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100
LICENSE
100
LICENSE
@@ -1,100 +0,0 @@
|
||||
COPYRIGHT NOTICE:
|
||||
|
||||
Copyright 1997-2000, University of Notre Dame.
|
||||
Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
|
||||
|
||||
The Boost Graph Library "Artistic License"
|
||||
|
||||
Preamble
|
||||
|
||||
The intent of this document is to state the conditions under which a
|
||||
Package may be copied, such that the Copyright Holder maintains some
|
||||
semblance of artistic control over the development of the package,
|
||||
while giving the users of the package the right to use and distribute
|
||||
the Package in a more-or-less free fashion, plus the right to make
|
||||
reasonable modifications.
|
||||
|
||||
Definitions
|
||||
|
||||
"Package" refers to the collection of files distributed by the
|
||||
Copyright Holder, and derivatives of that collection of files created
|
||||
through textual modification.
|
||||
|
||||
"Standard Version" refers to such a Package if it has not been
|
||||
modified, or has been modified in accordance with the wishes of the
|
||||
Copyright Holder as specified below.
|
||||
|
||||
"Copyright Holder" is whoever is named in the copyright or copyrights for the package.
|
||||
|
||||
"You" is you, if you're thinking about copying or distributing this Package.
|
||||
|
||||
"Reasonable copying fee" is whatever you can justify on the basis of
|
||||
media cost, duplication charges, time of people involved, and so
|
||||
on. (You will not be required to justify it to the Copyright Holder,
|
||||
but only to the computing community at large as a market that must
|
||||
bear the fee.)
|
||||
|
||||
"Freely Available" means that no fee is charged for the item itself,
|
||||
though there may be fees involved in handling the item. It also means
|
||||
that recipients of the item may redistribute it under the same
|
||||
conditions they received it.
|
||||
|
||||
1. You may make and give away verbatim copies of the source form of
|
||||
the Standard Version of this Package without restriction, provided
|
||||
that you duplicate all of the original copyright notices and
|
||||
associated disclaimers.
|
||||
|
||||
2. You may apply bug fixes, portability fixes and other modifications
|
||||
derived from the Public Domain or from the Copyright Holder. A Package
|
||||
modified in such a way shall still be considered the Standard Version.
|
||||
|
||||
3. You may otherwise modify your copy of this Package in any way,
|
||||
provided that you insert a prominent notice in each changed file
|
||||
stating how and when you changed that file, and provided that you do
|
||||
at least ONE of the following:
|
||||
|
||||
a. place your modifications in the Public Domain or otherwise make
|
||||
them Freely Available, such as by posting said modifications to Usenet
|
||||
or an equivalent medium, or placing the modifications on a major
|
||||
archive site such as uunet.uu.net, or by allowing the Copyright Holder
|
||||
to include your modifications in the Standard Version of the Package.
|
||||
b. use the modified Package only within your corporation or organization.
|
||||
c. rename any non-standard types and functions so the names do not
|
||||
conflict with Standard Vibrary, which must also be provided, and
|
||||
provide a separate documentation for each non-standard type of function
|
||||
that clearly documents how it differs from the Standard Version.
|
||||
d. make other distribution arrangements with the Copyright Holder.
|
||||
|
||||
4. You may charge a reasonable copying fee for any distribution of this
|
||||
Package. You may charge any fee you choose for support of this
|
||||
Package. You may not charge a fee for this Package itself. However,
|
||||
you may distribute this Package in aggregate with other (possibly
|
||||
commercial) programs as part of a larger (possibly commercial)
|
||||
software distribution provided that you do not advertise this Package
|
||||
as a product of your own.
|
||||
|
||||
5. The name of the Copyright Holder may not be used to endorse or
|
||||
promote products derived from this software without specific prior
|
||||
written permission.
|
||||
|
||||
DISCLAIMER:
|
||||
|
||||
LICENSOR MAKES NO REPRESENTATIONS OR WARRANTIES, EXPRESS OR IMPLIED.
|
||||
By way of example, but not limitation, Licensor MAKES NO
|
||||
REPRESENTATIONS OR WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY
|
||||
PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE COMPONENTS
|
||||
OR DOCUMENTATION WILL NOT INFRINGE ANY PATENTS, COPYRIGHTS, TRADEMARKS
|
||||
OR OTHER RIGHTS.
|
||||
|
||||
The Authors and the University of Notre Dame du Lac shall not be held
|
||||
liable for any liability nor for any direct, indirect or consequential
|
||||
damages with respect to any claim by LICENSEE or any third party on
|
||||
account of or arising from this Agreement or use of this software.
|
||||
|
||||
Any disputes arising out of this Agreement or LICENSEE'S use of the
|
||||
software at any time shall be resolved by the courts of the state of
|
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Indiana. LICENSEE hereby consents to the jurisdiction of the Indiana
|
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courts and waives the right to challenge the jurisdiction thereof in
|
||||
any dispute arising out of this Agreement or Licensee's use of the
|
||||
software.
|
||||
|
||||
@@ -1,164 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>AdjacencyGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
|
||||
<H2><A NAME="concept:AdjacencyGraph"></A>
|
||||
AdjacencyGraph
|
||||
</H2>
|
||||
|
||||
The AdjacencyGraph concept provides and interface for efficient access
|
||||
of the adjacent vertices to a vertex in a graph. This is quite similar
|
||||
to the <a href="./IncidenceGraph.html">IncidenceGraph</a> concept (the
|
||||
target of an out-edge is an adjacent vertex). Both concepts are
|
||||
provided because in some contexts there is only concern for the
|
||||
vertices, whereas in other contexts the edges are also important.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="Graph.html">Graph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>v</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<TR>
|
||||
<TD><pre>boost::graph_traits<G>::adjacency_iterator</pre>
|
||||
An adjacency iterator for a vertex <i>v</i> provides access to the
|
||||
vertices adjacent to <i>v</i>. As such, the value type of an
|
||||
adjacency iterator is the vertex descriptor type of its graph. An
|
||||
adjacency iterator must meet the requirements of <a
|
||||
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td><a name="sec:adjacent-vertices"><TT>adjacent_vertices(v, g)</TT></a></TD>
|
||||
<TD>
|
||||
Returns an iterator-range providing access to the vertices adjacent to
|
||||
vertex <TT>v</TT> in graph <TT>g</TT>.<a
|
||||
href="adjacencygraph.html#1">[1]</a>
|
||||
|
||||
<br> Return type:
|
||||
<TT>std::pair<adjacency_iterator, adjacency_iterator></TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Complexity guarantees</H3>
|
||||
|
||||
The <TT>adjacent_vertices()</TT> function must return in constant time.
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct AdjacencyGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::adjacency_iterator
|
||||
adjacency_iterator;
|
||||
void constraints() {
|
||||
function_requires< IncidenceGraphConcept<G> >();
|
||||
function_requires< MultiPassInputIteratorConcept<adjacency_iterator> >();
|
||||
|
||||
p = adjacent_vertices(v, g);
|
||||
v = *p.first;
|
||||
const_constraints(g);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
p = adjacent_vertices(v, g);
|
||||
}
|
||||
std::pair<adjacency_iterator,adjacency_iterator> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor v;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
<h3>Design Rationale</h3>
|
||||
|
||||
The AdjacencyGraph concept is somewhat frivolous since <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a> really covers the same
|
||||
functionality (and more). The AdjacencyGraph concept exists because
|
||||
there are situations when <tt>adjacent_vertices()</tt> is more
|
||||
convenient to use than <tt>out_edges()</tt>. If you are constructing a
|
||||
graph class and do not want to put in the extra work of creating an
|
||||
adjacency iterator, have no fear. There is an adaptor class in
|
||||
<tt>boost/graph/detail/adjacency_iterator.hpp</tt> that you can use to
|
||||
create an adjacency iterator out of an out-edge iterator.
|
||||
|
||||
<h3>Notes</h3>
|
||||
|
||||
<a name="1">[1]</a> The case of a
|
||||
<I>multigraph</I> (where multiple edges can connect the same two
|
||||
vertices) brings up an issue as to whether the iterators returned by
|
||||
the <TT>adjacent_vertices()</TT> function access a range that
|
||||
includes each adjacent vertex once, or whether it should match the
|
||||
behavior of the <TT>out_edges()</TT> function, and access a
|
||||
range that may include an adjacent vertex more than once. For now the
|
||||
behavior is defined to match that of <TT>out_edges()</TT>,
|
||||
though this decision may need to be reviewed in light of more
|
||||
experience with graph algorithm implementations.
|
||||
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,90 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>AdjacencyMatrix</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
|
||||
<H2><A NAME="concept:AdjacencyMatrix"></A>
|
||||
AdjacencyMatrix
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
The AdjacencyMatrix concept refines <a href="./Graph.html">Graph</a>
|
||||
concept and adds the requirement for efficient access to any edge in
|
||||
the graph given the source and target vertices. No Boost Graph Library
|
||||
algorithms currently use this concept. However there are algorithms
|
||||
not yet implemented such as Floyd-Warshall that would require this
|
||||
concept.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./Graph.html">Graph</a>
|
||||
|
||||
<H3>Valid Expressions</H3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Direct Edge Access</td>
|
||||
<TD><TT>edge(u,v,g)</TT></TD>
|
||||
<TD><TT>std::pair<edge_descriptor, bool></TT></TD>
|
||||
<TD>
|
||||
Returns a pair consisting of a flag saying whether there exists an
|
||||
edge between <TT>u</TT> and <TT>v</TT> in graph <TT>g</TT>, and
|
||||
consisting of the edge descriptor if the edge was found.
|
||||
</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
No models of this concept are currently in the Boost Graph Library.
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct AdjacencyMatrix
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
void constraints() {
|
||||
p = edge(u, v, g);
|
||||
}
|
||||
typename boost::graph_traits<G>::vertex_descriptor u, v;
|
||||
std::pair<bool, edge_descriptor> p;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,202 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: BFSVisitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>BFSVisitor Concept</H1>
|
||||
|
||||
This concept defines the visitor interface for <a
|
||||
href="./breadth_first_search.html"><tt>breadth_first_search()</tt></a>.
|
||||
Users can define a class with the BFSVisitor interface and pass and
|
||||
object of the class to <tt>breadth_first_search()</tt>, thereby
|
||||
augmenting the actions taken during the graph search.
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>V</tt></TD>
|
||||
<TD>A type that is a model of BFSVisitor.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>vis</tt></TD>
|
||||
<TD>An object of type <tt>V</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>s,u</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Initialize Vertex</td>
|
||||
<td><tt>vis.initialize_vertex(s, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every vertex of the graph before the start of the
|
||||
graph search.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Discover Vertex</td>
|
||||
<td><tt>vis.discover_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked when a vertex is encountered for the first time.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Examine Vertex</td>
|
||||
<td><tt>vis.examine_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on a vertex as it is popped from the queue. This
|
||||
happens immediately before <tt>examine_edge()</tt> is invoked
|
||||
on each of the out-edges of vertex <tt>u</tt>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Examine Edge</td>
|
||||
<td><tt>vis.examine_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every out-edge of each vertex after it is discovered.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>Tree Edge</td>
|
||||
<td><tt>vis.tree_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on each edge as it becomes a member of the edges that
|
||||
form the search tree.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Non-Tree Edge</td>
|
||||
<td><tt>vis.non_tree_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on back or cross edges for directed graphs and cross
|
||||
edges for undirected graphs.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Gray Target</td>
|
||||
<td><tt>vis.gray_target(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on the subset of non-tree edges who's target vertex is
|
||||
colored gray at the time of examination. The color gray indicates
|
||||
that the vertex is currently in the queue.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Black Target</td>
|
||||
<td><tt>vis.black_target(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on the subset of non-tree edges who's target vertex is
|
||||
colored black at the time of examination. The color black indicates
|
||||
that the vertex has been removed from the queue.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Finish Vertex</td>
|
||||
<td><tt>vis.finish_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This 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).
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="./bfs_visitor.html"><tt>bfs_visitor</tt></a>
|
||||
</ul>
|
||||
|
||||
|
||||
<h3>See also</h3>
|
||||
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,175 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: BellmanFordVisitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>BellmanFordVisitor Concept</H1>
|
||||
|
||||
This concept defines the visitor interface for <a
|
||||
href="./bellman_ford_shortest.html"><tt>bellman_ford_shortest_paths()</tt></a>.
|
||||
Users can define a class with the BellmanFordVisitor interface and
|
||||
pass and object of the class to <tt>bellman_ford_shortest_paths()</tt>,
|
||||
thereby augmenting the actions taken during the graph search.
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>V</tt></TD>
|
||||
<TD>A type that is a model of BellmanFordVisitor.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>vis</tt></TD>
|
||||
<TD>An object of type <tt>V</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>s,u</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Initialize Vertex</td>
|
||||
<td><tt>vis.initialize_vertex(s, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every vertex of the graph before the start of the
|
||||
graph search.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Examine Edge</td>
|
||||
<td><tt>vis.examine_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every edge in the graph <tt>num_vertices(g)</tt> times.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>Edge Relaxed</td>
|
||||
<td><tt>vis.edge_relaxed(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
Upon examination, if the following condition holds then the edge
|
||||
is relaxed (its distance is reduced), and this method is invoked.<br>
|
||||
<tt>
|
||||
tie(u,v) = incident(e, g);<br>
|
||||
D d_u = get(d, u), d_v = get(d, v);<br>
|
||||
W w_e = get(w, e);<br>
|
||||
assert(compare(combine(d_u, w_e), d_v));<br>
|
||||
</tt>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Edge Not Relaxed</td>
|
||||
<td><tt>edge_not_relaxed(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
Upon examination, if the edge is not relaxed (see above) then
|
||||
this method is invoked.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Edge Minimized</td>
|
||||
<td><tt>vis.edge_minimized(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
After the <tt>num_vertices(g)</tt> iterations through the edge set
|
||||
of the graph is complete, one last iteration is made to test whether
|
||||
each edge was minimized. If the edge is minimized then this function
|
||||
is invoked.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Edge Not Minimized</td>
|
||||
<td><tt>edge_not_minimized(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
If the edge is not minimized, this function is invoked. This happens
|
||||
when there is a negative cycle in the graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="./bellman_visitor.html"><tt>bellman_visitor</tt></a>
|
||||
</ul>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,173 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Bidirectional</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2>
|
||||
<A NAME="concept:BidirectionalGraph"></A>
|
||||
BidirectionalGraph
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
The BidirectionalGraph concept refines <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a> and adds the
|
||||
requirement for efficient access to the in-edges of each vertex. This
|
||||
concept is separated from <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a> because for directed
|
||||
graphs efficient access to in-edges typically requires more storage
|
||||
space, and many algorithms do not require access to in-edges. For
|
||||
undirected graphs this is not an issue, since the <TT>in_edges()</TT>
|
||||
and <TT>out_edges()</TT> functions are the same, they both return the
|
||||
edges incident to the vertex.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./IncidenceGraph.html">IncidenceGraph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>v</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<TR>
|
||||
<TD><pre>boost::graph_traits<G>::in_edge_iterator</pre>
|
||||
An in-edge iterator for a vertex <i>v</i> provides access to the
|
||||
in-edges of <i>v</i>. As such, the value type of an in-edge iterator
|
||||
is the edge descriptor type of its graph. An in-edge iterator must
|
||||
meet the requirements of <a href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</Table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<tr>
|
||||
<td><a name="sec:in-edges"><TT>in_edges(v, g)</TT></a></TD>
|
||||
<TD>
|
||||
Returns an iterator-range providing access to the
|
||||
in-edges (for directed graphs) or incident edges (for
|
||||
undirected graphs) of vertex <TT>v</TT> in graph <TT>g</TT>.
|
||||
For both directed and undirected graphs, the target of
|
||||
an out-edge is required to be vertex <tt>v</tt> and the
|
||||
source is required to be a vertex that is adjacent to <tt>v</tt>.
|
||||
<br>
|
||||
Return type: <TT>std::pair<in_edge_iterator, in_edge_iterator></TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>in_degree(v, g)</TT></TD>
|
||||
<TD>
|
||||
Returns the number of in-edges (for directed graphs) or the
|
||||
number of incident edges (for undirected graphs) of vertex <TT>v</TT>
|
||||
in graph <TT>g</TT>.<br>
|
||||
Return type: <TT>degree_size_type</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>degree(v, g)</TT></TD>
|
||||
<TD>Returns the number of in-edges plus out-edges (for directed graphs) or the
|
||||
number of incident edges (for undirected graphs) of vertex <TT>v</TT>
|
||||
in graph <TT>g</TT>.<br>
|
||||
Return type: <TT>degree_size_type</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</Table>
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
<ul>
|
||||
<li><a href="./adjacency_list.html"><tt>adjacency_list</tt></a> with <tt>Directed=bidirectionalS</tt></li>
|
||||
<li><a href="./adjacency_list.html"><tt>adjacency_list</tt></a> with <tt>Directed=undirectedS</tt></li>
|
||||
</ul>
|
||||
|
||||
|
||||
<H3>Complexity guarantees</H3>
|
||||
|
||||
The <TT>in_edges()</TT> function is required to be constant time. The
|
||||
<tt>in_degree()</tt> and <tt>degree()</tt> functions must be linear in
|
||||
the number of in-edges (for directed graphs) or incident edges (for
|
||||
undirected graphs).
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct BidirectionalGraph_concept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::in_edge_iterator
|
||||
in_edge_iterator;
|
||||
void constraints() {
|
||||
function_requires< IncidenceGraphConcept<G> >();
|
||||
function_requires< MultiPassInputIteratorConcept<in_edge_iterator> >();
|
||||
|
||||
p = in_edges(v, g);
|
||||
e = *p.first;
|
||||
const_constraints(g);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
p = in_edges(v, g);
|
||||
e = *p.first;
|
||||
}
|
||||
std::pair<in_edge_iterator, in_edge_iterator> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor v;
|
||||
typename boost::graph_traits<G>::edge_descriptor e;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
123
doc/Buffer.html
123
doc/Buffer.html
@@ -1,123 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Buffer</Title>
|
||||
</HEAD>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<h3>Buffer Concept</h3>
|
||||
|
||||
A Buffer is something in which items can be put and removed.
|
||||
The Buffer <i>concept</i> has very few requirements. It does
|
||||
not require any particular ordering of how the items are stored or in
|
||||
what order they will appear when removed, however, there is typically
|
||||
some sort of ordering policy.
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<table>
|
||||
<tr> <td> <tt>B</tt> </td> <td> is a type that models Buffer. </td></tr>
|
||||
<tr> <td> <tt>T</tt> </td> <td> is the value type of <tt>B</tt>. </td></tr>
|
||||
<tr> <td> <tt>t</tt> </td> <td> is an object of type <tt>T</tt>. </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
<h3>Members</h3>
|
||||
|
||||
For a type to model the Buffer concept it must have the following members.
|
||||
|
||||
<p>
|
||||
|
||||
<table border="1">
|
||||
|
||||
<tr> <td><b>Member</b></td> <td><b>Description</b></td> </tr>
|
||||
|
||||
<tr> <td> <tt>value_type</tt> </td>
|
||||
<td> The type of object stored in the Buffer. The value type
|
||||
must be <A href="http://www.sgi.com/tech/stl/Assignable.html">Assignable</a>.</td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>size_type</tt> </td>
|
||||
<td> An unsigned integral type for representing the number of
|
||||
objects in the Buffer.</td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>void push(const T& t)</tt> </td>
|
||||
<td> Inserts <tt>t</tt> into the Buffer. <tt>size()</tt> will be
|
||||
incremented by one.</td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>void pop()</tt> </td>
|
||||
<td> Removes an object from the Buffer. <tt>size()</tt> will be
|
||||
decremented by one. Precondition: <tt>empty()</tt>
|
||||
is <tt>false</tt>. </td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>T& top()</tt> </td>
|
||||
<td> Returns a mutable reference to some object in the Buffer.
|
||||
Precondition: <tt>empty()</tt> is <tt>false</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>const T& top() const</tt> </td>
|
||||
<td> Returns a const reference to some object in the Buffer.
|
||||
Precondition: <tt>empty()</tt> is <tt>false</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>void size() const</tt> </td>
|
||||
<td> Returns the number of objects in the Buffer.
|
||||
Invariant: <tt>size() >= 0</tt>. </td>
|
||||
</tr>
|
||||
|
||||
<tr> <td> <tt>bool empty() const</tt> </td>
|
||||
<td> Equivalent to <tt>b.size() == 0</tt>.</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Complexity Guarantees</h3>
|
||||
|
||||
<UL>
|
||||
|
||||
<LI> <tt>push()</tt>, <tt>pop()</tt>, and <tt>size()</tt> must be at
|
||||
most linear time complexity in the size of the Generalized Queue.
|
||||
|
||||
<LI> <tt>top()</tt> and <tt>empty()</tt> must be amortized constant time.
|
||||
|
||||
</UL>
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<UL>
|
||||
<LI><a href="http://www.sgi.com/tech/stl/stack.html"><tt>std::stack</tt></a>
|
||||
<LI><a href="../../pri_queue/queue.html"><tt>boost::queue</tt></a>
|
||||
<LI><a href="../../pri_queue/p_queue.html"><tt>boost::priority_queue</tt></a>
|
||||
</UL>
|
||||
|
||||
<p>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame and C++ Library & Compiler Group/SGI (<A HREF="mailto:jsiek@engr.sgi.com">jsiek@engr.sgi.com</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
|
||||
@@ -1,112 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: ColorValue Concept</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H1><A NAME="concept:ColorValue"></A>
|
||||
ColorValue
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
This concept describes the requirements for the type used for color
|
||||
values, as in for coloring a graph during a breath-first search to
|
||||
mark which vertices have been visited.
|
||||
|
||||
<P>
|
||||
|
||||
<h3>Refinement of</h3> <a
|
||||
href="http://www.sgi.com/tech/stl/EqualityComparable.html">EqualityComparable</a>
|
||||
and <a
|
||||
href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>
|
||||
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>T</tt></TD>
|
||||
<TD>A type that is a model of ColorValue.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>cv</tt></TD>
|
||||
<TD>An object of type <tt>T</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Get Color White </td>
|
||||
<TD><TT>color_traits<T>::white()</TT></TD>
|
||||
<TD><TT>T</TT></TD>
|
||||
<TD>Returns an object that represents the color white.</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td>Get Color Gray </td>
|
||||
<TD><TT>color_traits<T>::gray()</TT></TD>
|
||||
<TD><TT>T</TT></TD>
|
||||
<TD>Returns an object that represents the color gray.</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td>Get Color Black </td>
|
||||
<TD><TT>color_traits<T>::black()</TT></TD>
|
||||
<TD><TT>T</TT></TD>
|
||||
<TD>Returns an object that represents the color black.</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><tt>default_color_type</tt> (in <a href="../../../boost/graph/properties.hpp"><tt>boost/graph/properties.hpp</tt>)
|
||||
</ul>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,184 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>DFSVisitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>DFSVisitor Concept</H1>
|
||||
|
||||
This concept defines the visitor interface for <a
|
||||
href="./depth_first_search.html"><tt>depth_first_search()</tt></a>.
|
||||
Users can define a class with the DFSVisitor interface and pass and
|
||||
object of the class to <tt>depth_first_search()</tt>, thereby
|
||||
augmenting the actions taken during the graph search.
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>V</tt></TD>
|
||||
<TD>A type that is a model of DFSVisitor.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>vis</tt></TD>
|
||||
<TD>An object of type <tt>V</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>s,u</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Initialize Vertex</td>
|
||||
<td><tt>vis.initialize_vertex(s, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every vertex of the graph before the start of the
|
||||
graph search.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Start Vertex</td>
|
||||
<td><tt>vis.start_vertex(s, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on the source vertex once before the start of the
|
||||
search.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Discover Vertex</td>
|
||||
<td><tt>vis.discover_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked when a vertex is encountered for the first time.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Examine Edge</td>
|
||||
<td><tt>vis.examine_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every out-edge of each vertex after it is discovered.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>Tree Edge</td>
|
||||
<td><tt>vis.tree_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on each edge as it becomes a member of the edges that
|
||||
form the search tree.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Back Edge</td>
|
||||
<td><tt>vis.back_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on the back edges in the graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Forward or Cross Edge</td>
|
||||
<td><tt>vis.forward_or_cross_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on forward or cross edges in the graph. In an
|
||||
undirected graph this method is never called.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Finish Vertex</td>
|
||||
<td><tt>vis.finish_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This 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).
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="./dfs_visitor.html"><tt>dfs_visitor</tt></a>
|
||||
</ul>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,182 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>EdgeListGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2><A NAME="concept:EdgeListGraph"></A>
|
||||
EdgeListGraph
|
||||
</H2>
|
||||
|
||||
The EdgeListGraph concept refines the <a href="./Graph.html">Graph</a>
|
||||
concept, and adds the requirement for efficient access to all the
|
||||
edges in the graph.
|
||||
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./Graph.html">Graph</a>
|
||||
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of EdgeListGraph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::edge_iterator</pre>
|
||||
An edge iterator (obtained via <TT>edges(g)</TT>) provides access to
|
||||
all of the edges in a graph. An edge iterator type must meet the
|
||||
requirements of <a
|
||||
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>. The
|
||||
value type of the edge iterator must be the same as the edge
|
||||
descriptor of the graph.
