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diff --git a/lib/stdlib/doc/src/gb_sets.xml b/lib/stdlib/doc/src/gb_sets.xml new file mode 100644 index 0000000000..accec623b9 --- /dev/null +++ b/lib/stdlib/doc/src/gb_sets.xml @@ -0,0 +1,487 @@ +<?xml version="1.0" encoding="latin1" ?> +<!DOCTYPE erlref SYSTEM "erlref.dtd"> + +<erlref> + <header> + <copyright> + <year>2001</year><year>2009</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_sets</title> + <prepared></prepared> + <docno></docno> + <date></date> + <rev></rev> + </header> + <module>gb_sets</module> + <modulesummary>General Balanced Trees</modulesummary> + <description> + <p>An implementation of ordered sets using Prof. Arne Andersson's + General Balanced Trees. This can be much more efficient than + using ordered lists, for larger sets, but depends on the + application.</p> + </description> + + <section> + <title>Complexity note</title> + <p>The complexity on set operations is bounded by either O(|S|) or + O(|T| * log(|S|)), where S is the largest given set, depending + on which is fastest for any particular function call. 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, however, this solution can be + arbitrarily much faster; in practical cases, often between 10 + and 100 times. This implementation is particularly suited for + accumulating elements a few at a time, building up a large set + (more than 100-200 elements), and repeatedly testing for + membership in the current set.</p> + <p>As with normal tree structures, lookup (membership testing), + insertion and deletion have logarithmic complexity.</p> + </section> + + <section> + <title>Compatibility</title> + <p>All of the following functions in this module also exist + and do the same thing in the <c>sets</c> and <c>ordsets</c> + modules. That is, by only changing the module name for each call, + you can try out different set representations.</p> + <p></p> + <list type="bulleted"> + <item> + <p><c>add_element/2</c></p> + </item> + <item> + <p><c>del_element/2</c></p> + </item> + <item> + <p><c>filter/2</c></p> + </item> + <item> + <p><c>fold/3</c></p> + </item> + <item> + <p><c>from_list/1</c></p> + </item> + <item> + <p><c>intersection/1</c></p> + </item> + <item> + <p><c>intersection/2</c></p> + </item> + <item> + <p><c>is_element/2</c></p> + </item> + <item> + <p><c>is_set/1</c></p> + </item> + <item> + <p><c>is_subset/2</c></p> + </item> + <item> + <p><c>new/0</c></p> + </item> + <item> + <p><c>size/1</c></p> + </item> + <item> + <p><c>subtract/2</c></p> + </item> + <item> + <p><c>to_list/1</c></p> + </item> + <item> + <p><c>union/1</c></p> + </item> + <item> + <p><c>union/2</c></p> + </item> + </list> + </section> + + <section> + <title>DATA TYPES</title> + <code type="none"> +gb_set() = a GB set</code> + </section> + <funcs> + <func> + <name>add(Element, Set1) -> Set2</name> + <name>add_element(Element, Set1) -> Set2</name> + <fsummary>Add a (possibly existing) element to a gb_set</fsummary> + <type> + <v>Element = term()</v> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns a new gb_set formed from <c>Set1</c> with + <c>Element</c> inserted. If <c>Element</c> is already an + element in <c>Set1</c>, nothing is changed.</p> + </desc> + </func> + <func> + <name>balance(Set1) -> Set2</name> + <fsummary>Rebalance tree representation of a gb_set</fsummary> + <type> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Rebalances the tree representation of <c>Set1</c>. Note that + this is rarely necessary, but may be motivated when a large + number of elements 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(Element, Set1) -> Set2</name> + <fsummary>Remove an element from a gb_set</fsummary> + <type> + <v>Element = term()</v> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns a new gb_set formed from <c>Set1</c> with + <c>Element</c> removed. Assumes that <c>Element</c> is present + in <c>Set1</c>.</p> + </desc> + </func> + <func> + <name>delete_any(Element, Set1) -> Set2</name> + <name>del_element(Element, Set1) -> Set2</name> + <fsummary>Remove a (possibly non-existing) element from a gb_set</fsummary> + <type> + <v>Element = term()</v> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns a new gb_set formed from <c>Set1</c> with + <c>Element</c> removed. If <c>Element</c> is not an element + in <c>Set1</c>, nothing is changed.