mirror of
https://github.com/boostorg/disjoint_sets.git
synced 2026-01-19 04:12:08 +00:00
Redirect docs to Boost.Graph versions.
This commit is contained in:
jzmaddock
@@ -1,59 +1,15 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
|
||||
|
||||
<html>
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Language" content="en-us">
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
|
||||
|
||||
<title>Boost Utility Library: Bibliography</title>
|
||||
<meta http-equiv="refresh" content="0; URL=../graph/doc/disjoint_sets_biblio.html">
|
||||
</head>
|
||||
|
||||
<body bgcolor="#FFFFFF" link="#0000EE" text="#000000" vlink="#551A8B" alink=
|
||||
"#FF0000">
|
||||
<img src="../../boost.png" alt="C++ Boost" width="277" height=
|
||||
"86"><br clear="none">
|
||||
|
||||
<h2>Bibliography</h2>
|
||||
|
||||
<dl compact>
|
||||
<dt><a name="tarjan83:_data_struct_network_algo" id=
|
||||
"tarjan83:_data_struct_network_algo">1</a></dt>
|
||||
|
||||
<dd>R. E. Tarjan.<br>
|
||||
<em>Data Structures and Network Algorithms</em>.<br>
|
||||
Society for Industrial and Applied Mathematics, 1983.</dd>
|
||||
|
||||
<dt> </dt>
|
||||
|
||||
<dt><a name="clr90" id="clr90">2</a></dt>
|
||||
|
||||
<dd>T. Cormen, C. Leiserson, and R. Rivest.<br>
|
||||
<em>Introduction to Algorithms</em>.<br>
|
||||
McGraw-Hill, 1990.</dd>
|
||||
</dl><br>
|
||||
<hr>
|
||||
|
||||
<p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src=
|
||||
"../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional"
|
||||
height="31" width="88"></a></p>
|
||||
|
||||
<p>Revised
|
||||
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->01
|
||||
December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38508" --></p>
|
||||
|
||||
<table summary="">
|
||||
<tr valign="top">
|
||||
<td nowrap><i>Copyright © 2000</i></td>
|
||||
|
||||
<td><i><a href="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</a>, Univ.of
|
||||
Notre Dame (<a href=
|
||||
"mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</a>)</i></td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<p><i>Distributed under the Boost Software License, Version 1.0. (See
|
||||
accompanying file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or
|
||||
copy at <a href=
|
||||
"http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p>
|
||||
<body>
|
||||
Automatic redirection failed, please go to
|
||||
<a href="../graph/doc/disjoint_sets_biblio.html">disjoint_sets_biblio.html</a>. <hr>
|
||||
<p>© Copyright Beman Dawes, 2001</p>
|
||||
<p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy
|
||||
at <a href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -1,309 +1,15 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
|
||||
|
||||
<html>
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Language" content="en-us">
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
|
||||
|
||||
<title>Boost Disjoint Sets</title>
|
||||
<meta http-equiv="refresh" content="0; URL=../graph/doc/disjoint_sets.html">
|
||||
</head>
|
||||
|
||||
<body bgcolor="#FFFFFF" link="#0000EE" text="#000000" vlink="#551A8B" alink=
|
||||
"#FF0000">
|
||||
<img src="../../boost.png" alt="C++ Boost" width="277" height=
|
||||
"86"><br clear="none">
|
||||
|
||||
<h1><a name="sec:disjoint-sets" id="sec:disjoint-sets"></a> Disjoint
|
||||
Sets</h1>
|
||||
<pre>
|
||||
disjoint_sets<Rank, Parent, FindCompress>
|
||||
</pre>
|
||||
|
||||
<p>This is class that provides disjoint sets operations with <i>union by
|
||||
rank</i> and <i>path compression</i>. A disjoint-sets data structure
|
||||
maintains a collection <i>S = {S<sub>1</sub>, S<sub>2</sub>, ...,
|
||||
S<sub>k</sub>}</i> of disjoint sets. Each set is identified by a
|
||||
<i>representative</i> which is some member of of the set. Sets are
|
||||
represented by rooted trees which are encoded in the <tt>Parent</tt>
|
||||
property map. Two heuristics: "union by rank" and "path compression" are
|
||||
used to speed up the operations [<a href=
|
||||
"./bibliography.html#tarjan83:_data_struct_network_algo">1</a>, <a href=
|
||||
"./bibliography.html#clr90">2</a>].</p>
|
||||
|
||||
<h3>Where Defined</h3><a href=
|
||||
"../../boost/pending/disjoint_sets.hpp"><tt>boost/pending/disjoint_sets.hpp</tt></a>
|
||||
|
||||
<h3>Template Parameters</h3>
|
||||
|
||||
<table border summary="">
|
||||
<tr>
|
||||
<td><tt>Rank</tt></td>
|
||||
|
||||
<td>must be a model of <a href=
|
||||
"../property_map/doc/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
|
||||
with an integer value type and a key type equal to the set's element
|
||||
type.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>Parent</tt></td>
|
||||
|
||||
<td>must be a model of <a href=
|
||||
"../property_map/doc/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
|
||||
and the key and value type the same as the set's element type.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>FindCompress</tt></td>
|
||||
|
||||
<td>should be one of the find representative and path compress function
|
||||
objects.</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
<p>A typical usage pattern for <tt>disjoint_sets</tt> can be seen in the
|
||||
<a href=
|
||||
"../graph/doc/kruskal_min_spanning_tree.html"><tt>kruskal_minimum_spanning_tree()</tt></a>
|
||||
algorithm. In this example, we call <tt>link()</tt> instead of
|
||||
<tt>union_set()</tt> because <tt>u</tt> and <tt>v</tt> were obtained from
|
||||
<tt>find_set()</tt> and therefore are already the representatives for their
|
||||
sets.</p>
|
||||
<pre>
|
||||
...
