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321 lines
10 KiB
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<HTML>
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<!--
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Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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-->
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<Head>
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<Title>Boost Graph Library: Depth-First Search</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="../../../boost.png"
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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:depth-first-search"></A><img src="figs/python.gif" alt="(Python)"/>
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<TT>depth_first_search</TT>
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</H1>
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<P>
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<PRE>
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<i>// named parameter version</i>
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template <class Graph, class class P, class T, class R>
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void depth_first_search(Graph& G,
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const bgl_named_params<P, T, R>& params);
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<i>// non-named parameter version</i>
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template <class Graph, class <a href="DFSVisitor.html">DFSVisitor</a>, class ColorMap>
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void depth_first_search(const Graph& g, DFSVisitor vis, ColorMap color)
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template <class Graph, class <a href="DFSVisitor.html">DFSVisitor</a>, class ColorMap>
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void depth_first_search(const Graph& g, DFSVisitor vis, ColorMap color,
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typename graph_traits<Graph>::vertex_descriptor start)
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</PRE>
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<p>
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The <tt>depth_first_search()</tt> function performs a depth-first
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traversal of the vertices in a directed graph. When
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possible, a depth-first traversal chooses a vertex adjacent to the
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current vertex to visit next. If all adjacent vertices have already
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been discovered, or there are no adjacent vertices, then the algorithm
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backtracks to the last vertex that had undiscovered neighbors. Once
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all reachable vertices have been visited, the algorithm selects from
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any remaining undiscovered vertices and continues the traversal. The
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algorithm finishes when all vertices have been visited. Depth-first
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search is useful for categorizing edges in a graph, and for imposing
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an ordering on the vertices. Section <a
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href="./graph_theory_review.html#sec:dfs-algorithm">Depth-First
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Search</a> describes the various properties of DFS and walks through
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an example.
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</p>
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<p>
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Similar to BFS, color markers are used to keep track of which vertices
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have been discovered. White marks vertices that have yet to be
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discovered, gray marks a vertex that is discovered but still has
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vertices adjacent to it that are undiscovered. A black vertex is
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discovered vertex that is not adjacent to any white vertices.
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<p>
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<p>
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The <tt>depth_first_search()</tt> function invokes user-defined
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actions at certain event-points within the algorithm. This provides a
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mechanism for adapting the generic DFS algorithm to the many
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situations in which it can be used. In the pseudo-code below, the
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event points for DFS are the labels on
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the right. The user-defined actions must be provided in the form of a
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visitor object, that is, an object whose type meets the requirements
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for a <a href="./DFSVisitor.html">DFS Visitor</a>. In the pseudo-code
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we show the algorithm computing predecessors <i>p</i>, discover time
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<i>d</i> and finish time <i>t</i>. By default, the
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<tt>depth_first_search()</tt> function does not compute these
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properties, however there are pre-defined visitors such as <a
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href="./predecessor_recorder.html"><tt>predecessor_recorder</tt></a>
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and <a href="./time_stamper.html"><tt>time_stamper</tt></a> that can
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be used to do this.
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</p>
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<table>
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<tr>
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<td valign="top">
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<pre>
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DFS(<i>G</i>)
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<b>for</b> each vertex <i>u in V</i>
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<i>color[u] :=</i> WHITE
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<i>p[u] = u</i>
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<b>end for</b>
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<i>time := 0</i>
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<b>if</b> there is a starting vertex <i>s</i>
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<b>call</b> DFS-VISIT(<i>G</i>, <i>s</i>)
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<b>for</b> each vertex <i>u in V</i>
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<b>if</b> <i>color[u] =</i> WHITE
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<b>call</b> DFS-VISIT(<i>G</i>, <i>u</i>)
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<b>end for</b>
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return (<i>p</i>,<i>d_time</i>,<i>f_time</i>) <br>
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DFS-VISIT(<i>G</i>, <i>u</i>)
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<i>color[u] :=</i> GRAY
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<i>d_time[u] := time := time + 1</i>
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<b>for</b> each <i>v in Adj[u]</i>
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<b>if</b> (<i>color[v] =</i> WHITE)
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<i>p[v] = u</i>
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<b>call</b> DFS-VISIT(<i>G</i>, <i>v</i>)
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<b>else if</b> (<i>color[v] =</i> GRAY)
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<i>...</i>
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<b>else if</b> (<i>color[v] =</i> BLACK)
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<i>...</i>
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<i>...</i>
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<b>end for</b>
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<i>color[u] :=</i> BLACK
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<i>f_time[u] := time := time + 1</i>
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<pre>
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</td>
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<td valign="top">
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<pre>
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-
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-
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initialize vertex <i>u</i>
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-
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-
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start vertex <i>s</i>
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-
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start vertex <i>u</i>
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-
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discover vertex <i>u</i>
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-
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examine edge <i>(u,v)</i>
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-
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<i>(u,v)</i> is a tree edge
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-
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<i>(u,v)</i> is a back edge
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-
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<i>(u,v)</i> is a cross or forward edge
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-
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finish edge <i>(u,v)</i>
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-
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finish vertex <i>u</i>
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-
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</pre>
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</td>
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</tr>
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</table>
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/depth_first_search.hpp"><TT>boost/graph/depth_first_search.hpp</TT></a>
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<h3>Parameters</h3>
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IN: <tt>Graph& g</tt>
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<blockquote>
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A directed graph. The graph type must
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be a model of <a href="./IncidenceGraph.html">Incidence Graph</a>
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and <a href="./VertexListGraph.html">Vertex List Graph</a>.<br>
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<b>Python</b>: The parameter is named <tt>graph</tt>.
