gb_sets(3)

📦
version 29.0.6 · 3 versions
, in ubuntu stonking

🎀 gb_sets — wait, this is gb_sets(3), Erlang Module Definition

Bestie. Sit down. We're doing ordered sets today and honestly? They're iconic.

🌸 NAME

gb_sets — sets represented by general balanced trees. That's it, that's the name, periodt.

✨ DESCRIPTION

Okay so this module gives you ordered sets using Prof. Arne Andersson's General Balanced Trees. No cap. For bigger sets, ordered sets can be way more efficient than just using ordered lists — but lowkey it depends on what your app is actually doing, so like, vibe check your use case first.

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 that assumes it knows the internal format is running on thin ice 💀 — do not do that to yourself.

This module considers two elements as different if and only if they do not compare equal (==).

🔥 Complexity

The complexity on set operations is bounded by either O(|S|) or O(|T| log(|S|))*, where S is the largest given set — which one you get depends on which is fastest for that particular function call. Fancy, right?

  • 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, though, this solution can be arbitrarily much faster — in practical cases, often 10-100 times. Slay.

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.

And as with normal tree structures, lookup (membership testing), insertion, and deletion all 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

gb_trees, ordsets, sets

🦋 DATA TYPES

  • iter() :: iter(_).
  • -opaque iter(Element) — a general balanced set iterator.
  • set() :: set(_).
  • -opaque set(Element) — a general balanced set.

💅 FUNCTIONS

add_element

add_element(Element, Set1) -> Set2
                     when Set1 :: set(Element), Set2 :: set(Element).

Returns a new set formed from Set1 with Element inserted. 🫶

If Element is already an element in Set1, nothing is changed. So it's giving "no duplicates allowed, bestie."

🍓 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]

balance

balance(Set1) -> Set2
                 when Set1 :: set(Element), Set2 :: set(Element).

Rebalances the tree representation of Set1. 🌳✨

This is rarely necessary, but it can be motivated when a large number of elements have been deleted from the tree without further insertions. Forcing rebalancing can minimize lookup times, because deletion does not rebalance the tree. So if you've been deleting like it's your job, maybe balance. Just a thought. 💅

🍓 Examples

1> S0 = gb_sets:from_list(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).

delete

delete(Element, Set1) -> Set2
                when Set1 :: set(Element), Set2 :: set(Element).

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. Don't be out here deleting stuff that might not exist, that's not the vibe.

🍓 Examples

1> S = gb_sets:from_list([a,b]).
2> gb_sets:to_list(gb_sets:delete(b, S)).
[a]

delete_any

delete_any(Element, Set1) -> Set2
                    when Set1 :: set(Element), Set2 :: set(Element).

Returns a new set formed from Set1 with Element removed. The safe, chill version. 🧚

If Element is not an element in Set1, nothing is changed. No drama, no crash, we love that for us.

🍓 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).

empty

empty() -> Set when Set :: set(none()).

Returns a new empty set. Yes bestie, the empty set. The blank canvas. The clean slate. 🎀

🍓 Examples

1> gb_sets:to_list(gb_sets:empty()).
[]

filter

filter(Pred, Set1) -> Set2
                when
                    Pred :: fun((Element) -> boolean()),
                    Set1 :: set(Element),
                    Set2 :: set(Element).

Filters elements in Set1 using the predicate function Pred. Only the ones that pass the vibe check survive. 🌈

🍓 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]

filtermap

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. It's giving glow-up and ghosting, both at once. 💅

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, gb_sets:to_list(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]

fold

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. Main character energy: everything goes in, one value comes out. 👑

🍓 Examples

1> S = gb_sets:from_list([1,2,3,4]).
2> Plus = fun erlang:'+'/2.
3> gb_sets:fold(Plus, 0, S).
10

from_list

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. Chaotic input, organized output. We love a transformation arc. 🦋

🍓 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]

from_ordset

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. Different function, different rules, know the difference bestie. 💖

🍓 Examples

1> Ordset = [1,2,3].
2> gb_sets:to_list(gb_sets:from_ordset(Ordset)).
[1,2,3]

insert

insert(Element, Set1) -> Set2
                when Set1 :: set(Element), Set2 :: set(Element).

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. Pick the right one, okay? It literally matters.

