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diff --git a/lib/stdlib/doc/src/gb_sets.xml b/lib/stdlib/doc/src/gb_sets.xml index f91fac9c82..d677dd6f83 100644 --- a/lib/stdlib/doc/src/gb_sets.xml +++ b/lib/stdlib/doc/src/gb_sets.xml @@ -1,23 +1,24 @@ -<?xml version="1.0" encoding="latin1" ?> +<?xml version="1.0" encoding="utf-8" ?> <!DOCTYPE erlref SYSTEM "erlref.dtd"> <erlref> <header> <copyright> - <year>2001</year><year>2011</year> + <year>2001</year><year>2015</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/. + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 - 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. + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. </legalnotice> @@ -28,361 +29,445 @@ <rev></rev> </header> <module>gb_sets</module> - <modulesummary>General Balanced Trees</modulesummary> + <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 + <p>This module provides ordered sets using Prof. Arne Andersson's + General Balanced Trees. Ordered sets can be much more efficient than using ordered lists, for larger sets, but depends on the application.</p> + <p>This module considers two elements as different if and only if they do not compare equal (<c>==</c>).</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 + <title>Complexity Note</title> + <p>The complexity on set operations is bounded by either <em>O(|S|)</em> or + <em>O(|T| * log(|S|))</em>, 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 + arbitrarily much faster; in practical cases, often + 10-100 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 + (> 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> + 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> + <p>The following functions in this module also exist and provides + the same functionality in the + <seealso marker="sets"><c>sets(3)</c></seealso> and + <seealso marker="ordsets"><c>ordsets(3)</c></seealso> modules. That is, by only changing the module name for each call, you can try out different set representations.</p> <list type="bulleted"> - <item> - <p><c>add_element/2</c></p> + <item><seealso marker="#add_element/2"><c>add_element/2</c></seealso> </item> - <item> - <p><c>del_element/2</c></p> + <item><seealso marker="#del_element/2"><c>del_element/2</c></seealso> </item> - <item> - <p><c>filter/2</c></p> + <item><seealso marker="#filter/2"><c>filter/2</c></seealso> </item> - <item> - <p><c>fold/3</c></p> + <item><seealso marker="#fold/3"><c>fold/3</c></seealso> </item> - <item> - <p><c>from_list/1</c></p> + <item><seealso marker="#from_list/1"><c>from_list/1</c></seealso> </item> - <item> - <p><c>intersection/1</c></p> + <item><seealso marker="#intersection/1"><c>intersection/1</c></seealso> </item> - <item> - <p><c>intersection/2</c></p> + <item><seealso marker="#intersection/2"><c>intersection/2</c></seealso> </item> - <item> - <p><c>is_element/2</c></p> + <item><seealso marker="#is_element/2"><c>is_element/2</c></seealso> </item> - <item> - <p><c>is_set/1</c></p> + <item><seealso marker="#is_set/1"><c>is_set/1</c></seealso> </item> - <item> - <p><c>is_subset/2</c></p> + <item><seealso marker="#is_subset/2"><c>is_subset/2</c></seealso> </item> - <item> - <p><c>new/0</c></p> + <item><seealso marker="#new/0"><c>new/0</c></seealso> </item> - <item> - <p><c>size/1</c></p> + <item><seealso marker="#size/1"><c>size/1</c></seealso> </item> - <item> - <p><c>subtract/2</c></p> + <item><seealso marker="#subtract/2"><c>subtract/2</c></seealso> </item> - <item> - <p><c>to_list/1</c></p> + <item><seealso marker="#to_list/1"><c>to_list/1</c></seealso> </item> - <item> - <p><c>union/1</c></p> + <item><seealso marker="#union/1"><c>union/1</c></seealso> </item> - <item> - <p><c>union/2</c></p> + <item><seealso marker="#union/2"><c>union/2</c></seealso> </item> </list> </section> <datatypes> <datatype> - <name><marker id="type-gb_set">gb_set()</marker></name> - <desc><p>A GB set.