<HTML>
<!--
Copyright (c) Jeremy Siek 2000
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
-->
<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.sgi.com/tech/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>adjacenty_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>
