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     Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2002
    
     Distributed under the Boost Software License, Version 1.0.
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<Head>
<Title>Boost Graph Library: Undirected 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>undirected_dfs</TT>
</H1>

<P>
<PRE>
<i>// named parameter version</i>
template &lt;typename Graph, typename P, typename T, typename R&gt;
void undirected_dfs(Graph&amp; G, const bgl_named_params&lt;P, T, R&gt;&amp; params);

<i>// non-named parameter version</i>
template &lt;typename Graph, typename <a href="DFSVisitor.html">DFSVisitor</a>, typename VertexColorMap, typename EdgeColorMap&gt;
void undirected_dfs(const Graph&amp; g, DFSVisitor vis, VertexColorMap vertex_color, EdgeColorMap edge_color)

template &lt;typename Graph, typename <a href="DFSVisitor.html">DFSVisitor</a>, typename VertexColorMap, typename EdgeColorMap&gt;
void undirected_dfs(const Graph&amp; g, DFSVisitor vis,
                    VertexColorMap vertex_color, EdgeColorMap edge_color,
                    typename graph_traits&lt;Graph&gt;::vertex_descriptor start)

</PRE>

<p>
The <tt>undirected_dfs()</tt> function performs a depth-first
traversal of the vertices in an undirected 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>
Edges are also colored during the search to disambiguate tree and back
edges.
</p>

<p>
The <tt>undirected_dfs()</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 indicated in by the triangles and 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>undirected_dfs()</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>vcolor[u] :=</i> WHITE
    <i>p[u] := u</i> 
  <b>end for</b>
  <b>for</b> each edge <i>e in E</i> 
    <i>ecolor[u] :=</i> WHITE
  <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>vcolor[u] =</i> WHITE
      <b>call</b> DFS-VISIT(<i>G</i>, <i>u</i>)
  <b>end for</b>
  <b>return</b> (<i>p</i>,<i>d_time</i>,<i>f_time</i>) <br>
DFS-VISIT(<i>G</i>, <i>u</i>) 
  <i>vcolor[u] :=</i> GRAY
  <i>d_time[u] := time := time + 1</i> 
  <b>for</b> each <i>e in Out[u]</i> 
    <b>var</b> <i>ec := ecolor[e]</i>
    <i>ecolor[e] :=</i> BLACK
    <b>if</b> (<i>vcolor[v] =</i> WHITE)
      <i>p[v] := u</i> 
      <b>call</b> DFS-VISIT(<i>G</i>, <i>v</i>)
    <b>else if</b> (<i>vcolor[v] =</i> GRAY and <i>ec =</i> WHITE)
      <i>...</i>
    <i>...</i>
  <b>end for</b>
  <i>vcolor[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
-
-
finish edge <i>(u,v)</i>
-
finish vertex <i>u</i>
-
</pre>
</td>
</tr>
</table>


<H3>Where Defined</H3>

<P>
<a href="../../../boost/graph/undirected_dfs.hpp"><TT>boost/graph/undirected_dfs.hpp</TT></a>

<h3>Parameters</h3>

IN: <tt>Graph&amp; g</tt>
<blockquote>
  An undirected graph. The graph type must
  be a model of <a href="./IncidenceGraph.html">Incidence Graph</a>,
  <a href="./VertexListGraph.html">Vertex List Graph</a>,
  and <a href="./EdgeListGraph.html">Edge 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&lt;null_visitor&gt;</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>vertex_color_map(VertexColorMap vertex_color)</tt>
<blockquote>
  This is used by the algorithm to keep track of its progress through
  the graph. The type <tt>VertexColorMap</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>

UTIL: <tt>edge_color_map(EdgeColorMap edge_color)</tt>
<blockquote>
  This is used by the algorithm to keep track of which edges
  have been visited. The type <tt>EdgeColorMap</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 edge
  descriptor type and the value type of the color map must model
  <a href="./ColorValue.html">ColorValue</a>.<br>
  <b>Default:</b> none.<br>

  <b>Python</b>: The color map must be an <tt>edge_color_map</tt> for
  the graph.
</blockquote>

IN: <tt>root_vertex(typename
graph_traits&lt;VertexListGraph&gt;::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>
</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.finish_edge(e, g)</tt></b> is invoked on the back 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>
An example is in <a href="../example/undirected_dfs.cpp">
<TT>examples/undirected_dfs.cpp</TT></a>.

<h3>See Also</h3>

<a href="./depth_first_search.html"><tt>depth_first_search</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 &copy; 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>

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