gb_sets (stdlib v7.0)
View SourceSets 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.
Rebalances the tree representation of Set1.
Equivalent to delete_any(Element, Set1).
Returns a new set formed from Set1 with Element removed, assuming
Element is present in Set1.
Returns a new set formed from Set1 with Element removed.
Equivalent to subtract(Set1, Set2).
Returns a new empty set.
Filters elements in Set1 using predicate function Pred.
Calls Fun(Elem) for each Elem of Set1 to update or remove
elements from Set1.
Folds Function over every element in Set and returns 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 list without duplicates List into a set.
Returns a new set formed from Set1 with Element inserted,
assuming Element is not already present.
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; otherwise, returns
false.
Equivalent to is_member(Element, Set).
Returns true if Set is an empty set; otherwise, returns false.
Returns true if Set1 and Set2 are equal, that is, if every element
of one set is also a member of the other set; otherwise, returns false.
Returns true if Element is an element of Set; otherwise, returns
false.
Returns true if Term appears to be a set; otherwise, returns false.
Returns true when every element of Set1 is also a member of Set2;
otherwise, returns 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.
Returns an iterator that can be used for traversing the entries of Set; see
next/1.
Returns {found, Element2}, where Element2 is the least element strictly
greater than Element1.
Returns the largest element in Set.
Maps elements in Set1 with mapping function Fun.
Returns a new empty set.
Returns {Element, Iter2}, where Element is the first 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.
Returns the elements of Set1 that are not elements in Set2.
Returns {Element, Set2}, where Element is the largest element in
Set1, and Set2 is this set with Element deleted.
Returns {Element, Set2}, where Element is the smallest element in
Set1, and Set2 is this set with Element deleted.
Returns the elements of Set as an ordered list.
Returns the union of a list of sets.
Returns the union 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.
Examples
1> S0 = gb_sets:new().
2> S1 = gb_sets:add_element(7, S0).
3> gb_sets:to_list(S1).
[7]
4> S2 = gb_sets:add_element(42, S1).
5> S2 = gb_sets:add_element(42, S1).
6> gb_sets:to_list(S2).
[7,42]Rebalances the tree representation of Set1.
This is rarely necessary, but can be motivated when a large number of elements have been deleted from the tree without further insertions. Forcing rebalancing can minimize lookup times, as deletion does not rebalance the tree.
Examples
1> S0 = gb_sets:from_ordset(lists:seq(1, 100)).
2> Delete = fun(E, Set) -> gb_sets:delete(E, Set) end.
3> S1 = lists:foldl(Delete, S0, lists:seq(1, 50)).
4> gb_sets:size(S1).
50
5> S2 = gb_sets:balance(S1).Equivalent to delete_any(Element, Set1).
Returns a new set formed from Set1 with Element removed, assuming
Element is present in Set1.
Use delete_any/2 when deleting from a set where Element is potentially
missing.
Examples
1> S = gb_sets:from_list([a,b]).
2> gb_sets:to_list(gb_sets:delete(b, S)).
[a]Returns a new set formed from Set1 with Element removed.
If Element is not an element in Set1, nothing is changed.
Examples
1> S = gb_sets:from_list([a,b]).
2> gb_sets:to_list(gb_sets:delete_any(b, S)).
[a]
3> S = gb_sets:delete_any(x, S).-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.
Examples
1> gb_sets:to_list(gb_sets:empty()).
[]-spec filter(Pred, Set1) -> Set2 when Pred :: fun((Element) -> boolean()), Set1 :: set(Element), Set2 :: set(Element).
Filters elements in Set1 using predicate function Pred.
Examples
1> S = gb_sets:from_list([1,2,3,4,5,6,7]).
2> IsEven = fun(N) -> N rem 2 =:= 0 end.
3> Filtered = gb_sets:filter(IsEven, S).
4> gb_sets:to_list(Filtered).
[2,4,6]-spec filtermap(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> boolean() | {true, Element2}), Set1 :: set(Element1), Set2 :: set(Element1 | Element2).
Calls Fun(Elem) for each Elem of Set1 to update or remove
elements from Set1.
Fun/1 must return either a Boolean or a tuple {true, Value}. The
function returns the set of elements for which Fun returns a new
value, with true being equivalent to {true, Elem}.
gb_sets:filtermap/2 behaves as if it were defined as follows:
filtermap(Fun, Set1) ->
gb_sets:from_list(lists:filtermap(Fun, Set1)).Examples
1> S = gb_sets:from_list([2,4,5,6,8,9])
2> F = fun(X) ->
case X rem 2 of
0 -> {true, X div 2};
1 -> false
end
end.
