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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
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. 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.
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)