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::edges_size_type</pre>
|
||||
The unsigned integer type used to represent the number of edges in the
|
||||
graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<TD><a name="sec:edges"><TT>edges(g)</TT></a></TD>
|
||||
<TD>Returns an iterator-range providing access to all
|
||||
the edges in the graph <TT>g</TT>.<br>
|
||||
Return type: <TT>std::pair<edge_iterator, edge_iterator></TT>
|
||||
</td>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>num_edges(g)</TT></TD>
|
||||
<TD>Returns the number of edges in the graph <TT>g</TT>.<br>
|
||||
Return type: <TT>edges_size_type</TT>
|
||||
</td>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>source(e, g)</TT></TD>
|
||||
<TD>
|
||||
Returns the vertex descriptor for <i>u</i> of the edge <i>(u,v)</i>
|
||||
represented by <TT>e</TT>.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<TD><TT>target(e, g)</TT></TD>
|
||||
<TD>
|
||||
Returns the vertex descriptor for
|
||||
<i>v</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
<UL>
|
||||
<LI><a href="./adjacency_list.html"><TT>adjacency_list</TT></a></LI>
|
||||
<LI><a href="./edge_list.html"><TT>edge_list</TT></a></LI>
|
||||
</UL>
|
||||
|
||||
|
||||
<H3>Complexity guarantees</H3>
|
||||
|
||||
The <TT>edges()</TT>, <TT>source()</TT>, and <TT>target()</TT> functions
|
||||
must all return in constant time.
|
||||
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct EdgeListGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::edge_iterator
|
||||
edge_iterator;
|
||||
void constraints() {
|
||||
function_requires< GraphConcept<G> >();
|
||||
function_requires< MultiPassInputIteratorConcept<edge_iterator> >();
|
||||
|
||||
p = edges(g);
|
||||
E = num_edges(g);
|
||||
e = *p.first;
|
||||
u = source(e, g);
|
||||
v = target(e, g);
|
||||
const_constraints(g);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
p = edges(g);
|
||||
E = num_edges(g);
|
||||
e = *p.first;
|
||||
u = source(e, g);
|
||||
v = target(e, g);
|
||||
}
|
||||
std::pair<edge_iterator,edge_iterator> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u, v;
|
||||
typename boost::graph_traits<G>::edge_descriptor e;
|
||||
typename boost::graph_traits<G>::edges_size_type E;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,165 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: EventVisitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>EventVisitor Concept</H1>
|
||||
|
||||
This concept defines the interface for single-event visitors. An
|
||||
EventVisitor has an apply member function (<tt>operator()</tt>) which
|
||||
is invoked within the graph algorithm at the event-point specified by
|
||||
the <tt>event_filter</tt> typedef within the
|
||||
EventVisitor. EventVisitor's can be combined into an <a
|
||||
href="./EventVisitorList.html">EventVistorList</a>.
|
||||
|
||||
<p>
|
||||
The following is the list of event tags that can be invoked in BGL
|
||||
algorithms. Each tag corresponds to a member function of the visitor
|
||||
for an algorithm. For example, the <a
|
||||
href="./BFSVisitor.html">BFSVisitor</a> of <a
|
||||
href="./breadth_first_search.html"><tt>breadth_first_search()</tt></a>
|
||||
has a <tt>cycle_edge()</tt> member function. The corresponding tag is
|
||||
<tt>on_cycle_edge</tt>. The first argument is the event visitor's
|
||||
<tt>operator()</tt> must be either an edge or vertex descriptor
|
||||
depending on the event tag.
|
||||
|
||||
<pre>
|
||||
namespace boost {
|
||||
struct on_initialize_vertex { };
|
||||
struct on_start_vertex { };
|
||||
struct on_discover_vertex { };
|
||||
struct on_examine_edge { };
|
||||
struct on_tree_edge { };
|
||||
struct on_cycle_edge { };
|
||||
struct on_finish_vertex { };
|
||||
struct on_forward_or_cross_edge { };
|
||||
struct on_back_edge { };
|
||||
struct on_edge_relaxed { };
|
||||
struct on_edge_not_relaxed { };
|
||||
struct on_edge_minimized { };
|
||||
struct on_edge_not_minimized { };
|
||||
} // namespace boost
|
||||
</pre>
|
||||
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of <a href="./Graph.html">Graph</a>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>V</tt></TD>
|
||||
<TD>A type that is a model of EventVisitor.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>vis</tt></TD>
|
||||
<TD>An object of type <tt>V</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>x</tt></TD>
|
||||
<TD>An object of type
|
||||
<tt>boost::graph_traits<G>::vertex_descriptor</tt>
|
||||
or <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<TR>
|
||||
<TD>Event Filter </TD>
|
||||
<TD><TT>V::event_filter</TT></TD>
|
||||
<TD>
|
||||
A tag struct to specify on which event the visitor should be invoked.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Apply Visitor</td>
|
||||
<td><TT>vis(x, g)</TT></TD>
|
||||
<TD><TT>void</TT></TD>
|
||||
<TD>
|
||||
Invokes the visitor operation on object <tt>x</tt>, which is
|
||||
either a vertex or edge descriptor of the graph.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
</table>
|
||||
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><a
|
||||
href="./predecessor_recorder.html"><tt>predecessor_recorder</tt></a>
|
||||
<li><a href="./distance_recorder.html"><tt>distance_recorder</tt></a>
|
||||
<li><a href="./time_stamper.html"><tt>time_stamper</tt></a>
|
||||
<li><a href="./property_writer.html"><tt>property_writer</tt></a>
|
||||
<li><a href="./null_visitor.html"><tt>null_visitor</tt></a>
|
||||
</ul>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./EventVisitorList.html">EventVisitorList</a>,
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,131 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: EventVisitorList</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>EventVisitorList Concept</H1>
|
||||
|
||||
An EventVisitorList is either an <a
|
||||
href="./EventVisitor.html">EventVisitor</a>, or a list of
|
||||
EventVisitor's combined using <tt>std::pair</tt>. Each graph algorithm
|
||||
defines visitor adaptors that convert an EventVisitorList into the
|
||||
particular kind of visitor needed by the algorithm.
|
||||
|
||||
In the following example we will show how to combine event visitors
|
||||
into a list using <tt>std::pair</tt> and how to use an algorithm's
|
||||
visitor adaptor class.
|
||||
|
||||
<p>
|
||||
Suppose we would like to print out the parenthesis
|
||||
structure of the discover/finish times of vertices in a <a
|
||||
href="./graph_theory_review.html#sec:dfs-algorithm">depth-first
|
||||
search</a>. We can use the BGL algorithm <a
|
||||
href="./depth_first_search.html"><tt>depth_first_search()</tt></a> and
|
||||
two event visitors to accomplish this. The complete source code for
|
||||
the following example is in <a href="../example/dfs_parenthesis.cpp">
|
||||
<tt>examples/dfs_parenthesis.cpp</tt></a>. First we define the two
|
||||
event visitors. We use <tt>on_discover_vertex</tt> and
|
||||
<tt>on_finish_vertex</tt> as the event points, selected from the list
|
||||
of event points specified in <a
|
||||
href="./DFSVisitor.html">DFSVisitor</a>.
|
||||
|
||||
<pre>
|
||||
struct open_paren : public base_visitor<open_paren> {
|
||||
typedef on_discover_vertex event_filter;
|
||||
template <class Vertex, class Graph>
|
||||
void operator()(Vertex v, Graph& G) {
|
||||
std::cout << "(" << v;
|
||||
}
|
||||
};
|
||||
struct close_paren : public base_visitor<close_paren> {
|
||||
typedef on_finish_vertex event_filter;
|
||||
template <class Vertex, class Graph>
|
||||
void operator()(Vertex v, Graph& G) {
|
||||
std::cout << v << ")";
|
||||
}
|
||||
};
|
||||
</pre>
|
||||
|
||||
Next we create two event visitor objects and make an EventVisitorList
|
||||
out of them using a <tt>std::pair</tt> which created by
|
||||
<tt>std::make_pair</tt>.
|
||||
|
||||
<pre>
|
||||
std::make_pair(open_paren(), close_paren())
|
||||
</pre>
|
||||
|
||||
Next we want to pass this list into <tt>depth_first_search()</tt>, but
|
||||
<tt>depth_first_search()</tt> is expecting a <a
|
||||
href="./DFSVisitor.html">DFSVisitor</a>, not a EventVisitorList. We
|
||||
therefore use the <a
|
||||
href="./dfs_visitor.html"><tt>dfs_visitor</tt></a> adaptor which turns
|
||||
an EventVisitor list into a DFSVisitor. Like all of the visitor
|
||||
adaptors, <tt>dfs_visitor</tt> has a creation function called
|
||||
<tt>make_dfs_visitor()</tt>.
|
||||
|
||||
<pre>
|
||||
make_dfs_visitor(std::make_pair(open_paren(), close_paren()))
|
||||
</pre>
|
||||
|
||||
Now we can pass the resulting visitor object into
|
||||
<tt>depth_first_search()</tt> as follows.
|
||||
|
||||
<pre>
|
||||
// graph object G is created ...
|
||||
|
||||
std::vector<default_color_type> color(num_vertices(G));
|
||||
|
||||
depth_first_search(G, make_dfs_visitor(std::make_pair(open_paren(), close_paren())),
|
||||
color.begin());
|
||||
</pre>
|
||||
|
||||
For creating a list of more than two event visitors, nest calls to
|
||||
<tt>std::make_pair</tt> in the following way:
|
||||
|
||||
<pre>
|
||||
std::make_pair(<i>visitor1</i>,
|
||||
std::make_pair(<i>visitor2</i>,
|
||||
...
|
||||
std::make_pair(<i>visitorN-1</i>, <i>visitorN</i>)...));
|
||||
</pre>
|
||||
|
||||
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./EventVisitor.html">EventVisitor</a>,
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
133
doc/Graph.html
133
doc/Graph.html
@@ -1,133 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Graph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H2><A NAME="concept:Graph"></A>
|
||||
Graph
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
The Graph concept contains a few requirements that are common to all
|
||||
the graph concepts. These include some associated types for
|
||||
<tt>vertex_descriptor</tt>, <tt>edge_descriptor</tt>, etc., and the
|
||||
<tt>num_vertices()</tt> and <tt>num_edges()</tt> functions. One should
|
||||
note that a model of Graph is <B>not</B> required to be a model of <a
|
||||
href="http://www.sgi.com/tech/stl/Assignable.html">Assignable</a>,
|
||||
so algorithms should pass graph objects by reference.
|
||||
|
||||
<P>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
</table>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::vertex_descriptor</pre>
|
||||
A vertex descriptor corresponds to a unique vertex in an abstract
|
||||
graph instance. A vertex descriptor must be
|
||||
<a
|
||||
href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>,
|
||||
<a href="http://www.sgi.com/tech/stl/Assignable.html">Assignable</a>, and
|
||||
<a href="http://www.sgi.com/tech/stl/EqualityComparable.html">EqualityComparable</a>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::edge_descriptor</pre>
|
||||
An edge descriptor corresponds to a unique edge <i>(u,v)</i> in a
|
||||
graph. An edge descriptor must be <a
|
||||
href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</I>,
|
||||
<a
|
||||
href="http://www.sgi.com/tech/stl/Assignable.html">Assignable</a>,
|
||||
and <a href="http://www.sgi.com/tech/stl/EqualityComparable.html">EqualityComparable</a>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::directed_category</pre>
|
||||
The choices are <TT>directed_tag</TT> and <TT>undirected_tag</TT>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::graph_traits<G>::edge_parallel_category</pre>
|
||||
This describes whether the graph class allows the insertion of
|
||||
parallel edges (edges with the same source and target). The two tags
|
||||
are <TT>allow_parallel_edge_tag</TT> and <TT>disallow_parallel_edge_tag</TT>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Valid Expressions</H3>
|
||||
|
||||
None required.
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct GraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::vertex_descriptor vertex_descriptor;
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
typedef typename boost::graph_traits<G>::directed_category directed_category;
|
||||
typedef typename boost::graph_traits<G>::edge_parallel_category edge_parallel_category;
|
||||
|
||||
void constraints() {
|
||||
function_requires< DefaultConstructibleConcept<vertex_descriptor> >();
|
||||
function_requires< EqualityComparableConcept<vertex_descriptor> >();
|
||||
function_requires< AssignableConcept<vertex_descriptor> >();
|
||||
function_requires< DefaultConstructibleConcept<edge_descriptor> >();
|
||||
function_requires< EqualityComparableConcept<edge_descriptor> >();
|
||||
function_requires< AssignableConcept<edge_descriptor> >();
|
||||
}
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,199 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>IncidenceGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="concept:IncidenceGraph"></A>
|
||||
IncidenceGraph
|
||||
</H1>
|
||||
|
||||
The IncidenceGraph concept provides an interface for
|
||||
efficient access to the out-edges of each vertex in the graph.
|
||||
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./Graph.html">Graph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of IncidenceGraph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>u, v</tt></TD>
|
||||
<TD>Are objects of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<TR>
|
||||
<TD>
|
||||
<pre>boost::graph_traits<G>::out_edge_iterator</pre>
|
||||
An out-edge iterator for a vertex <i>v</i> provides access to the
|
||||
out-edges of the vertex. As such, the value type of an out-edge
|
||||
iterator is the edge descriptor type of its graph. An out-edge
|
||||
iterator must meet the requirements of <a
|
||||
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><pre>boost::graph_traits<G>::degree_size_type</pre>
|
||||
The unsigned intergral type used for representing the number
|
||||
out-edges or incident edges of a vertex.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<tr>
|
||||
<td><a name="sec:source"><TT>source(e, g)</TT></a></TD>
|
||||
<TD>Returns the vertex descriptor for <i>u</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
<tr>
|
||||
<td><a name="sec:target"><TT>target(e, g)</TT></a></TD>
|
||||
<TD>Returns the vertex descriptor for <i>v</i> of the edge <i>(u,v)</i> represented by <TT>e</TT>.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</td></tr>
|
||||
|
||||
<tr>
|
||||
<td><a name="sec:out-edges"><TT>out_edges(u, g)</TT></a></TD>
|
||||
<TD>Returns an iterator-range providing access to the out-edges (for
|
||||
directed graphs) or incident edges (for undirected graphs) of vertex
|
||||
<TT>u</TT> in graph <TT>g</TT>. The source vertex of an edge obtained
|
||||
via and out edge iterator is guaranteed (for both directed and
|
||||
undirected graphs) to be the vertex <tt>u</tt> used in the call to
|
||||
<tt>out_edges(u, g)</tt> and the target vertex must the a vertex
|
||||
adjacent to <tt>u</tt>.<a href="">[1]</a>
|
||||
<br>
|
||||
Return type: <TT>std::pair<out_edge_iterator, out_edge_iterator></TT>
|
||||
</TD>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<TD><TT>out_degree(u, g)</TT></TD>
|
||||
<TD>Returns the number of out-edges (for directed graphs) or the
|
||||
number of incident edges (for undirected graphs) of vertex <TT>u</TT>
|
||||
in graph <TT>g</TT>.<br>
|
||||
Return type: <TT>degree_size_type</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Complexity guarantees</H3>
|
||||
|
||||
<P>
|
||||
The <TT>source()</TT>, <TT>target()</TT>, and <TT>out_edges()</TT>
|
||||
functions must all be constant time. The <tt>out_degree()</tt>
|
||||
function must be linear in the number of out-edges.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<H3>Notes</H3>
|
||||
|
||||
<a name="1">[1]</a> For undirected graphs, the edge <tt>(u,v)</tt> is
|
||||
the same as edge <tt>(v,u)</tt>, so without some extra guarantee an
|
||||
implementation would be free use any ordering for the pair of vertices
|
||||
in an out-edge. For example, if you call <tt>out_edges(u, g)</tt>, and
|
||||
<tt>v</tt> is one of the vertices adjacent to <tt>u</tt>, then the
|
||||
implementation would be free to return <tt>(v,u)</tt> as an out-edge
|
||||
which would be non-intuitive and cause trouble for algorithms.
|
||||
Therefore, the extra requirement is added that the out-edge connecting
|
||||
<tt>u</tt> and <tt>v</tt> must be given as <tt>(u,v)</tt> and not
|
||||
<tt>(v,u)</tt>.
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct IncidenceGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::out_edge_iterator out_edge_iterator;
|
||||
void constraints() {
|
||||
function_requires< GraphConcept<G> >();
|
||||
function_requires< MultiPassInputIteratorConcept<out_edge_iterator> >();
|
||||
|
||||
p = out_edges(v, g);
|
||||
e = *p.first;
|
||||
u = source(e, g);
|
||||
v = target(e, g);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
p = out_edges(v, g);
|
||||
e = *p.first;
|
||||
u = source(e, g);
|
||||
v = target(e, g);
|
||||
}
|
||||
std::pair<out_edge_iterator, out_edge_iterator> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u, v;
|
||||
typename boost::graph_traits<G>::edge_descriptor e;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,165 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>IteratorConstructibleGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="concept:IteratorConstructibleGraph"></A>
|
||||
IteratorConstructibleGraph
|
||||
</H1>
|
||||
|
||||
The IteratorConstructibleGraph concept describes the interface for
|
||||
graph types that can be constructed using a kind of edge iterator. The
|
||||
edge iterator can be any <a
|
||||
href="http://www.sgi.com/tech/stl/InputIterator.html">InputIterator</a>
|
||||
that dereferences to a pair of integers <i>(i,j)</i>, which represent
|
||||
an edge that should be in the graph. The two integers <i>i</i> and
|
||||
<i>j</i> represent vertices where <i>0 <= i < |V|</i> and <i>0 <= j <
|
||||
|V|</i>. The edge iterator's value type should be
|
||||
<tt>std::pair<T,T></tt> (or at least be a structure that has
|
||||
members <tt>first</tt> and <tt>second</tt>) and the value type
|
||||
<tt>T</tt> of the pair must be convertible to the
|
||||
<tt>vertices_size_type</tt> of the graph (an integer).
|
||||
|
||||
There are two valid expressions required by this concept, both of
|
||||
which are constructors. The first creates a graph object from a
|
||||
first/last iterator range. The second constructor also takes a
|
||||
first/last iterator range and in addition requires the number of
|
||||
vertices and number of edges. For some graph and edge iterator types
|
||||
the second constructor can be more efficient than the first.
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
The following exampe creates two graph objects from an array of edges
|
||||
(vertex pairs). The type <tt>Edge*</tt> satisfies the requirements for
|
||||
an <a
|
||||
href="http://www.sgi.com/tech/stl/InputIterator.html">InputIterator</a>
|
||||
and can therefore be used to construct a graph.
|
||||
|
||||
<pre>
|
||||
typedef ... IteratorConstructibleGraph;
|
||||
typedef boost::graph_traits<IteratorConstructibleGraph> Traits;
|
||||
|
||||
typedef std::pair<Traits::vertices_size_type,
|
||||
Traits::vertices_size_type> Edge;
|
||||
Edge edge_array[] =
|
||||
{ Edge(0,1), Edge(0,2), Edge(0,3), Edge(0,4), Edge(0,5),
|
||||
Edge(1, 2), Edge(1,5), Edge(1,3),
|
||||
Edge(2, 4), Edge(2,5),
|
||||
Edge(3, 2),
|
||||
Edge(4, 3), Edge(4,1),
|
||||
Edge(5, 4) };
|
||||
Edge* first = edge_array,
|
||||
last = edge_array + sizeof(edge_array)/sizeof(Edge);
|
||||
|
||||
IteratorConstructibleGraph G1(first, last);
|
||||
// do something with G1 ...
|
||||
|
||||
Traits::vertices_size_type size_V = 6;
|
||||
Traits::edges_size_type size_E = sizeof(edge_array)/sizeof(Edge);
|
||||
IteratorConstructibleGraph G2(first, last, size_V, size_E);
|
||||
// do something with G2 ...
|
||||
</pre>
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
<a href="Graph.html">Graph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<tr>
|
||||
<td><tt>G</tt></td>
|
||||
<td>is a graph type that models IteratorConstructibleGraph.</td>
|
||||
<tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>g</tt></td>
|
||||
<td>is an object of type <tt>G</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>first, last</tt></td>
|
||||
<td>are edge iterators (see above).</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>Tr</tt></td>
|
||||
<td>is an object of type <tt>graph_traits<G></tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>n_vertices</tt></td>
|
||||
<td>is an object of type <tt>Tr::vertices_size_type</tt>.</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>n_edges</tt></td>
|
||||
<td>is an object of type <tt>Tr::edges_size_type</tt>.</td>
|
||||
</tr>
|
||||
|
||||
</Table>
|
||||
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<pre>G g(first, last);</pre>
|
||||
Construct graph object <tt>g</tt> given an edge range <tt>[first,last)</tt>.
|
||||
</td>
|
||||
<tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<pre>G g(first, last, n_vertices, n_edges);</pre>
|
||||
Construct graph object <tt>g</tt> given an edge range
|
||||
<tt>[first,last)</tt>, the number of vertices, and the number of
|
||||
edges. Sometimes this constructor is more efficient than the
|
||||
constructor lacking the graph size information.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</Table>
|
||||
|
||||
|
||||
<!--
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
</PRE>
|
||||
-->
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,303 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>MutableGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2><A NAME="sec:MutableGraph"></A>
|
||||
MutableGraph
|
||||
</H2>
|
||||
|
||||
A MutableGraph can be changed via the addition or removal of
|
||||
edges and vertices.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./Graph.html">Graph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>u,v</tt></TD>
|
||||
<TD>are objects of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>iter</tt></TD>
|
||||
<TD>is an object of type <tt>boost::graph_traits<G>::out_edge_iterator</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>p</tt></TD>
|
||||
<TD>is an object of a type that models <a
|
||||
href="http://www.sgi.com/tech/stl/Predicate.html">Predicate</a>
|
||||
and whose argument type matches the <tt>edge_descriptor</tt> type.
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Valid Expressions</H3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<TD><a name="sec:add-edge"><TT>add_edge(u, v, g)</TT></a></TD>
|
||||
<TD>
|
||||
Inserts the edge <i>(u,v)</i> into the graph, and returns an edge
|
||||
descriptor pointing to the new edge. If the graph disallows parallel
|
||||
edges, and the edge <i>(u,v)</i> is already in the graph, then the
|
||||
<tt>bool</tt> flag returned is <tt>false</tt> and the returned edge
|
||||
descriptor points to the already existing edge. Note that for
|
||||
undirected graphs, <i>(u,v)</i> is the same edge as <i>(v,u)</i>, so
|
||||
after a call to the function <tt>add_edge()</tt>, this implies that
|
||||
edge <i>(u,v)</i> will appear in the out-edges of <i>u</i> and
|
||||
<i>(u,v)</i> (or equivalently <i>(v,u)</i>) will appear in the
|
||||
out-edges of <i>v</i>. Put another way, <i>v</i> will be adjacent to
|
||||
<i>u</i> and <i>u</i> will be adjacent to <i>v</i>.
|
||||
<br>
|
||||
Return type: <TT>std::pair<edge_descriptor, bool></TT>
|
||||
</TD>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<TD><a name="sec:remove_edge"><TT>remove_edge(u, v, g)</TT></a></TD>
|
||||
<TD>
|
||||
Remove the edge <i>(u,v)</i> from the graph. If the
|
||||
graph allows parallel edges this remove all occurances of
|
||||
<i>(u,v)</i>.<br>
|
||||
Return type: <TT>void</TT><br>
|
||||
Precondition: <i>u</i> and <i>v</i> are vertices in the graph.<br>
|
||||
Postcondition: <i>(u,v)</i> is no longer in the edge set for
|
||||
<TT>g</TT>.<br>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
<tr>
|
||||
<TD><TT>remove_edge(e, g)</TT></TD>
|
||||
<TD>Remove the edge <i>e</i> from the graph.<br>
|
||||
Return type: <TT>void</TT><br>
|
||||
Precondition: <i>e</i> is an edge in the graph.<br>
|
||||
Postcondition: <i>e</i> is no longer in the edge set for <TT>g</TT>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>remove_edge(iter, g)</TT></TD>
|
||||
<TD>Remove the edge pointed to be <tt>iter</tt> from the graph. This
|
||||
expression is only required when the graph also models <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a>.<br>
|
||||
Return type: <TT>void</TT><br>
|
||||
Precondition: <tt>*iter</tt> is an edge in the graph.<br>
|
||||
Postcondition: <tt>*iter</tt> is no longer in the edge set for <TT>g</TT>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>remove_edge_if(p, g)</TT></TD>
|
||||
<TD>Remove all the edges from graph <tt>g</tt> for which
|
||||
the predicate <tt>p</tt> returns true.<br>
|
||||
Return type: <TT>void</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>remove_out_edge_if(u, p, g)</TT></TD>
|
||||
<TD>Remove all the out-edges of vertex <tt>u</tt> for which the
|
||||
predicate <tt>p</tt> returns true. This expression is only required
|
||||
when the graph also models <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a>.<br>
|
||||
Return type: <TT>void</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>remove_in_edge_if(u, p, g)</TT></TD>
|
||||
<TD>Remove all the in-edges of vertex <tt>u</tt> for which the
|
||||
predicate <tt>p</tt> returns true. This expression is only required when the
|
||||
graph also models <a
|
||||
href="./BidirectionalGraph.html">BidirectionalGraph</a>.<br>
|
||||
Return type: <TT>void</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
<tr>
|
||||
<TD><a name="sec:add-vertex"><TT>add_vertex(g)</TT></a></TD>
|
||||
<TD>
|
||||
Add a new vertex to the graph. The <TT>vertex_descriptor</TT> for the
|
||||
new vertex is returned.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
<tr>
|
||||
<TD><TT>clear_vertex(u, g)</TT></TD>
|
||||
<TD>
|
||||
Remove all edges to and from vertex <tt>u</tt> from the graph.<br>
|
||||
Return type: <TT>void</TT><br>
|
||||
Precondition: <tt>u</tt> is a valid vertex descriptor of <TT>g</TT>.<br>
|
||||
Postcondition: <tt>u</tt> does not appear as a source or target of
|
||||
any edge in <TT>g</TT>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><a name="sec:remove-vertex"><TT>remove_vertex(u, g)</TT></a></TD>
|
||||
<TD>
|
||||
Remove <i>u</i> from the vertex set of the graph. Note that undefined
|
||||
behavior may result if there are edges remaining in the graph who's
|
||||
target is <i>u</i>. Typically the <TT>clear_vertex()</TT> function
|
||||
should be called first.<br>
|
||||
Return type: <TT>void</TT><br>
|
||||
Precondition: <TT>u</TT> is a valid vertex descriptor of <TT>g</TT>.<br>
|
||||
Postcondition: <TT>num_vertices(g)</TT> is one less, <TT>u</TT>
|
||||
no longer appears in the vertex set of the graph and it
|
||||
is no longer a valid vertex descriptor.
|
||||
</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Complexity Guarantees</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>Edge insertion must be either amortized constant time or it
|
||||
can be <i>O(log(E/V))</i> if the insertion also checks to
|
||||
prevent the addition of parallel edges (which is a ``feature'' of
|
||||
some graph types).
|
||||
</LI>
|
||||
<LI>Edge removal is guaranteed to be <i>O(E)</i>.</LI>
|
||||
<LI>Vertex insertion is guaranteed to be amortized constant time.</LI>
|
||||
<LI>Clearing a vertex is <i>O(E + V)</i>.</LI>
|
||||
<LI>Vertex removal is <i>O(E + V)</i>.</LI>
|
||||
</UL>
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
<UL>
|
||||
<LI><TT>adjacency_list</TT>
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct MutableGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
void constraints() {
|
||||
v = add_vertex(g);
|
||||
clear_vertex(v, g);
|
||||
remove_vertex(v, g);
|
||||
e_b = add_edge(u, v, g);
|
||||
remove_edge(u, v, g);
|
||||
remove_edge(e, g);
|
||||
}
|
||||
G g;
|
||||
edge_descriptor e;
|
||||
std::pair<edge_descriptor, bool> e_b;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u, v;
|
||||
typename boost::graph_traits<G>::out_edge_iterator iter;
|
||||
};
|
||||
|
||||
template <class edge_descriptor>
|
||||
struct dummy_edge_predicate {
|
||||
bool operator()(const edge_descriptor& e) const {
|
||||
return false;
|
||||
}
|
||||
};
|
||||
|
||||
template <class G>
|
||||
struct MutableIncidenceGraphConcept
|
||||
{
|
||||
void constraints() {
|
||||
function_requires< MutableGraph<G> >();
|
||||
remove_edge(iter, g);
|
||||
remove_out_edge_if(u, p, g);
|
||||
}
|
||||
G g;
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
dummy_edge_predicate<edge_descriptor> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u;
|
||||
typename boost::graph_traits<G>::out_edge_iterator iter;
|
||||
};
|
||||
|
||||
template <class G>
|
||||
struct MutableBidirectionalGraphConcept
|
||||
{
|
||||
void constraints() {
|
||||
function_requires< MutableIncidenceGraph<G> >();
|
||||
remove_in_edge_if(u, p, g);
|
||||
}
|
||||
G g;
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
dummy_edge_predicate<edge_descriptor> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u;
|
||||
};
|
||||
|
||||
template <class G>
|
||||
struct MutableEdgeListGraphConcept
|
||||
{
|
||||
void constraints() {
|
||||
function_requires< MutableGraph<G> >();
|
||||
remove_edge_if(p, g);
|
||||
}
|
||||
G g;
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
dummy_edge_predicate<edge_descriptor> p;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,154 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>MutablePropertyGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
|
||||
<H2>
|
||||
<A NAME="sec:MutablePropertyGraph"></A>
|
||||
MutablePropertyGraph
|
||||
</H2>
|
||||
|
||||
A MutablePropertyGraph is a <a
|
||||
href="./MutableGraph.html">MutableGraph</a> with properties attached
|
||||
internally to the vertices and edges. When adding vertices and edges
|
||||
the value of the properties can be given.
|
||||
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./MutableGraph.html">MutableGraph</a> and
|
||||
<a href="./PropertyGraph.html">PropertyGraph</a>
|
||||
|
||||
<H3>Notation</H3>
|
||||
|
||||
|
||||
<TABLE>
|
||||
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>u,v</tt></TD>
|
||||
<TD>are objects of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><TT>ep</TT></TD><TD>is an object of type <TT>G::edge_property_type</TT></TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><TT>vp</TT></TD><TD>is an object of type <TT>G::vertex_property_type</TT></TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td>Edge Property Type </td>
|
||||
<td><TT>graph_traits<G>::edge_property_type</TT></td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Vertex Property Type </td>
|
||||
<td><TT>graph_traits<G>::vertex_property_type</TT> </td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<TD><TT>add_edge(u, v, ep, g)</TT></TD>
|
||||
<TD>Inserts the edge <i>(u,v)</i> into the graph, and
|
||||
copies object <TT>ep</TT> into the property property for that edge.<br>
|
||||
Return type: <TT>std::pair<edge_descriptor, bool></TT></TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<TD><TT>add_vertex(vp, g)</TT></TD>
|
||||
<TD>
|
||||
Add a new vertex to the graph and copy <TT>vp</TT> into the property
|
||||
property for the new vertex. The <TT>vertex_descriptor</TT> for the new
|
||||
vertex is returned.<br>
|
||||
Return type: <TT>vertex_descriptor</TT>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
<UL>
|
||||
<LI><TT>adjacency_list</TT></LI>
|
||||
</UL>
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct MutablePropertyGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::edge_descriptor edge_descriptor;
|
||||
void constraints() {
|
||||
function_requires< MutableGraphConcept<G> >();
|
||||
v = add_vertex(vp, g);
|
||||
p = add_edge(u, v, ep, g);
|
||||
}
|
||||
G g;
|
||||
std::pair<edge_descriptor, bool> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor u, v;
|
||||
typename boost::graph_traits<G>::vertex_property_type vp;
|
||||
typename boost::graph_traits<G>::edge_property_type ep;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,105 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Property</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H2><A NAME="concept:Property"></A>
|
||||
Property
|
||||
</H2>
|
||||
|
||||
A Property type is a type used to name or identify properties that are
|
||||
attached to the vertices and edges of a graph. A Property type is not
|
||||
the type of the actual property values. Objects of the Property type
|
||||
are not used except to carry the type information which specifies the
|
||||
property.