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</blockquote>
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<h3>Named Parameters</h3>
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IN: <tt>visitor(DFSVisitor vis)</tt>
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<blockquote>
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A visitor object that is invoked inside the algorithm at the
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event-points specified by the <a href="./DFSVisitor.html">DFS
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Visitor</a> concept. The visitor object is passed by value <a
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href="#1">[1]</a>. <br> <b>Default:</b>
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<tt>dfs_visitor<null_visitor></tt><br>
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<b>Python</b>: The parameter should be an object that derives from
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the <a href="DFSVisitor.html#python"><tt>DFSVisitor</tt></a> type of
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the graph.
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</blockquote>
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UTIL/OUT: <tt>color_map(ColorMap color)</tt>
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<blockquote>
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This is used by the algorithm to keep track of its progress through
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the graph. The type <tt>ColorMap</tt> must be a model of <a
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href="../../property_map/doc/ReadWritePropertyMap.html">Read/Write
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Property Map</a> and its key type must be the graph's vertex
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descriptor type and the value type of the color map must model
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<a href="./ColorValue.html">ColorValue</a>.<br>
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<b>Default:</b> an <a
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href="../../property_map/doc/iterator_property_map.html">
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</tt>iterator_property_map</tt></a> created from a
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<tt>std::vector</tt> of <tt>default_color_type</tt> of size
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<tt>num_vertices(g)</tt> and using the <tt>i_map</tt> for the index
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map.<br>
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<b>Python</b>: The color map must be a <tt>vertex_color_map</tt> for
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the graph.
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</blockquote>
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IN: <tt>root_vertex(typename
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graph_traits<VertexListGraph>::vertex_descriptor start)</tt>
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<blockquote>
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This specifies the vertex that the depth-first search should
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originate from. The type is the type of a vertex descriptor for the
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given graph.<br>
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<b>Default:</b> <tt>*vertices(g).first</tt><br>
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</blockquote>
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IN: <tt>vertex_index_map(VertexIndexMap i_map)</tt>
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<blockquote>
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This maps each vertex to an integer in the range <tt>[0,
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num_vertices(g))</tt>. This parameter is only necessary when the
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default color property map is used. The type <tt>VertexIndexMap</tt>
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must be a model of <a
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href="../../property_map/doc/ReadablePropertyMap.html">Readable Property
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Map</a>. The value type of the map must be an integer type. The
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vertex descriptor type of the graph needs to be usable as the key
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type of the map.<br>
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<b>Default:</b> <tt>get(vertex_index, g)</tt>.
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Note: if you use this default, make sure your graph has
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an internal <tt>vertex_index</tt> property. For example,
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<tt>adjacency_list</tt> with <tt>VertexList=listS</tt> does
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not have an internal <tt>vertex_index</tt> property.<br>
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<b>Python</b>: Unsupported parameter.
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</blockquote>
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<P>
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<H3><A NAME="SECTION001340300000000000000">
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Complexity</A>
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</H3>
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<P>
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The time complexity is <i>O(E + V)</i>.
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<P>
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<h3>Visitor Event Points</h3>
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<ul>
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<li><b><tt>vis.initialize_vertex(s, g)</tt></b> is invoked on every
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vertex of the graph before the start of the graph search.
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<li><b><tt>vis.start_vertex(s, g)</tt></b> is invoked on the source
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vertex once before the start of the search.
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<li><b><tt>vis.discover_vertex(u, g)</tt></b> is invoked when a vertex
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is encountered for the first time.
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<li><b><tt>vis.examine_edge(e, g)</tt></b> is invoked on every out-edge
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of each vertex after it is discovered.
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<li><b><tt>vis.tree_edge(e, g)</tt></b> is invoked on each edge as it
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becomes a member of the edges that form the search tree. If you
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wish to record predecessors, do so at this event point.
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<li><b><tt>vis.back_edge(e, g)</tt></b> is invoked on the back edges in
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the graph.
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<li><b><tt>vis.forward_or_cross_edge(e, g)</tt></b> is invoked on
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forward or cross edges in the graph. In an undirected graph this
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method is never called.
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<li><b><tt>vis.finish_edge(e, g)</tt></b> is invoked on the non-tree edges in
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the graph as well as on each tree edge after its target vertex is finished.
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<li><b><tt>vis.finish_vertex(u, g)</tt></b> is invoked on a vertex after
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all of its out edges have been added to the search tree and all of
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the adjacent vertices have been discovered (but before their
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out-edges have been examined).
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</ul>
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<H3>Example</H3>
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<P>
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The example in <a href="../example/dfs-example.cpp">
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<TT>examples/dfs-example.cpp</TT></a> shows DFS applied to the graph in
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<A HREF="./graph_theory_review.html#fig:dfs-example">Figure 1</A>.
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<h3>See Also</h3>
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<a href="./depth_first_visit.html"><tt>depth_first_visit</tt></a>
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<a href="./undirected_dfs.html"><tt>undirected_dfs</tt></a>
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<h3>Notes</h3>
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<p><a name="1">[1]</a>
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Since the visitor parameter is passed by value, if your visitor
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contains state then any changes to the state during the algorithm
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will be made to a copy of the visitor object, not the visitor object
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passed in. Therefore you may want the visitor to hold this state by
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pointer or reference.
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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 © 2000-2001</TD><TD>
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<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>,
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Indiana University (<A
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HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)<br>
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<A HREF="http://www.boost.org/people/liequan_lee.htm">Lie-Quan Lee</A>, Indiana University (<A HREF="mailto:llee@cs.indiana.edu">llee@cs.indiana.edu</A>)<br>
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<A HREF="https://homes.cs.washington.edu/~al75">Andrew Lumsdaine</A>,
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Indiana University (<A
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HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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