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251 lines
8.5 KiB
HTML
<HTML>
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<!--
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-- Copyright (c) Jeremy Siek 2000
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--
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-- Permission to use, copy, modify, distribute and sell this software
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-- and its documentation for any purpose is hereby granted without fee,
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-- provided that the above copyright notice appears in all copies and
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-- that both that copyright notice and this permission notice appear
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-- in supporting documentation. Silicon Graphics makes no
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-- representations about the suitability of this software for any
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-- purpose. It is provided "as is" without express or implied warranty.
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-->
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<Head>
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<Title>Boost Graph Library: Breadth-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="../../../c++boost.gif"
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ALT="C++ Boost">
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<BR Clear>
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<H1><A NAME="sec:bfs">
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<TT>breadth_first_search</TT>
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</H1>
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<P>
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<DIV ALIGN="LEFT">
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<TABLE CELLPADDING=3 border>
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<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
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<TD ALIGN="LEFT">directed and undirected</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
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<TD ALIGN="LEFT">color</TD>
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</TR>
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<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
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<TD ALIGN="LEFT">time: <i>O(V + E)</i></TD>
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</TR>
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</TABLE>
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</DIV>
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<P>
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<PRE>
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(1)
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template <class VertexListGraph, class BFSVisitor>
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void breadth_first_search(VertexListGraph& G,
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typename graph_traits<VertexListGraph>::vertex_descriptor s,
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BFSVisitor vis);
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(2)
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template <class VertexListGraph, class BFSVisitor, class ColorPA>
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void breadth_first_search(VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor s,
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BFSVisitor vis, ColorPA color);
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(3)
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template <class VertexListGraph, class BFSVisitor, class ColorPA>
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void breadth_first_search(VertexListGraph& g,
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typename graph_traits<VertexListGraph>::vertex_descriptor s,
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Buffer& Q, BFSVisitor vis, ColorPA color)
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</PRE>
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<P>
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The breadth-first search (BFS) algorithm is not really an algorithm in
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the sense that it has a particular purpose. Instead BFS is more like
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an algorithm <I>pattern</I>. One can do many different things with
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BFS. For example, the BFS pattern is used in the BGL to build several
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other algorithms: Dijkstra's shortest paths, Prim's Minimum Spanning
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Tree and best-first search. The definition of a <I>breadth-first
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search</I> is given in Section <A HREF="./graph_theory_review.html#sec:bfs-algorithm"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/local/src/teTeX00/lib/latex2html/icons/crossref.gif"></A>.
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<P>
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The BGL BFS functions are highly
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parameterized so that they can be used in a wide variety of places.
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The way to customize the BFS algorithm to perform different operations
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is to supply a visitor, which is a function object with multiple
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functions. Each member function of the visitor gets invoked at special
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times during the algorithm. Also, visitors can be layered on top of
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each other so that one can do lots of things during a single run of
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BFS. See Chapter <A HREF="./visitor_classes.html"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="file:/usr/local/src/teTeX00/lib/latex2html/icons/crossref.gif"></A> for more details.
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<P>
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Another way to customize the BFS algorithm is change the type of queue
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used. For instance, <TT>dijkstra_shortest_paths()</TT> uses a priority
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queue.
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<P>
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Version 1 of the algorithm takes only three arguments: the graph
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object, the source vertex, and a visitor to specify the actions to be
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taken during the graph search. The algorithm will need to use a color
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property which must be provided by the graph object (through a color
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plugin).
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<P>
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Version 2 of the algorithm adds a color property argument to
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accommodate the use of an external property accessor.
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<P>
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Version 3 of the algorithm is the most generalized. It adds a
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parameter for the queue. Version 1 and 2 of
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<TT>breadth_first_search()</TT> are implemented using this generalized
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version. This version does not initialize the color of all the
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vertices to white at the start of the algorithm or invoke the
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<tt>initialize_vertex()</tt> visitor method.
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<P>
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<H3>Where Defined</H3>
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<P>
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<a href="../../../boost/graph/breadth_first_search.hpp"><TT>boost/graph/breadth_first_search.hpp</TT></a>
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<P>
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<H3>Requirements on Types</H3>
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<P>
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<UL>
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<LI>The type <TT>IncidenceGraph</TT> must be a model of <a href="./IncidenceGraph.html">IncidenceGraph</a>.
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</LI>
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<LI>The type <TT>VertexListGraph</TT> must be a model of <a href="./VertexListGraph.html">VertexListGraph</a>.
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</LI>
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<LI>The type <TT>Vertex</TT> must be convertible to type <TT>graph_traits<VertexListGraph>::vertex_descriptor</TT>.
