<?xml version="1.0" encoding="latin1" ?> <!DOCTYPE erlref SYSTEM "erlref.dtd"> <erlref> <header> <copyright> <year>2001</year><year>2010</year> <holder>Ericsson AB. All Rights Reserved.</holder> </copyright> <legalnotice> The contents of this file are subject to the Erlang Public License, Version 1.1, (the "License"); you may not use this file except in compliance with the License. You should have received a copy of the Erlang Public License along with this software. If not, it can be retrieved online at http://www.erlang.org/. Software distributed under the License is distributed on an "AS IS" basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License for the specific language governing rights and limitations under the License. </legalnotice> <title>gb_trees</title> <prepared></prepared> <docno></docno> <date></date> <rev></rev> </header> <module>gb_trees</module> <modulesummary>General Balanced Trees</modulesummary> <description> <p>An efficient implementation of Prof. Arne Andersson's General Balanced Trees. These have no storage overhead compared to unbalanced binary trees, and their performance is in general better than AVL trees.</p> <p>This module considers two keys as different if and only if they do not compare equal (<c>==</c>).</p> </description> <section> <title>Data structure</title> <p>Data structure:</p> <code type="none"> - {Size, Tree}, where `Tree' is composed of nodes of the form: - {Key, Value, Smaller, Bigger}, and the "empty tree" node: - nil.</code> <p>There is no attempt to balance trees after deletions. Since deletions do not increase the height of a tree, this should be OK.</p> <p>Original balance condition <em>h(T) <= ceil(c * log(|T|))</em> has been changed to the similar (but not quite equivalent) condition <em>2 ^ h(T) <= |T| ^ c</em>. This should also be OK.</p> <p>Performance is comparable to the AVL trees in the Erlang book (and faster in general due to less overhead); the difference is that deletion works for these trees, but not for the book's trees. Behaviour is logarithmic (as it should be).</p> </section> <section> <title>DATA TYPES</title> <code type="none"> gb_tree() = a GB tree</code> </section> <funcs> <func> <name>balance(Tree1) -> Tree2</name> <fsummary>Rebalance a tree</fsummary> <type> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Rebalances <c>Tree1</c>. Note that this is rarely necessary, but may be motivated when a large number of nodes have been deleted from the tree without further insertions. Rebalancing could then be forced in order to minimise lookup times, since deletion only does not rebalance the tree.</p> </desc> </func> <func> <name>delete(Key, Tree1) -> Tree2</name> <fsummary>Remove a node from a tree</fsummary> <type> <v>Key = term()</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Removes the node with key <c>Key</c> from <c>Tree1</c>; returns new tree. Assumes that the key is present in the tree, crashes otherwise.</p> </desc> </func> <func> <name>delete_any(Key, Tree1) -> Tree2</name> <fsummary>Remove a (possibly non-existing) node from a tree</fsummary> <type> <v>Key = term()</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Removes the node with key <c>Key</c> from <c>Tree1</c> if the key is present in the tree, otherwise does nothing; returns new tree.</p> </desc> </func> <func> <name>empty() -> Tree</name> <fsummary>Return an empty tree</fsummary> <type> <v>Tree = gb_tree()</v> </type> <desc> <p>Returns a new empty tree</p> </desc> </func> <func> <name>enter(Key, Val, Tree1) -> Tree2</name> <fsummary>Insert or update key with value in a tree</fsummary> <type> <v>Key = Val = term()</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Inserts <c>Key</c> with value <c>Val</c> into <c>Tree1</c> if the key is not present in the tree, otherwise updates <c>Key</c> to value <c>Val</c> in <c>Tree1</c>. Returns the new tree.</p> </desc> </func> <func> <name>from_orddict(List) -> Tree</name> <fsummary>Make a tree from an orddict</fsummary> <type> <v>List = [{Key, Val}]</v> <v> Key = Val = term()</v> <v>Tree = gb_tree()</v> </type> <desc> <p>Turns an ordered list <c>List</c> of key-value tuples into a tree. The list must not contain duplicate keys.</p> </desc> </func> <func> <name>get(Key, Tree) -> Val</name> <fsummary>Look up a key in a tree, if present</fsummary> <type> <v>Key = Val = term()</v> <v>Tree = gb_tree()</v> </type> <desc> <p>Retrieves the value stored with <c>Key</c> in <c>Tree</c>. Assumes that the key is present in the tree, crashes otherwise.</p> </desc> </func> <func> <name>lookup(Key, Tree) -> {value, Val} | none</name> <fsummary>Look up a key in a tree</fsummary> <type> <v>Key = Val = term()</v> <v>Tree = gb_tree()</v> </type> <desc> <p>Looks up <c>Key</c> in <c>Tree</c>; returns <c>{value, Val}</c>, or <c>none</c> if <c>Key</c> is not present.</p> </desc> </func> <func> <name>insert(Key, Val, Tree1) -> Tree2</name> <fsummary>Insert a new key and value in a tree</fsummary> <type> <v>Key = Val = term()</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Inserts <c>Key</c> with value <c>Val</c> into <c>Tree1</c>; returns the new tree. Assumes that the key is not present in the tree, crashes otherwise.