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140 lines
4.0 KiB
HTML
140 lines
4.0 KiB
HTML
<HTML>
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<!--
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-- Copyright (c) Jeremy Siek 2000
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--
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-- Permission to use, copy, modify, distribute and sell this software
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-- and its documentation for any purpose is hereby granted without fee,
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-- provided that the above copyright notice appears in all copies and
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-- that both that copyright notice and this permission notice appear
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-- in supporting documentation. Jeremy Siek makes no
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-- representations about the suitability of this software for any
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-- purpose. It is provided "as is" without express or implied warranty.
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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="../../../c++boost.gif"
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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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<TT>topological_sort</TT>
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</H1>
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<P>
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<DIV ALIGN="left">
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<TABLE CELLPADDING=3 border>
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<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
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<TD ALIGN="LEFT">directed acyclic</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
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<TD ALIGN="LEFT">color</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
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<TD ALIGN="LEFT">time: <i>O(V + E)</i></TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Where Defined:</B></TH>
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<TD ALIGN="LEFT">
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<a href="../../../boost/graph/topological_sort.hpp"><TT>boost/graph/topological_sort.hpp</TT></a>
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</TD>
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</TR>
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</TABLE>
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</DIV>
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<P>
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<PRE>
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(1)
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template <class VertexListGraph, class OutputIterator>
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void topological_sort(VertexListGraph& G, OutputIterator iter)
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(2)
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template <class VertexListGraph, class OutputIterator, class Visitor>
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void topological_sort(VertexListGraph& G, OutputIterator iter,
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Visitor visit)
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(3)
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template <class VertexListGraph, class OutputIterator,
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class ColorMap, class DFSVisitor>
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void topological_sort(VertexListGraph& G, OutputIterator iter,
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ColorMap color, DFSVisitor visit)
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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>u</i> comes before <i>v</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>Requirements on Types</H3>
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<P>
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<UL>
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<LI>The graph type must be a model of <a
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href="./VertexListGraph.html">VertexListGraph</a>.
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</LI>
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<LI>Vertex descriptors of the graph will be output to the
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<TT>OutputIterator</TT>, which must model <a
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href="http://www.sgi.com/tech/stl/OutputIterator.html">OutputIterator</a>.
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</LI>
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<LI>The type <TT>Visitor</TT> must be a model of <I>Visitor</I>.
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</LI>
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<LI>The <TT>ColorMap</TT> must be a <a
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href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
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and vertex descriptors from the graph must be usable as the
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map's key type.
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</LI>
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<LI>The <TT>DFSVisitor</TT> type must be a model of <a href="./DFSVisitor.html">DFSVisitor</a>.
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</UL>
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<P>
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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[7] = { 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), Pair(5,5) };
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Graph G(6, edges, edges + 7);
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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</TD><TD>
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<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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