</p> + </desc> + </func> + <func> + <name>difference(Set1, Set2) -> Set3</name> + <name>subtract(Set1, Set2) -> Set3</name> + <fsummary>Return the difference of two gb_sets</fsummary> + <type> + <v>Set1 = Set2 = Set3 = gb_set()</v> + </type> + <desc> + <p>Returns only the elements of <c>Set1</c> which are not also + elements of <c>Set2</c>.</p> + </desc> + </func> + <func> + <name>empty() -> Set</name> + <name>new() -> Set</name> + <fsummary>Return an empty gb_set</fsummary> + <type> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns a new empty gb_set.</p> + </desc> + </func> + <func> + <name>filter(Pred, Set1) -> Set2</name> + <fsummary>Filter gb_set elements</fsummary> + <type> + <v>Pred = fun (E) -> bool()</v> + <v> E = term()</v> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Filters elements in <c>Set1</c> using predicate function + <c>Pred</c>.</p> + </desc> + </func> + <func> + <name>fold(Function, Acc0, Set) -> Acc1</name> + <fsummary>Fold over gb_set elements</fsummary> + <type> + <v>Function = fun (E, AccIn) -> AccOut</v> + <v>Acc0 = Acc1 = AccIn = AccOut = term()</v> + <v> E = term()</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Folds <c>Function</c> over every element in <c>Set</c> + returning the final value of the accumulator.</p> + </desc> + </func> + <func> + <name>from_list(List) -> Set</name> + <fsummary>Convert a list into a gb_set</fsummary> + <type> + <v>List = [term()]</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns a gb_set of the elements in <c>List</c>, where + <c>List</c> may be unordered and contain duplicates.</p> + </desc> + </func> + <func> + <name>from_ordset(List) -> Set</name> + <fsummary>Make a gb_set from an ordset list</fsummary> + <type> + <v>List = [term()]</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Turns an ordered-set list <c>List</c> into a gb_set. The list + must not contain duplicates.</p> + </desc> + </func> + <func> + <name>insert(Element, Set1) -> Set2</name> + <fsummary>Add a new element to a gb_set</fsummary> + <type> + <v>Element = term()</v> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns a new gb_set formed from <c>Set1</c> with + <c>Element</c> inserted. Assumes that <c>Element</c> is not + present in <c>Set1</c>.</p> + </desc> + </func> + <func> + <name>intersection(Set1, Set2) -> Set3</name> + <fsummary>Return the intersection of two gb_sets</fsummary> + <type> + <v>Set1 = Set2 = Set3 = gb_set()</v> + </type> + <desc> + <p>Returns the intersection of <c>Set1</c> and <c>Set2</c>.</p> + </desc> + </func> + <func> + <name>intersection(SetList) -> Set</name> + <fsummary>Return the intersection of a list of gb_sets</fsummary> + <type> + <v>SetList = [gb_set()]</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns the intersection of the non-empty list of gb_sets.</p> + </desc> + </func> + <func> + <name>is_disjoint(Set1, Set2) -> bool()</name> + <fsummary>Check whether two gb_sets are disjoint</fsummary> + <type> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns <c>true</c> if <c>Set1</c> and + <c>Set2</c> are disjoint (have no elements in common), + and <c>false</c> otherwise.</p> + </desc> + </func> + <func> + <name>is_empty(Set) -> bool()</name> + <fsummary>Test for empty gb_set</fsummary> + <type> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns <c>true</c> if <c>Set</c> is an empty set, and + <c>false</c> otherwise.</p> + </desc> + </func> + <func> + <name>is_member(Element, Set) -> bool()</name> + <name>is_element(Element, Set) -> bool()</name> + <fsummary>Test for membership of a gb_set</fsummary> + <type> + <v>Element = term()</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns <c>true</c> if <c>Element</c> is an element of + <c>Set</c>, otherwise <c>false</c>.</p> + </desc> + </func> + <func> + <name>is_set(Term) -> bool()</name> + <fsummary>Test for a gb_set</fsummary> + <type> + <v>Term = term()</v> + </type> + <desc> + <p>Returns <c>true</c> if <c>Set</c> appears to be a gb_set, + otherwise <c>false</c>.