View Source gb_sets (stdlib v6.0)
Sets represented by general balanced trees.
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
See the Compatibility Section in the sets module
for information about the compatibility of the different implementations of sets
in the Standard Library.
See Also
Summary
Functions
Equivalent to add_element(Element, Set1)
Returns a new set formed from Set1 with Element inserted. If Element is
already an element in Set1, nothing is changed.
Rebalances the tree representation of Set1.
Equivalent to delete_any(Element, Set1)
Returns a new set formed from Set1 with Element removed. Assumes that
Element is present in Set1.
Returns a new set formed from Set1 with Element removed. If Element is not
an element in Set1, nothing is changed.
Equivalent to subtract(Set1, Set2)
Returns a new empty set.
Filters elements in Set1 using predicate function Pred.
Filters and maps elements in Set1 using function Fun.
Folds Function over every element in Set returning the final value of the
accumulator.
Returns a set of the elements in List, where List can be unordered and
contain duplicates.
Turns an ordered-set list List into a set. The list must not contain
duplicates.
Returns a new set formed from Set1 with Element inserted. Assumes that
Element is not present in Set1.
Returns the intersection of the non-empty list of sets.
Returns the intersection of Set1 and Set2.
Returns true if Set1 and Set2 are disjoint (have no elements in common),
otherwise false.
Equivalent to is_member(Element, Set)
Returns true if Set is an empty set, otherwise false.
Returns true if Set1 and Set2 are equal, that is when every element of one
set is also a member of the respective other set, otherwise false.
Returns true if Element is an member of Set, otherwise false.
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.
Returns true when every element of Set1 is also a member of Set2,
otherwise false.
Returns an iterator that can be used for traversing the entries of Set; see
next/1.
Returns an iterator that can be used for traversing the entries of Set in
either ordered or reversed direction; see next/1.
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 iterator starts with the first element greater than or equal to
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/2 is
that the iterator starts with the first element next to or equal to Element.
Returns {found, Element2}, where Element2 is the least element strictly
greater than Element1.
Returns the largest element in Set. Assumes that Set is not empty.
Maps elements in Set1 using mapping function Fun.
Returns a new empty set.
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.
Returns a set containing only element Element.
Returns the number of elements in Set.
Returns {found, Element2}, where Element2 is the greatest element strictly
less than Element1.
Returns the smallest element in Set. Assumes that Set is not empty.
Returns only the elements of Set1 that are not also elements of Set2.
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.
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.
Returns the elements of Set as a list.
Returns the merged (union) set of the list of sets.
Returns the merged (union) set of Set1 and Set2.
Types
Functions
Equivalent to add_element(Element, Set1)
Returns a new set formed from Set1 with Element inserted. If Element is
already an element in Set1, nothing is changed.
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.
Equivalent to delete_any(Element, Set1)
Returns a new set formed from Set1 with Element removed. Assumes that
Element is present in Set1.
Returns a new set formed from Set1 with Element removed. If Element is not
an element in Set1, nothing is changed.
-spec difference(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Equivalent to subtract(Set1, Set2)
Returns a new empty set.
-spec filter(Pred, Set1) -> Set2 when Pred :: fun((Element) -> boolean()), Set1 :: set(Element), Set2 :: set(Element).
Filters elements in Set1 using predicate function Pred.
-spec filtermap(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> boolean() | {true, Element2}), Set1 :: set(Element1), Set2 :: set(Element1 | Element2).
Filters and maps elements in Set1 using function Fun.
-spec fold(Function, Acc0, Set) -> Acc1 when Function :: fun((Element, AccIn) -> AccOut), Acc0 :: Acc, Acc1 :: Acc, AccIn :: Acc, AccOut :: Acc, Set :: set(Element).
Folds Function over every element in Set returning the final value of the
accumulator.
-spec from_list(List) -> Set when List :: [Element], Set :: set(Element).
Returns a set of the elements in List, where List can be unordered and
contain duplicates.
-spec from_ordset(List) -> Set when List :: [Element], Set :: set(Element).
Turns an ordered-set list List into a set. The list must not contain
duplicates.
Returns a new set formed from Set1 with Element inserted. Assumes that
Element is not present in Set1.
Returns the intersection of the non-empty list of sets.
-spec intersection(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns the intersection of Set1 and Set2.
Returns true if Set1 and Set2 are disjoint (have no elements in common),
otherwise false.
Equivalent to is_member(Element, Set)
Returns true if Set is an empty set, otherwise false.
Returns true if Set1 and Set2 are equal, that is when every element of one
set is also a member of the respective other set, otherwise false.
Returns true if Element is an member of Set, otherwise false.
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.
Returns true when every element of Set1 is also a member of Set2,
otherwise false.
Returns an iterator that can be used for traversing the entries of Set; see
next/1.
Equivalent to iterator(Set, ordered).
-spec iterator(Set, Order) -> Iter when Set :: set(Element), Iter :: iter(Element), Order :: ordered | reversed.
Returns an iterator that can be used for traversing the entries of Set in
either ordered or reversed direction; 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.
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 iterator starts with the first element greater than or equal to
Element.
Equivalent to iterator_from(Element, Set, ordered).
-spec iterator_from(Element, Set, Order) -> Iter when Set :: set(Element), Iter :: iter(Element), Order :: ordered | reversed.
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/2 is
that the iterator starts with the first element next to or equal to Element.
-spec larger(Element1, Set) -> none | {found, Element2} when Element1 :: Element, Element2 :: Element, Set :: set(Element).
Returns {found, Element2}, where Element2 is the least element strictly
greater than Element1.
Returns none if no such element exists.
-spec largest(Set) -> Element when Set :: set(Element).
Returns the largest element in Set. Assumes that Set is not empty.
-spec map(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> Element2), Set1 :: set(Element1), Set2 :: set(Element2).
Maps elements in Set1 using mapping function Fun.
Returns a new empty set.
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.
-spec singleton(Element) -> set(Element).
Returns a set containing only element Element.
-spec size(Set) -> non_neg_integer() when Set :: set().
Returns the number of elements in Set.
-spec smaller(Element1, Set) -> none | {found, Element2} when Element1 :: Element, Element2 :: Element, Set :: set(Element).
Returns {found, Element2}, where Element2 is the greatest element strictly
less than Element1.
Returns none if no such element exists.
-spec smallest(Set) -> Element when Set :: set(Element).
Returns the smallest element in Set. Assumes that Set is not empty.
-spec subtract(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns only the elements of Set1 that are not also elements of Set2.
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.
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.
-spec to_list(Set) -> List when Set :: set(Element), List :: [Element].
Returns the elements of Set as a list.
Returns the merged (union) set of the list of sets.
-spec union(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns the merged (union) set of Set1 and Set2.