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td>Property Kind </td>
|
||||
<td><TT>property_kind<Property>::type</TT> </td>
|
||||
<td>
|
||||
|
||||
This specifies whether the property is a <a
|
||||
name="VertexProperty">VertexProperty</a>
|
||||
(<tt>vertex_property_tag</tt>), an <a
|
||||
name="EdgeProperty">EdgeProperty</a> (<tt>edge_property_tag</tt>), or
|
||||
a <a name="GraphProperty">GraphProperty</a> which is attached to the
|
||||
graph object itself (<tt>graph_property_tag</tt>). The tags are
|
||||
defined in <a
|
||||
href="../../../boost/graph/properties.hpp"><tt>boost/graph/properties.hpp</tt></a>
|
||||
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
<a
|
||||
href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a>
|
||||
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
The following models of the Property concept are defined
|
||||
in <a
|
||||
href="../../../boost/graph/properties.hpp"><tt>boost/graph/properties.hpp</tt></a>.
|
||||
|
||||
<ul>
|
||||
<li><tt>vertex_index_t</tt></li>
|
||||
<li><tt>edge_index_t</tt></li>
|
||||
<li><tt>graph_name_t</tt></li>
|
||||
<li><tt>vertex_name_t</tt></li>
|
||||
<li><tt>edge_name_t</tt></li>
|
||||
<li><tt>edge_weight_t</tt></li>
|
||||
<li><tt>vertex_distance_t</tt></li>
|
||||
<li><tt>vertex_color_t</tt></li>
|
||||
<li><tt>vertex_degree_t</tt></li>
|
||||
<li><tt>vertex_out_degree_t</tt></li>
|
||||
<li><tt>vertex_in_degree_t</tt></li>
|
||||
<li><tt>vertex_discover_time_t</tt></li>
|
||||
<li><tt>vertex_finish_time_t</tt></li>
|
||||
</ul>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./PropertyGraph.html">PropertyGraph</a>
|
||||
and
|
||||
<a href="../../property_map/property_map.html">Property Map Concepts</a>
|
||||
|
||||
<h3>Notes</h3>
|
||||
|
||||
On compilers that do not support partial specialization, each Property
|
||||
type is also required to specialize
|
||||
<tt>property_num<Property></tt> to contain an enum named
|
||||
<tt>value</tt> which uniquely identifies the property type.
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,213 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>PropertyGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H2><A NAME="concept:PropertyGraph"></A>
|
||||
PropertyGraph
|
||||
</H2>
|
||||
|
||||
A PropertyGraph is a graph that has some property associated with each
|
||||
of the vertices or edges in the graph. As a given graph may have
|
||||
several properties associated with each vertex or edge, a tag is used
|
||||
to identity which property is being accessed. The graph provides a
|
||||
function which returns a property map object.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./Graph.html">Graph</a>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of PropertyGraph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>X</tt></TD>
|
||||
<TD>Either the vertex or edge descriptor type for <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>x</tt></TD>
|
||||
<TD>An object of type <tt>X</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
|
||||
<TR>
|
||||
<TD><tt>Map</tt></TD>
|
||||
<TD>The type <tt>boost::property_map<G, Property>::const_type</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>v</tt></TD>
|
||||
<TD>An object of type <tt>boost::property_traits<Map>::value_type</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>Property</tt></TD>
|
||||
<TD>A type that models the <a href="./Property.html">Property</a> concept.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>p</tt></TD>
|
||||
<TD>An object of type <tt>Property</tt>.</td>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>pmap</tt></TD>
|
||||
<TD>An object of type <tt>Map</tt>.</td>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Associated types</H3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::property_map<G, Property>::type</pre>
|
||||
The type of the property map for the property specified by
|
||||
<TT>Property</TT>. This type must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a> with a key type the same as the graph's vertex or descriptor type.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><pre>boost::property_map<G, Property>::const_type</pre>
|
||||
The type of the const property map for the property specified by
|
||||
<TT>Property</TT>. This type must be a model of <a
|
||||
href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>
|
||||
with a key type the same as the graph's vertex or edge descriptor type.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<td> <TT>get(p, g)</TT> </td>
|
||||
<td>
|
||||
Returns the property map for the property specified by the
|
||||
<tt>Property</tt> type. The object <tt>p</tt> is only used to
|
||||
carry the type.<br>
|
||||
Return type: <TT>boost::property_map<G, Property>::type</TT> if <TT>g</TT> is mutable and <br><TT>boost::property_map<G, Property>::const_type</TT> otherwise.
|
||||
</td>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td> <TT>get(p, g, x)</TT> </td>
|
||||
<td>
|
||||
Returns the property value (specified by the <tt>Property</tt> type)
|
||||
associated with object <tt>x</tt> (a vertex or edge).
|
||||
The object <tt>p</tt> is only used to carry the type.
|
||||
This function is equivalent to:<br>
|
||||
<tt>get(get(p, g), x)</tt><br>
|
||||
Return type: <tt>boost::property_traits<Map>::value_type</tt>
|
||||
</td>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td> <TT>put(p, g, x, v)</TT> </td>
|
||||
<td>
|
||||
Set the property (specified by the <tt>Property</tt> type)
|
||||
associated with object <tt>x</tt> (a vertex or edge) to
|
||||
the value <tt>v</tt>. The object <tt>p</tt> is only used to carry the type.
|
||||
This function is equivalent to:<br>
|
||||
<tt>
|
||||
pmap = get(p, g);<br>
|
||||
put(pmap, x, v)
|
||||
</tt><br>
|
||||
Return type: <TT>void</TT>
|
||||
</td>
|
||||
</TR>
|
||||
|
||||
|
||||
</TABLE>
|
||||
|
||||
<H3>Complexity</H3>
|
||||
|
||||
The <tt>get()</tt> property map function must be constant time.
|
||||
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
|
||||
<UL>
|
||||
<LI><tt>adjacency_list</tt> with <tt>VertexProperty=property<vertex_distance_t,int,property<vertex_in_degree_t,int> ></tt> and <tt>Property=vertex_distance_t</tt>.</li>
|
||||
<li><tt>adjacency_list</tt> with <tt>VertexProperty=property<vertex_distance_t,int,property<vertex_in_degree_t,int> ></TT> and <tt>Property=vertex_in_degree_t</tt>.</li>
|
||||
</UL>
|
||||
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<PRE>
|
||||
template <class Graph, class X, class Property>
|
||||
struct PropertyGraphConcept
|
||||
{
|
||||
typedef typename property_map<G, Property>::type Map;
|
||||
typedef typename property_map<G, Property>::const_type const_Map;
|
||||
void constraints() {
|
||||
function_requires< GraphConcept<G> >();
|
||||
function_requires< ReadWritePropertyMapConcept<Map, X> >();
|
||||
function_requires< ReadablePropertyMapConcept<const_Map, X> >();
|
||||
|
||||
Map pmap = get(Property(), g);
|
||||
pval = get(Property(), g, x);
|
||||
put(Property(), g, x, pval);
|
||||
ignore_unused_variable_warning(pmap);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
const_Map pmap = get(Property(), g);
|
||||
pval = get(Property(), g, x);
|
||||
ignore_unused_variable_warning(pmap);
|
||||
}
|
||||
G g;
|
||||
X x;
|
||||
typename property_traits<Map>::value_type pval;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./property_map.html"><tt>property_map</tt></a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,199 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: UniformCostVisitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>UniformCostVisitor Concept</H1>
|
||||
|
||||
This concept defines the visitor interface for <a
|
||||
href="./uniform_cost_search.html"><tt>uniform_cost_search()</tt></a>
|
||||
and related algorithms. The user can create a class that matches this
|
||||
interface, and then pass objects of the class into
|
||||
<tt>uniform_cost_search()</tt> to augment the actions taken during the
|
||||
search.
|
||||
|
||||
<h3>Refinement of</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Notation</h3>
|
||||
|
||||
<Table>
|
||||
<TR>
|
||||
<TD><tt>V</tt></TD>
|
||||
<TD>A type that is a model of UniformCostVisitor.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>vis</tt></TD>
|
||||
<TD>An object of type <tt>V</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>G</tt></TD>
|
||||
<TD>A type that is a model of Graph.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>g</tt></TD>
|
||||
<TD>An object of type <tt>G</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>e</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::edge_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>s,u,v</tt></TD>
|
||||
<TD>An object of type <tt>boost::graph_traits<G>::vertex_descriptor</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>DistanceMap</tt></TD>
|
||||
<TD>A type that is a model of <a href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>d</tt></TD>
|
||||
<TD>An object of type <tt>DistanceMap</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>WeightMap</tt></TD>
|
||||
<TD>A type that is a model of <a href="../../property_map/ReadWritePropertyMap.html">ReadablePropertyMap</a>.</TD>
|
||||
</TR>
|
||||
|
||||
<TR>
|
||||
<TD><tt>w</tt></TD>
|
||||
<TD>An object of type <tt>DistanceMap</tt>.</TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Associated Types</h3>
|
||||
|
||||
none
|
||||
<p>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Initialize Vertex</td>
|
||||
<td><tt>vis.initialize_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked one each vertex of the graph when it is initialized.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Start Vertex</td>
|
||||
<td><tt>vis.start_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on the source vertex at the beginning of the algorithm.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Discover Vertex</td>
|
||||
<td><tt>vis.discover_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked when a vertex is encountered for the first time.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Examine Edge</td>
|
||||
<td><tt>vis.examine_edge(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This is invoked on every out-edge of each vertex after it is discovered.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Edge Relaxed</td>
|
||||
<td><tt>vis.edge_relaxed(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
Upon examination, if the following condition holds then the edge
|
||||
is relaxed (its distance is reduced), and this method is invoked.<br>
|
||||
<tt>
|
||||
tie(u,v) = incident(e, g);<br>
|
||||
D d_u = get(d, u), d_v = get(d, v);<br>
|
||||
W w_e = get(w, e);<br>
|
||||
assert(compare(combine(d_u, w_e), d_v));<br>
|
||||
</tt>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Edge Not Relaxed</td>
|
||||
<td><tt>vis.edge_not_relaxed(e, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
Upon examination, if the edge is not relaxed (see above) then
|
||||
this method is invoked.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Finish Vertex</td>
|
||||
<td><tt>vis.finish_vertex(u, g)</tt></td>
|
||||
<td><tt>void</tt></td>
|
||||
<td>
|
||||
This 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).
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Models</h3>
|
||||
|
||||
<ul>
|
||||
<li><a href="./ucs_visitor.html"><tt>ucs_visitor</tt></a>
|
||||
</ul>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,74 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>VertexAndEdgeListGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2><A NAME="concept:VertexAndEdgeListGraph"></A>
|
||||
VertexAndEdgeListGraph
|
||||
</H2>
|
||||
|
||||
The VertexAndEdgeListGraph concept refines the <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a> and the <a
|
||||
href="./EdgeListGraph.html">EdgeListGraph</a> concepts. No further
|
||||
requirements are added.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./VertexListGraph.html">VertexListGraph</a>,
|
||||
<a href="./EdgeListGraph.html">EdgeListGraph</a>
|
||||
|
||||
|
||||
<H3>Models</H3>
|
||||
|
||||
<UL>
|
||||
<LI><TT>adjacency_list</TT></LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct VertexAndEdgeListGraph
|
||||
{
|
||||
void constraints() {
|
||||
function_requires< VertexListGraphConcept<G> >();
|
||||
function_requires< EdgeListGraphConcept<G> >();
|
||||
}
|
||||
};
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,153 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>VertexListGraph</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2><A NAME="concept:VertexListGraph">
|
||||
VertexListGraph
|
||||
</H2>
|
||||
|
||||
The VertexListGraph</I> concept refines the <a
|
||||
href="./AdjacencyGraph.html">AdjacencyGraph</a> concept, and adds the
|
||||
requirement for efficient traversal of all the vertices in the graph.
|
||||
|
||||
<H3>Refinement of</H3>
|
||||
|
||||
<a href="./IncidenceGraph.html">IncidenceGraph</a>
|
||||
and <a href="./AdjacencyGraph.html">AdjacencyGraph</a>
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<Table border>
|
||||
|
||||
<TR>
|
||||
<TD><tt>boost::graph_traits<G>::vertex_iterator</tt><br><br>
|
||||
A vertex iterator (obtained via <TT>vertices(g)</TT>) provides access
|
||||
to all of the vertices in a graph. A vertex iterator type must meet
|
||||
the requirements of <a
|
||||
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>. The
|
||||
value type of the vertex iterator must be the vertex descriptor of the
|
||||
graph.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td><tt>boost::graph_traits<G>::vertices_size_type</tt><br><br>
|
||||
The unsigned integer type used to represent the number of vertices
|
||||
in the graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Valid Expressions</h3>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Vertex Set of the Graph</td>
|
||||
<td><a name="sec:vertices"><TT>vertices(g)</TT></a></TD>
|
||||
<TD><TT>std::pair<vertex_iterator, vertex_iterator></TT></TD>
|
||||
<TD>
|
||||
Returns an iterator-range providing access to all the vertices in the
|
||||
graph<TT>g</TT>.
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
<tr>
|
||||
<td>Number of Vertices in the Graph </td>
|
||||
<td><TT>num_vertices(g)</TT></TD>
|
||||
<TD><TT>vertices_size_type</TT></TD>
|
||||
<TD>Returns the number of vertices in the graph <TT>g</TT>.</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
|
||||
|
||||
<H3>Complexity guarantees</H3>
|
||||
|
||||
<P>
|
||||
The <TT>vertices()</TT> function must return in constant time.
|
||||
|
||||
<H3>See Also</H3>
|
||||
|
||||
<a href="./graph_concepts.html">Graph concepts</a>
|
||||
|
||||
|
||||
<H3>Design Rationale</H3>
|
||||
|
||||
One issue in the design of this concept is whether to include the
|
||||
refinement from the <a href="./IncidenceGraph.html">IncidenceGraph</a>
|
||||
and <a href="./AdjacencyGraph.html">AdjacencyGraph</a> concepts. The
|
||||
ability to traverse the vertices of a graph is orthogonal to
|
||||
traversing out-edges, so it would make sense to have a VertexListGraph
|
||||
concept that only includes vertex traversal. However, such a concept
|
||||
would no longer really be a graph, but would just be a set, and the
|
||||
STL already has concepts for dealing with such things. However, there
|
||||
are many BGL algorithms that need to traverse the vertices and
|
||||
out-edges of a graph, so for convenience a concept is needed that
|
||||
groups these requirements together, hence the VertexListGraph concept.
|
||||
|
||||
|
||||
<H3>Concept Checking Class</H3>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
template <class G>
|
||||
struct VertexListGraphConcept
|
||||
{
|
||||
typedef typename boost::graph_traits<G>::vertex_iterator
|
||||
vertex_iterator;
|
||||
void constraints() {
|
||||
function_requires< IncidenceGraphConcept<G> >();
|
||||
function_requires< AdjacencyGraphConcept<G> >();
|
||||
function_requires< MultiPassInputIteratorConcept<vertex_iterator> >();
|
||||
|
||||
p = vertices(g);
|
||||
V = num_vertices(g);
|
||||
v = *p.first;
|
||||
const_constraints(g);
|
||||
}
|
||||
void const_constraints(const G& g) {
|
||||
p = vertices(g);
|
||||
V = num_vertices(g);
|
||||
v = *p.first;
|
||||
}
|
||||
std::pair<vertex_iterator, vertex_iterator> p;
|
||||
typename boost::graph_traits<G>::vertex_descriptor v;
|
||||
typename boost::graph_traits<G>::vertices_size_type V;
|
||||
G g;
|
||||
};
|
||||
</PRE>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,80 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Acknowledgements</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<h1>Acknowledgements</h1>
|
||||
|
||||
We owe many debts of thanks to a number of individuals who both
|
||||
inspired and encouraged us in developing the Boost Graph Library.
|
||||
|
||||
<p>
|
||||
A most profound thanks goes to Alexander Stepanov for his pioneering
|
||||
work in generic programming, for his encouragement, and for his
|
||||
algorithm contributions to the BGL. We thank Matthew Austern for his
|
||||
work on documenting the concepts of STL which provided a foundation
|
||||
for creating the concepts in the BGL. We thank Dietmar Kühl for
|
||||
his work on generic graph algorithms and design patterns; especially
|
||||
for the property map abstraction.
|
||||
|
||||
<p>
|
||||
Dave Abrahams, Jens Maurer, Beman Dawes, Gary Powell, Greg Colvin,
|
||||
Valentin Bonnard, and the rest of the group at Boost provided valuable
|
||||
input to the BGL interface, numerous suggestions for improvement,
|
||||
proof reads of the documentation, and help with polishing the code. A
|
||||
special thanks to Dave Abrahams for managing the formal review.
|
||||
|
||||
<p>
|
||||
We also thank the following BGL users whose questions helped to
|
||||
improve the BGL: Gordon Woodhull, Dave Longhorn, Joel Phillips, and
|
||||
Edward Luke.
|
||||
|
||||
<p>
|
||||
A special thanks to Jeffrey Squyres for editing and proof reading
|
||||
of the documentation.
|
||||
|
||||
<p>
|
||||
Our original work on the Boost Graph Library was supported in part by
|
||||
NSF grant ACI-9982205 and by the Director, Office of Science, Division
|
||||
of Mathematical, Information, and Computational Sciences of the U.S.
|
||||
Department of Energy under contract number DE-AC03-76SF00098.
|
||||
<p>
|
||||
In our work we also used resources of the National Energy Research
|
||||
Scientific Computing Center, which is supported by the Office of
|
||||
Science of the U.S. Department of Energy.
|
||||
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
File diff suppressed because it is too large
Load Diff
@@ -1,162 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Graph Traits</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME=""></A>
|
||||
<pre>
|
||||
adjacency_list_traits<EdgeList, VertexList, Directed>
|
||||
</pre>
|
||||
</H1>
|
||||
|
||||
This class provides an alternate method for accessing some of the
|
||||
associated types of the <tt>adjacency_list</tt> class. The main reason
|
||||
for this class is that sometimes one would like to create graph
|
||||
properties whose values are vertex or edge descriptors. If you try to
|
||||
use <tt>graph_traits</tt> for this you will run into a problem with
|
||||
mutually recursive types. To get around this problem, the
|
||||
<tt>adjacency_list_traits</tt> class is provided, which gives the user
|
||||
access to the vertex and edge descriptor types without requiring the
|
||||
user to provide the property types for the graph.
|
||||
|
||||
<pre>
|
||||
template <class EdgeList, class VertexList, class Directed>
|
||||
struct adjacency_list_traits {
|
||||
typedef ... vertex_descriptor;
|
||||
typedef ... edge_descriptor;
|
||||
typedef ... directed_category;
|
||||
typedef ... edge_parallel_category;
|
||||
};
|
||||
</pre>
|
||||
|
||||
<h3>Where Defined</h3>
|
||||
|
||||
<a href="../../../boost/graph/adjacency_list.hpp"><tt>boost/graph/adjacency_list.hpp</tt></a>
|
||||
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th><th>Default</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>EdgeList</TT></TD>
|
||||
<TD>
|
||||
The selector type for the edge container implementation.
|
||||
</TD>
|
||||
<td><tt>vecS</tt></td>
|
||||
</TR>
|
||||
|
||||
<TR><TD><TT>VertexList</TT></TD>
|
||||
<TD>
|
||||
The selector type for the vertex container implementation.
|
||||
</TD>
|
||||
<td><tt>vecS</tt></td>
|
||||
</TR>
|
||||
|
||||
<TR><TD><TT>Directed</TT></TD>
|
||||
<TD>
|
||||
The selector type whether the graph is directed or undirected.
|
||||
</TD>
|
||||
<td><tt>directedS</tt></td>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Model of</h3>
|
||||
|
||||
<a
|
||||
href="http://www.sgi.com/tech/stl/DefaultConstructible.html">DefaultConstructible</a> and
|
||||
<a href="http://www.sgi.com/tech/stl/Assignable.html">Assignable</a>
|
||||
|
||||
<h3>Type Requirements</h3>
|
||||
|
||||
Under construction.
|
||||
|
||||
<H2>Members</H2>
|
||||
|
||||
<p>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Member</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
vertex_descriptor
|
||||
</tt></td>
|
||||
<td>
|
||||
The type for the objects used to identify vertices in the graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
edge_descriptor
|
||||
</tt></td>
|
||||
<td>
|
||||
The type for the objects used to identify edges in the graph.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
directed_category
|
||||
</tt></td>
|
||||
<td>
|
||||
This says whether the graph is undirected (<tt>undirected_tag</tt>)
|
||||
or directed (<tt>directed_tag</tt>).
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
edge_parallel_category
|
||||
</tt></td>
|
||||
<td>
|
||||
This says whether the graph allows parallel edges to be inserted
|
||||
(<tt>allow_parallel_edge_tag</tt>) or if it automatically removes
|
||||
parallel edges (<tt>disallow_parallel_edge_tag</tt>).
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./adjacency_list.html"><tt>adjacency_list</tt></a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,97 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Bandwidth</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:bandwidth">
|
||||
<TT>bandwidth</TT>
|
||||
</H1>
|
||||
|
||||
<pre>
|
||||
(1)
|
||||
template <typename Graph>
|
||||
typename graph_traits<Graph>::vertices_size_type
|
||||
bandwidth(const Graph& g)
|
||||
|
||||
(2)
|
||||
template <typename Graph, typename VertexIndexMap>
|
||||
typename graph_traits<Graph>::vertices_size_type
|
||||
bandwidth(const Graph& g, VertexIndexMap index_map)
|
||||
</pre>
|
||||
|
||||
The <b><i>bandwidth</i></b> of an undirected graph is the maximum
|
||||
distance between two adjacent vertices, with distance measured on a
|
||||
line upon which the vertices have been placed at unit intervals. To
|
||||
put it another way, if the vertices of an undirected graph
|
||||
<i>G=(V,E)</i> are each assigned an index from zero to <i>|V| - 1</i>
|
||||
given by <i>index[v]</i>, then the bandwidth of <i>G</i> is<br>
|
||||
<br>
|
||||
<i>B(G) = max { |index[u] - index[v]| | (u,v) in E }</i><br>
|
||||
|
||||
|
||||
<h3>Defined in</h3>
|
||||
|
||||
<a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>
|
||||
|
||||
|
||||
<hr>
|
||||
|
||||
<H1><A NAME="sec:ith-bandwidth">
|
||||
<TT>ith_bandwidth</TT>
|
||||
</H1>
|
||||
|
||||
<pre>
|
||||
(1)
|
||||
template <typename Graph>
|
||||
typename graph_traits<Graph>::vertices_size_type
|
||||
ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
|
||||
const Graph& g)
|
||||
|
||||
(2)
|
||||
template <typename Graph, typename VertexIndexMap>
|
||||
typename graph_traits<Graph>::vertices_size_type
|
||||
ith_bandwidth(typename graph_traits<Graph>::vertex_descriptor i,
|
||||
const Graph& g,
|
||||
VertexIndexMap index)
|
||||
</pre>
|
||||
|
||||
The <b><i>i-th bandwidth</i></b> a graph is the maximum distance
|
||||
between the <i>i-th</i> vertex and any of its neighbors.<br>
|
||||
<br>
|
||||
<i>B<sub>i</sub>(G) = max { |index[i] - index[j]| | (i,j) in E }</i><br>
|
||||
<br>
|
||||
So the bandwidth <i>B(G)</i> can be expressed as the maximum
|
||||
of the i-th bandwidths <i>B<sub>i</sub>(G)</i>.<br>
|
||||
<br>
|
||||
<i>B(G) = max { B<sub>i</sub>(G) | i=0...|V|-1 }</i><br>
|
||||
|
||||
<h3>Defined in</h3>
|
||||
|
||||
<a href="../../../boost/graph/bandwidth.hpp"><tt>boost/graph/bandwidth.hpp</tt></a>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,180 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Bellman Ford Shortest Paths</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H1><A NAME="sec:bellman-ford"></A>
|
||||
<TT>bellman_ford_shortest_paths</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="left">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed or undirected</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">distance, weight</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT"><i>O(V E)</i></TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Where Defined:</B></TH>
|
||||
<TD ALIGN="LEFT">
|
||||
<a href="../../../boost/graph/bellman_ford_shortest_paths.hpp"><TT>boost/graph/bellman_ford_shortest_paths.hpp</TT></a>
|
||||
</TD>
|
||||
</TR></TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(1)
|
||||
template <class <a href="./EdgeListGraph.html">EdgeListGraph</a>, class Size, class WeightMap, class DistanceMap>
|
||||
bool bellman_ford_shortest_paths(EdgeListGraph& g, Size N,
|
||||
WeightMap w, DistanceMap d)
|
||||
|
||||
(2)
|
||||
template <class <a href="./EdgeListGraph.html">EdgeListGraph</a>, class Size, class WeightMap, class DistanceMap,
|
||||
class <a href="./BellmanFordVisitor.html">BellmanFordVisitor</a>>
|
||||
bool bellman_ford_shortest_paths(EdgeListGraph& g, Size N, WeightMap w,
|
||||
DistanceMap d, BellmanFordVisitor visit)
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
The Bellman-Ford algorithm [<A
|
||||
HREF="bibliography.html#bellman58">4</A>,<A
|
||||
HREF="bibliography.html#ford62:_flows">11</A>,<A
|
||||
HREF="bibliography.html#lawler76:_comb_opt">20</A>,<A
|
||||
HREF="bibliography.html#clr90">8</A>] solves the single-source
|
||||
shortest paths problem for a graph with both positive and negative
|
||||
edge weights. See Section <A
|
||||
HREF="./graph_theory_review.html#sec:shortest-paths-algorithms">Shortest-Paths
|
||||
Algorithms</A> for a description of the single-source shortest paths
|
||||
problem. If a cycle with negative length is detected, the algorithm
|
||||
returns <TT>false</TT>. The argument <TT>N</TT> should be the number
|
||||
of vertices in the graph. The source vertex is indicated by
|
||||
initializing the distance of the source vertex to zero and the
|
||||
distances of the rest of the vertices to
|
||||
<TT>std::numeric_limits<T>::max()</TT>.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The type <TT>EdgeListGraph</TT> must be a model of
|
||||
<a href="./EdgeListGraph.html">EdgeListGraph</a>.
|
||||
</LI>
|
||||
<LI>The type <TT>Distance</TT> must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The
|
||||
vertex descriptor type of the graph needs to be usable as the key
|
||||
type of the distance map. The value type of the distance
|
||||
map must be <a
|
||||
href="http://www.sgi.com/tech/stl/LessThanComparable.html">LessThanComparable</a>.
|
||||
</LI>
|
||||
<LI>The <TT>Weight</TT> type must be a model of
|
||||
<a href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>.
|
||||
The edge descriptor of the graph needs to be usable as the key
|
||||
type for the weight map. The value type for the
|
||||
weight map must be <I>Addable</I> with the
|
||||
distance map's value type.
|
||||
</LI>
|
||||
<LI>The <TT>Parent</TT> type must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The
|
||||
value type and key type should be the graph's vertex descriptor
|
||||
type.
|
||||
</LI>
|
||||
<LI>The type <TT>BellmanFordVisitor</TT> must be a model of <a href="./BellmanFordVisitor.html">BellmanFordVisitor</a>.
