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1 | <HTML> |
2 | <!-- | |
3 | Copyright (c) Jeremy Siek 2000 | |
4 | ||
5 | Distributed under the Boost Software License, Version 1.0. | |
6 | (See accompanying file LICENSE_1_0.txt or copy at | |
7 | http://www.boost.org/LICENSE_1_0.txt) | |
8 | --> | |
9 | <Head> | |
10 | <Title>Boost Graph Library: Topological Sort</Title> | |
11 | <BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" | |
12 | ALINK="#ff0000"> | |
13 | <IMG SRC="../../../boost.png" | |
14 | ALT="C++ Boost" width="277" height="86"> | |
15 | ||
16 | <BR Clear> | |
17 | ||
18 | ||
19 | <H1><A NAME="sec:topological-sort"> | |
20 | <img src="figs/python.gif" alt="(Python)"/> | |
21 | <TT>topological_sort</TT> | |
22 | </H1> | |
23 | ||
24 | <PRE> | |
25 | template <typename VertexListGraph, typename OutputIterator, | |
26 | typename P, typename T, typename R> | |
27 | void topological_sort(VertexListGraph& g, OutputIterator result, | |
28 | const bgl_named_params<P, T, R>& params = <i>all defaults</i>) | |
29 | </PRE> | |
30 | ||
31 | <P> | |
32 | The topological sort algorithm creates a linear ordering of the | |
33 | vertices such that if edge <i>(u,v)</i> appears in the graph, then | |
34 | <i>v</i> comes before <i>u</i> in the ordering. The graph must be a | |
35 | directed acyclic graph (DAG). The implementation consists mainly of a | |
36 | call to <a | |
37 | href="./depth_first_search.html"><tt>depth_first_search()</tt></a>. | |
38 | </p> | |
39 | ||
40 | <h3>Where Defined:</h3> | |
41 | <a href="../../../boost/graph/topological_sort.hpp"><TT>boost/graph/topological_sort.hpp</TT></a> | |
42 | ||
43 | <h3>Parameters</h3> | |
44 | ||
45 | IN: <tt>VertexListGraph& g</tt> | |
46 | <blockquote> | |
47 | A directed acylic graph (DAG). The graph type must | |
48 | be a model of <a href="./VertexListGraph.html">Vertex List Graph</a> | |
49 | and <a href="./IncidenceGraph.html">Incidence Graph</a>. | |
50 | If the graph is not a DAG then a <a href="./exception.html#not_a_dag"><tt>not_a_dag</tt></a> | |
51 | exception will be thrown and the | |
52 | user should discard the contents of <tt>result</tt> range.<br> | |
53 | <b>Python</b>: The parameter is named <tt>graph</tt>. | |
54 | </blockquote> | |
55 | ||
56 | OUT: <tt>OutputIterator result</tt> | |
57 | <blockquote> | |
58 | The vertex descriptors of the graph will be output to the | |
59 | <TT>result</TT> output iterator in <b>reverse</b> topological order. The | |
60 | iterator type must model <a | |
61 | href="http://www.sgi.com/tech/stl/OutputIterator.html">Output | |
62 | Iterator</a>.<br> | |
63 | ||
64 | <b>Python</b>: This parameter is not used in Python. Instead, a | |
65 | Python <tt>list</tt> containing the vertices in topological order is | |
66 | returned. | |
67 | </blockquote> | |
68 | ||
69 | <h3>Named Parameters</h3> | |
70 | ||
71 | UTIL/OUT: <tt>color_map(ColorMap color)</tt> | |
72 | <blockquote> | |
73 | This is used by the algorithm to keep track of its progress through | |
74 | the graph. The type <tt>ColorMap</tt> must be a model of <a | |
75 | href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write | |
76 | Property Map</a> and its key type must be the graph's vertex | |
77 | descriptor type and the value type of the color map must model | |
78 | <a href="./ColorValue.html">ColorValue</a>.<br> | |
79 | <b>Default:</b> an <a | |
80 | href="../../property_map/doc/iterator_property_map.html"> | |
81 | </tt>iterator_property_map</tt></a> created from a | |
82 | <tt>std::vector</tt> of <tt>default_color_type</tt> of size | |
83 | <tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index | |
84 | map.<br> | |
85 | ||
86 | <b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for | |
87 | the graph. | |
88 | </blockquote> | |
89 | ||
90 | IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt> | |
91 | <blockquote> | |
92 | This maps each vertex to an integer in the range <tt>[0, | |
93 | num_vertices(g))</tt>. This parameter is only necessary when the | |
94 | default color property map is used. The type <tt>VertexIndexMap</tt> | |
95 | must be a model of <a | |
96 | href="../../property_map/doc/ReadablePropertyMap.html">Readable Property | |
97 | Map</a>. The value type of the map must be an integer type. The | |
98 | vertex descriptor type of the graph needs to be usable as the key | |
99 | type of the map.<br> | |
100 | ||
101 | <b>Default:</b> <tt>get(vertex_index, g)</tt> | |
102 | Note: if you use this default, make sure your graph has | |
103 | an internal <tt>vertex_index</tt> property. For example, | |
104 | <tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does | |
105 | not have an internal <tt>vertex_index</tt> property. | |
106 | <br> | |
107 | ||
108 | <b>Python</b>: Unsupported parameter. | |
109 | </blockquote> | |
110 | ||
111 | ||
112 | <H3>Complexity</H3> | |
113 | ||
114 | The time complexity is <i>O(V + E)</i>. | |
115 | ||
116 | ||
117 | <H3>Example</H3> | |
118 | ||
119 | <P> | |
120 | Calculate a topological ordering of the vertices. | |
121 | ||
122 | <P> | |
123 | <PRE> | |
124 | typedef adjacency_list< vecS, vecS, directedS, color_property<> > Graph; | |
125 | typedef boost::graph_traits<Graph>::vertex_descriptor Vertex; | |
126 | Pair edges[6] = { Pair(0,1), Pair(2,4), | |
127 | Pair(2,5), | |
128 | Pair(0,3), Pair(1,4), | |
129 | Pair(4,3) }; | |
130 | Graph G(6, edges, edges + 6); | |
131 | ||
132 | typedef std::vector< Vertex > container; | |
133 | container c; | |
134 | topological_sort(G, std::back_inserter(c)); | |
135 | ||
136 | cout << "A topological ordering: "; | |
137 | for ( container::reverse_iterator ii=c.rbegin(); ii!=c.rend(); ++ii) | |
138 | cout << index(*ii) << " "; | |
139 | cout << endl; | |
140 | </PRE> | |
141 | The output is: | |
142 | <PRE> | |
143 | A topological ordering: 2 5 0 1 4 3 | |
144 | </PRE> | |
145 | ||
146 | ||
147 | <br> | |
148 | <HR> | |
149 | <TABLE> | |
150 | <TR valign=top> | |
151 | <TD nowrap>Copyright © 2000-2001</TD><TD> | |
152 | <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>) | |
153 | </TD></TR></TABLE> | |
154 | ||
155 | </BODY> | |
156 | </HTML> |