|
||||
disjoint_sets<Rank, Parent, FindCompress> dsets(rank, p);
|
||||
|
||||
for (ui = vertices(G).first; ui != vertices(G).second; ++ui)
|
||||
dsets.make_set(*ui);
|
||||
...
|
||||
while ( !Q.empty() ) {
|
||||
e = Q.front();
|
||||
Q.pop();
|
||||
u = dsets.find_set(source(e));
|
||||
v = dsets.find_set(target(e));
|
||||
if ( u != v ) {
|
||||
*out++ = e;
|
||||
dsets.link(u, v);
|
||||
}
|
||||
}
|
||||
</pre>
|
||||
|
||||
<h3>Members</h3>
|
||||
|
||||
<table border summary="">
|
||||
<tr>
|
||||
<th>Member</th>
|
||||
|
||||
<th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>disjoint_sets(Rank r, Parent p)</tt></td>
|
||||
|
||||
<td>Constructor.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>disjoint_sets(const disjoint_sets& x)</tt></td>
|
||||
|
||||
<td>Copy constructor.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class Element><br>
|
||||
void make_set(Element x)</tt></td>
|
||||
|
||||
<td>Creates a singleton set containing Element <tt>x</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class Element><br>
|
||||
void link(Element x, Element y)</tt></td>
|
||||
|
||||
<td>Union the two sets <i>represented</i> by element <tt>x</tt> and
|
||||
<tt>y</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class Element><br>
|
||||
void union_set(Element x, Element y)</tt></td>
|
||||
|
||||
<td>Union the two sets that <i>contain</i> elements <tt>x</tt> and
|
||||
<tt>y</tt>. This is equivalent to
|
||||
<tt>link(find_set(x),find_set(y))</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class Element><br>
|
||||
Element find_set(Element x)</tt></td>
|
||||
|
||||
<td>Return the representative for the set containing element
|
||||
<tt>x</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class ElementIterator><br>
|
||||
std::size_t count_sets(ElementIterator first, ElementIterator
|
||||
last)</tt></td>
|
||||
|
||||
<td>Returns the number of disjoint sets.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>template <class ElementIterator><br>
|
||||
void compress_sets(ElementIterator first, ElementIterator
|
||||
last)</tt></td>
|
||||
|
||||
<td>Flatten the parents tree so that the parent of every element is its
|
||||
representative.</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<h3>Complexity</h3>
|
||||
|
||||
<p>The time complexity is <i>O(m alpha(m,n))</i>, where <i>alpha</i> is the
|
||||
inverse Ackermann's function, <i>m</i> is the number of disjoint-set
|
||||
operations (<tt>make_set()</tt>, <tt>find_set()</tt>, and <tt>link()</tt>
|
||||
and <i>n</i> is the number of elements. The <i>alpha</i> function grows
|
||||
very slowly, much more slowly than the <i>log</i> function.</p>
|
||||
|
||||
<h3>See Also</h3><a href=
|
||||
"../graph/doc/incremental_components.html"><tt>incremental_connected_components()</tt></a>
|
||||
<hr>
|
||||
<pre>
|
||||
disjoint_sets_with_storage<ID,InverseID,FindCompress>
|
||||
</pre>
|
||||
|
||||
<p>This class manages the storage for the rank and parent properties
|
||||
internally. The storage is in arrays, which are indexed by element ID,
|
||||
hence the requirement for the <tt>ID</tt> and <tt>InverseID</tt> functors.
