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-rw-r--r--lib/stdlib/doc/src/gb_sets.xml325
1 files changed, 196 insertions, 129 deletions
diff --git a/lib/stdlib/doc/src/gb_sets.xml b/lib/stdlib/doc/src/gb_sets.xml
index 84609a0f7c..d677dd6f83 100644
--- a/lib/stdlib/doc/src/gb_sets.xml
+++ b/lib/stdlib/doc/src/gb_sets.xml
@@ -29,87 +29,75 @@
<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
+ (&gt; 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>
@@ -117,290 +105,369 @@
<datatypes>
<datatype>
<name name="set" n_vars="1"/>
- <desc><p>A GB set.</p></desc>
+ <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 GB set iterator.</p></desc>
+ <desc><p>A general balanced set iterator.</p></desc>
</datatype>
<datatype>
<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 set</fsummary>
+ <fsummary>Add a (possibly existing) element to a set.</fsummary>
<desc>
<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
+ <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 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 set</fsummary>
+ <fsummary>Remove an 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. Assumes that <c><anno>Element</anno></c> is present
+ <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 set</fsummary>
+ <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
+ <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 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 set</fsummary>
+ <fsummary>Return an empty set.</fsummary>
<desc>
<p>Returns a new empty set.</p>
</desc>
</func>
+
<func>
<name name="filter" arity="2"/>
- <fsummary>Filter 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 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 set</fsummary>
+ <fsummary>Convert a list into a set.</fsummary>
<desc>
<p>Returns a set of the elements in <c><anno>List</anno></c>, where
- <c><anno>List</anno></c> may be unordered and contain duplicates.</p>
+ <c><anno>List</anno></c> can be unordered and contain duplicates.</p>
</desc>
</func>
+
<func>
<name name="from_ordset" arity="1"/>
- <fsummary>Make a 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 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 set</fsummary>
+ <fsummary>Add a new element to a set.</fsummary>
<desc>
<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
+ <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 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 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 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 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 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 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 set</fsummary>
+ <fsummary>Test for a set.</fsummary>
<desc>
<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 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>
+ <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 <c>next/1</c>.
+ 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
- <c>iterator/1</c> is that the first element greater than
+ <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 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 set with one element</fsummary>
+ <fsummary>Return a set with one element.</fsummary>
<desc>
- <p>Returns a 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 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 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 sets</fsummary>
+ <name name="union" arity="1"/>
+ <fsummary>Return the union of a list of sets.</fsummary>
<desc>
- <p>Returns the merged (union) 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 sets</fsummary>
+ <name name="union" arity="2"/>
+ <fsummary>Return the union of two sets.</fsummary>
<desc>
- <p>Returns the merged (union) set of the list of 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>