1gb_sets(3) Erlang Module Definition gb_sets(3)
2
6 gb_sets - 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 This module considers two elements as different if and only if they do
14 not compare equal (==).
15
17 The complexity on set operations is bounded by either O(|S|) or O(|T| *
18 log(|S|)), where S is the largest given set, depending on which is
19 fastest for any particular function call. For operating on sets of al‐
20 most equal size, this implementation is about 3 times slower than using
21 ordered-list sets directly. For sets of very different sizes, however,
22 this solution can be arbitrarily much faster; in practical cases, often
23 10-100 times. This implementation is particularly suited for accumulat‐
24 ing elements a few at a time, building up a large set (> 100-200 ele‐
25 ments), and repeatedly testing for membership in the current set.
26 As with normal tree structures, lookup (membership testing), insertion,
28 and deletion have logarithmic complexity.
29
31 The following functions in this module also exist and provides the same
32 functionality in the sets(3) and ordsets(3) modules. That is, by only
33 changing the module name for each call, you can try out different set
34 representations.
35 * add_element/2
37 * del_element/2
39 * filter/2
41 * fold/3
43 * from_list/1
45 * intersection/1
47 * intersection/2
49 * is_element/2
51 * is_empty/1
53 * is_set/1
55 * is_subset/2
57 * new/0
59 * size/1
61 * subtract/2
63 * to_list/1
65 * union/1
67 * union/2
69
71 set(Element)
72 A general balanced set.
74 set() = set(term())
76 iter(Element)
78 A general balanced set iterator.
80 iter() = iter(term())
82
84 add(Element, Set1) -> Set2
85 add_element(Element, Set1) -> Set2
87 Types:
89 Set1 = Set2 = set(Element)
91 Returns a new set formed from Set1 with Element inserted. If El‐
93 ement is already an element in Set1, nothing is changed.
94 balance(Set1) -> Set2
96 Types:
98 Set1 = Set2 = set(Element)
100 Rebalances the tree representation of Set1. Notice that this is
102 rarely necessary, but can be motivated when a large number of
103 elements have been deleted from the tree without further inser‐
104 tions. Rebalancing can then be forced to minimise lookup times,
105 as deletion does not rebalance the tree.
106 del_element(Element, Set1) -> Set2
108 Types:
110 Set1 = Set2 = set(Element)
112 Returns a new set formed from Set1 with Element removed. If Ele‐
114 ment is not an element in Set1, nothing is changed.
115 delete(Element, Set1) -> Set2
117 Types:
119 Set1 = Set2 = set(Element)
121 Returns a new set formed from Set1 with Element removed. Assumes
123 that Element is present in Set1.
124 delete_any(Element, Set1) -> Set2
126 Types:
128 Set1 = Set2 = set(Element)
130 Returns a new set formed from Set1 with Element removed. If Ele‐
132 ment is not an element in Set1, nothing is changed.
133 difference(Set1, Set2) -> Set3
135 Types:
137 Set1 = Set2 = Set3 = set(Element)
139 Returns only the elements of Set1 that are not also elements of
141 Set2.
142 empty() -> Set
144 Types:
146 Set = set()
148 Returns a new empty set.
150 filter(Pred, Set1) -> Set2
152 Types:
154 Pred = fun((Element) -> boolean())
156 Set1 = Set2 = set(Element)
157 Filters elements in Set1 using predicate function Pred.
159 fold(Function, Acc0, Set) -> Acc1
161 Types:
163 Function = fun((Element, AccIn) -> AccOut)
165 Acc0 = Acc1 = AccIn = AccOut = Acc
166 Set = set(Element)
167 Folds Function over every element in Set returning the final
169 value of the accumulator.
170 from_list(List) -> Set
172 Types:
174 List = [Element]
176 Set = set(Element)
177 Returns a set of the elements in List, where List can be un‐
179 ordered and contain duplicates.
180 from_ordset(List) -> Set
182 Types:
184 List = [Element]
186 Set = set(Element)
187 Turns an ordered-set list List into a set. The list must not
189 contain duplicates.
190 insert(Element, Set1) -> Set2
192 Types:
194 Set1 = Set2 = set(Element)
196 Returns a new set formed from Set1 with Element inserted. As‐
198 sumes that Element is not present in Set1.