</p> + </desc> + </func> + <func> + <name>is_subset(Set1, Set2) -> bool()</name> + <fsummary>Test for subset</fsummary> + <type> + <v>Set1 = Set2 = gb_set()</v> + </type> + <desc> + <p>Returns <c>true</c> when every element of <c>Set1</c> is + also a member of <c>Set2</c>, otherwise <c>false</c>.</p> + </desc> + </func> + <func> + <name>iterator(Set) -> Iter</name> + <fsummary>Return an iterator for a gb_set</fsummary> + <type> + <v>Set = gb_set()</v> + <v>Iter = term()</v> + </type> + <desc> + <p>Returns an iterator that can be used for traversing the + entries of <c>Set</c>; see <c>next/1</c>. The implementation + of this is very efficient; traversing the whole set 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>largest(Set) -> term()</name> + <fsummary>Return largest element</fsummary> + <type> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns the largest element in <c>Set</c>. Assumes that + <c>Set</c> is nonempty.</p> + </desc> + </func> + <func> + <name>next(Iter1) -> {Element, Iter2} | none</name> + <fsummary>Traverse a gb_set with an iterator</fsummary> + <type> + <v>Iter1 = Iter2 = Element = term()</v> + </type> + <desc> + <p>Returns <c>{Element, Iter2}</c> where <c>Element</c> is the + smallest element referred to by the iterator <c>Iter1</c>, + and <c>Iter2</c> is the new iterator to be used for + traversing the remaining elements, or the atom <c>none</c> if + no elements remain.</p> + </desc> + </func> + <func> + <name>singleton(Element) -> gb_set()</name> + <fsummary>Return a gb_set with one element</fsummary> + <type> + <v>Element = term()</v> + </type> + <desc> + <p>Returns a gb_set containing only the element <c>Element</c>.</p> + </desc> + </func> + <func> + <name>size(Set) -> int()</name> + <fsummary>Return the number of elements in a gb_set</fsummary> + <type> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns the number of elements in <c>Set</c>.</p> + </desc> + </func> + <func> + <name>smallest(Set) -> term()</name> + <fsummary>Return smallest element</fsummary> + <type> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns the smallest element in <c>Set</c>. Assumes that + <c>Set</c> is nonempty.</p> + </desc> + </func> + <func> + <name>take_largest(Set1) -> {Element, Set2}</name> + <fsummary>Extract largest element</fsummary> + <type> + <v>Set1 = Set2 = gb_set()</v> + <v>Element = term()</v> + </type> + <desc> + <p>Returns <c>{Element, Set2}</c>, where <c>Element</c> is the + largest element in <c>Set1</c>, and <c>Set2</c> is this set + with <c>Element</c> deleted. Assumes that <c>Set1</c> is + nonempty.</p> + </desc> + </func> + <func> + <name>take_smallest(Set1) -> {Element, Set2}</name> + <fsummary>Extract smallest element</fsummary> + <type> + <v>Set1 = Set2 = gb_set()</v> + <v>Element = term()</v> + </type> + <desc> + <p>Returns <c>{Element, Set2}</c>, where <c>Element</c> is the + smallest element in <c>Set1</c>, and <c>Set2</c> is this set + with <c>Element</c> deleted. Assumes that <c>Set1</c> is + nonempty.</p> + </desc> + </func> + <func> + <name>to_list(Set) -> List</name> + <fsummary>Convert a gb_set into a list</fsummary> + <type> + <v>Set = gb_set()</v> + <v>List = [term()]</v> + </type> + <desc> + <p>Returns the elements of <c>Set</c> as a list.</p> + </desc> + </func> + <func> + <name>union(Set1, Set2) -> Set3</name> + <fsummary>Return the union of two gb_sets</fsummary> + <type> + <v>Set1 = Set2 = Set3 = gb_set()</v> + </type> + <desc> + <p>Returns the merged (union) gb_set of <c>Set1</c> and + <c>Set2</c>.</p> + </desc> + </func> + <func> + <name>union(SetList) -> Set</name> + <fsummary>Return the union of a list of gb_sets</fsummary> + <type> + <v>SetList = [gb_set()]</v> + <v>Set = gb_set()</v> + </type> + <desc> + <p>Returns the merged (union) gb_set of the list of gb_sets.</p> + </desc> + </func> + </funcs> + + <section> + <title>SEE ALSO</title> + <p><seealso marker="gb_trees">gb_trees(3)</seealso>, + <seealso marker="ordsets">ordsets(3)</seealso>, + <seealso marker="sets">sets(3)</seealso></p> + </section> +</erlref> + |