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Complexity</H3>
|
||||
|
||||
<P>
|
||||
The time complexity is <i>O(V E)</i>.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Example</H3>
|
||||
|
||||
<P>
|
||||
The source code for this example is in <a
|
||||
href="../example/bellman_ford.cpp"><TT>examples/bellman_ford.cpp</TT></a>.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
enum { u, v, x, y, z, N };
|
||||
char name[] = { 'u', 'v', 'x', 'y', 'z' };
|
||||
|
||||
typedef std::pair<int,int> E;
|
||||
E edges[] = { E(u,y), E(u,x), E(u,v),
|
||||
E(v,u),
|
||||
E(x,y), E(x,v),
|
||||
E(y,v), E(y,z),
|
||||
E(z,u), E(z,x) };
|
||||
|
||||
int weight[] = { -4, 8, 5,
|
||||
-2,
|
||||
9, -3,
|
||||
7, 2,
|
||||
6, 7 };
|
||||
|
||||
typedef edge_list<E*,E,ptrdiff_t> Graph;
|
||||
Graph g(edges, edges + sizeof(edges)/sizeof(E));
|
||||
|
||||
vector<int> distance(N,std::numeric_limits<short>::max());
|
||||
vector<int> parent(N,-1);
|
||||
|
||||
distance[z] = 0;
|
||||
parent[z] = z;
|
||||
bool r = bellman_ford_shortest_paths(g, int(N), weight,
|
||||
distance.begin(),
|
||||
parent.begin());
|
||||
if (r)
|
||||
for (int i = 0; i < N; ++i)
|
||||
std::cout << name[i] << ": " << distance[i]
|
||||
<< " " << name[parent[i]] << std::endl;
|
||||
else
|
||||
std::cout << "negative cycle" << std::endl;
|
||||
</PRE>
|
||||
The distance and predecessor for each vertex is:
|
||||
<PRE>
|
||||
u: 2 v
|
||||
v: 4 x
|
||||
x: 7 z
|
||||
y: -2 u
|
||||
z: 0 z
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,115 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: bellman_visitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>
|
||||
<pre>
|
||||
bellman_visitor<EventVisitorList>
|
||||
</pre>
|
||||
</H1>
|
||||
|
||||
This class is an adapter that converts a list of <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s (constructed using
|
||||
<tt>std::pair</tt>) into a <a
|
||||
href="./BellmanFordVisitor.html">BellmanFordVisitor</a>.
|
||||
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
|
||||
<h3>Model of</h3>
|
||||
|
||||
<a href="./BellmanFordVisitor.html">BellmanFordVisitor</a>
|
||||
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th><th>Default</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>EventVisitorList</TT></TD>
|
||||
<TD>
|
||||
A list of <a href="./EventVisitor.html">EventVisitor</a>'s created
|
||||
with <tt>std::pair</tt>.
|
||||
</TD>
|
||||
<TD><TT><a href="./null_visitor.html"><tt>null_visitor</tt></a></TT></TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/bellman_ford_shortest_paths.hpp">
|
||||
<TT>boost/graph/bellman_ford_shortest_paths.hpp</TT></a>
|
||||
|
||||
<h3>Member Functions</h3>
|
||||
|
||||
This class implements all of the member functions required by <a
|
||||
href="./BellmanFordVisitor.html">BellmanFordVisitor</a>. In each function the
|
||||
appropriate event is dispatched to the <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s in the EventVisitorList.
|
||||
|
||||
<h3>Non-Member Functions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Function</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr><td><tt>
|
||||
template <class EventVisitorList><br>
|
||||
bellman_visitor<EventVisitorList><br>
|
||||
make_bellman_visitor(EventVisitorList ev_list);
|
||||
</tt></td><td>
|
||||
Returns the event visitor list adapted to be a BellmanFordVisitor.
|
||||
</td></tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
<p>
|
||||
The following are event visitors: <a
|
||||
href="./predecessor_recorder.html"><tt>predecessor_recorder</tt></a>,
|
||||
<a href="./distance_recorder.html"><tt>distance_recorder</tt></a>
|
||||
<a href="./time_stamper.html"><tt>time_stamper</tt></a>,
|
||||
and <a href="./property_writer.html"><tt>property_writer</tt></a>.
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,132 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: bfs_visitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>
|
||||
<pre>
|
||||
bfs_visitor<EventVisitorList>
|
||||
</pre>
|
||||
</H1>
|
||||
|
||||
This class is an adapter that converts a list of <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s (constructed using
|
||||
<tt>std::pair</tt>) into a <a href="./BFSVisitor.html">BFSVisitor</a>.
|
||||
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
This is an excerpt from <a
|
||||
href="../example/bfs.cpp"><tt>examples/bfs.cpp</tt></a> where three
|
||||
event-visitors are combined to make a BFS visitor. The functions
|
||||
<tt>boost::record_distances</tt>, <tt>boost::record_predecessors</tt>,
|
||||
and <tt>copy_graph</tt> are all functions that create an event
|
||||
visitor.
|
||||
|
||||
<pre>
|
||||
// Construct graph G and obtain the source vertex s ...
|
||||
|
||||
boost::breadth_first_search(G, s,
|
||||
make_bfs_visitor(
|
||||
std::make_pair(boost::record_distances(d, boost::on_tree_edge()),
|
||||
std::make_pair(boost::record_predecessors(p.begin(),
|
||||
boost::on_tree_edge()),
|
||||
copy_graph(G_copy, boost::on_examine_edge())))) );
|
||||
</pre>
|
||||
|
||||
|
||||
<h3>Model of</h3>
|
||||
|
||||
<a href="./BFSVisitor.html">BFSVisitor</a>
|
||||
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th><th>Default</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>EventVisitorList</TT></TD>
|
||||
<TD>
|
||||
A list of <a href="./EventVisitor.html">EventVisitor</a>'s created
|
||||
with <tt>std::pair</tt>.
|
||||
</TD>
|
||||
<TD><a href="./null_visitor.html"><tt>null_visitor</tt></a></TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/breadth_first_search.hpp">
|
||||
<TT>boost/graph/breadth_first_search.hpp</TT></a>
|
||||
|
||||
<h3>Member Functions</h3>
|
||||
|
||||
This class implements all of the member functions required by <a
|
||||
href="./BFSVisitor.html">BFSVisitor</a>. In each function the
|
||||
appropriate event is dispatched to the <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s in the EventVisitorList.
|
||||
|
||||
<h3>Non-Member Functions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Function</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr><td><tt>
|
||||
template <class EventVisitorList><br>
|
||||
bfs_visitor<EventVisitorList><br>
|
||||
make_bfs_visitor(EventVisitorList ev_list);
|
||||
</tt></td><td>
|
||||
Returns the event visitor list adapted to be a BFS visitor.
|
||||
</td></tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
<p>
|
||||
The following are event visitors: <a
|
||||
href="./predecessor_recorder.html"><tt>predecessor_recorder</tt></a>,
|
||||
<a href="./distance_recorder.html"><tt>distance_recorder</tt></a>,
|
||||
<a href="./time_stamper.html"><tt>time_stamper</tt></a>,
|
||||
and <a href="./property_writer.html"><tt>property_writer</tt></a>.
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,302 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Bibliography</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H2>Bibliography</H2>
|
||||
|
||||
<DL COMMapCT><DD><P></P><DT><A NAME="aho83:_data_struct_algo">1</A>
|
||||
<DD>
|
||||
A. V. Aho, J. E. Hopcroft, and J. D. Ullman.
|
||||
<BR><EM>Data Structures and Algorithms</EM>.
|
||||
<BR>Addison-Wesley, 1983.
|
||||
|
||||
<P></P><DT><A NAME="austern99:_gener_progr_stl">2</A>
|
||||
<DD>
|
||||
M. H. Austern.
|
||||
<BR><EM>Generic Programming and the STL</EM>.
|
||||
<BR>Professional computing series. Addison-Wesley, 1999.
|
||||
|
||||
<P></P><DT><A NAME="baumgartner95:_signatures">3</A>
|
||||
<DD>
|
||||
G. Baumgartner and V. F. Russo.
|
||||
<BR>Signatures: A language extension for improving type abstraction and
|
||||
subtype polymorphism in C++.
|
||||
<BR><EM>Software-Practice and Experience</EM>, 25(8):863-889, August 1995.
|
||||
|
||||
<P></P><DT><A NAME="bellman58">4</A>
|
||||
<DD>
|
||||
R. Bellman.
|
||||
<BR>On a routing problem.
|
||||
<BR><EM>Quarterly of Applied Mathematics</EM>, 16(1):87-90, 1958.
|
||||
|
||||
<P></P><DT><A NAME="bruce95">5</A>
|
||||
<DD>
|
||||
K. B. Bruce, L. Cardelli, G. Castagna, the Hopkins Objects Group, G. T.
|
||||
Leavens, and B. Pierce.
|
||||
<BR>On binary methods.
|
||||
<BR><EM>Theory and Practice of Object Systems</EM>, 1:221-242, 1995.
|
||||
|
||||
<P></P><DT><A NAME="coleman85:_algor">6</A>
|
||||
<DD>
|
||||
T. F. Coleman, B. S. Garbow, and J. J. Mor'e.
|
||||
<BR>Algorithm 649: Fortran subroutines for estimating sparse hessian
|
||||
matrices.
|
||||
<BR><EM>ACM Transactions on Mathematical Software</EM>, 11(4):378, December
|
||||
1985.
|
||||
|
||||
<P></P><DT><A NAME="coleman84:_estim_jacob">7</A>
|
||||
<DD>
|
||||
T. F. Coleman and J. J. Mor'e.
|
||||
<BR>Estimation of sparse jacobian matrices and graph coloring problems.
|
||||
<BR><EM>SIAM Journal on Numerical Analysis</EM>, 20:187-209,, 1984.
|
||||
|
||||
<P></P><DT><A NAME="clr90">8</A>
|
||||
<DD>
|
||||
T. Cormen, C. Leiserson, and R. Rivest.
|
||||
<BR><EM>Introduction to Algorithms</EM>.
|
||||
<BR>McGraw-Hill, 1990.
|
||||
|
||||
<P></P><DT><A NAME="curtis74:_jacob">9</A>
|
||||
<DD>
|
||||
A. Curtis, M. Powell, and J. Reid.
|
||||
<BR>On the estimation of sparse jacobian matrices.
|
||||
<BR><EM>Journal of the Institute of Mathematics and its Applications</EM>,
|
||||
13:117-119, 1974.
|
||||
|
||||
<P></P><DT><A NAME="dijkstra59">10</A>
|
||||
<DD>
|
||||
E. Dijkstra.
|
||||
<BR>A note on two problems in connexion with graphs.
|
||||
<BR><EM>Numerische Mathematik</EM>, 1:269-271, 1959.
|
||||
|
||||
<P></P><DT><A NAME="ford62:_flows">11</A>
|
||||
<DD>
|
||||
L. R. Ford and D. R. Fulkerson.
|
||||
<BR><EM>Flows in networks</EM>.
|
||||
<BR>Princeton University Press, 1962.
|
||||
|
||||
<P></P><DT><A NAME="gamma95:_design_patterns">12</A>
|
||||
<DD>
|
||||
E. Gamma, R. Helm, R. Johnson, and J. Vlissides.
|
||||
<BR><EM>Design Patterns: Elements of Reusable Object-Oriented Software</EM>.
|
||||
<BR>Professional Computing. Addison-Welsey, 1995.
|
||||
|
||||
<P></P><DT><A NAME="george93:graphtheory">13</A>
|
||||
<DD>
|
||||
A. George, J. R. Gilbert, and J. W. Liu, editors.
|
||||
<BR><EM>Graph Theory and Sparse Matrix Computation</EM>.
|
||||
<BR>Springer-Verlag New York, Inc, 1993.
|
||||
|
||||
<P></P><DT><A NAME="george81:__sparse_pos_def">14</A>
|
||||
<DD>
|
||||
A. George and J. W.-H. Liu.
|
||||
<BR><EM>Computer Solution of Large Sparse Positive Definite Systems</EM>.
|
||||
<BR>Computational Mathematics. Prentice-Hall, 1981.
|
||||
|
||||
<P></P><DT><A NAME="graham85">15</A>
|
||||
<DD>
|
||||
R. Graham and P. Hell.
|
||||
<BR>On the history of the minimum spanning tree problem.
|
||||
<BR><EM>Annals of the History of Computing</EM>, 7(1):43-57, 1985.
|
||||
|
||||
<P></P><DT><A NAME="hart68">16</A>
|
||||
<DD>
|
||||
P. E. Hart, N. J. Nilsson, and B. Raphael.
|
||||
<BR>A formal basis for the heuristic determination of minimum cost paths.
|
||||
<BR><EM>IEEE Transactions on Systems Science and Cybernetics</EM>,
|
||||
4(2):100-107, 1968.
|
||||
|
||||
<P></P><DT><A NAME="kruskal56">18</A>
|
||||
<DD>
|
||||
J. B. Kruskal.
|
||||
<BR>On the shortest spanning subtree of a graph and the traveling
|
||||
salesman problem.
|
||||
<BR>In <EM>Proceedings of the American Mathematical Sofiety</EM>, volume 7,
|
||||
pages 48-50, 1956.
|
||||
|
||||
<P></P><DT><A NAME="kuehl96:_design_patterns_for_graph_algo">19</A>
|
||||
<DD>
|
||||
D. Kühl.
|
||||
<BR>Design patterns for the implementation of graph algorithms.
|
||||
<BR>Master's thesis, Technische Universität Berlin, July 1996.
|
||||
|
||||
<P></P><DT><A NAME="lawler76:_comb_opt">20</A>
|
||||
<DD>
|
||||
E. L. Lawler.
|
||||
<BR><EM>Combinatorial Opimization: Networks and Matroids</EM>.
|
||||
<BR>Holt, Rinehart, and Winston, 1976.
|
||||
|
||||
<P></P><DT><A NAME="LIU:MMD">21</A>
|
||||
<DD>
|
||||
J. W. H. Liu.
|
||||
<BR>Modification of the minimum-degree algorithm by multiple elimination.
|
||||
<BR><EM>ACM Transaction on Mathematical Software</EM>, 11(2):141-153, 1985.
|
||||
|
||||
<P></P><DT><A NAME="mehlhorn99:_leda">22</A>
|
||||
<DD>
|
||||
K. Mehlhorn and S. Näher.
|
||||
<BR><EM>The LEDA Platform of Combinatorial and Geometric Computing</EM>.
|
||||
<BR>Cambridge University Press, 1999.
|
||||
|
||||
<P></P><DT><A NAME="meyer88:_object_soft_const">23</A>
|
||||
<DD>
|
||||
B. Meyer.
|
||||
<BR><EM>Object-oriented Software Construction</EM>.
|
||||
<BR>Prentice Hall International Series in Computer Science. Prentice
|
||||
Hall, 1988.
|
||||
|
||||
<P></P><DT><A NAME="myers95:_trait">24</A>
|
||||
<DD>
|
||||
N. C. Myers.
|
||||
<BR>Traits: a new and useful template technique.
|
||||
<BR><EM>C++ Report</EM>, June 1995.
|
||||
|
||||
<P></P><DT><A NAME="prim57:_short">25</A>
|
||||
<DD>
|
||||
R. Prim.
|
||||
<BR>Shortest connection networks and some generalizations.
|
||||
<BR><EM>Bell System Technical Journal</EM>, 36:1389-1401, 1957.
|
||||
|
||||
<P></P><DT><A NAME="saad96:imsms">26</A>
|
||||
<DD>
|
||||
Y. Saad.
|
||||
<BR><EM>Iterative Methods for Sparse Minear System</EM>.
|
||||
<BR>PWS Publishing Company, 1996.
|
||||
|
||||
<P></P><DT><A NAME="tarjan83:_data_struct_network_algo">27</A>
|
||||
<DD>
|
||||
R. E. Tarjan.
|
||||
<BR><EM>Data Structures and Network Algorithms</EM>.
|
||||
<BR>Society for Industrial and Applied Mathematics, 1983.
|
||||
|
||||
<P></P><DT><A NAME="parter61:_gauss">28</A>
|
||||
<DD>
|
||||
Seymour Parter.
|
||||
<BR><EM>The use of linear graphs in Gauss elimination</EM>.
|
||||
<BR>SIAM Review, 1961 3:119-130.
|
||||
|
||||
<P></P><DT><A NAME="matula72:_graph_theory_computing">29</A>
|
||||
<DD>
|
||||
D. Matula, G. Marble, and J. Isaacson
|
||||
<BR><EM>Graph coloring algorithms in Graph Theory and
|
||||
Computing</EM>.<BR>
|
||||
Academic Press, pp.104-122, 1972.
|
||||
|
||||
<P></P><DT><A NAME="garey79:computers-and-intractability">30</a>
|
||||
<DD>
|
||||
M.R. Garey and D.S. Johnson<BR>
|
||||
<EM>Computers and Intractibility: A Guide to the Theory of
|
||||
NP-Completeness</EM><BR>
|
||||
W.H. Freeman, New York, 1979.
|
||||
|
||||
<P></P><DT><A NAME="welsch67">31</a>
|
||||
<DD>D. Welsch and M. B. Powel<BR>
|
||||
<EM>An upper bound for the chromatic number of a graph and its
|
||||
application to timetabling problems</EM>
|
||||
Computer Journal, 10:85-86, 1967.
|
||||
|
||||
<P></P><DT><A NAME="brelaz79:_new">32</a>
|
||||
<DD>D. Br'elaz<BR>
|
||||
<EM>New methods to color the vertices of a graph</EM><br>
|
||||
Communications of the ACM, vol. 22, 1979, pp. 251-256.
|
||||
|
||||
<P></P><DT><A NAME="heber99:_saw">33</a>
|
||||
<DD>G. Heber, R. Biswas, G.R. Gao<BR>
|
||||
<EM>Self-Avoiding Walks over Adaptive Unstructured Grids</EM><br>
|
||||
Parallel and Distributed Processing, LNCS 1586,
|
||||
Springer-Verlag, 1999, pp. 968-977
|
||||
|
||||
|
||||
<P></P><DT><A NAME="ng-raghavan">34</a>
|
||||
<DD>Esmond G. Ng amd Padma Raghavan<BR>
|
||||
<EM>Performance of greedy ordering heuristics for sparse {C}holesky factorization</EM><br>
|
||||
SIAM Journal on Matrix Analysis and Applications (To appear)
|
||||
|
||||
<P></P><DT><A NAME="George:evolution">35</a>
|
||||
<DD>Alan George and Joseph W. H. Liu<BR>
|
||||
<EM>The Evolution of the Minimum Degree Ordering Algorithm</EM><br>
|
||||
SIAM Review, March 1989, vol. 31, num. 1, pp. 1-19.
|
||||
|
||||
<P></P><DT><A NAME="ford56:_maxim">36</a>
|
||||
<DD>L. R. Ford and D. R. Fulkerson<BR>
|
||||
<EM>Maximal flow through a network.</EM><br>
|
||||
Can. Journal of Mathematics 1956 pp.399-404
|
||||
|
||||
<P></P><DT><A NAME="goldberg85:_new_max_flow_algor">37</a>
|
||||
<DD>A. V. Goldberg<BR>
|
||||
<EM>A New Max-Flow Algorithm.</EM><br>
|
||||
MIT Tehnical report MIT/LCS/TM-291, 1985.
|
||||
|
||||
<P></P><DT><A NAME="karzanov74:_deter">38</a>
|
||||
<DD>A. V. Karzanov<BR>
|
||||
<EM>Determining the maximal flow in a network by the method of preflows.</EM><br>
|
||||
Sov. Math. Dokl. 1974
|
||||
|
||||
<P></P><DT><A NAME="ahuja93:_network_flows">39</a>
|
||||
<DD>Ravindra K. Ahuja and Thomas L. Magnanti and James B. Orlin<BR>
|
||||
<EM>Network Flows: Theory, Algorithms, and Applications.</EM><br>
|
||||
Prentice Hall, 1993.
|
||||
|
||||
<P></P><DT><A NAME="edmonds72:_improvements_netflow">40</a>
|
||||
<DD>Jack Edmonds and Richard M. Karp<BR>
|
||||
<EM>Theoretical improvements in the algorithmic efficiency for network flow problems.</EM><br>
|
||||
Journal of the ACM, 1972 19:248-264
|
||||
|
||||
<P></P><DT><A NAME="tarjan72:dfs_and_linear_algo">41</a>
|
||||
<DD>Robert E. Tarjan<BR>
|
||||
<EM>Depth first search and linear graph algorithms.</EM><br>
|
||||
SIAM Journal on Computing, 1(2):146-160, 1972
|
||||
|
||||
<P></P><DT><A NAME="eppstein97:dynamic_graph">42</a>
|
||||
<DD>David Eppstein, Zvi Galil, and Giuseppe F. Italiano<BR>
|
||||
<EM>Dynamic Graph Algorithms.</EM><br>
|
||||
Chapter 22, CRC Handbook of Algorithms and Theory of Computation, 1997.
|
||||
|
||||
<P></P><DT><A NAME="cuthill69:reducing_bandwith">43</a>
|
||||
<DD>E. Cuthill and J. McKee<BR>
|
||||
<EM>Reducing the bandwidth of sparse symmetric matrices.</EM><br>
|
||||
Proceedings of the 24th National Conference of the ACM, 1969.
|
||||
|
||||
<P></P><DT><A NAME="liu75:anal_cm_rcm">44</a>
|
||||
<DD>J. Liu and A. Sherman<BR>
|
||||
<EM>Comparative analysis of the Cuthill-Mckee and the reverse
|
||||
Cuthill-Mckee ordering algorithms for sparse matrices.</EM><br>
|
||||
SIAM Journal of Numerical Analysis. 13 (1975), pp. 198-213.
|
||||
|
||||
<P></P><DT><A NAME="george71:fem">45</a>
|
||||
<DD>Alan George<BR>
|
||||
<EM>Computer implementation of the finite element method</EM><br>
|
||||
Technical Report STAN-CS-208, Stanford University (1971).
|
||||
|
||||
|
||||
|
||||
</DL>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,246 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Breadth-First Search</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:bfs">
|
||||
<TT>breadth_first_search</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="LEFT">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed and undirected</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">color</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT">time: <i>O(V + E)</i></TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(1)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./BFSVisitor.html">BFSVisitor</a>>
|
||||
void breadth_first_search(VertexListGraph& G,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
BFSVisitor vis);
|
||||
|
||||
(2)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./BFSVisitor.html">BFSVisitor</a>, class <a href="#ColorMap">ColorMap</a>>
|
||||
void breadth_first_search(const VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
BFSVisitor vis, ColorMap color);
|
||||
|
||||
(3)
|
||||
template <class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./Buffer.html">Buffer</a>, <a href="./BFSVisitor.html">BFSVisitor</a>, class <a href="#ColorMap">ColorMap</a>>
|
||||
void breadth_first_search(const VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
Buffer& Q, BFSVisitor vis, ColorMap color)
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
The breadth-first search (BFS) algorithm is not really an algorithm in
|
||||
the sense that it has a particular purpose. Instead BFS is more like
|
||||
an algorithm <I>pattern</I>. One can do many different things with
|
||||
BFS. For example, the BFS pattern is used in the BGL to build several
|
||||
other algorithms: Dijkstra's shortest paths, Prim's Minimum Spanning
|
||||
Tree and best-first search. The definition of a <I>breadth-first
|
||||
search</I> is given in Section <A
|
||||
HREF="./graph_theory_review.html#sec:bfs-algorithm">Breadth-First
|
||||
Search</A>.
|
||||
|
||||
<P>
|
||||
The BGL BFS functions are highly parameterized so that they can be
|
||||
used in a wide variety of places. The way to customize the BFS
|
||||
algorithm to perform different operations is to supply a visitor,
|
||||
which is a function object with multiple functions. Each member
|
||||
function of the visitor gets invoked at special times during the
|
||||
algorithm as specified by <a
|
||||
href="./BFSVisitor.html">BFSVisitor</a>. Also, visitors can be layered
|
||||
on top of each other so that one can do lots of things during a single
|
||||
run of BFS. See the <a href="./bfs_visitor.html">bfs_visitor</a> class
|
||||
and the <A HREF="./EventVisitor.html">EventVisitor</A> concept for
|
||||
more details.
|
||||
|
||||
<P>
|
||||
Another way to customize the BFS algorithm is change the type of queue
|
||||
used. For instance, <TT>dijkstra_shortest_paths()</TT> uses a priority
|
||||
queue.
|
||||
|
||||
<p>
|
||||
The <tt>ColorMap</tt> is used by BFS to keep track of which vertices
|
||||
have been visited. At the beginning of the algorithm all vertices are
|
||||
white. As the algorithm proceeds, vertices are colored gray as they
|
||||
are inserted into the queue, and then colored black when they are
|
||||
finished and removed from queue.
|
||||
|
||||
|
||||
<P>
|
||||
Version 1 of the algorithm takes only three arguments: the graph
|
||||
object, the source vertex, and a visitor to specify the actions to be
|
||||
taken during the graph search. The algorithm will need to use a color
|
||||
property which must be provided by the graph object (through a vertex
|
||||
color property).
|
||||
|
||||
<P>
|
||||
Version 2 of the algorithm adds a color property argument to
|
||||
accommodate the use of an external property map.
|
||||
|
||||
<P>
|
||||
Version 3 of the algorithm is the most generalized. It adds a
|
||||
parameter for the queue. This version does not initialize the color of
|
||||
all the vertices to white at the start of the algorithm or invoke the
|
||||
<tt>initialize_vertex()</tt> visitor method, so that must be taken
|
||||
care of before calling this versin of <tt>breadth_first_search()</tt>.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/breadth_first_search.hpp"><TT>boost/graph/breadth_first_search.hpp</TT></a>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The type <TT>IncidenceGraph</TT> must be a model of <a href="./IncidenceGraph.html">IncidenceGraph</a>.
|
||||
</LI>
|
||||
<LI>The type <TT>VertexListGraph</TT> must be a model of <a href="./VertexListGraph.html">VertexListGraph</a>.
|
||||
</LI>
|
||||
<LI>The type <TT>BFSVisitor</TT> must be a model of <a href="./BFSVisitor.html">BFSVisitor</a>.
|
||||
</LI>
|
||||
<LI>In version (1) of the algorithm the graph must be a model
|
||||
of <a href="./PropertyGraph.html">PropertyGraph</a> for
|
||||
<TT>vertex_color_t</TT> and
|
||||
the color property map for the graph must meet the
|
||||
same requirements as <TT>ColorMap</TT>.
|
||||
</LI>
|
||||
<LI><a name="ColorMap">The type <TT>ColorMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>.
|
||||
A vertex descriptor must be usable as the key type of the map,
|
||||
and the value type of the map must be a model of <a
|
||||
href="./ColorValue.html">ColorValue</a>.</a>
|
||||
</LI>
|
||||
<LI>The type <TT>Buffer</TT> must be a model of <a href="./Buffer.html">Buffer</a>.