</p> </desc> </func> <func> <name>is_defined(Key, Tree) -> bool()</name> <fsummary>Test for membership of a tree</fsummary> <type> <v>Tree = gb_tree()</v> </type> <desc> <p>Returns <c>true</c> if <c>Key</c> is present in <c>Tree</c>, otherwise <c>false</c>.</p> </desc> </func> <func> <name>is_empty(Tree) -> bool()</name> <fsummary>Test for empty tree</fsummary> <type> <v>Tree = gb_tree()</v> </type> <desc> <p>Returns <c>true</c> if <c>Tree</c> is an empty tree, and <c>false</c> otherwise.</p> </desc> </func> <func> <name>iterator(Tree) -> Iter</name> <fsummary>Return an iterator for a tree</fsummary> <type> <v>Tree = gb_tree()</v> <v>Iter = term()</v> </type> <desc> <p>Returns an iterator that can be used for traversing the entries of <c>Tree</c>; see <c>next/1</c>. The implementation of this is very efficient; traversing the whole tree using <c>next/1</c> is only slightly slower than getting the list of all elements using <c>to_list/1</c> and traversing that. The main advantage of the iterator approach is that it does not require the complete list of all elements to be built in memory at one time.</p> </desc> </func> <func> <name>keys(Tree) -> [Key]</name> <fsummary>Return a list of the keys in a tree</fsummary> <type> <v>Tree = gb_tree()</v> <v>Key = term()</v> </type> <desc> <p>Returns the keys in <c>Tree</c> as an ordered list.</p> </desc> </func> <func> <name>largest(Tree) -> {Key, Val}</name> <fsummary>Return largest key and value</fsummary> <type> <v>Tree = gb_tree()</v> <v>Key = Val = term()</v> </type> <desc> <p>Returns <c>{Key, Val}</c>, where <c>Key</c> is the largest key in <c>Tree</c>, and <c>Val</c> is the value associated with this key. Assumes that the tree is nonempty.</p> </desc> </func> <func> <name>map(Function, Tree1) -> Tree2</name> <fsummary>Return largest key and value</fsummary> <type> <v>Function = fun(K, V1) -> V2</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc><p>maps the function F(K, V1) -> V2 to all key-value pairs of the tree Tree1 and returns a new tree Tree2 with the same set of keys as Tree1 and the new set of values V2.</p> </desc> </func> <func> <name>next(Iter1) -> {Key, Val, Iter2} | none</name> <fsummary>Traverse a tree with an iterator</fsummary> <type> <v>Iter1 = Iter2 = Key = Val = term()</v> </type> <desc> <p>Returns <c>{Key, Val, Iter2}</c> where <c>Key</c> is the smallest key referred to by the iterator <c>Iter1</c>, and <c>Iter2</c> is the new iterator to be used for traversing the remaining nodes, or the atom <c>none</c> if no nodes remain.</p> </desc> </func> <func> <name>size(Tree) -> int()</name> <fsummary>Return the number of nodes in a tree</fsummary> <type> <v>Tree = gb_tree()</v> </type> <desc> <p>Returns the number of nodes in <c>Tree</c>.</p> </desc> </func> <func> <name>smallest(Tree) -> {Key, Val}</name> <fsummary>Return smallest key and value</fsummary> <type> <v>Tree = gb_tree()</v> <v>Key = Val = term()</v> </type> <desc> <p>Returns <c>{Key, Val}</c>, where <c>Key</c> is the smallest key in <c>Tree</c>, and <c>Val</c> is the value associated with this key. Assumes that the tree is nonempty.</p> </desc> </func> <func> <name>take_largest(Tree1) -> {Key, Val, Tree2}</name> <fsummary>Extract largest key and value</fsummary> <type> <v>Tree1 = Tree2 = gb_tree()</v> <v>Key = Val = term()</v> </type> <desc> <p>Returns <c>{Key, Val, Tree2}</c>, where <c>Key</c> is the largest key in <c>Tree1</c>, <c>Val</c> is the value associated with this key, and <c>Tree2</c> is this tree with the corresponding node deleted. Assumes that the tree is nonempty.</p> </desc> </func> <func> <name>take_smallest(Tree1) -> {Key, Val, Tree2}</name> <fsummary>Extract smallest key and value</fsummary> <type> <v>Tree1 = Tree2 = gb_tree()</v> <v>Key = Val = term()</v> </type> <desc> <p>Returns <c>{Key, Val, Tree2}</c>, where <c>Key</c> is the smallest key in <c>Tree1</c>, <c>Val</c> is the value associated with this key, and <c>Tree2</c> is this tree with the corresponding node deleted. Assumes that the tree is nonempty.</p> </desc> </func> <func> <name>to_list(Tree) -> [{Key, Val}]</name> <fsummary>Convert a tree into a list</fsummary> <type> <v>Tree = gb_tree()</v> <v>Key = Val = term()</v> </type> <desc> <p>Converts a tree into an ordered list of key-value tuples.</p> </desc> </func> <func> <name>update(Key, Val, Tree1) -> Tree2</name> <fsummary>Update a key to new value in a tree</fsummary> <type> <v>Key = Val = term()</v> <v>Tree1 = Tree2 = gb_tree()</v> </type> <desc> <p>Updates <c>Key</c> to value <c>Val</c> in <c>Tree1</c>; returns the new tree. Assumes that the key is present in the tree.</p> </desc> </func> <func> <name>values(Tree) -> [Val]</name> <fsummary>Return a list of the values in a tree</fsummary> <type> <v>Tree = gb_tree()</v> <v>Val = term()</v> </type> <desc> <p>Returns the values in <c>Tree</c> as an ordered list, sorted by their corresponding keys. Duplicates are not removed.</p> </desc> </func> </funcs> <section> <title>SEE ALSO</title> <p><seealso marker="gb_sets">gb_sets(3)</seealso>, <seealso marker="dict">dict(3)</seealso></p> </section> </erlref>