</p></desc> + <name name="set" n_vars="1"/> + <desc><p>A general balanced set.</p></desc> + </datatype> + <datatype> + <name name="set" n_vars="0"/> + </datatype> + <datatype> + <name name="iter" n_vars="1"/> + <desc><p>A general balanced set iterator.</p></desc> </datatype> <datatype> - <name name="iter"/> - <desc><p>A GB set iterator.</p></desc> + <name name="iter" n_vars="0"/> </datatype> </datatypes> + <funcs> <func> <name name="add" arity="2"/> <name name="add_element" arity="2"/> - <fsummary>Add a (possibly existing) element to a gb_set</fsummary> + <fsummary>Add a (possibly existing) element to a set.</fsummary> <desc> - <p>Returns a new gb_set formed from <c><anno>Set1</anno></c> with - <c><anno>Element</anno></c> inserted. If <c><anno>Element</anno></c> is already an + <p>Returns a new set formed from <c><anno>Set1</anno></c> with + <c><anno>Element</anno></c> inserted. If <c><anno>Element</anno></c> + is already an element in <c><anno>Set1</anno></c>, nothing is changed.</p> </desc> </func> + <func> <name name="balance" arity="1"/> - <fsummary>Rebalance tree representation of a gb_set</fsummary> + <fsummary>Rebalance tree representation of a set.</fsummary> <desc> - <p>Rebalances the tree representation of <c><anno>Set1</anno></c>. Note that - this is rarely necessary, but may be motivated when a large + <p>Rebalances the tree representation of <c><anno>Set1</anno></c>. + Notice that + this is rarely necessary, but can 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 + further insertions. Rebalancing can then be forced + to minimise lookup times, as deletion does not rebalance the tree.</p> </desc> </func> + + <func> + <name name="del_element" arity="2"/> + <fsummary>Remove a (possibly non-existing) element from a set.</fsummary> + <desc> + <p>Returns a new set formed from <c><anno>Set1</anno></c> with + <c><anno>Element</anno></c> removed. If <c><anno>Element</anno></c> + is not an element + in <c><anno>Set1</anno></c>, nothing is changed.</p> + </desc> + </func> + <func> <name name="delete" arity="2"/> - <fsummary>Remove an element from a gb_set</fsummary> + <fsummary>Remove an element from a set.</fsummary> <desc> - <p>Returns a new gb_set formed from <c><anno>Set1</anno></c> with - <c><anno>Element</anno></c> removed. Assumes that <c><anno>Element</anno></c> is present + <p>Returns a new set formed from <c><anno>Set1</anno></c> with + <c><anno>Element</anno></c> removed. Assumes that + <c><anno>Element</anno></c> is present in <c><anno>Set1</anno></c>.</p> </desc> </func> + <func> <name name="delete_any" arity="2"/> - <name name="del_element" arity="2"/> - <fsummary>Remove a (possibly non-existing) element from a gb_set</fsummary> + <fsummary>Remove a (possibly non-existing) element from a set.</fsummary> <desc> - <p>Returns a new gb_set formed from <c><anno>Set1</anno></c> with - <c><anno>Element</anno></c> removed. If <c><anno>Element</anno></c> is not an element + <p>Returns a new set formed from <c><anno>Set1</anno></c> with + <c><anno>Element</anno></c> removed. If <c><anno>Element</anno></c> + is not an element in <c><anno>Set1</anno></c>, nothing is changed.</p> </desc> </func> + <func> <name name="difference" arity="2"/> - <name name="subtract" arity="2"/> - <fsummary>Return the difference of two gb_sets</fsummary> + <fsummary>Return the difference of two sets.</fsummary> <desc> - <p>Returns only the elements of <c><anno>Set1</anno></c> which are not also - elements of <c><anno>Set2</anno></c>.</p> + <p>Returns only the elements of <c><anno>Set1</anno></c> that are not + also elements of <c><anno>Set2</anno></c>.