1gb_trees(3) Erlang Module Definition gb_trees(3)
2
6 gb_trees - General balanced trees.
7
9 This module provides Prof. Arne Andersson's General Balanced Trees.
10 These have no storage overhead compared to unbalanced binary trees, and
11 their performance is better than AVL trees.
12 This module considers two keys as different if and only if they do not
14 compare equal (==).
15
17 {Size, Tree}
18 Tree is composed of nodes of the form {Key, Value, Smaller, Bigger} and
20 the "empty tree" node nil.
21 There is no attempt to balance trees after deletions. As deletions do
23 not increase the height of a tree, this should be OK.
24 The original balance condition h(T) <= ceil(c * log(|T|)) has been
26 changed to the similar (but not quite equivalent) condition 2 ^ h(T) <=
27 |T| ^ c. This should also be OK.
28
30 tree(Key, Value)
31 A general balanced tree.
33 tree() = tree(term(), term())
35 iter(Key, Value)
37 A general balanced tree iterator.
39 iter() = iter(term(), term())
41
43 balance(Tree1) -> Tree2
44 Types:
46 Tree1 = Tree2 = tree(Key, Value)
48 Rebalances Tree1. Notice that this is rarely necessary, but can
50 be motivated when many nodes have been deleted from the tree
51 without further insertions. Rebalancing can then be forced to
52 minimize lookup times, as deletion does not rebalance the tree.
53 delete(Key, Tree1) -> Tree2
55 Types:
57 Tree1 = Tree2 = tree(Key, Value)
59 Removes the node with key Key from Tree1 and returns the new
61 tree. Assumes that the key is present in the tree, crashes oth‐
62 erwise.
63 delete_any(Key, Tree1) -> Tree2
65 Types:
67 Tree1 = Tree2 = tree(Key, Value)
69 Removes the node with key Key from Tree1 if the key is present
71 in the tree, otherwise does nothing. Returns the new tree.
72 take(Key, Tree1) -> {Value, Tree2}
74 Types:
76 Tree1 = Tree2 = tree(Key, term())
78 Key = Value = term()
79 Returns a value Value from node with key Key and new Tree2 with‐
81 out the node with this value. Assumes that the node with key is
82 present in the tree, crashes otherwise.
83 take_any(Key, Tree1) -> {Value, Tree2} | error
85 Types:
87 Tree1 = Tree2 = tree(Key, term())
89 Key = Value = term()
90 Returns a value Value from node with key Key and new Tree2 with‐
92 out the node with this value. Returns error if the node with the
93 key is not present in the tree.
94 empty() -> tree()
96 Returns a new empty tree.
98 enter(Key, Value, Tree1) -> Tree2
100 Types:
102 Tree1 = Tree2 = tree(Key, Value)
104 Inserts Key with value Value into Tree1 if the key is not
106 present in the tree, otherwise updates Key to value Value in
107 Tree1. Returns the new tree.
108 from_orddict(List) -> Tree
110 Types:
112 List = [{Key, Value}]
114 Tree = tree(Key, Value)
115 Turns an ordered list List of key-value tuples into a tree. The
117 list must not contain duplicate keys.
118 get(Key, Tree) -> Value
120 Types:
122 Tree = tree(Key, Value)
124 Retrieves the value stored with Key in Tree. Assumes that the
126 key is present in the tree, crashes otherwise.
127 insert(Key, Value, Tree1) -> Tree2
129 Types:
131 Tree1 = Tree2 = tree(Key, Value)
133 Inserts Key with value Value into Tree1 and returns the new
135 tree. Assumes that the key is not present in the tree, crashes
136 otherwise.