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3><A NAME="SECTION001330300000000000000">
|
||||
Complexity</A>
|
||||
</H3>
|
||||
|
||||
<P>
|
||||
The time complexity is <i>O(E + V)</i>.
|
||||
|
||||
<P>
|
||||
|
||||
<H3><A NAME="SECTION001330400000000000000">
|
||||
Example</A>
|
||||
</H3>
|
||||
|
||||
<P>
|
||||
This example demonstrates using the BGL Breadth-first search algorithm
|
||||
on the graph from <A
|
||||
HREF="./graph_theory_review.html#fig:bfs-example">Figure 5</A>. The
|
||||
source code for this example is in <a
|
||||
href="../example/bfs_basics.cpp"><TT>examples/bfs_basics.cpp</TT></a>.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
// Select the graph type we wish to use
|
||||
typedef adjacency_list<vecS, undirectedS> Graph;
|
||||
// Set up the vertex ID's and names
|
||||
enum { r, s, t, u, v, w, x, y, N };
|
||||
char name[] = { 'r', 's', 't', 'u', 'v', 'w', 'x', 'y' };
|
||||
// Specify the edges in the graph
|
||||
typedef pair<int,int> E;
|
||||
E edge_array[] = { E(r,s), E(r,v), E(s,w), E(w,r), E(w,t),
|
||||
E(w,x), E(x,t), E(t,u), E(x,y), E(u,y) };
|
||||
// Create the graph object
|
||||
Graph G(N, edge_array, edge_array + sizeof(edge_array)/sizeof(E));
|
||||
|
||||
// Some typedef's to save a little typing
|
||||
typedef Graph::vertex_descriptor Vertex;
|
||||
typedef std::vector<Vertex>::iterator Piter;
|
||||
typedef std::vector<Graph::size_type>::iterator Iiter;
|
||||
|
||||
// vectors to hold color, discover time, and finish time properties
|
||||
std::vector<default_color_type> color(num_vertices(G));
|
||||
std::vector<Graph::size_type> dtime(num_vertices(G));
|
||||
std::vector<Graph::size_type> ftime(num_vertices(G));
|
||||
|
||||
breadth_first_search(G, vertex(s,G),
|
||||
visit_timestamp(dtime.begin(), ftime.begin()),
|
||||
color.begin());
|
||||
|
||||
// Use std::sort to order the vertices by their discover time
|
||||
vector<Graph::size_type> discover_order(N);
|
||||
iota(discover_order.begin(), discover_order.end(), 0);
|
||||
std::sort(discover_order.begin(), discover_order.end(),
|
||||
indirect_cmp<Iiter, std::less<Graph::size_type> >(dtime.begin()));
|
||||
|
||||
cout << "order of discovery: ";
|
||||
for (int i = 0; i < N; ++i)
|
||||
cout << name[ discover_order[i] ] << " ";
|
||||
|
||||
vector<Graph::size_type> finish_order(N);
|
||||
iota(finish_order.begin(), finish_order.end(), 0);
|
||||
std::sort(finish_order.begin(), finish_order.end(),
|
||||
indirect_cmp<Iiter, std::less<Graph::size_type> >(ftime.begin()));
|
||||
|
||||
cout << endl << "order of finish: ";
|
||||
for (int i = 0; i < N; ++i)
|
||||
cout << name[ finish_order[i] ] << " ";
|
||||
cout << endl;
|
||||
</PRE>
|
||||
The output is:
|
||||
<PRE>
|
||||
order of discovery: s r w v t x u y
|
||||
order of finish: s r w v t x u y
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./bfs_visitor.html"><tt>bfs_visitor</tt></a> and
|
||||
<a href="./depth_first_search.html"><tt>depth_first_search()</tt></a>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,108 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Challenge</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<h2>Boost Graph Library Challenge and To-Do Items</h2>
|
||||
|
||||
|
||||
<ul>
|
||||
|
||||
<li>Polish up code/docs for pending items and champion the formal
|
||||
review. The pending items are:</li>
|
||||
<ul>
|
||||
<li><tt>container_traits.hpp</tt> (this should also include
|
||||
the work Matt Austern is doing on this topic)</li>
|
||||
|
||||
<li><tt>property.hpp</tt></li>
|
||||
|
||||
<li>The queues and heaps: <tt>queue.hpp</tt>,
|
||||
<tt>mutable_queue.hpp</tt>, <tt>fibonacci_heap.hpp</tt>.
|
||||
Somehow merge implementation with Dietmer's heaps and queues.</li>
|
||||
|
||||
<li><tt>disjoint_sets</tt> </li>
|
||||
</ul>
|
||||
|
||||
<li>Port the graph library to Borland C++</li>
|
||||
|
||||
<li>Construct a set of planar graph algorithms.</li>
|
||||
<ul>
|
||||
<li> Is the graph planar?</li>
|
||||
<li> "Walk around the block" and similar open and closed neighborhood
|
||||
traversals. Note that edge traversals need to resolve to particular ends
|
||||
and sides (see below), not just to the edge as a whole.</li>
|
||||
<li> Given a point, find the nearest vertex, edge, or bounded polygon.
|
||||
Again, edges are viewed as having left and right sides.</li>
|
||||
<li> Given a line segment, find intersecting vertices, edges, or bounded
|
||||
polygons.</li>
|
||||
<li> Given a polygon, find intersecting whatever...</li>
|
||||
<li> Various minimum bounding rectangle and clipping problems.</li>
|
||||
<li> Construct a planar embedding of a planar graph.</li>
|
||||
<li> Find a balanced separator of a graph.</li>
|
||||
<li> Modify adjacency_list so that the out-edges can be ordered
|
||||
according to a user defined comparison object.</li>
|
||||
</ul>
|
||||
|
||||
<li>Floyd-Warshall algorithm.</li>
|
||||
|
||||
<li>Rewrite the Qhull algorithm using the Boost Graph Library.</li>
|
||||
|
||||
<li>Explore the use of Algorithm Objects as an alternative to
|
||||
the current approach with visitors.</li>
|
||||
|
||||
<li>Analyze the algorithms that do not yet have visitors, and
|
||||
come up with visitor interfaces for them.</li>
|
||||
|
||||
<li>Add a check in the adjacency_list class to make sure
|
||||
all the vertex property template arguments have kind=vertex_property_tag
|
||||
and all edge property template arguments have kind=edge_property_tag.</li>
|
||||
|
||||
<li>Clean up the output functions in graph_utility.hpp to
|
||||
use streams, and document all the utility functions. Replace
|
||||
the random number stuff with calls to the boost random number generator.</li>
|
||||
|
||||
<li>Modularize the tests in test/graph.cpp to apply to particular
|
||||
concepts. Make sure there are run-time tests for every BGL concept.</li>
|
||||
|
||||
<li>Write tests for the BGL algorithms. Currently the examples
|
||||
are used as a sanity check, but they do not constitute a real test. </li>
|
||||
|
||||
<li>Write up the examples from Knuth's <i>Stanford GraphBase</i> using
|
||||
the BGL. The file <a
|
||||
href="../example/miles_span.cpp"><tt>examples/miles_span.cpp</tt></a>
|
||||
is a start.
|
||||
|
||||
<li>Create a class to support sub-graph views of a graph, where a
|
||||
sub-graph behaves just like a graph, but shares vertex and edge
|
||||
properties with the original graph. Perhaps even support sub-graphs
|
||||
of sub-graphs, etc.
|
||||
|
||||
</ul>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,193 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Jeremy Siek makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Connected Components</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H1>
|
||||
<A NAME="sec:connected-components"></A><A NAME="sec:strongly-connected-components"></A>
|
||||
<TT>connected_components</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="left">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">see below</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">components, color</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT"><i>O(V + E)</i></TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(2)
|
||||
template <class VertexListGraph, class ComponentMap, class ColorMap>
|
||||
typename property_traits<ComponentMap>::value_type
|
||||
connected_components(VertexListGraph& G, ComponentMap comp, ColorMap color);
|
||||
|
||||
(2)
|
||||
template <class VertexListGraph,
|
||||
class ComponentMap, class ColorMap, class DFSVisitor>
|
||||
typename property_traits<ComponentMap>::value_type
|
||||
connected_components(VertexListGraph& G, ComponentMap comp, ColorMap color,
|
||||
DFSVisitor v);
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
The <TT>connected_components()</TT> functions compute the connected
|
||||
components of an undirected graph using a DFS-based approach. If the
|
||||
connected-components are to be calculated over and over while a graph
|
||||
is changing the disjoint-set based approach of function
|
||||
<TT>dynamic_connected_components()</TT> is faster. For ``static''
|
||||
graphs this DFS-based approach is faster [<A
|
||||
HREF="bibliography.html#clr90">8</A>].
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
The output of the algorithm is recorded in the component property
|
||||
map <TT>comp</TT>, which will contain numbers giving the component ID
|
||||
assigned to each vertex. The number of components is the return value
|
||||
of the function.
|
||||
|
||||
<P>
|
||||
The algorithm requires the use of several property maps: color,
|
||||
discover time, and finish time. There are several versions of this
|
||||
algorithm to accommodate whether you wish to use interior or exterior
|
||||
property maps.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/connected_components.hpp"><TT>boost/graph/connected_components.hpp</TT></a>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Definitions</H3>
|
||||
|
||||
<P>
|
||||
A <b><I>connected component</I></b> of an undirected graph is a set of
|
||||
vertices that are all reachable from each other.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The graph type must be a model of <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a>.
|
||||
|
||||
</LI>
|
||||
<LI>The <TT>ComponentMap</TT> type must be a model of <a
|
||||
href="../../property_map/WritablePropertyMap.html">WritablePropertyMap</a>. The
|
||||
value type of the <TT>ComponentMap</TT> property map should be
|
||||
an integer type, preferably the same as the <TT>size_type</TT> of
|
||||
the graph. The key type should be the graph's vertex descriptor
|
||||
type.
|
||||
</LI>
|
||||
<LI>The <TT>ColorMap</TT> map must be a <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>
|
||||
and the graph's vertex descriptor type should be usable as the
|
||||
map's key type. The value type of the map must be a
|
||||
model of <I>ColorValue</I>.
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Complexity</H3>
|
||||
|
||||
<P>
|
||||
The time complexity for the connected components algorithm is also
|
||||
<i>O(V + E)</i>.
|
||||
|
||||
<P>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./strong_components.html"><tt>strong_components()</tt></a>
|
||||
and <a href="./dynamic_components.html"><tt>dynamic_components()</tt></a>
|
||||
|
||||
<H3>Example</H3>
|
||||
|
||||
<P>
|
||||
Calculating the connected components of an undirected graph. The
|
||||
complete source is in file <a
|
||||
href="../example/connected_components.cpp"><tt>examples/connected_components.cpp</tt></a>.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
typedef discover_time_property< finish_time_property
|
||||
< color_property<> > > VertexProperty;
|
||||
typedef adjacency_list <vecS, vecS, undirectedS, VertexProperty> Graph;
|
||||
typedef graph_traits<Graph>::vertex_descriptor Vertex;
|
||||
|
||||
const int N = 6;
|
||||
Graph G(N);
|
||||
add_edge(0, 1, G);
|
||||
add_edge(1, 4, G);
|
||||
add_edge(4, 0, G);
|
||||
add_edge(2, 5, G);
|
||||
|
||||
std::vector<int> c(num_vertices(G));
|
||||
int num = connected_components(G, c.begin(),
|
||||
get_color_map(G), null_visitor());
|
||||
|
||||
cout << endl;
|
||||
std::vector<int>::iterator i;
|
||||
cout << "Total number of components: " << num << endl;
|
||||
for (i = c.begin(); i != c.end(); ++i)
|
||||
cout << "Vertex " << i - c.begin()
|
||||
<< " is in component " << *i << endl;
|
||||
cout << endl;
|
||||
</PRE>
|
||||
The output is:
|
||||
<PRE>
|
||||
Total number of components: 3
|
||||
Vertex 0 is in component 1
|
||||
Vertex 1 is in component 1
|
||||
Vertex 2 is in component 2
|
||||
Vertex 3 is in component 3
|
||||
Vertex 4 is in component 1
|
||||
Vertex 5 is in component 2
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,187 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Constructing Graph Algorithms</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>Constructing graph algorithms with BGL</H1>
|
||||
|
||||
<P>
|
||||
The <I>main</I> goal of BGL is not to provide a nice graph class, or
|
||||
to provide a comprehensive set of reusable graph algorithms (though
|
||||
these are goals). The main goal of BGL is to encourage others to
|
||||
write reusable graph algorithms. By reusable we mean maximally
|
||||
reusable. Generic programming is a methodology for making algorithms
|
||||
maximally reusable, and in this section we will discuss how to apply
|
||||
generic programming to constructing graph algorithms.
|
||||
|
||||
<P>
|
||||
To illustrate the generic programming process we will step though the
|
||||
construction of a graph coloring algorithm. The graph coloring problem
|
||||
(or more specifically, the vertex coloring problem) is to label each
|
||||
vertex in a graph <i>G</i> with a color such that no two adjacent
|
||||
vertices are labeled with the same color and such that the minimum
|
||||
number of colors are used. In general, the graph coloring problem is
|
||||
NP-complete, and therefore it is impossible to find an optimal
|
||||
solution in a reasonable amount of time. However, there are many
|
||||
algorithms that use heuristics to find colorings that are close to the
|
||||
minimum.
|
||||
|
||||
<P>
|
||||
The particular algorithm we present here is based on the linear time
|
||||
<TT>SEQ</TT> subroutine that is used in the estimation of sparse
|
||||
Jacobian and Hessian matrices [<A
|
||||
HREF="bibliography.html#curtis74:_jacob">9</A>,<A
|
||||
HREF="bibliography.html#coleman84:_estim_jacob">7</A>,<A
|
||||
HREF="bibliography.html#coleman85:_algor">6</A>]. This algorithm
|
||||
visits all of the vertices in the graph according to the order defined
|
||||
by the input order. At each vertex the algorithm marks the colors of
|
||||
the adjacent vertices, and then chooses the smallest unmarked color
|
||||
for the color of the current vertex. If all of the colors are already
|
||||
marked, a new color is created. A color is considered marked if its
|
||||
mark number is equal to the current vertex number. This saves the
|
||||
trouble of having to reset the marks for each vertex. The
|
||||
effectiveness of this algorithm is highly dependent on the input
|
||||
vertex order. There are several ordering algorithms, including the
|
||||
<I>largest-first</I> [<A HREF="bibliography.html#welsch67">31</A>],
|
||||
<I>smallest-last</I> [<a
|
||||
href="bibliography.html#matula72:_graph_theory_computing">29</a>], and
|
||||
<I>incidence degree</I> [<a
|
||||
href="bibliography.html#brelaz79:_new">32</a>] algorithms, which
|
||||
improve the effectiveness of this coloring algorithm.
|
||||
|
||||
<P>
|
||||
The first decision to make when constructing a generic graph algorithm
|
||||
is to decide what graph operations are necessary for implementing the
|
||||
algorithm, and which graph concepts the operations map to. In this
|
||||
algorithm we will need to traverse through all of the vertices to
|
||||
intialize the vertex colors. We also need to access the adjacent
|
||||
vertices. Therefore, we will choose the <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a> concept because it
|
||||
is the minimum concept that includes these operations. The graph type
|
||||
will be parameterized in the template function for this algorithm. We
|
||||
do not restrict the graph type to a particular graph class, such as
|
||||
the BGL <a href="./adjacency_list.html"><TT>adjacency_list</TT></a>,
|
||||
for this would drastically limit the reusability of the algorithm (as
|
||||
most algorithms written to date are). We do restrict the graph type to
|
||||
those types that model <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a>. This is enforced by
|
||||
the use of those graph operations in the algorithm, and furthermore by
|
||||
our explicit requirement added as a concept check with
|
||||
<TT>function_requires()</TT> (see Section <A
|
||||
HREF="../../concept_check/concept_check.htm">Concept
|
||||
Checking</A> for more details about concept checking).
|
||||
|
||||
<P>
|
||||
Next we need to think about what vertex or edge properties will be
|
||||
used in the algorithm. In this case, the only property is vertex
|
||||
color. The most flexible way to specify access to vertex color is to
|
||||
use the propery map interface. This gives the user of the
|
||||
algorithm the ability to decide how they want to store the properties.
|
||||
Since we will need to both read and write the colors we specify the
|
||||
requirements as <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The
|
||||
<TT>key_type</TT> of the color map must be the
|
||||
<TT>vertex_descriptor</TT> from the graph, and the <TT>value_type</TT>
|
||||
must be some kind of integer. We also specify the interface for the
|
||||
<TT>order</TT> parameter as a property map, in this case a <a
|
||||
href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>. For
|
||||
order, the <TT>key_type</TT> is an integer offset and the
|
||||
<TT>value_type</TT> is a <TT>vertex_descriptor</TT>. Again we enforce
|
||||
these requirements with concept checks. The return value of this
|
||||
algorithm is the number of colors that were needed to color the graph,
|
||||
hence the return type of the function is the graph's
|
||||
<TT>vertices_size_type</TT>. The following code shows the interface for our
|
||||
graph algorithm as a template function, the concept checks, and some
|
||||
typedefs. The implementation is straightforward, the only step not
|
||||
discussed above is the color initialization step, where we set the
|
||||
color of all the vertices to ``uncolored''.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
namespace boost {
|
||||
template <class VertexListGraph, class Order, class Color>
|
||||
typename graph_traits<VertexListGraph>::vertices_size_type
|
||||
sequential_vertex_color_ting(const VertexListGraph& G,
|
||||
Order order, Color color)
|
||||
{
|
||||
typedef graph_traits<VertexListGraph> GraphTraits;
|
||||
typedef typename GraphTraits::vertex_descriptor vertex_descriptor;
|
||||
typedef typename GraphTraits::vertices_size_type size_type;
|
||||
typedef typename property_traits<Color>::value_type ColorType;
|
||||
typedef typename property_traits<Order>::value_type OrderType;
|
||||
|
||||
function_requires< VertexListGraphConcept<VertexListGraph> >();
|
||||
function_requires< ReadWritePropertyMapConcept<Color, vertex_descriptor> >();
|
||||
function_requires< IntegerConcept<ColorType> >();
|
||||
function_requires< size_type, ReadablePropertyMapConcept<Order> >();
|
||||
typedef typename same_type<OrderType, vertex_descriptor>::type req_same;
|
||||
|
||||
size_type max_color = 0;
|
||||
const size_type V = num_vertices(G);
|
||||
std::vector<size_type>
|
||||
mark(V, numeric_limits_max(max_color));
|
||||
|
||||
typename GraphTraits::vertex_iterator v, vend;
|
||||
for (tie(v, vend) = vertices(G); v != vend; ++v)
|
||||
color[*v] = V - 1; // which means "not colored"
|
||||
|
||||
for (size_type i = 0; i < V; i++) {
|
||||
vertex_descriptor current = order[i];
|
||||
|
||||
// mark all the colors of the adjacent vertices
|
||||
typename GraphTraits::adjacency_iterator ai, aend;
|
||||
for (tie(ai, aend) = adjacent_vertices(current, G); ai != aend; ++ai)
|
||||
mark[color[*ai]] = i;
|
||||
|
||||
// find the smallest color unused by the adjacent vertices
|
||||
size_type smallest_color = 0;
|
||||
while (smallest_color < max_color && mark[smallest_color] == i)
|
||||
++smallest_color;
|
||||
|
||||
// if all the colors are used up, increase the number of colors
|
||||
if (smallest_color == max_color)
|
||||
++max_color;
|
||||
|
||||
color[current] = smallest_color;
|
||||
}
|
||||
return max_color;
|
||||
}
|
||||
} // namespace boost
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,182 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Cuthill-Mckee Ordering</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:bfs">
|
||||
<TT>cuthill_mckee_ordering</TT>
|
||||
</H1>
|
||||
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="LEFT">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">undirected</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">color, degree</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT">time: <i>O(log(m)|E|)</i> where <i>m = max { degree(v) | v in V }</i> </TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
|
||||
<pre>
|
||||
(1)
|
||||
template <class IncidenceGraph, class OutputIterator,
|
||||
class ColorMap, class DegreeMap>
|
||||
void
|
||||
cuthill_mckee_ordering(IncidenceGraph& g,
|
||||
typename graph_traits<Graph>::vertex_descriptor s,
|
||||
OutputIterator inverse_permutation,
|
||||
ColorMap color, DegreeMap degree)
|
||||
|
||||
(2)
|
||||
template <class VertexListGraph, class OutputIterator,
|
||||
class ColorMap, class DegreeMap>
|
||||
void
|
||||
cuthill_mckee_ordering(VertexListGraph& G, OutputIterator inverse_permutation,
|
||||
ColorMap color, DegreeMap degree)
|
||||
</pre>
|
||||
|
||||
The goal of the Cuthill-Mckee (and reverse Cuthill-Mckee) ordering
|
||||
algorithm[<A
|
||||
HREF="bibliography.html#george81:__sparse_pos_def">14</A>, <A
|
||||
HREF="bibliography.html#cuthill69:reducing_bandwith">43</A>, <a
|
||||
href="bibliography.html#liu75:rcm">44</a>, <a
|
||||
href="bibliography.html#george71:fem">45</a> ] is to reduce the <a
|
||||
href="./bandwidth.html">bandwidth</a> of a graph by reordering the
|
||||
indices assigned to each vertex. The Cuthill-Mckee ordering algorithm
|
||||
works by a local minimization of the i-th bandwidths. The vertices are
|
||||
basically assigned a breadth-first search order, except that at each
|
||||
step, the adjacent vertices are placed in the queue in order of
|
||||
increasing degree.
|
||||
|
||||
<p>
|
||||
Version 1 of the algorithm lets the user choose the ``starting
|
||||
vertex'' whereas version 2 finds a good starting vertex using the
|
||||
pseudo-peripheral pair heuristic. The choice of the ``starting
|
||||
vertex'' can have a significant effect on the quality of the ordering.
|
||||
|
||||
<p>
|
||||
The output of the algorithm are the vertices in the new ordering.
|
||||
Depending on what kind of output iterator you use, you can get either
|
||||
the Cuthill-Mckee ordering or the reverse Cuthill-McKee ordering. For
|
||||
example, if you store the output into a vector using the vector's
|
||||
reverse iterator, then you get the reverse Cuthill-McKee ordering.
|
||||
|
||||
<pre>
|
||||
std::vector<vertex_descriptor> inv_perm(num_vertices(G));
|
||||
cuthill_mckee_ordering(G, inv_perm.rbegin());
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
Either way, storing the output into a vector gives you the
|
||||
permutation from the new ordering to the old ordering.
|
||||
|
||||
<pre>
|
||||
inv_perm[new_index[u]] == old_index[u]
|
||||
</pre>
|
||||
|
||||
<p>
|
||||
Often times, it is the opposite permutation that you want, the
|
||||
permutation from the old index to the new index. This can easily be
|
||||
computed in the following way.
|
||||
|
||||
<pre>
|
||||
for (size_type i = 0; i != inv_perm.size(); ++i)
|
||||
perm[inv_perm[i]] = i;
|
||||
</pre>
|
||||
|
||||
|
||||
|
||||
<h3>Parameters</h3>
|
||||
|
||||
For version 1:
|
||||
|
||||
<ul>
|
||||
|
||||
<li> <tt>IncidenceGraph& g</tt> (IN) <br>
|
||||
An undirected graph. The graph's type must be a model of <a
|
||||
href="./IncidenceGraph.html">IncidenceGraph</a>.
|
||||
|
||||
<li> <tt>vertex_descriptor s</tt>  (IN) <br>
|
||||
The starting vertex.
|
||||
|
||||
<li> <tt>OutputIterator inverse_permutation</tt>  (OUT) <br>
|
||||
The new vertex ordering. The vertices are written to the <a
|
||||
href="http://www.sgi.com/tech/stl/OutputIterator.html">output
|
||||
iterator</a> in their new order.
|
||||
|
||||
<li> <tt>ColorMap color_map</tt>  (WORK) <br>
|
||||
Used internally to keep track of the progress of the algorithm
|
||||
(to avoid visiting the same vertex twice).
|
||||
|
||||
<li> <tt>DegreeMap degree_map</tt>  (IN) <br>
|
||||
This must map vertices to their degree.
|
||||
|
||||
</ul>
|
||||
|
||||
|
||||
For version 2:
|
||||
|
||||
<ul>
|
||||
|
||||
<li> <tt>VertexListGraph& g</tt> (IN) <br>
|
||||
An undirected graph. The graph's type must be a model of <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a>.
|
||||
|
||||
<li> <tt><a href="http://www.sgi.com/tech/stl/OutputIterator.html">
|
||||
OutputIterator</a> inverse_permutation</tt>  (OUT) <br>
|
||||
The new vertex ordering. The vertices are written to the
|
||||
output iterator in their new order.
|
||||
|
||||
<li> <tt>ColorMap color_map</tt>  (WORK) <br>
|
||||
Used internally to keep track of the progress of the algorithm
|
||||
(to avoid visiting the same vertex twice).
|
||||
|
||||
<li> <tt>DegreeMap degree_map</tt>  (IN) <br>
|
||||
This must map vertices to their degree.
|
||||
|
||||
</ul>
|
||||
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
See <a
|
||||
href="../example/cuthill_mckee_ordering.cpp"><tt>example/cuthill_mckee_ordering.cpp</tt></a>.
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./bandwidth.html">bandwidth</tt></a>,
|
||||
and <tt>degree_property_map</tt> in <tt>boost/graph/properties.hpp</tt>.
