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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.
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.
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/2del_element/2filter/2fold/3from_list/1intersection/1intersection/2is_element/2is_set/1is_subset/2new/0size/1subtract/2to_list/1union/1union/2
gb_set() = a GB set
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.
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.
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.
Types:
Set = gb_set()
Returns a new empty gb_set.
Types:
Pred = fun (E) -> bool()
E = term()
Set1 = Set2 = gb_set()
Filters elements in Set1 using predicate function
Pred.
fold(Function, Acc0, Set) -> Acc1
Types:
Function = fun (E, AccIn) -> AccOut
Acc0 = Acc1 = AccIn = AccOut = term()
E = term()
Set = gb_set()
Folds Function over every element in Set
returning the final value of the accumulator.
Types:
List = [term()]
Set = gb_set()
Returns a gb_set of the elements in List, where
List may be unordered and contain duplicates.
Types:
List = [term()]
Set = gb_set()
Turns an ordered-set list List into a gb_set. The list
must not contain duplicates.
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.
Types:
SetList = [gb_set()]
Set = gb_set()
Returns the intersection of the non-empty list of gb_sets.
Types:
Set = gb_set()
Returns true if Set is an empty set, and
false otherwise.
is_member(Element, Set) -> bool()
is_element(Element, Set) -> bool()
Types:
Element = term()
Set = gb_set()
Returns true if Element is an element of
Set, otherwise false.
Types:
Set = gb_set()
Returns true if Set appears to be a gb_set,
otherwise false.
is_subset(Set1, Set2) -> bool()
Types:
Set1 = Set2 = gb_set()
Returns true when every element of Set1 is
also a member of Set2, otherwise false.
Types:
Set = gb_set()
Iter = term()
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.
Types:
Set = gb_set()
Returns the largest element in Set. Assumes that
Set is nonempty.
next(Iter1) -> {Element, Iter2 | none}
Types:
Iter1 = Iter2 = 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.
Types:
Set = gb_set()
Returns the number of elements in Set.
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.
Types:
Set = gb_set()
List = [term()]
Returns the elements of Set as a list.
Types:
Set1 = Set2 = Set3 = gb_set()
Returns the merged (union) gb_set of Set1 and
Set2.
Types:
SetList = [gb_set()]
Set = gb_set()
Returns the merged (union) gb_set of the list of gb_sets.