1gb_sets(3) Erlang Module Definition gb_sets(3)
2
6 gb_sets - Sets represented by general balanced trees.
7
9 This module provides ordered sets using Prof. Arne Andersson's General
10 Balanced Trees. Ordered sets can be much more efficient than using or‐
11 dered lists, for larger sets, but depends on the application.
12 The data representing a set as used by this module is to be regarded as
14 opaque by other modules. In abstract terms, the representation is a
15 composite type of existing Erlang terms. See note on data types. Any
16 code assuming knowledge of the format is running on thin ice.
17 This module considers two elements as different if and only if they do
19 not compare equal (==).
20
22 The complexity on set operations is bounded by either O(|S|) or O(|T| *
23 log(|S|)), where S is the largest given set, depending on which is
24 fastest for any particular function call. For operating on sets of al‐
25 most equal size, this implementation is about 3 times slower than using
26 ordered-list sets directly. For sets of very different sizes, however,
27 this solution can be arbitrarily much faster; in practical cases, often
28 10-100 times. This implementation is particularly suited for accumulat‐
29 ing elements a few at a time, building up a large set (> 100-200 ele‐
30 ments), and repeatedly testing for membership in the current set.
31 As with normal tree structures, lookup (membership testing), insertion,
33 and deletion have logarithmic complexity.
34
36 See the Compatibility Section in the sets(3) module for information
37 about the compatibility of the different implementations of sets in the
38 Standard Library.
39
41 set(Element)
42 A general balanced set.
44 set() = set(term())
46 iter(Element)
48 A general balanced set iterator.
50 iter() = iter(term())
52
54 add(Element, Set1) -> Set2
55 add_element(Element, Set1) -> Set2
57 Types:
59 Set1 = Set2 = set(Element)
61 Returns a new set formed from Set1 with Element inserted. If El‐
63 ement is already an element in Set1, nothing is changed.
64 balance(Set1) -> Set2
66 Types:
68 Set1 = Set2 = set(Element)
70 Rebalances the tree representation of Set1. Notice that this is
72 rarely necessary, but can be motivated when a large number of
73 elements have been deleted from the tree without further inser‐
74 tions. Rebalancing can then be forced to minimise lookup times,
75 as deletion does not rebalance the tree.
76 del_element(Element, Set1) -> Set2
78 Types:
80 Set1 = Set2 = set(Element)
82 Returns a new set formed from Set1 with Element removed. If Ele‐
84 ment is not an element in Set1, nothing is changed.
85 delete(Element, Set1) -> Set2
87 Types:
89 Set1 = Set2 = set(Element)
91 Returns a new set formed from Set1 with Element removed. Assumes
93 that Element is present in Set1.
94 delete_any(Element, Set1) -> Set2
96 Types:
98 Set1 = Set2 = set(Element)
100 Returns a new set formed from Set1 with Element removed. If Ele‐
102 ment is not an element in Set1, nothing is changed.
103 difference(Set1, Set2) -> Set3
105 Types:
107 Set1 = Set2 = Set3 = set(Element)
109 Returns only the elements of Set1 that are not also elements of
111 Set2.
112 empty() -> Set
114 Types:
116 Set = set(none())
118 Returns a new empty set.
120 filter(Pred, Set1) -> Set2
122 Types:
124 Pred = fun((Element) -> boolean())
126 Set1 = Set2 = set(Element)
127 Filters elements in Set1 using predicate function Pred.
129 fold(Function, Acc0, Set) -> Acc1
131 Types:
133 Function = fun((Element, AccIn) -> AccOut)
135 Acc0 = Acc1 = AccIn = AccOut = Acc
136 Set = set(Element)
137 Folds Function over every element in Set returning the final
139 value of the accumulator.
140 from_list(List) -> Set
142 Types:
144 List = [Element]
146 Set = set(Element)
147 Returns a set of the elements in List, where List can be un‐
149 ordered and contain duplicates.
150 from_ordset(List) -> Set
152 Types:
154 List = [Element]
156 Set = set(Element)
157 Turns an ordered-set list List into a set. The list must not
159 contain duplicates.
160 insert(Element, Set1) -> Set2
162 Types:
164 Set1 = Set2 = set(Element)
166 Returns a new set formed from Set1 with Element inserted. As‐
168 sumes that Element is not present in Set1.