</p> </desc> </func> + <func> <name name="empty" arity="0"/> - <name name="new" arity="0"/> - <fsummary>Return an empty gb_set</fsummary> + <fsummary>Return an empty set.</fsummary> <desc> - <p>Returns a new empty gb_set.</p> + <p>Returns a new empty set.</p> </desc> </func> + <func> <name name="filter" arity="2"/> - <fsummary>Filter gb_set elements</fsummary> + <fsummary>Filter set elements.</fsummary> <desc> <p>Filters elements in <c><anno>Set1</anno></c> using predicate function <c><anno>Pred</anno></c>.</p> </desc> </func> + <func> <name name="fold" arity="3"/> - <fsummary>Fold over gb_set elements</fsummary> + <fsummary>Fold over set elements.</fsummary> <desc> - <p>Folds <c><anno>Function</anno></c> over every element in <c><anno>Set</anno></c> + <p>Folds <c><anno>Function</anno></c> over every element in + <c><anno>Set</anno></c> returning the final value of the accumulator.</p> </desc> </func> + <func> <name name="from_list" arity="1"/> - <fsummary>Convert a list into a gb_set</fsummary> + <fsummary>Convert a list into a set.</fsummary> <desc> - <p>Returns a gb_set of the elements in <c><anno>List</anno></c>, where - <c><anno>List</anno></c> may be unordered and contain duplicates.</p> + <p>Returns a set of the elements in <c><anno>List</anno></c>, where + <c><anno>List</anno></c> can be unordered and contain duplicates.</p> </desc> </func> + <func> <name name="from_ordset" arity="1"/> - <fsummary>Make a gb_set from an ordset list</fsummary> + <fsummary>Make a set from an ordset list.</fsummary> <desc> - <p>Turns an ordered-set list <c><anno>List</anno></c> into a gb_set. The list - must not contain duplicates.</p> + <p>Turns an ordered-set list <c><anno>List</anno></c> into a set. + The list must not contain duplicates.</p> </desc> </func> + <func> <name name="insert" arity="2"/> - <fsummary>Add a new element to a gb_set</fsummary> + <fsummary>Add a new element to a set.</fsummary> <desc> - <p>Returns a new gb_set formed from <c><anno>Set1</anno></c> with - <c><anno>Element</anno></c> inserted. Assumes that <c><anno>Element</anno></c> is not + <p>Returns a new set formed from <c><anno>Set1</anno></c> with + <c><anno>Element</anno></c> inserted. Assumes that + <c><anno>Element</anno></c> is not present in <c><anno>Set1</anno></c>.</p> </desc> </func> + <func> - <name name="intersection" arity="2"/> - <fsummary>Return the intersection of two gb_sets</fsummary> + <name name="intersection" arity="1"/> + <fsummary>Return the intersection of a list of sets.</fsummary> <desc> - <p>Returns the intersection of <c><anno>Set1</anno></c> and <c><anno>Set2</anno></c>.</p> + <p>Returns the intersection of the non-empty list of sets.</p> </desc> </func> + <func> - <name name="intersection" arity="1"/> - <fsummary>Return the intersection of a list of gb_sets</fsummary> + <name name="intersection" arity="2"/> + <fsummary>Return the intersection of two sets.</fsummary> <desc> - <p>Returns the intersection of the non-empty list of gb_sets.</p> + <p>Returns the intersection of <c><anno>Set1</anno></c> and + <c><anno>Set2</anno></c>.</p> </desc> </func> + <func> <name name="is_disjoint" arity="2"/> - <fsummary>Check whether two gb_sets are disjoint</fsummary> + <fsummary>Check whether two sets are disjoint.</fsummary> <desc> <p>Returns <c>true</c> if <c><anno>Set1</anno></c> and <c><anno>Set2</anno></c> are disjoint (have no elements in common), - and <c>false</c> otherwise.</p> + otherwise <c>false</c>.</p> </desc> </func> + + <func> + <name name="is_element" arity="2"/> + <fsummary>Test for membership of a set.</fsummary> + <desc> + <p>Returns <c>true</c> if <c><anno>Element</anno></c> is an element of + <c><anno>Set</anno></c>, otherwise <c>false</c>.