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