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