator.from_list(List)->SetTypes: List = [term()] Set = gb_set() Returns a gb_set of the elements inList, whereListmay be unordered and contain duplicates.from_ordset(List)->SetTypes: List = [term()] Set = gb_set() Turns an ordered-set listListinto a gb_set. The list must not contain duplicates.insert(Element,Set1)->Set2Types: Element = term() Set1 = Set2 = gb_set() Returns a new gb_set formed fromSet1withElementinserted. Assumes thatElementis not present inSet1.intersection(Set1,Set2)->Set3Types: Set1 = Set2 = Set3 = gb_set() Returns the intersection ofSet1andSet2.intersection(SetList)->SetTypes: 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() ReturnstrueifSet1andSet2are disjoint (have no elements in common), andfalseotherwise.is_empty(Set)->boolean()Types: Set = gb_set() ReturnstrueifSetis an empty set, andfalseotherwise.is_member(Element,Set)->boolean()is_element(Element,Set)->boolean()Types: Element = term() Set = gb_set() ReturnstrueifElementis an element ofSet, otherwisefalse.is_set(Term)->boolean()Types: Term = term() ReturnstrueifTermappears to be a gb_set, otherwisefalse.is_subset(Set1,Set2)->boolean()Types: Set1 = Set2 = gb_set() Returnstruewhen every element ofSet1is also a member ofSet2, otherwisefalse.iterator(Set)->IterTypes: Set = gb_set() Iter =iter()Returns an iterator that can be used for traversing the entries ofSet; seenext/1. The implementation of this is very efficient; traversing the whole set usingnext/1is only slightly slower than getting the list of all elements usingto_list/1and 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 inSet. Assumes thatSetis nonempty.next(Iter1)->{Element,Iter2}|noneTypes: Iter1 = Iter2 =iter()Element = term() Returns{Element,Iter2}whereElementis the smallest element referred to by the iteratorIter1, andIter2is the new iterator to be used for traversing the remaining elements, or the atomnoneif no elements remain.singleton(Element)->gb_set()Types: Element = term() Returns a gb_set containing only the elementElement.size(Set)->integer()>=0Types: Set = gb_set() Returns the number of elements inSet.smallest(Set)->term()Types: Set = gb_set() Returns the smallest element inSet. Assumes thatSetis nonempty.take_largest(Set1)->{Element,Set2}Types: Set1 = Set2 = gb_set() Element = term() Returns{Element,Set2}, whereElementis the largest element inSet1, andSet2is this set withElementdeleted. Assumes thatSet1is nonempty.take_smallest(Set1)->{Element,Set2}Types: Set1 = Set2 = gb_set() Element = term() Returns{Element,Set2}, whereElementis the smallest element inSet1, andSet2is this set withElementdeleted. Assumes thatSet1is nonempty.to_list(Set)->ListTypes: Set = gb_set() List = [term()] Returns the elements ofSetas a list.union(Set1,Set2)->Set3Types: Set1 = Set2 = Set3 = gb_set() Returns the merged (union) gb_set ofSet1andSet2.union(SetList)->SetTypes: 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)