199 intersection(SetList) -> Set
201 Types:
203 SetList = [set(Element), ...]
205 Set = set(Element)
206 Returns the intersection of the non-empty list of sets.
208 intersection(Set1, Set2) -> Set3
210 Types:
212 Set1 = Set2 = Set3 = set(Element)
214 Returns the intersection of Set1 and Set2.
216 is_disjoint(Set1, Set2) -> boolean()
218 Types:
220 Set1 = Set2 = set(Element)
222 Returns true if Set1 and Set2 are disjoint (have no elements in
224 common), otherwise false.
225 is_element(Element, Set) -> boolean()
227 Types:
229 Set = set(Element)
231 Returns true if Element is an element of Set, otherwise false.
233 is_empty(Set) -> boolean()
235 Types:
237 Set = set()
239 Returns true if Set is an empty set, otherwise false.
241 is_member(Element, Set) -> boolean()
243 Types:
245 Set = set(Element)
247 Returns true if Element is an element of Set, otherwise false.
249 is_set(Term) -> boolean()
251 Types:
253 Term = term()
255 Returns true if Term appears to be a set, otherwise false.
257 is_subset(Set1, Set2) -> boolean()
259 Types:
261 Set1 = Set2 = set(Element)
263 Returns true when every element of Set1 is also a member of
265 Set2, otherwise false.
266 iterator(Set) -> Iter
268 Types:
270 Set = set(Element)
272 Iter = iter(Element)
273 Returns an iterator that can be used for traversing the entries
275 of Set; see next/1. The implementation of this is very effi‐
276 cient; traversing the whole set using next/1 is only slightly
277 slower than getting the list of all elements using to_list/1 and
278 traversing that. The main advantage of the iterator approach is
279 that it does not require the complete list of all elements to be
280 built in memory at one time.
281 iterator_from(Element, Set) -> Iter
283 Types:
285 Set = set(Element)
287 Iter = iter(Element)
288 Returns an iterator that can be used for traversing the entries
290 of Set; see next/1. The difference as compared to the iterator
291 returned by iterator/1 is that the first element greater than or
292 equal to Element is returned.
293 largest(Set) -> Element
295 Types:
297 Set = set(Element)
299 Returns the largest element in Set. Assumes that Set is not
301 empty.
302 new() -> Set
304 Types:
306 Set = set()
308 Returns a new empty set.
310 next(Iter1) -> {Element, Iter2} | none
312 Types:
314 Iter1 = Iter2 = iter(Element)
316 Returns {Element, Iter2}, where Element is the smallest element
318 referred to by iterator Iter1, and Iter2 is the new iterator to
319 be used for traversing the remaining elements, or the atom none
320 if no elements remain.
321 singleton(Element) -> set(Element)
323 Returns a set containing only element Element.
325 size(Set) -> integer() >= 0
327 Types:
329 Set = set()
331 Returns the number of elements in Set.
333 smallest(Set) -> Element
335 Types:
337 Set = set(Element)
339 Returns the smallest element in Set. Assumes that Set is not
341 empty.
342 subtract(Set1, Set2) -> Set3
344 Types:
346 Set1 = Set2 = Set3 = set(Element)
348 Returns only the elements of Set1 that are not also elements of
350 Set2.
351 take_largest(Set1) -> {Element, Set2}
353 Types:
355 Set1 = Set2 = set(Element)
357 Returns {Element, Set2}, where Element is the largest element in
359 Set1, and Set2 is this set with Element deleted. Assumes that
360 Set1 is not empty.
361 take_smallest(Set1) -> {Element, Set2}
363 Types:
365 Set1 = Set2 = set(Element)
367 Returns {Element, Set2}, where Element is the smallest element
369 in Set1, and Set2 is this set with Element deleted. Assumes that
370 Set1 is not empty.
371 to_list(Set) -> List
373 Types:
375 Set = set(Element)
377 List = [Element]
378 Returns the elements of Set as a list.
380 union(SetList) -> Set
382 Types:
384 SetList = [set(Element), ...]
386 Set = set(Element)
387 Returns the merged (union) set of the list of sets.
389 union(Set1, Set2) -> Set3
391 Types:
393 Set1 = Set2 = Set3 = set(Element)
395 Returns the merged (union) set of Set1 and Set2.
397
399 gb_trees(3), ordsets(3), sets(3)
400Ericsson AB stdlib 3.14.2.1 gb_sets(3)