157 lines
5.0 KiB
HTML
157 lines
5.0 KiB
HTML
<HTML>
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<!--
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Copyright (c) Jeremy Siek 2000
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Topological Sort</Title>
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<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
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ALINK="#ff0000">
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<IMG SRC="../../../boost.png"
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ALT="C++ Boost" width="277" height="86">
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<BR Clear>
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<H1><A NAME="sec:topological-sort">
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<img src="figs/python.gif" alt="(Python)"/>
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<TT>topological_sort</TT>
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</H1>
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<PRE>
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template <typename VertexListGraph, typename OutputIterator,
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typename P, typename T, typename R>
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void topological_sort(VertexListGraph& g, OutputIterator result,
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const bgl_named_params<P, T, R>& params = <i>all defaults</i>)
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</PRE>
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<P>
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The topological sort algorithm creates a linear ordering of the
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vertices such that if edge <i>(u,v)</i> appears in the graph, then
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<i>v</i> comes before <i>u</i> in the ordering. The graph must be a
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directed acyclic graph (DAG). The implementation consists mainly of a
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call to <a
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href="./depth_first_search.html"><tt>depth_first_search()</tt></a>.
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</p>
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<h3>Where Defined:</h3>
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<a href="../../../boost/graph/topological_sort.hpp"><TT>boost/graph/topological_sort.hpp</TT></a>
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<h3>Parameters</h3>
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IN: <tt>VertexListGraph& g</tt>
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<blockquote>
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A directed acylic graph (DAG). The graph type must
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be a model of <a href="./VertexListGraph.html">Vertex List Graph</a>
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and <a href="./IncidenceGraph.html">Incidence Graph</a>.
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If the graph is not a DAG then a <a href="./exception.html#not_a_dag"><tt>not_a_dag</tt></a>
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exception will be thrown and the
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user should discard the contents of <tt>result</tt> range.<br>
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<b>Python</b>: The parameter is named <tt>graph</tt>.
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</blockquote>
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OUT: <tt>OutputIterator result</tt>
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<blockquote>
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The vertex descriptors of the graph will be output to the
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<TT>result</TT> output iterator in <b>reverse</b> topological order. The
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iterator type must model <a
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href="http://www.boost.org/sgi/stl/OutputIterator.html">Output
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Iterator</a>.<br>
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<b>Python</b>: This parameter is not used in Python. Instead, a
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Python <tt>list</tt> containing the vertices in topological order is
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returned.
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</blockquote>
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<h3>Named Parameters</h3>
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UTIL/OUT: <tt>color_map(ColorMap color)</tt>
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<blockquote>
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This is used by the algorithm to keep track of its progress through
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the graph. The type <tt>ColorMap</tt> must be a model of <a
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href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
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Property Map</a> and its key type must be the graph's vertex
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descriptor type and the value type of the color map must model
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<a href="./ColorValue.html">ColorValue</a>.<br>
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<b>Default:</b> an <a
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href="../../property_map/doc/iterator_property_map.html">
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</tt>iterator_property_map</tt></a> created from a
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<tt>std::vector</tt> of <tt>default_color_type</tt> of size
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<tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
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map.<br>
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<b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for
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the graph.
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</blockquote>
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IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
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<blockquote>
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This maps each vertex to an integer in the range <tt>[0,
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num_vertices(g))</tt>. This parameter is only necessary when the
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default color property map is used. The type <tt>VertexIndexMap</tt>
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must be a model of <a
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href="../../property_map/doc/ReadablePropertyMap.html">Readable Property
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Map</a>. The value type of the map must be an integer type. The
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vertex descriptor type of the graph needs to be usable as the key
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type of the map.<br>
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<b>Default:</b> <tt>get(vertex_index, g)</tt>
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Note: if you use this default, make sure your graph has
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an internal <tt>vertex_index</tt> property. For example,
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<tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
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not have an internal <tt>vertex_index</tt> property.
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<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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<H3>Complexity</H3>
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The time complexity is <i>O(V + E)</i>.
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<H3>Example</H3>
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<P>
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Calculate a topological ordering of the vertices.
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<P>
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<PRE>
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typedef adjacency_list< vecS, vecS, directedS, color_property<> > Graph;
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typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
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Pair edges[6] = { Pair(0,1), Pair(2,4),
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Pair(2,5),
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Pair(0,3), Pair(1,4),
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Pair(4,3) };
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Graph G(6, edges, edges + 6);
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typedef std::vector< Vertex > container;
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container c;
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topological_sort(G, std::back_inserter(c));
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cout << "A topological ordering: ";
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for ( container::reverse_iterator ii=c.rbegin(); ii!=c.rend(); ++ii)
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cout << index(*ii) << " ";
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cout << endl;
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</PRE>
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The output is:
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<PRE>
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A topological ordering: 2 5 0 1 4 3
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</PRE>
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<br>
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<HR>
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<TABLE>
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<TR valign=top>
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<TD nowrap>Copyright © 2000-2001</TD><TD>
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<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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