🍓 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]

intersection

intersection(SetList) -> Set
                      when
                          SetList :: [set(Element), ...],
                          Set :: set(Element).

Returns the intersection of the non-empty list of sets. (Yes, note the non-empty. There's a whole example about what happens when you ignore that. 💀)

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([])

intersection

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)).
[]

is_disjoint

is_disjoint(Set1, Set2) -> boolean()
                     when Set1 :: set(Element), Set2 :: set(Element).

Returns true if Set1 and Set2 are disjoint; otherwise, returns false.

Two sets are disjoint if they have no elements in common. Like two friend groups that have literally never met. 🙈

This function is equivalent to gb_sets:is_empty(gb_sets:intersection(Set1, Set2)), but faster. Faster = better = slay.

🍓 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).
true

is_empty

is_empty(Set) -> boolean() when Set :: set().

Returns true if Set is an empty set; otherwise, returns false. Quick little vibe check. ✨

🍓 Examples

1> gb_sets:is_empty(gb_sets:new()).
true
2> gb_sets:is_empty(gb_sets:singleton(1)).
false

is_equal

is_equal(Set1, Set2) -> boolean()
                  when Set1 :: set(), Set2 :: set().

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. Same energy, different tree. 💜

🍓 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).
false

is_member

is_member(Element, Set) -> boolean() when Set :: set(Element).

Returns true if Element is an element of Set; otherwise, returns false. Are you in or are you out? 🎀

🍓 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).
true

is_set

is_set(Term) -> boolean() when Term :: term().

Okay so is_set is giving "is this actually a set?" energy — it returns true if Term appears to be a set; otherwise, it's a whole 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, so it might throw false positive results. See also the note on data types. And because gb_sets are opaque, calling this 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).
false

is_subset/2

is_subset(Set1, Set2) -> boolean()
                          when Set1 :: set(Element), Set2 :: set(Element).

Bestie, this one returns true when every single element of Set1 is also a member of Set2; otherwise, it's a 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).
true

iterator/2

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 in memory at once. 🧚

Examples:

1> S = gb_sets:from_list([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)).
5

iterator_from/3

iterator_from(Element, Set, Order) -> Iter
                        when
                            Set :: set(Element),
                            Iter :: iter(Element),
                            Order :: ordered | reversed.

Returns an iterator over members of Set in the given Order, starting from Element or, if absent, the first member that follows in the iteration order, if any; see next/1. 🦋

Examples:

1> S = gb_sets:from_list([10,20,30,40,50]).
2> Iter1 = gb_sets:iterator_from(17, S, ordered).
3> element(1, gb_sets:next(Iter1)).
20
4> Iter2 = gb_sets:iterator_from(17, S, reversed).
5> element(1, gb_sets:next(Iter2)).
10

larger/2

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

largest/1

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

map/2

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]

new/0

new() -> Set when Set :: set(none()).

Returns a new empty set. 🌸

Examples:

1> gb_sets:to_list(gb_sets:new()).
[]

next/1

next(Iter1) -> {Element, Iter2} | none
               when Iter1 :: iter(Element), Iter2 :: iter(Element).

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. ✨

Examples:

1> S = gb_sets:from_list([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

singleton/1

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]

size/1

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

smaller/2

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

smallest/1

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

subtract/2

subtract(Set1, Set2) -> Set3
                   when
                       Set1 :: set(Element),
                       Set2 :: set(Element),
                       Set3 :: set(Element).

Returns a new set containing 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]

take_largest/1

take_largest(Set1) -> {Element, Set2}
                     when Set1 :: set(Element), 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. ⚠️

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]

take_smallest/1

take_smallest(Set1) -> {Element, Set2}
                      when Set1 :: set(Element), 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. ⚠️

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]

to_list/1

to_list(Set) -> List when Set :: set(Element), List :: [Element].

Returns the elements of Set as an ordered list. 📝

Examples:

1> gb_sets:to_list(gb_sets:from_list([4,3,5,1,2])).
[1,2,3,4,5]

union/1

union(SetList) -> Set
                when SetList :: [set(Element)], Set :: set(Element).

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]

union/2

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]

And that's the whole vibe, bestie! This page was brought to you by Ericsson AB, stdlib 8.0.4, and gb_sets(3) — no date on the page, but it's serving pure OTP energy. Stay iconic, and may your sets always be balanced. 💅✨🦋

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