| <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> |
