| <HTML> |
| <!-- |
| Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2002 |
| |
| 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: 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 <typename Graph, typename P, typename T, typename R> |
| void undirected_dfs(Graph& G, const bgl_named_params<P, T, R>& params); |
| |
| <i>// non-named parameter version</i> |
| template <typename Graph, typename <a href="DFSVisitor.html">DFSVisitor</a>, typename VertexColorMap, typename EdgeColorMap> |
| void undirected_dfs(const Graph& g, DFSVisitor vis, VertexColorMap vertex_color, EdgeColorMap edge_color) |
| |
| template <typename Graph, typename <a href="DFSVisitor.html">DFSVisitor</a>, typename VertexColorMap, typename EdgeColorMap> |
| void undirected_dfs(const Graph& g, DFSVisitor vis, |
| VertexColorMap vertex_color, EdgeColorMap edge_color, |
| typename graph_traits<Graph>::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> |
| <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 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& 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<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>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<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> |
| </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> |
| |
| <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_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 © 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="http://www.osl.iu.edu/~lums">Andrew Lumsdaine</A>, |
| Indiana University (<A |
| HREF="mailto:lums@osl.iu.edu">lums@osl.iu.edu</A>) |
| </TD></TR></TABLE> |
| |
| </BODY> |
| </HTML> |