169 intersection(SetList) -> Set
171 Types:
173 SetList = [set(Element), ...]
175 Set = set(Element)
176 Returns the intersection of the non-empty list of sets.
178 intersection(Set1, Set2) -> Set3
180 Types:
182 Set1 = Set2 = Set3 = set(Element)
184 Returns the intersection of Set1 and Set2.
186 is_disjoint(Set1, Set2) -> boolean()
188 Types:
190 Set1 = Set2 = set(Element)
192 Returns true if Set1 and Set2 are disjoint (have no elements in
194 common), otherwise false.
195 is_element(Element, Set) -> boolean()
197 Types:
199 Set = set(Element)
201 Returns true if Element is an element of Set, otherwise false.
203 is_empty(Set) -> boolean()
205 Types:
207 Set = set()
209 Returns true if Set is an empty set, otherwise false.
211 is_member(Element, Set) -> boolean()
213 Types:
215 Set = set(Element)
217 Returns true if Element is an element of Set, otherwise false.
219 is_set(Term) -> boolean()
221 Types:
223 Term = term()
225 Returns true if Term appears to be a set, otherwise false. This
227 function will return true for any term that coincides with the
228 representation of a gb_set, while not really being a gb_set,
229 thus it might return false positive results. See also note on
230 data types.
231 is_subset(Set1, Set2) -> boolean()
233 Types:
235 Set1 = Set2 = set(Element)
237 Returns true when every element of Set1 is also a member of
239 Set2, otherwise false.
240 iterator(Set) -> Iter
242 Types:
244 Set = set(Element)
246 Iter = iter(Element)
247 Returns an iterator that can be used for traversing the entries
249 of Set; see next/1. The implementation of this is very effi‐
250 cient; traversing the whole set using next/1 is only slightly
251 slower than getting the list of all elements using to_list/1 and
252 traversing that. The main advantage of the iterator approach is
253 that it does not require the complete list of all elements to be
254 built in memory at one time.
255 iterator_from(Element, Set) -> Iter
257 Types:
259 Set = set(Element)
261 Iter = iter(Element)
262 Returns an iterator that can be used for traversing the entries
264 of Set; see next/1. The difference as compared to the iterator
265 returned by iterator/1 is that the first element greater than or
266 equal to Element is returned.
267 largest(Set) -> Element
269 Types:
271 Set = set(Element)
273 Returns the largest element in Set. Assumes that Set is not
275 empty.
276 new() -> Set
278 Types:
280 Set = set(none())
282 Returns a new empty set.
284 next(Iter1) -> {Element, Iter2} | none
286 Types:
288 Iter1 = Iter2 = iter(Element)
290 Returns {Element, Iter2}, where Element is the smallest element
292 referred to by iterator Iter1, and Iter2 is the new iterator to
293 be used for traversing the remaining elements, or the atom none
294 if no elements remain.
295 singleton(Element) -> set(Element)
297 Returns a set containing only element Element.
299 size(Set) -> integer() >= 0
301 Types:
303 Set = set()
305 Returns the number of elements in Set.
307 smallest(Set) -> Element
309 Types:
311 Set = set(Element)
313 Returns the smallest element in Set. Assumes that Set is not
315 empty.
316 subtract(Set1, Set2) -> Set3
318 Types:
320 Set1 = Set2 = Set3 = set(Element)
322 Returns only the elements of Set1 that are not also elements of
324 Set2.
325 take_largest(Set1) -> {Element, Set2}
327 Types:
329 Set1 = Set2 = set(Element)
331 Returns {Element, Set2}, where Element is the largest element in
333 Set1, and Set2 is this set with Element deleted. Assumes that
334 Set1 is not empty.
335 take_smallest(Set1) -> {Element, Set2}
337 Types:
339 Set1 = Set2 = set(Element)
341 Returns {Element, Set2}, where Element is the smallest element
343 in Set1, and Set2 is this set with Element deleted. Assumes that
344 Set1 is not empty.
345 to_list(Set) -> List
347 Types:
349 Set = set(Element)
351 List = [Element]
352 Returns the elements of Set as a list.
354 union(SetList) -> Set
356 Types:
358 SetList = [set(Element), ...]
360 Set = set(Element)
361 Returns the merged (union) set of the list of sets.
363 union(Set1, Set2) -> Set3
365 Types:
367 Set1 = Set2 = Set3 = set(Element)
369 Returns the merged (union) set of Set1 and Set2.
371
373 gb_trees(3), ordsets(3), sets(3)
374Ericsson AB stdlib 5.1.1 gb_sets(3)