137 is_defined(Key, Tree) -> boolean()
139 Types:
141 Tree = tree(Key, Value :: term())
143 Returns true if Key is present in Tree, otherwise false.
145 is_empty(Tree) -> boolean()
147 Types:
149 Tree = tree()
151 Returns true if Tree is an empty tree, othwewise false.
153 iterator(Tree) -> Iter
155 Types:
157 Tree = tree(Key, Value)
159 Iter = iter(Key, Value)
160 Returns an iterator that can be used for traversing the entries
162 of Tree; see next/1. The implementation of this is very effi‐
163 cient; traversing the whole tree using next/1 is only slightly
164 slower than getting the list of all elements using to_list/1 and
165 traversing that. The main advantage of the iterator approach is
166 that it does not require the complete list of all elements to be
167 built in memory at one time.
168 iterator_from(Key, Tree) -> Iter
170 Types:
172 Tree = tree(Key, Value)
174 Iter = iter(Key, Value)
175 Returns an iterator that can be used for traversing the entries
177 of Tree; see next/1. The difference as compared to the iterator
178 returned by iterator/1 is that the first key greater than or
179 equal to Key is returned.
180 keys(Tree) -> [Key]
182 Types:
184 Tree = tree(Key, Value :: term())
186 Returns the keys in Tree as an ordered list.
188 largest(Tree) -> {Key, Value}
190 Types:
192 Tree = tree(Key, Value)
194 Returns {Key, Value}, where Key is the largest key in Tree, and
196 Value is the value associated with this key. Assumes that the
197 tree is not empty.
198 lookup(Key, Tree) -> none | {value, Value}
200 Types:
202 Tree = tree(Key, Value)
204 Looks up Key in Tree. Returns {value, Value}, or none if Key is
206 not present.
207 map(Function, Tree1) -> Tree2
209 Types:
211 Function = fun((K :: Key, V1 :: Value1) -> V2 :: Value2)
213 Tree1 = tree(Key, Value1)
214 Tree2 = tree(Key, Value2)
215 Maps function F(K, V1) -> V2 to all key-value pairs of tree
217 Tree1. Returns a new tree Tree2 with the same set of keys as
218 Tree1 and the new set of values V2.
219 next(Iter1) -> none | {Key, Value, Iter2}
221 Types:
223 Iter1 = Iter2 = iter(Key, Value)
225 Returns {Key, Value, Iter2}, where Key is the smallest key
227 referred to by iterator Iter1, and Iter2 is the new iterator to
228 be used for traversing the remaining nodes, or the atom none if
229 no nodes remain.
230 size(Tree) -> integer() >= 0
232 Types:
234 Tree = tree()
236 Returns the number of nodes in Tree.
238 smallest(Tree) -> {Key, Value}
240 Types:
242 Tree = tree(Key, Value)
244 Returns {Key, Value}, where Key is the smallest key in Tree, and
246 Value is the value associated with this key. Assumes that the
247 tree is not empty.
248 take_largest(Tree1) -> {Key, Value, Tree2}
250 Types:
252 Tree1 = Tree2 = tree(Key, Value)
254 Returns {Key, Value, Tree2}, where Key is the largest key in
256 Tree1, Value is the value associated with this key, and Tree2 is
257 this tree with the corresponding node deleted. Assumes that the
258 tree is not empty.
259 take_smallest(Tree1) -> {Key, Value, Tree2}
261 Types:
263 Tree1 = Tree2 = tree(Key, Value)
265 Returns {Key, Value, Tree2}, where Key is the smallest key in
267 Tree1, Value is the value associated with this key, and Tree2 is
268 this tree with the corresponding node deleted. Assumes that the
269 tree is not empty.
270 to_list(Tree) -> [{Key, Value}]
272 Types:
274 Tree = tree(Key, Value)
276 Converts a tree into an ordered list of key-value tuples.
278 update(Key, Value, Tree1) -> Tree2
280 Types:
282 Tree1 = Tree2 = tree(Key, Value)
284 Updates Key to value Value in Tree1 and returns the new tree.
286 Assumes that the key is present in the tree.
287 values(Tree) -> [Value]
289 Types:
291 Tree = tree(Key :: term(), Value)
293 Returns the values in Tree as an ordered list, sorted by their
295 corresponding keys. Duplicates are not removed.
296
298 dict(3), gb_sets(3)
299Ericsson AB stdlib 3.8.2.1 gb_trees(3)