</p> + </desc> + </func> + <func> <name name="is_empty" arity="1"/> - <fsummary>Test for empty gb_set</fsummary> + <fsummary>Test for empty set.</fsummary> <desc> - <p>Returns <c>true</c> if <c><anno>Set</anno></c> is an empty set, and - <c>false</c> otherwise.</p> + <p>Returns <c>true</c> if <c><anno>Set</anno></c> is an empty set, + otherwise <c>false</c>.</p> </desc> </func> + <func> <name name="is_member" arity="2"/> - <name name="is_element" arity="2"/> - <fsummary>Test for membership of a gb_set</fsummary> + <fsummary>Test for membership of a set.</fsummary> <desc> <p>Returns <c>true</c> if <c><anno>Element</anno></c> is an element of <c><anno>Set</anno></c>, otherwise <c>false</c>.</p> </desc> </func> + <func> <name name="is_set" arity="1"/> - <fsummary>Test for a gb_set</fsummary> + <fsummary>Test for a set.</fsummary> <desc> - <p>Returns <c>true</c> if <c><anno>Term</anno></c> appears to be a gb_set, + <p>Returns <c>true</c> if <c><anno>Term</anno></c> appears to be a set, otherwise <c>false</c>.</p> </desc> </func> + <func> <name name="is_subset" arity="2"/> - <fsummary>Test for subset</fsummary> + <fsummary>Test for subset.</fsummary> <desc> <p>Returns <c>true</c> when every element of <c><anno>Set1</anno></c> is also a member of <c><anno>Set2</anno></c>, otherwise <c>false</c>.</p> </desc> </func> + <func> <name name="iterator" arity="1"/> - <fsummary>Return an iterator for a gb_set</fsummary> + <fsummary>Return an iterator for a set.</fsummary> <desc> - <p>Returns an iterator that can be used for traversing the - entries of <c><anno>Set</anno></c>; see <c>next/1</c>. The implementation + <p>Returns an iterator that can be used for traversing the entries of + <c><anno>Set</anno></c>; see + <seealso marker="#next/1"><c>next/1</c></seealso>. 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. + <c>next/1</c> is only slightly slower than getting the list of all + elements using <seealso marker="#to_list/1"><c>to_list/1</c></seealso> + 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 name="iterator_from" arity="2"/> + <fsummary>Return an iterator for a set starting from a specified element. + </fsummary> + <desc> + <p>Returns an iterator that can be used for traversing the + entries of <c><anno>Set</anno></c>; see + <seealso marker="#next/1"><c>next/1</c></seealso>. + The difference as compared to the iterator returned by + <seealso marker="#iterator/1"><c>iterator/1</c></seealso> + is that the first element greater than + or equal to <c><anno>Element</anno></c> is returned.</p> + </desc> + </func> + <func> <name name="largest" arity="1"/> - <fsummary>Return largest element</fsummary> + <fsummary>Return largest element.</fsummary> <desc> <p>Returns the largest element in <c><anno>Set</anno></c>. Assumes that - <c><anno>Set</anno></c> is nonempty.</p> + <c><anno>Set</anno></c> is not empty.</p> </desc> </func> + + <func> + <name name="new" arity="0"/> + <fsummary>Return an empty set.</fsummary> + <desc> + <p>Returns a new empty set.</p> + </desc> + </func> + <func> <name name="next" arity="1"/> - <fsummary>Traverse a gb_set with an iterator</fsummary> + <fsummary>Traverse a set with an iterator.</fsummary> <desc> - <p>Returns <c>{<anno>Element</anno>, <anno>Iter2</anno>}</c> where <c><anno>Element</anno></c> is the - smallest element referred to by the iterator <c><anno>Iter1</anno></c>, + <p>Returns <c>{<anno>Element</anno>, <anno>Iter2</anno>}</c>, where + <c><anno>Element</anno></c> is the smallest element referred to by + iterator <c><anno>Iter1</anno></c>, and <c><anno>Iter2</anno></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 name="singleton" arity="1"/> - <fsummary>Return a gb_set with one element</fsummary> + <fsummary>Return a set with one element.