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,223 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Depth-First Search</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:depth-first-search"></A>
|
||||
<TT>depth_first_search</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="LEFT">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed and undirected</TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">color</TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT">time: <i>O(V + E)</i></TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Where Defined:</B></TH>
|
||||
<TD ALIGN="LEFT">
|
||||
<a href="../../../boost/graph/depth_first_search.hpp"><TT>boost/graph/depth_first_search.hpp</TT></a>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(1)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>>
|
||||
void depth_first_search(VertexListGraph& G, DFSVisitor v);
|
||||
|
||||
(2)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>, class <a href="#ColorMap">ColorMap</a>>
|
||||
void depth_first_search(VertexListGraph& G, DFSVisitor v, ColorMap c);
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
The <TT>depth_first_search()</TT> algorithm performs a depth-first
|
||||
search (DFS) on a graph, invoking the methods of the graph search
|
||||
visitor at the appropriate event-points. A depth-first search visits
|
||||
all the vertices in a graph, starting with some arbitrary vertex and
|
||||
then always choosing the next adjacent unvisited vertex. Once the DFS
|
||||
reaches a vertex with no unvisited neighbors it backtracks to one of
|
||||
the previous vertices and continues from there. Once all of the
|
||||
vertices in the same connected component have been visited, another
|
||||
arbitrary unvisited vertex is choosen and the depth-first search
|
||||
resumes. A more detailed explanation of DFS is given in Section <A
|
||||
HREF="./graph_theory_review.html#sec:dfs-algorithm">Depth-First
|
||||
Search</A>. The depth-first exploration of each connected component is
|
||||
implemented by the function <a
|
||||
href="./depth_first_visit.html"><tt>depth_first_visit()</tt></a>.
|
||||
|
||||
|
||||
<p>
|
||||
The <tt>DFSVisitor</tt> supplied by the user determines what
|
||||
actions are taken at each event-point within the algorithm.
|
||||
|
||||
<p>
|
||||
The <tt>ColorMap</tt> is used by the algorithm to keep track
|
||||
of which vertices have been visited.
|
||||
|
||||
<P>
|
||||
DFS is used as the kernel for several other graph algorithms,
|
||||
including <a
|
||||
href="./topological_sort.html"><tt>topological_sort</tt></a> and two
|
||||
of the connected component algorithms.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The type <TT>VertexListGraph</TT> must be a model of <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a>.
|
||||
</LI>
|
||||
<LI>In version (1) of the algorithm the graph must be a model of <a
|
||||
href="./PropertyGraph.html">PropertyGraph</a> for
|
||||
<TT>vertex_color_t</TT> and the color property map for the graph
|
||||
must meet the same requirements as <TT>ColorMap</TT>.
|
||||
</LI>
|
||||
<LI><a name="ColorMap">The type <TT>ColorMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The key type of <tt>ColorMap</tt> must be the vertex descriptor type for the graph and the value type of <TT>ColorMap</TT> must be a model of
|
||||
<a href="./ColorValue.html">ColorValue</a>.</a>
|
||||
</LI>
|
||||
<LI>The <tt>DFSVisitor</tt> type must be a model of <a
|
||||
href="./DFSVisitor.html">DFSVisitor</a>.
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3><A NAME="SECTION001340300000000000000">
|
||||
Complexity</A>
|
||||
</H3>
|
||||
|
||||
<P>
|
||||
The time complexity is <i>O(E + V)</i>.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Example</H3>
|
||||
|
||||
<P>
|
||||
This example shows DFS applied to the graph in <A
|
||||
HREF="./graph_theory_review.html#fig:dfs-example">Figure 1</A>. The
|
||||
source code for this example is in <a
|
||||
href="../example/dfs_basics.cpp"><TT>examples/dfs_basics.cpp</TT></a>.
|
||||
|
||||
<P>
|
||||
<p></p>
|
||||
<DIV ALIGN="CENTER"><A NAME="fig:dfs-example"></A></A>
|
||||
<TABLE>
|
||||
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
|
||||
Depth-first search spreading through a graph.
|
||||
</CAPTION>
|
||||
<TR><TD><IMG SRC="./figs/dfs_example.gif" width="166" height="91"></TD></TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
<p></p>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
// Select the graph type we wish to use
|
||||
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS> Graph;
|
||||
// Set up the vertex names
|
||||
enum { u, v, w, x, y, z, N };
|
||||
char name[] = { 'u', 'v', 'w', 'x', 'y', 'z' };
|
||||
// Specify the edges in the graph
|
||||
typedef std::pair<int,int> E;
|
||||
E edge_array[] = { E(u,v), E(u,x), E(x,v), E(y,x),
|
||||
E(v,y), E(w,y), E(w,z), E(z,z) };
|
||||
Graph G(N, edge_array, edge_array + sizeof(edge_array)/sizeof(E));
|
||||
|
||||
// Some typedef's to save a little typing
|
||||
typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
|
||||
typedef boost::graph_traits<Graph>::vertices_size_type size_type;
|
||||
typedef std::vector<Vertex>::iterator Piter;
|
||||
typedef std::vector<size_type>::iterator Iiter;
|
||||
|
||||
// color, discover time, and finish time properties
|
||||
std::vector<default_color_type> color(num_vertices(G));
|
||||
std::vector<size_type> dtime(num_vertices(G));
|
||||
std::vector<size_type> ftime(num_vertices(G));
|
||||
|
||||
boost::depth_first_search(G, boost::visit_timestamp(dtime.begin(), ftime.begin()),
|
||||
color.begin());
|
||||
|
||||
// use std::sort to order the vertices by their discover time
|
||||
std::vector<size_type> discover_order(N);
|
||||
boost::iota(discover_order.begin(), discover_order.end(), 0);
|
||||
std::sort(discover_order.begin(), discover_order.end(),
|
||||
boost::indirect_cmp<Iiter, std::less<size_type> >(dtime.begin()));
|
||||
|
||||
std::cout << "order of discovery: ";
|
||||
for (int i = 0; i < N; ++i)
|
||||
std::cout << name[ discover_order[i] ] << " ";
|
||||
|
||||
std::vector<size_type> finish_order(N);
|
||||
boost::iota(finish_order.begin(), finish_order.end(), 0);
|
||||
std::sort(finish_order.begin(), finish_order.end(),
|
||||
boost::indirect_cmp<Iiter, std::less<size_type> >(ftime.begin()));
|
||||
|
||||
std::cout << endl << "order of finish: ";
|
||||
for (size_type i = 0; i < N; ++i)
|
||||
std::cout << name[ finish_order[i] ] << " ";
|
||||
std::cout << std::endl;
|
||||
</PRE>
|
||||
The output is:
|
||||
<PRE>
|
||||
order of discovery: u v y x w z
|
||||
order of finish: x y v u z w
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./depth_first_visit.html"><tt>depth_first_visit</tt></a>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,107 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Depth-First Visit</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H2><A NAME="sec:dfs"></A>
|
||||
<TT>depth_first_visit</TT>
|
||||
</H2>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="LEFT">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed and undirected</TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">color</TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT">time: <i>O(E)</i></TD>
|
||||
</TR>
|
||||
|
||||
<TR><TH ALIGN="LEFT"><B>Where Defined:</B></TH>
|
||||
<TD ALIGN="LEFT">
|
||||
<a href="../../../boost/graph/depth_first_search.hpp"><TT>boost/graph/depth_first_search.hpp</TT></a>
|
||||
</TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
template <class <a href="./IncidenceGraph.html">IncidenceGraph</a>, class <a href="./DFSVisitor.html">DFSVisitor</a>, class <a href="#ColorMap">ColorMap</a>>
|
||||
void depth_first_visit(IncidenceGraph& g,
|
||||
typename graph_traits<IncidenceGraph>::vertex_descriptor s,
|
||||
DFSVisitor& vis, ColorMap color)
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
This function visits all of the vertices in the same connected
|
||||
component as the source vertex <tt>s</tt>, using the <a
|
||||
href="./graph_theory_review.html#sec:dfs-algorithm">depth-first
|
||||
pattern</a>. The main purpose of the function is for the
|
||||
implementation of <TT>depth_first_search()</TT> though sometimes it is
|
||||
useful on its own.
|
||||
|
||||
<p>
|
||||
The <tt>DFSVisitor</tt> supplied by the user determines what
|
||||
actions are taken at each event-point within the algorithm.
|
||||
|
||||
<p>
|
||||
The <tt>ColorMap</tt> is used by the algorithm to keep track
|
||||
of which vertices have been visited.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The type <TT>IncidenceGraph</TT> must be a model of
|
||||
<a href="./IncidenceGraph.html">IncidenceGraph</a>.
|
||||
</LI>
|
||||
<LI>The type <TT>DFSVisitor</TT> must be a model of <a
|
||||
href="./DFSVisitor.html">DFSVisitor</a>.
|
||||
</LI>
|
||||
<LI><a name="ColorMap">The type <TT>ColorMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The key type of <tt>ColorMap</tt> must be the vertex descriptor type for the graph and the value type of <TT>ColorMap</TT> must be a model of
|
||||
<a href="./ColorValue.html">ColorValue</a>.</a>
|
||||
</LI>
|
||||
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,115 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: dfs_visitor</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>
|
||||
<pre>
|
||||
dfs_visitor<EventVisitorList>
|
||||
</pre>
|
||||
</H1>
|
||||
|
||||
This class is an adapter that converts a list of <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s (constructed using
|
||||
<tt>std::pair</tt>) into a <a href="./DFSVisitor.html">DFSVisitor</a>.
|
||||
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
See the example for <a href="./EventVisitor.html">EventVisitor</a>.
|
||||
|
||||
<h3>Model of</h3>
|
||||
|
||||
<a href="./DFSVisitor.html">DFSVisitor</a>
|
||||
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th><th>Default</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>EventVisitorList</TT></TD>
|
||||
<TD>
|
||||
A list of <a href="./EventVisitor.html">EventVisitor</a>'s created
|
||||
with <tt>std::pair</tt>.
|
||||
</TD>
|
||||
<TD><TT><a href="./null_visitor.html"><tt>null_visitor</tt></a></TT></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>Member Functions</h3>
|
||||
|
||||
This class implements all of the member functions required by <a
|
||||
href="./DFSVisitor.html">DFSVisitor</a>. In each function the
|
||||
appropriate event is dispatched to the <a
|
||||
href="./EventVisitor.html">EventVisitor</a>'s in the EventVisitorList.
|
||||
|
||||
<h3>Non-Member Functions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Function</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr><td><tt>
|
||||
template <class EventVisitorList><br>
|
||||
dfs_visitor<EventVisitorList><br>
|
||||
make_dfs_visitor(EventVisitorList ev_list);
|
||||
</tt></td><td>
|
||||
Returns the event visitor list adapted to be a DFS visitor.
|
||||
</td></tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
<p>
|
||||
The following are event visitors: <a
|
||||
href="./predecessor_recorder.html"><tt>predecessor_recorder</tt></a>,
|
||||
<a href="./distance_recorder.html"><tt>distance_recorder</tt></a>,
|
||||
<a href="./time_stamper.html"><tt>time_stamper</tt></a>,
|
||||
and <a href="./property_writer.html"><tt>property_writer</tt></a>.
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,236 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Jeremy Siek makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Dijkstra's Shortest Paths</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:dijkstra"></A>
|
||||
<TT>dijkstra_shortest_paths</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="left">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed and undirected</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">color, distance, weight, vertex index</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT"><i>O((V + E) log V)</i>
|
||||
</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Where Defined:</B></TH>
|
||||
<TD ALIGN="LEFT">
|
||||
<a href="../../../boost/graph/dijkstra_shortest_paths.hpp"><TT>boost/graph/dijkstra_shortest_paths.hpp</TT></a>
|
||||
</TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(1)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>>
|
||||
void
|
||||
dijkstra_shortest_paths(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s);
|
||||
|
||||
(2)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="#DistanceMap">DistanceMap</a>>
|
||||
void
|
||||
dijkstra_shortest_paths(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
DistanceMap d);
|
||||
|
||||
(3)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="#DistanceMap">DistanceMap</a>, class <a href="./UniformCostVisitor.html">UniformCostVisitor</a>>
|
||||
void
|
||||
dijkstra_shortest_paths(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
DistanceMap d, UniformCostVisitor visit);
|
||||
|
||||
(4)
|
||||
template <class <a href="./VertexListGraph.html">VertexListGraph</a>, class <a href="./UniformCostVisitor.html">UniformCostVisitor</a>,
|
||||
class <a href="#DistanceMap">DistanceMap</a>, class <a href="#WeightMap">WeightMap</a>, class <a href="#ColorMap">ColorMap</a>, class <a href="#VertexIndexMap">VertexIndexMap</a>>
|
||||
void
|
||||
dijkstra_shortest_paths(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor s,
|
||||
DistanceMap distance, WeightMap weight, ColorMap color, VertexIndexMap id,
|
||||
UniformCostVisitor vis);
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
This is the modified Dijkstra algorithm [<A
|
||||
HREF="bibliography.html#dijkstra59">10</A>,<A
|
||||
HREF="bibliography.html#clr90">8</A>] which solves the single-source
|
||||
shortest-paths problem on a weighted, directed graph for the case
|
||||
where all edge weights are nonnegative. See Section <A
|
||||
HREF="graph_theory_review.html#sec:shortest-path-algorithms">Shortest-Paths Algorithms</A>
|
||||
for some background to the shortest-path problem. The priority queue
|
||||
used inside the algorithm is implemented with a heap for efficiency.
|
||||
|
||||
<P>
|
||||
There are four versions of the algorithm to accommodate whether the
|
||||
necessary graph properties will be supplied by the graph object or
|
||||
externally via a argument to this function. The properties needed by
|
||||
the algorithm are distance, weight, color, and vertex index. Version 3
|
||||
and 4 of the algorithm also include a visitor argument for added
|
||||
extensibility.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Requirements on Types</H3>
|
||||
|
||||
<P>
|
||||
|
||||
<UL>
|
||||
<LI>The type <TT>VertexListGraph</TT> must be a model of <a href="./VertexListGraph.html">VertexListGraph</a>.
|
||||
</LI>
|
||||
<li>In version (1) of the algorithm, the graph must be a <a href="./PropertyGraph.html">PropertyGraph</a> with respect to <tt>vertex_color_t</tt>,
|
||||
<tt>vertex_distance_t</tt>, <tt>edge_weight_t</tt>, and <tt>vertex_index_t</tt></li>
|
||||
|
||||
<li>In version (2) of the algorithm, the graph must be a <a href="./PropertyGraph.html">PropertyGraph</a> with respect to <tt>vertex_color_t</tt>,
|
||||
<tt>edge_weight_t</tt>, and <tt>vertex_index_t</tt></li>
|
||||
|
||||
<li>In version (3) of the algorithm, the graph must be a <a href="./PropertyGraph.html">PropertyGraph</a> with respect to <tt>vertex_color_t</tt>,
|
||||
<tt>edge_weight_t</tt>, and <tt>vertex_index_t</tt></li>
|
||||
|
||||
<LI>The type <TT>UniformCostVisitor</TT> must be a model of <a href="./UniformCostVisitor.html">UniformCostVisitor</a>.
|
||||
</LI>
|
||||
<LI><a name="DistanceMap">The type <TT>DistanceMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. The
|
||||
vertex descriptor type of the graph needs to be usable as the key
|
||||
type of the distance map. The value type of the distance
|
||||
map must be <a href="http://www.sgi.com/tech/stl/LessThanComparable.html">LessThanComparable</a>.</a>
|
||||
</LI>
|
||||
<LI><a name="WeightMap">The type <TT>WeightMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>. The
|
||||
edge descriptor type of the graph needs to be usable as the key
|
||||
type for the weight map. The value type for the map
|
||||
must be <I>Addable</I> with the value type of the distance
|
||||
map.</a>
|
||||
</LI>
|
||||
<LI><a name="ColorMap">The type <TT>ColorMap</TT> must be a model of
|
||||
<a href="../../property_map/ReadWritePropertyMap.html">ReadWritePropertyMap</a>. A vertex descriptor must be
|
||||
usable as the key type of the map, and the value type of the
|
||||
map must be a model of <a href="./ColorValue.html">ColorValue</a>.</a>
|
||||
</LI>
|
||||
<LI><a name="VertexIndexMap">The type <TT>VertexIndexMap</TT> must be a model of <a
|
||||
href="../../property_map/ReadablePropertyMap.html">ReadablePropertyMap</a>. The
|
||||
value type of <TT>VertexIndexMap</TT> must be an integer type. The
|
||||
integers must map vertex descriptors to the integers zero through
|
||||
<tt>num_vertices(g) - 1</tt>. The vertex
|
||||
descriptor type of the graph needs to be usable as the key type
|
||||
of the vertex index map.</a>
|
||||
</LI>
|
||||
</UL>
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Complexity</H3>
|
||||
|
||||
<P>
|
||||
The time complexity is <i>O((V + E) log V)</i>, or just <i>O(E log V)</i>
|
||||
if all vertices are reachable from the source.
|
||||
|
||||
<H3>Example</H3>
|
||||
|
||||
<P>
|
||||
The source code for this example is in <a
|
||||
href="../example/dijkstra.cpp"><TT>examples/dijkstra.cpp</TT></a>.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
int
|
||||
main(int , char* [])
|
||||
{
|
||||
using namespace boost;
|
||||
|
||||
typedef property<edge_weight_t, int> weightp;
|
||||
typedef adjacency_list< listS, vecS, directedS,
|
||||
property<vertex_color_t,default_color_type>, weightp > Graph;
|
||||
typedef graph_traits<Graph>::vertex_descriptor Vertex;
|
||||
|
||||
typedef std::pair<int,int> E;
|
||||
|
||||
const int num_nodes = 5;
|
||||
E edges[] = { E(0,2),
|
||||
E(1,1), E(1,3), E(1,4),
|
||||
E(2,1), E(2,3),
|
||||
E(3,4),
|
||||
E(4,0), E(4,1) };
|
||||
int weights[] = { 1, 2, 1, 2, 7, 3, 1, 1, 1};
|
||||
|
||||
Graph G(num_nodes, edges, edges + sizeof(edges)/sizeof(E), weights);
|
||||
|
||||
std::vector<Vertex> p(num_vertices(G));
|
||||
std::vector<int> d(num_vertices(G));
|
||||
|
||||
Vertex s = *(vertices(G).first);
|
||||
p[s] = s;
|
||||
dijkstra_shortest_paths(G, s, &d[0],
|
||||
make_ucs_visitor(record_predecessors(&p[0], on_edge_relaxed())));
|
||||
|
||||
std::cout << "distances from start vertex:" << std::endl;
|
||||
graph_traits<Graph>::vertex_iterator vi, vend;
|
||||
for(tie(vi,vend) = vertices(G); vi != vend; ++vi)
|
||||
std::cout << "distance(" << *vi << ") = " << d[*vi] << std::endl;
|
||||
std::cout << std::endl;
|
||||
|
||||
std::cout << "shortest paths tree" << std::endl;
|
||||
adjacency_list<> tree(num_nodes);
|
||||
|
||||
for(tie(vi,vend) = vertices(G); vi != vend; ++vi)
|
||||
if (*vi != p[*vi])
|
||||
add_edge(p[*vi], *vi, tree);
|
||||
|
||||
print_graph(tree);
|
||||
|
||||
return 0;
|
||||
}
|
||||
</PRE>
|
||||
The output is:
|
||||
<PRE>
|
||||
distances from start vertex:
|
||||
distance(0) = 0
|
||||
distance(1) = 6
|
||||
distance(2) = 1
|
||||
distance(3) = 4
|
||||
distance(4) = 5
|
||||
|
||||
shortest paths tree
|
||||
0 --> 2
|
||||
1 -->
|
||||
2 --> 3
|
||||
3 --> 4
|
||||
4 --> 1
|
||||
</PRE>
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,186 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: distance_recorder</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1>
|
||||
<pre>
|
||||
distance_recorder<DistanceMap, EventTag>
|
||||
</pre>
|
||||
</H1>
|
||||
|
||||
This is an <a href="./EventVisitor.html">EventVisitor</a> that records
|
||||
the distance of a vertex (using a <a
|
||||
href="property_map.html">property map</a>) from some
|
||||
source vertex during a graph search. When applied to edge <i>e =
|
||||
(u,v)</i>, the distance of <i>v</i> is recorded to be one more than
|
||||
the distance of <i>u</i>. The distance recorder is typically used with
|
||||
the <tt>on_tree_edge</tt> or <tt>on_relax_edge</tt> events, and
|
||||
cannot be used with vertex events.
|
||||
|
||||
<p>
|
||||
<tt>distance_recorder</tt> can be used with graph algorithms by
|
||||
wrapping it with the algorithm specific adaptor, such as <a
|
||||
href="./bfs_visitor.html"><tt>bfs_visitor</tt></a> and <a
|
||||
href="./dfs_visitor.html"><tt>dfs_visitor</tt></a>. Also, this event
|
||||
visitor can be combined with other event visitors using
|
||||
<tt>std::pair</tt> to form an EventVisitorList.
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
See the example for <a href="./bfs_visitor.html"><tt>bfs_visitor</tt></a>.
|
||||
|
||||
<h3>Model of</h3>
|
||||
|
||||
<a href="./EventVisitor.html">EventVisitor</a>
|
||||
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/visitors.hpp">
|
||||
<TT>boost/graph/visitors.hpp</TT></a>
|
||||
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th><th>Default</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>DistanceMap</TT></TD>
|
||||
<TD>
|
||||
A <a
|
||||
href="../../property_map/WritablePropertyMap.html">WritablePropertyMap</a>,
|
||||
where the key type and the value type are the vertex descriptor type
|
||||
of the graph.
|
||||
</TD>
|
||||
<TD> </TD>
|
||||
</TR>
|
||||
|
||||
<TR><TD><TT>EventTag</TT></TD>
|
||||
<TD>
|
||||
The tag to specify when the <tt>distance_recorder</tt> should be
|
||||
applied during the graph algorithm. <tt>EventTag</tt> must be an
|
||||
edge event.
|
||||
</TD>
|
||||
<TD> </TD>
|
||||
</TR>
|
||||
|
||||
</table>
|
||||
|
||||
<H2>Associated Types</H2>
|
||||
|
||||
<table border>
|
||||
|
||||
<tr>
|
||||
<th>Type</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>distance_recorder::event_filter</tt></td>
|
||||
<td>
|
||||
This will be the same type as the template parameter <tt>EventTag</tt>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Member Functions</h3>
|
||||
|
||||
<p>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Member</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
distance_recorder(DistanceMap pa);
|
||||
</tt></td>
|
||||
<td>
|
||||
Construct a distance recorder object with distance property map
|
||||
<tt>pa</tt>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td><tt>
|
||||
template <class Edge, class Graph><br>
|
||||
void operator()(Edge e, const Graph& g);
|
||||
</tt></td>
|
||||
<td>
|
||||
Given edge <i>e = (u,v)</i>, this records the distance of <i>v</i> as
|
||||
one plus the distance of <i>u</i>.
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>Non-Member Functions</h3>
|
||||
|
||||
<table border>
|
||||
<tr>
|
||||
<th>Function</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<tr><td><tt>
|
||||
template <class DistanceMap, class Tag><br>
|
||||
distance_recorder<DistanceMap, Tag> <br>
|
||||
record_distances(DistanceMap pa, Tag);
|
||||
</tt></td><td>
|
||||
A convenient way to create a <tt>distance_recorder</tt>.
|
||||
</td></tr>
|
||||
|
||||
</table>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./visitor_concepts.html">Visitor concepts</a>
|
||||
<p>
|
||||
The following are other event visitors: <a
|
||||
href="./distance_recorder.html"><tt>predecessor_recorder</tt></a>,
|
||||
<a href="./time_stamper.html"><tt>time_stamper</tt></a>,
|
||||
and <a href="./property_writer.html"><tt>property_writer</tt></a>.
|
||||
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
<!-- LocalWords: DistanceMap EventTag EventVisitor map bfs dfs const Siek
|
||||
-->
|
||||
<!-- LocalWords: EventVisitorList WritablePropertyMap Univ Quan
|
||||
-->
|
||||
<!-- LocalWords: Lumsdaine
|
||||
-->
|
||||
@@ -1,225 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Edge List Class</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
|
||||
<H1><A NAME="sec:edge-list-class"></A>
|
||||
<PRE>
|
||||
edge_list<EdgeIterator, ValueType, DiffType>
|
||||
</PRE>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
The <TT>edge_list</TT> class is an adaptor that turns a pair of edge
|
||||
iterators into a class that models <TT>EdgeListGraph</TT>. The
|
||||
<TT>value_type</TT> of the edge iterator must be a <TT>std::pair</TT> (or
|
||||
at least have <TT>first</TT> and <TT>second</TT> members). The
|
||||
<TT>first_type</TT> and <TT>second_type</TT> of the pair must be the
|
||||
same and they will be used for the graph's <TT>vertex_descriptor</TT>.
|
||||
The <TT>ValueType</TT> and <TT>DiffType</TT> template parameters are only
|
||||
needed if your compiler does not support partial
|
||||
specialization. Otherwise they default to the correct types.
|
||||
|
||||
<P>
|
||||
|
||||
<H3>Example</H3>
|
||||
|
||||
<P>
|
||||
Applying the Bellman-Ford shortest paths algorithm to an
|
||||
<TT>edge_list</TT>.