|
||||
The rank and parent properties are initialized during construction so the
|
||||
each element is in a set by itself (so it is not necessary to initialize
|
||||
objects of this class with the <a href=
|
||||
"../graph/doc/incremental_components.html#sec:initialize-incremental-components">
|
||||
<tt>initialize_incremental_components()</tt></a> function). This class is
|
||||
especially useful when computing the (dynamic) connected components of an
|
||||
<tt>edge_list</tt> graph which does not provide a place to store vertex
|
||||
properties.</p>
|
||||
|
||||
<h3>Template Parameters</h3>
|
||||
|
||||
<table border summary="">
|
||||
<tr>
|
||||
<th>Parameter</th>
|
||||
|
||||
<th>Description</th>
|
||||
|
||||
<th>Default</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>ID</tt></td>
|
||||
|
||||
<td>must be a model of <a href=
|
||||
"../property_map/doc/ReadablePropertyMap.html">ReadablePropertyMap</a> that
|
||||
maps elements to integers between zero 0 and N, the total number of
|
||||
elements in the sets.</td>
|
||||
|
||||
<td><tt>boost::identity_property_map</tt></td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>InverseID</tt></td>
|
||||
|
||||
<td>must be a model of <a href=
|
||||
"../property_map/doc/ReadablePropertyMap.html">ReadablePropertyMap</a> that
|
||||
maps integers to elements.</td>
|
||||
|
||||
<td><tt>boost::identity_property_map</tt></td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>FindCompress</tt></td>
|
||||
|
||||
<td>should be one of the find representative and path compress function
|
||||
objects.</td>
|
||||
|
||||
<td><tt>representative_with_full_path_compression</tt></td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<h3>Members</h3>
|
||||
|
||||
<p>This class has all of the members in <tt>disjoint_sets</tt> as well as
|
||||
the following members.</p>
|
||||
<pre>
|
||||
disjoint_sets_with_storage(size_type n = 0,
|
||||
ID id = ID(),
|
||||
InverseID inv = InverseID())
|
||||
</pre>Constructor.
|
||||
<pre>
|
||||
template <class ElementIterator>
|
||||
void disjoint_sets_with_storage::
|
||||
normalize_sets(ElementIterator first, ElementIterator last)
|
||||
</pre>This rearranges the representatives such that the representative of
|
||||
each set is the element with the smallest ID.<br>
|
||||
Postcondition: <tt>v >= parent[v]</tt><br>
|
||||
Precondition: the disjoint sets structure must be compressed.<br>
|
||||
<hr>
|
||||
|
||||
<h2><a name="sec:representative-with-path-halving" id=
|
||||
"sec:representative-with-path-halving"></a></h2>
|
||||
<pre>
|
||||
representative_with_path_halving<Parent>
|
||||
</pre>
|
||||
|
||||
<p>This is a functor which finds the representative vertex for the same
|
||||
component as the element <tt>x</tt>. While traversing up the representative
|
||||
tree, the functor also applies the path halving technique to shorten the
|
||||
height of the tree.</p>
|
||||
<pre>
|
||||
Element operator()(Parent p, Element x)
|
||||
</pre>
|
||||
<hr>
|
||||
|
||||
<h2><a name="sec:representative-with-full-path-compression" id=
|
||||
"sec:representative-with-full-path-compression"></a><br></h2>
|
||||
<pre>
|
||||
representative_with_full_path_compression<Parent>
|
||||
</pre>
|
||||
|
||||
<p>This is a functor which finds the representative element for the set
|
||||
that element <tt>x</tt> belongs to.</p>
|
||||
<pre>
|
||||
Element operator()(Parent p, Element x)
|
||||
</pre>
|
||||
|
||||
<p><br></p>
|
||||
<hr>
|
||||
|
||||
<p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src=
|
||||
"../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional"
|
||||
height="31" width="88"></a></p>
|
||||
|
||||
<p>Revised
|
||||
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->01
|
||||
December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38508" --></p>
|
||||
|
||||
<table summary="">
|
||||
<tr valign="top">
|
||||
<td nowrap><i>Copyright © 2000</i></td>
|
||||
|
||||
<td><i><a href="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</a>, Univ.of
|
||||
Notre Dame (<a href="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</a>)<br>
|
||||
<a href="http://www.boost.org/people/liequan_lee.htm">Lie-Quan Lee</a>,
|
||||
Univ.of Notre Dame (<a href=
|
||||
"mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</a>)<br>
|
||||
<a href="http://www.lsc.nd.edu/~lums">Andrew Lumsdaine</a>, Univ.of
|
||||
Notre Dame (<a href=
|
||||
"mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</a>)</i></td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<p><i>Distributed under the Boost Software License, Version 1.0. (See
|
||||
accompanying file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or
|
||||
copy at <a href=
|
||||
"http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p>
|
||||
<body>
|
||||
Automatic redirection failed, please go to
|
||||
<a href="../graph/doc/disjoint_sets.html">disjoint_sets.html</a>. <hr>
|
||||
<p>© Copyright Beman Dawes, 2001</p>
|
||||
<p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy
|
||||
at <a href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@@ -1,14 +1,14 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="refresh" content="0; URL=disjoint_sets.html">
|
||||
<meta http-equiv="refresh" content="0; URL=../graph/doc/disjoint_sets.html">
|
||||
</head>
|
||||
<body>
|
||||
Automatic redirection failed, please go to
|
||||
<a href="disjoint_sets.html">disjoint_sets.html</a>. <hr>
|
||||
<a href="../graph/doc/disjoint_sets.html">disjoint_sets.html</a>. <hr>
|
||||
<p>© Copyright Beman Dawes, 2001</p>
|
||||
<p>Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy
|
||||
at <a href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</body>
|
||||
</html>
|
||||
</html>
|
||||
|
||||
Reference in New Issue
Block a user