3> Set = gb_sets:filtermap(F, S).
4> gb_sets:to_list(Set).
[1,2,3,4]-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 and returns the final value of
the accumulator.
Examples
1> S = gb_sets:from_list([1,2,3,4]).
2> Plus = fun erlang:'+'/2.
3> gb_sets:fold(Plus, 0, S).
10-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.
Examples
1> Unordered = [x,y,a,x,y,b,b,z]
2> gb_sets:to_list(gb_sets:from_list(Unordered)).
[a,b,x,y,z]-spec from_ordset(List) -> Set when List :: [Element], Set :: set(Element).
Turns an ordered list without duplicates List into a set.
See from_list/1 for a function that accepts unordered lists with
duplicates.
Examples
1> Ordset = [1,2,3].
2> gb_sets:to_list(gb_sets:from_ordset(Ordset)).
[1,2,3]Returns a new set formed from Set1 with Element inserted,
assuming Element is not already present.
Use add/2 for inserting into a set where Element is potentially
already present.
Examples
1> S0 = gb_sets:new().
2> S1 = gb_sets:insert(7, S0).
3> gb_sets:to_list(S1).
[7]
4> S2 = gb_sets:insert(42, S1).
5> gb_sets:to_list(S2).
[7,42]Returns the intersection of the non-empty list of sets.
The intersection of multiple sets is a new set that contains only the elements that are present in all sets.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([d,e,f]).
3> S2 = gb_sets:from_list([q,r])
4> Sets = [S0, S1, S2].
5> gb_sets:to_list(gb_sets:intersection([S0, S1, S2])).
[]
6> gb_sets:to_list(gb_sets:intersection([S0, S1])).
[d]
7> gb_sets:intersection([]).
** exception error: no function clause matching gb_sets:intersection([])-spec intersection(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns the intersection of Set1 and Set2.
The intersection of two sets is a new set that contains only the elements that are present in both sets.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([c,d,e,f]).
3> S2 = gb_sets:from_list([q,r]).
4> gb_sets:to_list(gb_sets:intersection(S0, S1)).
[c,d]
5> gb_sets:to_list(gb_sets:intersection(S1, S2)).
[]Returns true if Set1 and Set2 are disjoint; otherwise, returns
false.
Two sets are disjoint if they have no elements in common.
This function is equivalent to gb_sets:intersection(Set1, Set2) =:= [],
but faster.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([d,e,f]).
3> S2 = gb_sets:from_list([q,r])
4> gb_sets:is_disjoint(S0, S1).
false
5> gb_sets:is_disjoint(S1, S2).
trueEquivalent to is_member(Element, Set).
Returns true if Set is an empty set; otherwise, returns false.
Examples
1> gb_sets:is_empty(gb_sets:new()).
true
2> gb_sets:is_empty(gb_sets:singleton(1)).
falseReturns true if Set1 and Set2 are equal, that is, if every element
of one set is also a member of the other set; otherwise, returns false.
Examples
1> Empty = gb_sets:new().
2> S = gb_sets:from_list([a,b]).
3> gb_sets:is_equal(S, S)
true
4> gb_sets:is_equal(S, Empty)
falseReturns true if Element is an element of Set; otherwise, returns
false.
Examples
1> S = gb_sets:from_list([a,b,c]).
2> gb_sets:is_member(42, S).
false
3> gb_sets:is_member(b, S).
trueReturns true if Term appears to be a set; otherwise, returns false.
Note
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.
Furthermore, since gb_sets are opaque, calling this function on terms
that are not gb_sets could result in dialyzer warnings.
Examples
1> gb_sets:is_set(gb_sets:new()).
true
2> gb_sets:is_set(gb_sets:singleton(42)).
true
3> gb_sets:is_set(0).
falseReturns true when every element of Set1 is also a member of Set2;
otherwise, returns false.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([c,d]).
3> gb_sets:is_subset(S1, S0).
true
4> gb_sets:is_subset(S0, S1).
false
5> gb_sets:is_subset(S0, S0).
trueReturns 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 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 avoids building the complete list
of all elements to be built in memory at once.
1> S = gb_sets:from_ordset([1,2,3,4,5]).
2> Iter0 = gb_sets:iterator(S, ordered).
3> element(1, gb_sets:next(Iter0)).
1
4> Iter1 = gb_sets:iterator(S, reversed).
5> element(1, gb_sets:next(Iter1)).
5Returns an iterator that can be used for traversing the entries of Set; see
next/1.
Unlike the iterator returned by iterator/1 or iterator/2, this
iterator starts with the first element greater than or equal to
Element.
Equivalent to iterator_from(Element, Set, ordered).