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
enum { u, v, x, y, z, N };
|
||||
char name[] = { 'u', 'v', 'x', 'y', 'z' };
|
||||
|
||||
typedef std::pair<int,int> E;
|
||||
E edges[] = { E(u,y), E(u,x), E(u,v),
|
||||
E(v,u),
|
||||
E(x,y), E(x,v),
|
||||
E(y,v), E(y,z),
|
||||
E(z,u), E(z,x) };
|
||||
|
||||
int weight[] = { -4, 8, 5,
|
||||
-2,
|
||||
9, -3,
|
||||
7, 2,
|
||||
6, 7 };
|
||||
|
||||
typedef boost::edge_list<E*> Graph;
|
||||
Graph g(edges, edges + sizeof(edges) / sizeof(E));
|
||||
|
||||
std::vector<int> distance(N, std::numeric_limits<short>::max());
|
||||
std::vector<int> parent(N,-1);
|
||||
|
||||
distance[z] = 0;
|
||||
parent[z] = z;
|
||||
bool r = boost::bellman_ford_shortest_paths(g, int(N), weight,
|
||||
distance.begin(),
|
||||
parent.begin());
|
||||
if (r)
|
||||
for (int i = 0; i < N; ++i)
|
||||
std::cout << name[i] << ": " << distance[i]
|
||||
<< " " << name[parent[i]] << std::endl;
|
||||
else
|
||||
std::cout << "negative cycle" << std::endl;
|
||||
</PRE>
|
||||
The output is the distance from the root and the parent
|
||||
of each vertex in the shortest paths tree.
|
||||
<PRE>
|
||||
u: 2 v
|
||||
v: 4 x
|
||||
x: 7 z
|
||||
y: -2 u
|
||||
z: 0 z
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
<p>
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<a href="../../../boost/graph/edge_list.hpp"><TT>boost/graph/edge_list.hpp</TT></a>
|
||||
|
||||
<P>
|
||||
<H3>Template Parameters</H3>
|
||||
|
||||
<P>
|
||||
<TABLE border>
|
||||
<TR>
|
||||
<th>Parameter</th><th>Description</th>
|
||||
</tr>
|
||||
|
||||
<TR><TD><TT>EdgeIterator</TT></TD> <TD>Must be model of <a
|
||||
href="http://www.sgi.com/tech/stl/InputIterator.html">InputIterator</a>
|
||||
who's <TT>value_type</TT> must be a pair of vertex descriptors.</TD>
|
||||
</TR>
|
||||
|
||||
<TR><TD><TT>ValueType</TT></TD>
|
||||
<TD>The <TT>value_type</TT> of the <TT>EdgeIterator</TT>.<br>
|
||||
Default: <TT>std::iterator_traits<EdgeIterator>::value_type</TT></TD>
|
||||
</TR>
|
||||
|
||||
<TR><TD><TT>DiffType</TT></TD>
|
||||
<TD>The <TT>difference_type</TT> of the <TT>EdgeIterator</TT>.<br>
|
||||
Default: <TT>std::iterator_traits<EdgeIterator>::difference_type</TT></TD>
|
||||
</TR>
|
||||
|
||||
</TABLE>
|
||||
<P>
|
||||
|
||||
<H3>Model of</H3>
|
||||
|
||||
<a href="./EdgeListGraph.html">EdgeListGraph</a>
|
||||
|
||||
<P>
|
||||
|
||||
|
||||
<H3>Associated Types</H3>
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>boost::graph_traits<edge_list>::vertex_descriptor</tt>
|
||||
<br><br>
|
||||
The type for the vertex descriptors associated with the
|
||||
<TT>edge_list</TT>. This will be the same type as
|
||||
<TT>std::iterator_traits<EdgeIterator>::value_type::first_type</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
boost::graph_traits<edge_list>::edge_descriptor
|
||||
</tt>
|
||||
<br><br>
|
||||
The type for the edge descriptors associated with the
|
||||
<TT>edge_list</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
boost::graph_traits<edge_list>::edge_iterator
|
||||
</tt>
|
||||
<br><br>
|
||||
The type for the iterators returned by <TT>edges()</TT>. The iterator
|
||||
category of the <TT>edge_iterator</TT> will be the same as that of the
|
||||
<TT>EdgeIterator</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<h3>Member Functions</h3>
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
edge_list(EdgeIterator first, EdgeIterator last)
|
||||
</tt>
|
||||
<br><br>
|
||||
Creates a graph object with <TT>n</TT> vertices and with the
|
||||
edges specified in the edge list given by the range <TT>[first,last)</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<H3>Non-Member Functions</H3>
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
std::pair<edge_iterator, edge_iterator><br>
|
||||
edges(const edge_list& g)
|
||||
</tt>
|
||||
<br><br>
|
||||
Returns an iterator-range providing access to the edge set of graph <TT>g</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
vertex_descriptor<br>
|
||||
source(edge_descriptor e, const edge_list& g)
|
||||
</tt>
|
||||
<br><br>
|
||||
Returns the source vertex of edge <TT>e</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<tt>
|
||||
vertex_descriptor<br>
|
||||
target(edge_descriptor e, const edge_list& g)
|
||||
</tt>
|
||||
<br><br>
|
||||
Returns the target vertex of edge <TT>e</TT>.
|
||||
|
||||
<hr>
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)<br>
|
||||
<A HREF="../../../people/liequan_lee.htm">Lie-Quan Lee</A>, Univ.of Notre Dame (<A HREF="mailto:llee1@lsc.nd.edu">llee1@lsc.nd.edu</A>)<br>
|
||||
<A HREF=http://www.lsc.nd.edu/~lums>Andrew Lumsdaine</A>,
|
||||
Univ.of Notre Dame (<A
|
||||
HREF="mailto:lums@lsc.nd.edu">lums@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
@@ -1,306 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. Silicon Graphics makes no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: Edmunds-Karp Maximum Flow</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<H1><A NAME="sec:edmunds_karp_max_flow">
|
||||
<TT>edmunds_karp_max_flow</TT>
|
||||
</H1>
|
||||
|
||||
<P>
|
||||
<DIV ALIGN="LEFT">
|
||||
<TABLE CELLPADDING=3 border>
|
||||
<TR><TH ALIGN="LEFT"><B>Graphs:</B></TH>
|
||||
<TD ALIGN="LEFT">directed</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Properties:</B></TH>
|
||||
<TD ALIGN="LEFT">edge capacity, edge residual capacity, reverse edge,
|
||||
(vertex index | edge predecessor of vertex, vertex color)</TD>
|
||||
</TR>
|
||||
<TR><TH ALIGN="LEFT"><B>Complexity:</B></TH>
|
||||
<TD ALIGN="LEFT">time: <i>O(V E<sup>2</sup>)</i> or <i>O(V E U)</i> if capacity values are integers bounded by <i>U</i></TD>
|
||||
</TR>
|
||||
</TABLE>
|
||||
</DIV>
|
||||
|
||||
<P>
|
||||
<PRE>
|
||||
(1)
|
||||
template <typename VertexListGraph,
|
||||
typename CapacityEdgeMap, typename ResidualCapacityEdgeMap,
|
||||
typename ReverseEdgeMap, typename VertexIndexMap>
|
||||
typename property_traits<CapacityEdgeMap>::value_type
|
||||
edmunds_karp_max_flow
|
||||
(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor src,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor sink,
|
||||
CapacityEdgeMap cap,
|
||||
ResidualCapacityEdgeMap res,
|
||||
ReverseEdgeMap rev,
|
||||
VertexIndexMap index_map)
|
||||
|
||||
(2)
|
||||
template <typename VertexListGraph,
|
||||
typename CapacityEdgeMap, typename ResidualCapacityEdgeMap,
|
||||
typename ReverseEdgeMap, typename ColorMap, typename PredEdgeMap>
|
||||
typename property_traits<CapacityEdgeMap>::value_type
|
||||
edmunds_karp_max_flow
|
||||
(VertexListGraph& g,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor src,
|
||||
typename graph_traits<VertexListGraph>::vertex_descriptor sink,
|
||||
CapacityEdgeMap cap,
|
||||
ResidualCapacityEdgeMap res,
|
||||
ReverseEdgeMap rev,
|
||||
ColorMap color,
|
||||
PredEdgeMap pred)
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
The <tt>edmunds_karp_max_flow()</tt> function calculates the maximum flow
|
||||
of a network. See Section <a
|
||||
href="./graph_theory_review.html#sec:network-flow-algorithms">Network
|
||||
Flow Algorithms</a> for a description of maximum flow. The calculated
|
||||
maximum flow will be the return value of the function. The function
|
||||
also calculates the flow values <i>f(u,v)</i> for all <i>(u,v)</i> in
|
||||
<i>E</i>, which are returned in the form of the residual capacity
|
||||
<i>r(u,v) = c(u,v) - f(u,v)</i>.
|
||||
|
||||
<p>
|
||||
There are several special requirements on the input graph and property
|
||||
map parameters for this algorithm. First, the directed graph
|
||||
<i>G=(V,E)</i> that represents the network must be augmented to
|
||||
include the reverse edge for every edge in <i>E</i>. That is, the
|
||||
input graph should be <i>G<sub>in</sub> = (V,{E U
|
||||
E<sup>T</sup>})</i>. The <tt>ReverseEdgeMap</tt> argument <tt>rev</tt>
|
||||
must map each edge in the original graph to its reverse edge, that is
|
||||
<i>(u,v) -> (v,u)</i> for all <i>(u,v)</i> in <i>E</i>. The
|
||||
<tt>CapacityEdgeMap</tt> argument <tt>cap</tt> must map each edge in
|
||||
<i>E</i> to a positive number, and each edge in <i>E<sup>T</sup></i>
|
||||
to 0.
|
||||
|
||||
<p>
|
||||
The algorithm is due to <a
|
||||
href="./bibliography.html#edmonds72:_improvements_netflow">Edmonds and
|
||||
Karp</a>, though we are using the variation called the ``labeling
|
||||
algorithm'' described in <a
|
||||
href="./bibliography.html#ahuja93:_network_flows">Network Flows</a>.
|
||||
|
||||
<p>
|
||||
This algorithm provides a very simple an easy to implement solution to
|
||||
the maximum flow problem. However, there are several reasons why this
|
||||
algorithm is not as good as the <a
|
||||
href="./push_relabel_max_flow.html"><tt>push_relabel_max_flow()</tt></a>
|
||||
algorithm.
|
||||
|
||||
<ul>
|
||||
<li>In the non-integer capacity case, the time complexity is <i>O(V
|
||||
E<sup>2</sup>)</i> which is worse than the time complexity of the
|
||||
push-relabel algorithm <i>O(V<sup>2</sup>E<sup>1/2</sup>)</i>
|
||||
for all but the sparsest of graphs.</li>
|
||||
|
||||
<li>In the integer capacity case, if the capacity bound <i>U</i> is
|
||||
very large then the algorithm will take a long time.</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<H3>Where Defined</H3>
|
||||
|
||||
<P>
|
||||
<a href="../../../boost/graph/edmunds_karp_max_flow.hpp"><TT>boost/graph/edmunds_karp_max_flow.hpp</TT></a>
|
||||
|
||||
<P>
|
||||
|
||||
<h3>Parameters</h3>
|
||||
|
||||
<p>
|
||||
For version 1:
|
||||
|
||||
<ul>
|
||||
|
||||
<li> <tt>VertexListGraph& g</tt> (IN) <br>
|
||||
A directed graph. The
|
||||
graph's type must be a model of <a
|
||||
href="./VertexListGraph.html">VertexListGraph</a>. For each edge
|
||||
<i>(u,v)</i> in the graph, the reverse edge <i>(v,u)</i> must also
|
||||
be in the graph.
|
||||
|
||||
<li> <tt>vertex_descriptor src</tt>  (IN) <br>
|
||||
The source vertex for the flow network graph.
|
||||
|
||||
<li> <tt>vertex_descriptor sink</tt>  (IN) <br>
|
||||
The sink vertex for the flow network graph.
|
||||
|
||||
<li> <tt>CapacityEdgeMap cap</tt>  (IN) <br>
|
||||
The edge capacity property map. The type must be a model of a
|
||||
constant <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>. The
|
||||
key type of the map must be the graph's edge descriptor type.
|
||||
|
||||
<li> <tt>ResidualCapacityEdgeMap res</tt> (OUT) <br>
|
||||
The edge residual capacity property map. The type must be a model of
|
||||
a mutable <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>. The
|
||||
key type of the map must be the graph's edge descriptor type.
|
||||
|
||||
<li> <tt>ReverseEdgeMap rev</tt> (OUT) <br>
|
||||
An edge property map that maps every edge <i>(u,v)</i> in the graph
|
||||
to the reverse edge <i>(v,u)</i>. The map must be a model of
|
||||
constant <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>. The
|
||||
key type of the map must be the graph's edge descriptor type.
|
||||
|
||||
<li> <tt>VertexIndexMap index_map</tt>  (IN) <br>
|
||||
Maps each vertex of the graph to a unique integer in the range
|
||||
<tt>[0, num_vertices(g))</tt>. The map must be a model of constant <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>. The
|
||||
key type of the map must be the graph's vertex descriptor type.
|
||||
</ul>
|
||||
|
||||
<p>
|
||||
For version 2 (all of the above, minus the vertex index map, plus the
|
||||
following):
|
||||
|
||||
<ul>
|
||||
<li> <tt>ColorMap color</tt> (WORK) <br>
|
||||
Used by the algorithm to keep track of progress during the
|
||||
breadth-first search stage. At the end of the algorithm, the white
|
||||
vertices define the minimum cut set. The map must be a model of
|
||||
mutable <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>.
|
||||
The key type of the map should be the graph's vertex descriptor type, and
|
||||
the value type must be a model of <a
|
||||
href="./ColorValue.html">ColorValue</a>.</li>
|
||||
|
||||
<li> <tt>PredEdgeMap pred</tt> (WORK) <br>
|
||||
Use by the algorithm to store augmenting paths. The map must be a
|
||||
model of mutable <a
|
||||
href="../../property_map/LvaluePropertyMap.html">LvaluePropertyMap</a>.
|
||||
The key type must be the graph's vertex descriptor type and the
|
||||
value type must be the graph's edge descriptor type.
|
||||
|
||||
</ul>
|
||||
|
||||
|
||||
<h3>Example</h3>
|
||||
|
||||
This reads in an example maximum flow problem (a graph with edge
|
||||
capacities) from a file in the DIMACS format. The source for this
|
||||
example can be found in <a
|
||||
href="../example/edmunds_karp_max_flow.cpp"><tt>example/edmunds_karp_max_flow.cpp</tt></a>.
|
||||
|
||||
<pre>
|
||||
#include <boost/config.hpp>
|
||||
#include <iostream>
|
||||
#include <string>
|
||||
#include <boost/graph/edmunds_karp_map_flow.hpp>
|
||||
#include <boost/graph/adjacency_list.hpp>
|
||||
#include <boost/graph/read_dimacs.hpp>
|
||||
|
||||
int
|
||||
main()
|
||||
{
|
||||
using namespace boost;
|
||||
|
||||
typedef adjacency_list_traits<vecS, vecS, directedS> Traits;
|
||||
typedef adjacency_list<vecS, vecS, directedS,
|
||||
property<vertex_name_t, std::string>,
|
||||
property<edge_capacity_t, long,
|
||||
property<edge_residual_capacity_t, long,
|
||||
property<edge_reverse_t, Traits::edge_descriptor> > >
|
||||
> Graph;
|
||||
|
||||
Graph g;
|
||||
long flow;
|
||||
|
||||
property_map<Graph, edge_capacity_t>::type
|
||||
capacity = get(edge_capacity, g);
|
||||
property_map<Graph, edge_residual_capacity_t>::type
|
||||
residual_capacity = get(edge_residual_capacity, g);
|
||||
property_map<Graph, edge_reverse_t>::type
|
||||
reverse_edge = get(edge_reverse, g);
|
||||
|
||||
Traits::vertex_descriptor s, t;
|
||||
read_dimacs_max_flow(g, capacity, residual_capacity, reverse_edge, s, t);
|
||||
|
||||
flow = edmunds_karp_max_flow(g, s, t, capacity, residual_capacity,
|
||||
reverse_edge, get(vertex_index, g));
|
||||
|
||||
std::cout << "c The total flow:" << std::endl;
|
||||
std::cout << "s " << flow << std::endl << std::endl;
|
||||
|
||||
std::cout << "c flow values:" << std::endl;
|
||||
graph_traits<Graph>::vertex_iterator u_iter, u_end;
|
||||
graph_traits<Graph>::out_edge_iterator ei, e_end;
|
||||
for (tie(u_iter, u_end) = vertices(g); u_iter != u_end; ++u_iter)
|
||||
for (tie(ei, e_end) = out_edges(*u_iter, g); ei != e_end; ++ei)
|
||||
if (capacity[*ei] > 0)
|
||||
std::cout << "f " << *u_iter << " " << target(*ei, g) << " "
|
||||
<< (capacity[*ei] - residual_capacity[*ei]) << std::endl;
|
||||
return 0;
|
||||
}
|
||||
</pre>
|
||||
The output is:
|
||||
<pre>
|
||||
c The total flow:
|
||||
s 4
|
||||
|
||||
c flow values:
|
||||
f 0 1 4
|
||||
f 1 2 4
|
||||
f 2 3 2
|
||||
f 2 4 2
|
||||
f 3 1 0
|
||||
f 3 6 2
|
||||
f 4 5 3
|
||||
f 5 6 0
|
||||
f 5 7 3
|
||||
f 6 4 1
|
||||
f 6 7 1
|
||||
</pre>
|
||||
|
||||
<h3>See Also</h3>
|
||||
|
||||
<a href="./push_relabel_max_flow.html"><tt>push_relabel_max_flow()</tt></a>.
|
||||
|
||||
<br>
|
||||
<HR>
|
||||
<TABLE>
|
||||
<TR valign=top>
|
||||
<TD nowrap>Copyright © 2000</TD><TD>
|
||||
<A HREF="../../../people/jeremy_siek.htm">Jeremy Siek</A>, Univ.of Notre Dame (<A HREF="mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</A>)
|
||||
</TD></TR></TABLE>
|
||||
|
||||
</BODY>
|
||||
</HTML>
|
||||
<!-- LocalWords: HTML Siek Edmunds BGCOLOR ffffff ee VLINK ALINK ff IMG SRC
|
||||
-->
|
||||
<!-- LocalWords: gif ALT BR sec edmunds karp TT DIV CELLPADDING TR TD PRE lt
|
||||
-->
|
||||
<!-- LocalWords: typename VertexListGraph CapacityEdgeMap ReverseEdgeMap gt
|
||||
-->
|
||||
<!-- LocalWords: ResidualCapacityEdgeMap VertexIndexMap src rev ColorMap pred
|
||||
-->
|
||||
<!-- LocalWords: PredEdgeMap tt href html hpp ul li nbsp br LvaluePropertyMap
|
||||
-->
|
||||
<!-- LocalWords: num ColorValue DIMACS cpp pre config iostream dimacs int std
|
||||
-->
|
||||
<!-- LocalWords: namespace vecS directedS cout endl iter ei HR valign nowrap
|
||||
-->
|
||||
<!-- LocalWords: jeremy siek htm Univ mailto jsiek lsc edu
|
||||
p -->
|
||||
78
doc/faq.html
78
doc/faq.html
@@ -1,78 +0,0 @@
|
||||
<HTML>
|
||||
<!--
|
||||
-- Copyright (c) Jeremy Siek, Lie-Quan Lee, and Andrew Lumsdaine 2000
|
||||
--
|
||||
-- Permission to use, copy, modify, distribute and sell this software
|
||||
-- and its documentation for any purpose is hereby granted without fee,
|
||||
-- provided that the above copyright notice appears in all copies and
|
||||
-- that both that copyright notice and this permission notice appear
|
||||
-- in supporting documentation. We make no
|
||||
-- representations about the suitability of this software for any
|
||||
-- purpose. It is provided "as is" without express or implied warranty.
|
||||
-->
|
||||
<Head>
|
||||
<Title>Boost Graph Library: FAQ</Title>
|
||||
<BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b"
|
||||
ALINK="#ff0000">
|
||||
<IMG SRC="../../../c++boost.gif"
|
||||
ALT="C++ Boost" width="277" height="86">
|
||||
|
||||
<BR Clear>
|
||||
|
||||
<h1>Frequently Asked Questions</h1>
|
||||
|
||||
|
||||
<ol>
|
||||
|
||||
<li>Why does the algorithm X work with <tt>adjacency_list</tt> where
|
||||
<tt>VertexList=vecS</tt> but not when <tt>VertexList=listS</tt>? <br><br>
|
||||
Often the reason is that the algorithm expects to find the
|
||||
<tt>vertex_index</tt> property stored in the graph. When
|
||||
<tt>VertexList=vecS</tt>, the <tt>adjacency_list</tt> automatically
|
||||
has a <tt>vertex_index</tt> property. However, when <tt>VertexList=listS</tt>
|
||||
this is not the case, and the <tt>vertex_index</tt> property must be
|
||||
explicitly added, and initialized. For example,
|
||||
<pre>
|
||||
// specify the graph type
|
||||
typedef adjacency_list<listS, listS, undirectedS,
|
||||
property<vertex_index_t, std::size_t>,
|
||||
no_property
|
||||
> graph_t;
|
||||
|
||||
// construct a graph object
|
||||
graph_t G(num_nodes);
|
||||
// obtain a property map for the vertex_index property
|
||||
property_map<graph_t, vertex_index_t>::type
|
||||
index = get(vertex_index, G);
|
||||
// initialize the vertex_index property values
|
||||
graph_traits<graph_t>::vertex_iterator vi, vend;
|
||||
graph_traits<graph_t>::vertices_size_type cnt = 0;
|
||||
for(tie(vi,vend) = vertices(G); vi != vend; ++vi)
|
||||
put(index, *vi, cnt++);
|
||||
</pre>
|
||||
</li>
|
||||
|
||||
<li>When using algorithm X, why do I get an error about a property
|
||||
not being found, such as:
|
||||
<pre>
|
||||
../../../boost/concept_check.hpp:209: no match for
|
||||
`boost::detail::error_property_not_found & ==
|
||||
boost::detail::error_property_not_found &'
|
||||
</pre>
|
||||
or a message such as:
|
||||
<pre>
|
||||
../../..\boost/graph/depth_first_search.hpp(78) : error C2664: 'white'
|
||||
: cannot convert parameter 1 from
|
||||
'struct boost::detail::error_property_not_found'
|
||||
to 'enum boost::default_color_type'
|
||||
</pre>
|
||||
|
||||
The reason is that the algorithm expected to find some property (like color or
|
||||
weight) attached to the vertices or edges of the graph, but didn't
|
||||
find it. You need to either add an interior property to the graph, or
|
||||
create an exterior property map for the property and pass it as an
|
||||
argument to the algorithm.</li>
|
||||
|
||||
|
||||
|
||||
</ol>
|
||||
@@ -1,40 +0,0 @@
|
||||
# -*- makefile -*-
|
||||
|
||||
.SUFFIXES: .fig .gif .tif .jpeg
|
||||
|
||||
.fig.gif:
|
||||
fig2dev -L gif $*.fig > $*.gif
|
||||
|
||||
.fig.tif:
|
||||
fig2dev -L tiff $*.fig > $*.tif
|
||||
|
||||
.fig.jpeg:
|
||||
fig2dev -L jpeg $*.fig > $*.jpg
|
||||
|
||||
|
||||
|
||||
FIG = \
|
||||
analogy.fig dfs_example.fig quick_start.fig \
|
||||
back_edges.fig dfs_family.fig stl_iter.fig \
|
||||
bfs_example.fig dfs_visitor.fig tree_edges.fig \
|
||||
bfs_family.fig disjoint_set_family.fig visitor.fig \
|
||||
bfs_visitor.fig file_dep.fig \
|
||||
concepts.fig forward_or_cross_edges.fig digraph.fig \
|
||||
undigraph.fig adj_matrix.fig adj_list.fig \
|
||||
edge_list.fig dfs.fig knights_tour.fig \
|
||||
search_states.fig graph_search.fig
|
||||
|
||||
|
||||
GIF = $(FIG:.fig=.gif)
|
||||
TIFF = $(FIG:.fig=.tif)
|
||||
JPEG = $(FIG:.fig=.jpg)
|
||||
|
||||
gifs: $(GIF)
|
||||
tiffs: $(TIFF)
|
||||
jpegs: $(JPEG)
|
||||
|
||||
clean:
|
||||
/bin/rm -f *.gif *.tif *.jpg
|
||||
|
||||
|
||||
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 613 B |
Binary file not shown.
|
Before Width: | Height: | Size: 10 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 968 B |
@@ -1,59 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1156 2519 150 150 1156 2519 1306 2519
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1598 2541 150 150 1598 2541 1748 2541
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1148 2841 150 150 1148 2841 1298 2841
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1148 3141 150 150 1148 3141 1298 3141
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1150 3442 150 150 1150 3442 1300 3442
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1143 3746 150 150 1143 3746 1293 3746
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1592 2844 150 150 1592 2844 1742 2844
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2048 2541 150 150 2048 2541 2198 2541
|
||||
2 2 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 5
|
||||
600 2100 900 2100 900 3900 600 3900 600 2100
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
600 2400 900 2400
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
600 2700 900 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
600 3000 900 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
600 3300 900 3300
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
600 3600 900 3600
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
900 2550 975 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1350 2550 1425 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
900 2850 975 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1275 2850 1425 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
900 3150 975 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
900 3450 975 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
900 3750 975 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1770 2565 1890 2565
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 2325 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 675 2625 b\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 2925 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 75 675 3225 z\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 75 675 3525 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 675 3825 y\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1125 2625 y\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1575 2625 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1125 2925 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1575 2925 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 75 1125 3525 z\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 75 1125 3225 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1125 3825 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2025 2625 y\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 800 B |
@@ -1,31 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 2 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 5
|
||||
900 2100 2700 2100 2700 3900 900 3900 900 2100
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 2325 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 675 2625 b\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 2925 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 3225 z\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 675 3525 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 675 3825 y\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 1620 975 2025 v b x z a y\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2475 2625 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 975 3825 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2175 3225 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2925 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2625 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 975 2925 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1875 3525 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1575 975 2325 0 0 0 0 0 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1350 975 2625 0 0 0 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1305 1275 2925 0 0 0 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1575 975 3225 0 0 0 0 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1575 975 3525 0 0 0 0 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 1305 1275 3825 0 0 0 0 0\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 947 B |
@@ -1,35 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 2400 1200 1200 675 2400 1200 1200 1875
|
||||
1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 2320 4269 1200 675 2320 4269 1120 4944
|
||||
1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 6000 1200 1200 675 6000 1200 4800 1875
|
||||
1 1 0 1 0 7 0 0 -1 0.000 1 0.0000 6000 4350 1200 675 6000 4350 4800 5025
|
||||
2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 1 2
|
||||
0 0 1.00 60.00 120.00
|
||||
0 0 1.00 60.00 120.00
|
||||
2325 1875 2325 3600
|
||||
2 1 0 1 0 7 0 0 -1 0.000 0 0 -1 1 1 2
|
||||
0 0 1.00 60.00 120.00
|
||||
0 0 1.00 60.00 120.00
|
||||
5700 1875 5700 3675
|
||||
2 1 2 1 0 7 0 0 -1 3.000 0 0 -1 0 0 2
|
||||
4200 600 4200 4875
|
||||
4 0 0 0 0 0 18 0.0000 4 240 1770 1575 4350 STL Algorithms\001
|
||||
4 0 0 0 0 0 18 0.0000 4 210 1710 1650 1275 STL Containers\001
|
||||
4 0 0 0 0 0 18 0.0000 4 225 300 2025 5475 (a)\001
|
||||
4 0 0 0 0 0 18 0.0000 4 225 315 5700 5550 (b)\001
|
||||
4 0 0 0 0 0 18 0.0000 4 240 1965 5100 4425 Graph Algorithms\001
|
||||
4 0 0 0 0 0 18 0.0000 4 240 675 5700 1050 Graph\001
|
||||
4 0 0 0 0 0 18 0.0000 4 210 1665 5175 1350 Data Structures\001
|
||||
4 0 0 0 0 0 18 0.0000 4 180 795 2475 2700 Iterator\001
|
||||
4 0 0 0 0 0 18 0.0000 4 180 840 2475 3000 Functor\001
|
||||
4 0 0 0 0 0 18 0.0000 4 210 1590 5850 2475 Vertex Iterator\001
|
||||
4 0 0 100 0 0 18 0.0000 4 240 2010 5850 2850 Adjacency Iterator\001
|
||||
4 0 0 0 0 0 18 0.0000 4 240 2355 5850 3225 Visitor, Property Map\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 3.9 KiB |
@@ -1,45 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 6
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 2925 1575 3150 1275 3225 1200 2775 1425 2550 1650 2775
|
||||
0.000 1.000 1.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3750 2550 3600 2100 3300 1950 2925
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3300 2700 3300 2400 3000 2100 2700 2100
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 2700 2775 2550 2175 2550 1875 2700
|
||||
0.000 1.000 1.000 0.000
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 744 B |
@@ -1,72 +0,0 @@
|
||||
#FIG 3.2
|
||||
Portrait
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1057 3147 168 168 1057 3147 1207 3222
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1057 4046 168 168 1057 4046 1207 4121
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1963 3144 168 168 1963 3144 2113 3219
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1964 4033 168 168 1964 4033 2114 4108
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2850 3150 168 168 2850 3150 3000 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2850 4050 168 168 2850 4050 3000 4125
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3750 3150 168 168 3750 3150 3900 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3750 4050 168 168 3750 4050 3900 4125
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1050 3300 1050 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1200 3150 1800 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1950 3300 1950 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2700 3300 2100 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2175 4050 2700 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2850 3900 2850 3300
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3000 3150 3600 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3750 3300 3750 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3600 4050 3000 4050
|
||||
3 1 1 1 0 7 100 0 -1 4.000 0 0 0 13
|
||||
2250 3000 2100 2775 1950 2925 1725 2775 1725 3000 1500 3075
|
||||
1725 3300 1725 3525 2250 3450 2175 3375 2625 3300 2175 3150
|
||||
2325 3075
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000 1.000
|
||||
3 1 1 1 0 7 100 0 -1 4.000 0 0 0 18
|
||||
1875 2625 1500 2850 1050 2700 750 2925 750 3450 975 3450
|
||||
1275 3750 1500 3525 1650 3900 1650 4200 1950 4425 2475 4650
|
||||
2325 4125 2550 3975 2325 3675 2700 3450 2550 2925 2250 2700
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000
|
||||
3 1 1 1 0 7 100 0 -1 4.000 0 0 0 20
|
||||
2325 2625 1500 2625 900 2700 675 3000 675 3525 825 3750
|
||||
675 4050 900 4500 1125 4275 1500 4650 1725 4500 2400 4650
|
||||
2925 4350 3300 4350 3075 3900 3225 3600 3000 3450 3150 3000
|
||||
2625 2850 2625 2625
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000
|
||||
3 1 1 1 0 7 100 0 -1 4.000 0 0 0 19
|
||||
1800 2550 900 2625 675 2925 525 3525 675 4275 1050 4575
|
||||
1800 4725 3375 4500 4050 4275 4275 3900 3900 3675 4050 3450
|
||||
4050 3075 4050 2700 3600 2775 3300 2925 3075 2775 3000 2550
|
||||
2175 2550
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000
|
||||
4 0 0 100 0 0 12 0.0000 4 90 105 975 3225 r\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 135 975 4125 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 135 1875 3225 s\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 225 1875 4125 w \001
|
||||
4 0 0 100 0 0 12 0.0000 4 105 105 2775 3225 t\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 135 2775 4125 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 135 3675 3225 u\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3675 4125 y\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.7 KiB |
@@ -1,50 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3600 2550 4500 2100
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4800 3750 3750 3300
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4950 3750 3450 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4800 1950 4800 1500
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6000 2550 5100 2100
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3900 1425 2025 1425
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3975 2025 3000 2025
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3975 2025 3000 1800
|
||||
4 0 0 100 0 14 12 0.0000 4 165 2100 3900 1500 breadth_first_search\001
|
||||
4 0 0 100 0 14 12 0.0000 4 165 1785 4050 2100 best_first_search\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 2730 5100 2700 prim_minimum_spanning_tree\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 2415 2400 2700 dijkstra_shortest_paths\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 2835 900 3300 bellman_ford_shortest_paths\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 1470 1500 2100 fibonacci_heap\001
|
||||
4 0 0 100 0 14 12 0.0000 4 135 525 1500 1500 queue\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 3360 3300 3900 johnson_all_pairs_shortest_paths\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 4350 3225 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 3600 3600 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 5700 2400 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 4875 1800 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 3000 1350 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 3450 1875 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 3975 2475 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 3225 2250 <<uses>>\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 1365 1650 1800 mutable_queue\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 2.3 KiB |
@@ -1,73 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1500 4425 2025 4425
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1500 4650 2025 4650
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2250 2550 2850 2400 3375 2100 3675
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 6
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 2925 1575 3150 1275 3225 1200 2775 1425 2550 1650 2775
|
||||
0.000 1.000 1.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2775 2400 2850 2925 3225 3150 3600
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1875 3600 1650 3450 1650 3225 1725 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2100 3825 2400 4050 2850 4050 3075 3900
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3750 2550 3600 2100 3300 1950 2925
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 3600 3450 3450 3525 3225 3375 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3300 2700 3300 2400 3000 2100 2700 2100
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 2700 2775 2550 2175 2550 1875 2700
|
||||
0.000 1.000 1.000 0.000
|
||||
4 0 0 100 0 0 12 0.0000 4 180 780 2100 4500 Tree Edge\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 1515 2100 4725 Back or Cross Edge\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.3 KiB |
@@ -1,44 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6975 3150 7500 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6525 3825 7650 3075
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6975 2175 7575 2775
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3300 2025 5100 2025
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6975 2625 7575 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4350 2625 4800 2625
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4350 2550 5175 2100
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3075 2850 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3900 3225 4875 3225
|
||||
4 0 0 100 0 19 18 0.0000 4 255 2070 4350 3900 AdacencyMatrix\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 2040 5175 2100 IncidenceGraph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 2430 900 2100 BidirectionalGraph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 1935 4950 3300 EdgeListGraph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 795 7575 3000 Graph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 2145 4800 2700 AdjacencyGraph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 2100 2175 2700 VertexListGraph\001
|
||||
4 0 0 100 0 19 18 0.0000 4 255 3285 600 3300 VertexAndEdgeListGraph\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 2.5 KiB |
@@ -1,77 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2100 150 150 1800 2100 1800 2250
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2700 2100 150 150 2700 2100 2700 2250
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 3000 150 150 1800 3000 1800 3150
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2700 3000 150 150 2700 3000 2700 3150
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3600 2100 150 150 3600 2100 3600 2250
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3600 3000 150 150 3600 3000 3600 3150
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 3900 150 150 1800 3900 1800 4050
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2700 3900 150 150 2700 3900 2700 4050
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2700 4800 150 150 2700 4800 2700 4950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1950 2100 2550 2100
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1875 2250 2625 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1800 2250 1800 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1950 3000 2550 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2700 2250 2700 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2775 2850 3450 2175
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3600 2250 3600 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3450 3000 2850 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1950 3900 2550 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2625 4650 1950 3975
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2700 4050 2700 4650
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
1950 2100 2550 2100
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
2700 2250 2700 2850
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
2550 3000 1950 3000
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
2775 2850 3450 2175
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
3600 2250 3600 2850
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
1950 3900 2550 3900
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 3.00 90.00 150.00
|
||||
2700 4050 2700 4650
|
||||
4 0 0 100 0 0 12 0.0000 4 90 120 1725 2175 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2625 2175 b\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 120 3525 2175 c\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1725 3075 d\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 75 2625 3075 e\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 105 3525 3075 f\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1800 3975 g\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2625 3975 h\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2625 4875 i\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2100 2025 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2550 2550 2\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2250 2925 3\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2925 2550 4\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 3375 2625 5\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2100 3825 6\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2775 4275 7\001
|
||||
BIN
doc/figs/dfs.gif
BIN
doc/figs/dfs.gif
Binary file not shown.