</fsummary> <desc> - <p>Returns a gb_set containing only the element <c><anno>Element</anno></c>.</p> + <p>Returns a set containing only element <c><anno>Element</anno></c>. + </p> </desc> </func> + <func> <name name="size" arity="1"/> - <fsummary>Return the number of elements in a gb_set</fsummary> + <fsummary>Return the number of elements in a set.</fsummary> <desc> <p>Returns the number of elements in <c><anno>Set</anno></c>.</p> </desc> </func> + <func> <name name="smallest" arity="1"/> - <fsummary>Return smallest element</fsummary> + <fsummary>Return smallest element.</fsummary> <desc> <p>Returns the smallest element in <c><anno>Set</anno></c>. Assumes that - <c><anno>Set</anno></c> is nonempty.</p> + <c><anno>Set</anno></c> is not empty.</p> + </desc> + </func> + + <func> + <name name="subtract" arity="2"/> + <fsummary>Return the difference of two sets.</fsummary> + <desc> + <p>Returns only the elements of <c><anno>Set1</anno></c> that are not + also elements of <c><anno>Set2</anno></c>.</p> </desc> </func> + <func> <name name="take_largest" arity="1"/> - <fsummary>Extract largest element</fsummary> + <fsummary>Extract largest element.</fsummary> <desc> - <p>Returns <c>{<anno>Element</anno>, <anno>Set2</anno>}</c>, where <c><anno>Element</anno></c> is the - largest element in <c><anno>Set1</anno></c>, and <c><anno>Set2</anno></c> is this set - with <c><anno>Element</anno></c> deleted. Assumes that <c><anno>Set1</anno></c> is - nonempty.</p> + <p>Returns <c>{<anno>Element</anno>, <anno>Set2</anno>}</c>, where + <c><anno>Element</anno></c> is the largest element in + <c><anno>Set1</anno></c>, and <c><anno>Set2</anno></c> is this set + with <c><anno>Element</anno></c> deleted. Assumes that + <c><anno>Set1</anno></c> is not empty.</p> </desc> </func> + <func> <name name="take_smallest" arity="1"/> - <fsummary>Extract smallest element</fsummary> + <fsummary>Extract smallest element.</fsummary> <desc> - <p>Returns <c>{<anno>Element</anno>, <anno>Set2</anno>}</c>, where <c><anno>Element</anno></c> is the - smallest element in <c><anno>Set1</anno></c>, and <c><anno>Set2</anno></c> is this set - with <c><anno>Element</anno></c> deleted. Assumes that <c><anno>Set1</anno></c> is - nonempty.</p> + <p>Returns <c>{<anno>Element</anno>, <anno>Set2</anno>}</c>, where + <c><anno>Element</anno></c> is the smallest element in + <c><anno>Set1</anno></c>, and <c><anno>Set2</anno></c> is this set + with <c><anno>Element</anno></c> deleted. Assumes that + <c><anno>Set1</anno></c> is not empty.</p> </desc> </func> + <func> <name name="to_list" arity="1"/> - <fsummary>Convert a gb_set into a list</fsummary> + <fsummary>Convert a set into a list.</fsummary> <desc> <p>Returns the elements of <c><anno>Set</anno></c> as a list.</p> </desc> </func> + <func> - <name name="union" arity="2"/> - <fsummary>Return the union of two gb_sets</fsummary> + <name name="union" arity="1"/> + <fsummary>Return the union of a list of sets.</fsummary> <desc> - <p>Returns the merged (union) gb_set of <c><anno>Set1</anno></c> and - <c><anno>Set2</anno></c>.</p> + <p>Returns the merged (union) set of the list of sets.</p> </desc> </func> + <func> - <name name="union" arity="1"/> - <fsummary>Return the union of a list of gb_sets</fsummary> + <name name="union" arity="2"/> + <fsummary>Return the union of two sets.</fsummary> <desc> - <p>Returns the merged (union) gb_set of the list of gb_sets.</p> + <p>Returns the merged (union) set of <c><anno>Set1</anno></c> and + <c><anno>Set2</anno></c>.</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> + <title>See Also</title> + <p><seealso marker="gb_trees"><c>gb_trees(3)</c></seealso>, + <seealso marker="ordsets"><c>ordsets(3)</c></seealso>, + <seealso marker="sets"><c>sets(3)</c></seealso></p> </section> </erlref> |