Examples
1> S = gb_sets:from_ordset([10,20,30,40,50]).
2> Iter = gb_sets:iterator_from(17, S).
3> element(1, gb_sets:next(Iter)).
20-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.
Unlike the iterator returned by iterator/1 or iterator/2, this
iterator starts with the first element greater than or equal to
Element.
Examples
1> S = gb_sets:from_ordset([10,20,30,40,50]).
2> Iter = gb_sets:iterator_from(17, S, reversed).
3> element(1, gb_sets:next(Iter)).
10-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.
Examples
1> S = gb_sets:from_list([10,20,30]).
2> gb_sets:larger(1, S).
{found,10}
3> gb_sets:larger(10, S).
{found,20}
4> gb_sets:larger(19, S).
{found,20}
5> gb_sets:larger(30, S).
none-spec largest(Set) -> Element when Set :: set(Element).
Returns the largest element in Set.
Assumes that Set is not empty.
Examples
1> S = gb_sets:from_list([a,b,c]).
2> gb_sets:largest(S).
c-spec map(Fun, Set1) -> Set2 when Fun :: fun((Element1) -> Element2), Set1 :: set(Element1), Set2 :: set(Element2).
Maps elements in Set1 with mapping function Fun.
Examples
1> S = gb_sets:from_list([1,2,3,4,5,6,7]).
2> F = fun(N) -> N div 2 end.
3> Mapped = gb_sets:map(F, S).
4> gb_sets:to_list(Mapped).
[0,1,2,3]Returns a new empty set.
Examples
1> gb_sets:to_list(gb_sets:new()).
[]Returns {Element, Iter2}, where Element is the first 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.
1> S = gb_sets:from_ordset([1,2,3,4,5]).
2> Iter0 = gb_sets:iterator(S).
3> {Element0, Iter1} = gb_sets:next(Iter0).
4> Element0.
1
5> {Element1, Iter2} = gb_sets:next(Iter1).
6> Element1.
2-spec singleton(Element) -> set(Element).
Returns a set containing only element Element.
Examples
1> S = gb_sets:singleton(42).
2> gb_sets:to_list(S).
[42]-spec size(Set) -> non_neg_integer() when Set :: set().
Returns the number of elements in Set.
Examples
1> gb_sets:size(gb_sets:new()).
0
2> gb_sets:size(gb_sets:from_list([4,5,6])).
3-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.
Examples
1> S = gb_sets:from_list([a,b,c]).
2> gb_sets:smaller(b, S).
{found,a}
3> gb_sets:smaller(z, S).
{found,c}
4> gb_sets:smaller(a, S).
none-spec smallest(Set) -> Element when Set :: set(Element).
Returns the smallest element in Set.
Assumes that Set is not empty.
Examples
1> S = gb_sets:from_list([a,b,c]).
2> gb_sets:smallest(S).
a-spec subtract(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns the elements of Set1 that are not elements in Set2.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([c,d,e,f]).
3> gb_sets:to_list(gb_sets:subtract(S0, S1)).
[a,b]
4> gb_sets:to_list(gb_sets:subtract(S1, S0)).
[e,f]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.
Examples
1> S0 = gb_sets:from_list([a,b,c]).
2> {Largest,S1} = gb_sets:take_largest(S0).
3> Largest.
c
4> gb_sets:to_list(S1).
[a,b]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.
Examples
1> S0 = gb_sets:from_list([a,b,c]).
2> {Smallest,S1} = gb_sets:take_smallest(S0).
3> Smallest.
a
4> gb_sets:to_list(S1).
[b,c]-spec to_list(Set) -> List when Set :: set(Element), List :: [Element].
Returns the elements of Set as an ordered list.
1> gb_sets:to_list(gb_sets:from_list([4,3,5,1,2])).
[1,2,3,4,5]Returns the union of a list of sets.
The union of multiple sets is a new set that contains all the elements from all sets, without duplicates.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([d,e,f]).
3> S2 = gb_sets:from_list([q,r])
4> Sets = [S0, S1, S2].
5> Union = gb_sets:union(Sets).
6> gb_sets:to_list(Union).
[a,b,c,d,e,f,q,r]-spec union(Set1, Set2) -> Set3 when Set1 :: set(Element), Set2 :: set(Element), Set3 :: set(Element).
Returns the union of Set1 and Set2.
The union of two sets is a new set that contains all the elements from both sets, without duplicates.
Examples
1> S0 = gb_sets:from_list([a,b,c,d]).
2> S1 = gb_sets:from_list([c,d,e,f]).
3> Union = gb_sets:union(S0, S1).
4> gb_sets:to_list(Union).
[a,b,c,d,e,f]