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</LI>
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<LI>The type <TT>BFSVisitor</TT> must be a model of <a href="./BFSVisitor.html">BFSVisitor</a>.
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</LI>
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<LI>In version (1) of the algorithm the graph must be a model
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of <a href="./VertexPropertyGraph.html">VertexPropertyGraph</a> for <TT>color_tag</TT> and
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the color property accessor for the graph must meet the
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same requirements as <TT>Color</TT>.
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</LI>
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<LI>The type <TT>Color</TT> must be a model of <a
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href="../../property_accessor/ReadWritePropertyAccessor.html">ReadWritePropertyAccessor</a>.
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A vertex descriptor must be usable as the key type of the accessor,
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and the value type of the accessor must be a model of <a
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href="./ColorValue.html">ColorValue</a>.
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</LI>
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<LI>The type <TT>Buffer</TT> must be a model of <I>Buffer</I>.
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</LI>
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<LI>The <TT>VisitedFunc</TT> type is a functor with an apply
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method that looks like this:
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<PRE>
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template <class Visitor, class Buffer, class Vertex>
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void operator()(Visitor v, Buffer& Q, Vertex target);}
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</PRE>
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<P>
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</LI>
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</UL>
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<P>
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<H3><A NAME="SECTION001330300000000000000">
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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><A NAME="SECTION001330400000000000000">
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Example</A>
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</H3>
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<P>
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This example demonstrates using the BGL Breadth-first search algorithm
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on the graph from Figure <A
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HREF="./graph_theory_review.html#fig:bfs-example"><IMG ALIGN="BOTTOM" BORDER="1"
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ALT="[*]"
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SRC="file:/usr/local/src/teTeX00/lib/latex2html/icons/crossref.gif"></A>.
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The source code for this example is in <a
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href="../examples/bfs_basics.cpp"><TT>examples/bfs_basics.cpp</TT></a>.
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<P>
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<PRE>
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// Select the graph type we wish to use
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typedef adjacency_list<vecS, undirectedS> Graph;
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// Set up the vertex ID's and names
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enum { r, s, t, u, v, w, x, y, N };
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char name[] = { 'r', 's', 't', 'u', 'v', 'w', 'x', 'y' };
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// Specify the edges in the graph
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typedef pair<int,int> E;
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E edge_array[] = { E(r,s), E(r,v), E(s,w), E(w,r), E(w,t),
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E(w,x), E(x,t), E(t,u), E(x,y), E(u,y) };
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// Create the graph object
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Graph G(N, edge_array, edge_array + sizeof(edge_array)/sizeof(E));
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// Some typedef's to save a little typing
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typedef Graph::vertex_descriptor Vertex;
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typedef std::vector<Vertex>::iterator Piter;
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typedef std::vector<Graph::size_type>::iterator Iiter;
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// vectors to hold color, discover time, and finish time properties
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std::vector<default_color_type> color(num_vertices(G));
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std::vector<Graph::size_type> dtime(num_vertices(G));
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std::vector<Graph::size_type> ftime(num_vertices(G));
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breadth_first_search(G, vertex(s,G),
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visit_timestamp(dtime.begin(), ftime.begin()),
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color.begin());
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// Use std::sort to order the vertices by their discover time
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vector<Graph::size_type> discover_order(N);
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iota(discover_order.begin(), discover_order.end(), 0);
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std::sort(discover_order.begin(), discover_order.end(),
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indirect_cmp<Iiter, std::less<Graph::size_type> >(dtime.begin()));
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cout << "order of discovery: ";
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for (int i = 0; i < N; ++i)
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cout << name[ discover_order[i] ] << " ";
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vector<Graph::size_type> finish_order(N);
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iota(finish_order.begin(), finish_order.end(), 0);
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std::sort(finish_order.begin(), finish_order.end(),
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indirect_cmp<Iiter, std::less<Graph::size_type> >(ftime.begin()));
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cout << endl << "order of finish: ";
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for (int i = 0; i < N; ++i)
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cout << name[ finish_order[i] ] << " ";
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cout << endl;
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</PRE>
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The output is:
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<PRE>
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order of discovery: s r w v t x u y
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order of finish: s r w v t x u y
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</PRE>
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<P>
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<h3>See Also</h3>
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<a href="./graph_search.html"><tt>graph_search()</tt></a> and
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<a href="./depth_first_search.html"><tt>depth_first_search()</tt></a>
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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</TD><TD>
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<A HREF=http://www.boost.org/people/jeremy_siek.htm>Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
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</TD></TR></TABLE>
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</BODY>
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</HTML>
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