|
Before Width: | Height: | Size: 1.2 KiB |
@@ -1,46 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3150 168 168 1950 3150 2025 3300
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2850 3132 168 168 2850 3132 2925 3282
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3750 3132 168 168 3750 3132 3825 3282
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1932 4050 168 168 1932 4050 2007 4200
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2832 4050 168 168 2832 4050 2907 4200
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3732 4050 168 168 3732 4050 3807 4200
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3300 1950 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2025 3975 2775 3225
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 90.00 120.00
|
||||
2700 4050 2100 4050
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 90.00 120.00
|
||||
2850 3300 2850 3900
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3600 3225 2925 3900
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 90.00 120.00
|
||||
3750 3300 3750 3900
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 90.00 120.00
|
||||
2100 3150 2700 3150
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 5
|
||||
1 1 1.00 60.00 120.00
|
||||
3825 4200 4050 4350 4275 4275 4200 3975 3900 4050
|
||||
0.000 1.000 1.000 1.000 0.000
|
||||
4 0 0 100 0 0 12 0.0000 4 90 180 1800 3225 u\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 180 2700 3225 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 225 3600 3225 w\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1875 4125 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2775 4125 y\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 3675 4125 z\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 813 B |
@@ -1,30 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 2250 4050 1800
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6000 2250 4950 1800
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2400 2700 3300 1875
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2400 2700 2100 2325
|
||||
4 0 0 100 0 14 12 0.0000 4 180 1890 3000 1800 depth_first_search\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 3255 1500 2925 connected_components (strongly)\001
|
||||
4 0 0 100 0 14 12 0.0000 4 165 945 1500 2325 transpose\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 2100 3075 2400 connected_components\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 1680 5400 2400 topological_sort\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 1725 2625 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 2625 2625 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 4125 2100 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 5550 2025 <<uses>>\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.2 KiB |
@@ -1,77 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4500 1800 4500
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4725 1800 4725
|
||||
2 1 1 1 0 7 100 0 -1 4.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4950 1800 4950
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 6
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 2925 1575 3150 1275 3225 1200 2775 1425 2550 1650 2775
|
||||
0.000 1.000 1.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2775 2400 2850 2925 3225 3150 3600
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1875 3600 1650 3450 1650 3225 1725 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3750 2550 3600 2100 3300 1950 2925
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 3600 3450 3450 3525 3225 3375 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3300 2700 3300 2400 3000 2100 2700 2100
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 2700 2775 2550 2175 2550 1875 2700
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2250 2550 2850 2400 3375 2100 3675
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 1 1 0 7 100 0 -1 4.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2100 3825 2400 4050 2850 4050 3075 3900
|
||||
0.000 1.000 1.000 0.000
|
||||
4 0 0 100 0 0 12 0.0000 4 180 780 2025 4575 Tree Edge\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 825 2025 4800 Back Edge\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 1755 2025 5025 Forward or Cross Edge\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.5 KiB |
@@ -1,53 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1650 2250 168 168 1650 2250 1800 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2232 1650 168 168 2232 1650 2382 1725
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2832 2250 168 168 2832 2250 2982 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2832 3150 168 168 2832 3150 2982 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1632 3150 168 168 1632 3150 1782 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2232 3750 168 168 2232 3750 2382 3825
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2700 3075 2325 2475 2250 1800
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2700 2175 2250 2100 1800 2175
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 2100 1725 1725 2100 1725
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 5
|
||||
1 1 1.00 60.00 120.00
|
||||
2925 3000 3225 2925 3300 3225 3150 3375 2925 3300
|
||||
0.000 -1.000 -1.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3600 2100 3225 1800 3150
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2775 2400 2700 2700 2775 3000
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 3300 1725 3600 2100 3750
|
||||
0.000 -1.000 0.000
|
||||
3 2 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2700 2325 2250 2250 1800 2325
|
||||
0.000 -1.000 0.000
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2175 1725 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2775 2325 b\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2775 3225 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2175 3825 z\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1575 3225 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2325 y\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 880 B |
@@ -1,20 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2925 2250 4275 1575
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6150 2250 4875 1575
|
||||
4 0 0 100 0 14 12 0.0000 4 180 2940 1500 2400 dynamic_connected_components\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 3045 4800 2400 kruskal_minimum_spanning_tree\001
|
||||
4 0 0 100 0 14 12 0.0000 4 180 1365 3975 1500 disjoint_sets\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 2925 1950 <<uses>>\001
|
||||
4 0 0 100 0 -1 10 0.0000 4 75 555 5700 1950 <<uses>>\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 988 B |
@@ -1,26 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 2 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 5
|
||||
600 2400 4800 2400 4800 2700 600 2700 600 2400
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1200 2400 1200 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1800 2400 1800 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2400 2400 2400 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3000 2400 3000 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
3600 2400 3600 2700
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
4200 2400 4200 2700
|
||||
2 2 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 5
|
||||
4800 2400 5400 2400 5400 2700 4800 2700 4800 2400
|
||||
4 0 0 100 0 0 12 0.0000 4 180 4545 720 2625 (b, y) (b, y) (y, v) (z, a) (x, x) (b, x) (x, v) (a, z)\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 562 B |
@@ -1,130 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 2100 3450 3000 3900
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 3675 450 225 2550 3675 3000 3900
|
||||
4 0 0 100 0 0 12 0.0000 4 180 555 2250 3750 foo.cpp\001
|
||||
-6
|
||||
6 2100 4200 3075 4725
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 2551 4428 450 225 2551 4428 3001 4653
|
||||
4 0 0 100 0 0 12 0.0000 4 135 375 2400 4500 foo.o\001
|
||||
-6
|
||||
6 3600 3450 4575 3975
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 4051 3678 450 225 4051 3678 4501 3903
|
||||
4 0 0 100 0 0 12 0.0000 4 180 555 3750 3750 bar.cpp\001
|
||||
-6
|
||||
6 3600 4200 4575 4650
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 4051 4425 450 225 4051 4425 4501 4650
|
||||
4 0 0 100 0 0 12 0.0000 4 135 375 3825 4500 bar.o\001
|
||||
-6
|
||||
6 2700 4950 3900 5400
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 5175 600 225 3300 5175 3900 5400
|
||||
4 0 0 100 0 0 12 0.0000 4 135 795 2925 5250 libfoobar.a\001
|
||||
-6
|
||||
6 4500 2250 5250 2700
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 4875 2475 375 225 4875 2475 5250 2700
|
||||
4 0 0 100 0 0 12 0.0000 4 180 450 4650 2550 yow.h\001
|
||||
-6
|
||||
6 2175 2250 2925 2700
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2475 375 225 2550 2475 2925 2700
|
||||
4 0 0 100 0 0 12 0.0000 4 135 450 2325 2550 zow.h\001
|
||||
-6
|
||||
6 3300 1650 4050 2100
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 3675 1875 375 225 3675 1875 4050 2100
|
||||
4 0 0 100 0 0 12 0.0000 4 135 405 3450 1950 dax.h\001
|
||||
-6
|
||||
6 4800 4200 5700 4650
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 5250 4425 450 225 5250 4425 5700 4650
|
||||
4 0 0 100 0 0 12 0.0000 4 180 540 5025 4500 zig.cpp\001
|
||||
-6
|
||||
6 4800 4950 5700 5400
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 5250 5175 450 225 5250 5175 5700 5400
|
||||
4 0 0 100 0 0 12 0.0000 4 180 360 5025 5250 zig.o\001
|
||||
-6
|
||||
6 6150 4200 7050 4650
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 6600 4425 450 225 6600 4425 7050 4650
|
||||
4 0 0 100 0 0 12 0.0000 4 135 585 6375 4500 zag.cpp\001
|
||||
-6
|
||||
6 6150 4950 7050 5400
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 6600 5175 450 225 6600 5175 7050 5400
|
||||
4 0 0 100 0 0 12 0.0000 4 135 405 6375 5250 zag.o\001
|
||||
-6
|
||||
6 4500 5850 5550 6300
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 5025 6075 525 225 5025 6075 5550 6300
|
||||
4 0 0 100 0 0 12 0.0000 4 180 810 4650 6150 libzigzag.a\001
|
||||
-6
|
||||
6 3000 6450 3900 6900
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 3450 6675 450 225 3450 6675 3900 6900
|
||||
4 0 0 100 0 0 12 0.0000 4 180 645 3150 6750 killerapp\001
|
||||
-6
|
||||
6 6000 2550 6750 3000
|
||||
1 1 0 1 0 7 100 0 -1 0.000 1 0.0000 6375 2775 375 225 6375 2775 6750 3000
|
||||
4 0 0 100 0 0 12 0.0000 4 135 405 6150 2850 boz.h\001
|
||||
-6
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2700 2550 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 3900 2550 4200
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 3900 4050 4200
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2700 4650 3000 4950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3975 4650 3675 4950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3825 5325 4650 5925
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4575 6150 3825 6525
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
5250 5400 5100 5850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6525 5400 5400 5925
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6600 4650 6600 4950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
5250 4650 5250 4950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 2025 2775 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3975 2025 4575 2400
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6075 2850 4425 3525
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6225 3000 5400 4200
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
6450 3000 6600 4200
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4725 2700 4200 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
5025 2700 6375 4275
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 2100 3975 3450
|
||||
3 0 1 1 0 7 100 0 -1 4.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3825 3450 3675 3150 3525 2550 3600 2100
|
||||
0.000 1.000 1.000 0.000
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 3.6 KiB |
@@ -1,33 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2100 3825 2400 4050 2850 4050 3075 3900
|
||||
0.000 1.000 1.000 0.000
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 537 B |
@@ -1,32 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 50 0 -1 4.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3675 5100 3675 6150
|
||||
2 1 0 1 0 7 50 0 -1 4.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 3450 3750 4350
|
||||
2 1 0 1 0 7 50 0 -1 4.000 0 0 -1 0 0 2
|
||||
1800 4500 5700 4500
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
1800 2700 5700 2700 5700 6900 1800 6900 1800 2700
|
||||
3 3 2 1 0 7 50 0 -1 4.000 0 0 0 24
|
||||
2625 4350 3075 4125 3375 4275 3825 4050 4200 4200 4425 4425
|
||||
4725 4200 5100 4125 5475 4350 5625 4725 5475 5100 4725 5400
|
||||
4125 5400 3975 5175 3525 5475 3075 5475 3000 5175 2625 5250
|
||||
2250 5475 1950 5175 1950 4350 2175 4425 2325 4200 2550 4125
|
||||
-1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
|
||||
-1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
|
||||
-1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
|
||||
4 0 0 50 0 19 18 0.0000 4 195 1275 3075 6600 Examined\001
|
||||
4 0 0 50 0 19 18 0.0000 4 255 3225 2175 4800 Target-To-Be-Examined\001
|
||||
4 0 0 50 0 14 14 0.0000 4 195 2970 2400 5775 p.examine_vertex(u, g)\001
|
||||
4 0 0 50 0 14 14 0.0000 4 195 2700 2475 3900 p.examine_edge(e, g)\001
|
||||
4 0 0 50 0 19 18 0.0000 4 195 1605 2925 3225 Unexamined\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 2.3 KiB |
@@ -1,211 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 0 0.000 1 0.0000 1950 1950 75 75 1950 1950 1950 2025
|
||||
1 3 0 1 0 7 100 0 0 0.000 1 0.0000 2850 3150 75 75 2850 3150 2850 3225
|
||||
2 2 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 5
|
||||
1800 1800 4200 1800 4200 4200 1800 4200 1800 1800
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 1950 2250 2625
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 2625 1950 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3150 2250 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3750 2850 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 4050 3450 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 3750 4050 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 4050 3750 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 3450 4050 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 2850 3750 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 2250 3150 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 1950 2550 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2250 1950 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2550 2250 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 1950 2850 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 2250 3450 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 1950 4050 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 2250 3450 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 2550 3750 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 1950 4050 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 2550 3750 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 3150 4050 3825
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 3825 3450 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 4050 3150 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 3450 3825 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3825 3750 4050 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 3150 3450 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 2850 3150 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 2250 2550 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 1950 1950 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2025 2250 2250 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 2850 1950 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3450 2250 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 4050 2850 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 3750 2550 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 3150 1950 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2850 2250 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 2325 2850 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 2550 3150 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 3150 2550 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 3450 1950 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3750 2550 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 4050 3225 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 3750 3750 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 4050 4050 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 3525 3750 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 2850 3450 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3525 2325 4050 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
4050 1950 3750 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3750 2550 3150 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 2850 3450 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 3450 3150 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 4050 2775 3375
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 3375 3450 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3450 3150 2850 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 2850 2250 3150
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3150 2550 3750
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 3675 1950 4050
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3975 2250 3450
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3525 2550 2850
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2925 3150 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3150 2625 2850 1950
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2850 1950 2550 2550
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2550 2850 3150
|
||||
4 0 0 100 0 0 12 0.0000 4 135 2205 1875 1725 0 1 2 3 4 5 6 7\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2025 0\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2325 1\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2700 2\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2925 3\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 3225 4\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 3525 5\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 3825 6\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 4125 7\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 2.4 KiB |
@@ -1,72 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1932 2832 2268 3168
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2100 3000 168 168 2100 3000 2250 3075
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2070 3075 0\001
|
||||
-6
|
||||
6 1350 4314 1686 4650
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1518 4482 168 168 1518 4482 1668 4557
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1473 4557 4\001
|
||||
-6
|
||||
6 1350 3414 1686 3750
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1518 3582 168 168 1518 3582 1668 3657
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1503 3657 1\001
|
||||
-6
|
||||
6 2550 3414 2886 3750
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2718 3582 168 168 2718 3582 2868 3657
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2718 3657 2\001
|
||||
-6
|
||||
6 2550 4314 2886 4650
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2718 4482 168 168 2718 4482 2868 4557
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2703 4557 3\001
|
||||
-6
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 3150 1650 3450
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2145 3180 2205 3900 2550 4365
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2640 4335 2520 3705 2220 3180
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2250 3090 2430 3420 2580 3450
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2670 3420 2580 3120 2280 3030
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2610 3690 2235 4140 1680 4455
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2535 4455 1905 4125 1635 3780
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2595 4560 2115 4710 1635 4635
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
1515 4290 1320 4020 1485 3765
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
2010 3150 1725 3705 1545 4335
|
||||
0.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 3
|
||||
1 1 1.00 60.00 120.00
|
||||
1635 4365 2055 3765 2070 3135
|
||||
0.000 1.000 0.000
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 923 B |
@@ -1,60 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
2 1 0 1 0 7 50 0 -1 3.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3300 3300 3300
|
||||
2 1 0 1 0 7 50 0 -1 3.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3600 3300 3600
|
||||
2 1 0 1 0 7 50 0 -1 3.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3900 3300 3900
|
||||
2 1 0 1 0 7 50 0 -1 3.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 4200 3300 4200
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
3300 2700 5400 2700 5400 3600 3300 3600 3300 2700
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
5400 2700 7800 2700 7800 3300 5400 3300 5400 2700
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
5400 3300 7800 3300 7800 3900 5400 3900 5400 3300
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
7800 2700 10200 2700 10200 3600 7800 3600 7800 2700
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
7800 3600 10200 3600 10200 4200 7800 4200 7800 3600
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
7800 4200 10200 4200 10200 4800 7800 4800 7800 4200
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
5400 3900 7800 3900 7800 4800 5400 4800 5400 3900
|
||||
2 2 0 1 0 7 50 0 -1 0.000 0 0 -1 0 0 5
|
||||
3300 3600 5400 3600 5400 4800 3300 4800 3300 3600
|
||||
3 0 2 1 0 7 50 0 -1 3.000 0 0 0 18
|
||||
3495 3705 3390 3510 3495 3315 3735 3390 3855 3240 4485 3360
|
||||
4845 3315 5160 3210 5340 3480 5295 4080 5070 4095 4785 3930
|
||||
4545 4110 3990 4185 3885 4035 3630 4200 3495 4140 3510 3705
|
||||
0.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
|
||||
1.000 0.000
|
||||
4 0 0 50 0 14 14 0.0000 4 195 2295 690 3345 examine_edge(u,v)\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 585 6270 3075 White\001
|
||||
4 0 0 50 0 19 14 0.0000 4 210 480 6315 3675 Gray\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 570 6300 4425 Black\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 585 8760 3240 White\001
|
||||
4 0 0 50 0 19 14 0.0000 4 210 480 8760 3975 Gray\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 570 8730 4560 Black\001
|
||||
4 0 0 50 0 14 14 0.0000 4 180 2295 690 3645 examine_vertex(v)\001
|
||||
4 0 0 50 0 14 14 0.0000 4 195 2835 150 3960 out_edges_examined(v)\001
|
||||
4 0 0 50 0 14 14 0.0000 4 195 2970 30 4260 previously_examined(v)\001
|
||||
4 0 0 50 0 18 14 0.0000 4 210 1395 3615 2505 Graph Search\001
|
||||
4 0 0 50 0 18 14 0.0000 4 165 1395 5880 2490 Breadth-First\001
|
||||
4 0 0 50 0 18 14 0.0000 4 210 1200 8370 2475 Depth-First\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 1275 3750 3075 Unexamined\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 1005 3825 4425 Examined\001
|
||||
4 0 0 50 0 19 14 0.0000 4 165 1740 3525 3675 To Be Processed\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 3.2 KiB |
@@ -1,14 +0,0 @@
|
||||
#FIG 3.1
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
1200 2
|
||||
1 3 0 3 -1 -1 0 0 0 0.000 1 0.0000 2250 1350 1045 1045 2250 1350 3295 2395
|
||||
1 3 0 3 -1 -1 0 0 0 0.000 1 0.0000 6179 1370 1045 1045 6179 1370 7224 2415
|
||||
2 1 0 3 -1 7 0 0 0 0.000 0 0 -1 1 1 2
|
||||
1 1 3.00 180.00 360.00
|
||||
1 1 3.00 180.00 360.00
|
||||
3375 1350 5025 1350
|
||||
4 0 -1 0 0 18 24 0.0000 4 255 1875 1275 1500 Containers\001
|
||||
4 0 -1 0 0 18 24 0.0000 4 255 1425 3450 825 Iterators\001
|
||||
4 0 -1 0 0 18 24 0.0000 4 330 1905 5250 1425 Algorithms\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.9 KiB |
@@ -1,45 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2250 2550 2850 2400 3375 2100 3675
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2775 2400 2850 2925 3225 3150 3600
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1875 3600 1650 3450 1650 3225 1725 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 3600 3450 3450 3525 3225 3375 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 733 B |
@@ -1,31 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1650 2250 168 168 1650 2250 1800 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2232 1650 168 168 2232 1650 2382 1725
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2832 2250 168 168 2832 2250 2982 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2832 3150 168 168 2832 3150 2982 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1632 3150 168 168 1632 3150 1782 3225
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2232 3750 168 168 2232 3750 2382 3825
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
1725 3300 2100 3675
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2325 1800 2775 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2850 2400 2850 3000
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2700 2250 1800 2250
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 0 0 2
|
||||
2100 1725 1800 2100
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2175 1725 v\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 2775 2325 b\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2775 3225 x\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 2175 3825 z\001
|
||||
4 0 0 100 0 0 12 0.0000 4 90 90 1575 3225 a\001
|
||||
4 0 0 100 0 0 12 0.0000 4 135 90 1575 2325 y\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 697 B |
Binary file not shown.
|
Before Width: | Height: | Size: 646 B |
Binary file not shown.
|
Before Width: | Height: | Size: 8.0 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 905 B |
@@ -1,77 +0,0 @@
|
||||
#FIG 3.2
|
||||
Landscape
|
||||
Center
|
||||
Inches
|
||||
Letter
|
||||
100.00
|
||||
Single
|
||||
-2
|
||||
1200 2
|
||||
6 1725 3525 2175 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1950 3732 168 168 1950 3732 2100 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1875 3825 2\001
|
||||
-6
|
||||
6 2925 3525 3375 3900
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3150 3732 168 168 3150 3732 3300 3807
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3075 3825 3\001
|
||||
-6
|
||||
6 2325 1875 2775 2325
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 2550 2100 168 168 2550 2100 2700 2175
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 2475 2175 0\001
|
||||
-6
|
||||
6 1575 2625 2025 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 1800 2832 168 168 1800 2832 1950 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 1725 2925 1\001
|
||||
-6
|
||||
6 3075 2625 3525 3000
|
||||
1 3 0 1 0 7 100 0 -1 0.000 1 0.0000 3300 2832 168 168 3300 2832 3450 2907
|
||||
4 0 0 100 0 0 12 0.0000 4 135 135 3225 2925 4\001
|
||||
-6
|
||||
2 1 0 3 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4500 1800 4500
|
||||
2 1 0 1 0 7 100 0 -1 0.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4725 1800 4725
|
||||
2 1 1 1 0 7 100 0 -1 4.000 0 0 -1 1 0 2
|
||||
1 1 1.00 60.00 120.00
|
||||
1350 4950 1800 4950
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 6
|
||||
1 1 1.00 60.00 120.00
|
||||
1650 2925 1575 3150 1275 3225 1200 2775 1425 2550 1650 2775
|
||||
0.000 1.000 1.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1950 2775 2400 2850 2925 3225 3150 3600
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
1875 3600 1650 3450 1650 3225 1725 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3000 3750 2550 3600 2100 3300 1950 2925
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 3600 3450 3450 3525 3225 3375 3000
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3300 2700 3300 2400 3000 2100 2700 2100
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 1 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
3225 2700 2775 2550 2175 2550 1875 2700
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 0 3 0 7 100 0 -1 0.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2550 2250 2550 2850 2400 3375 2100 3675
|
||||
0.000 1.000 1.000 0.000
|
||||
3 0 1 1 0 7 100 0 -1 4.000 0 1 0 4
|
||||
1 1 1.00 60.00 120.00
|
||||
2100 3825 2400 4050 2850 4050 3075 3900
|
||||
0.000 1.000 1.000 0.000
|
||||
4 0 0 100 0 0 12 0.0000 4 180 780 2025 4575 Tree Edge\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 825 2025 4800 Back Edge\001
|
||||
4 0 0 100 0 0 12 0.0000 4 180 1755 2025 5025 Forward or Cross Edge\001
|
||||
Binary file not shown.
|
Before Width: | Height: | Size: 1.5 KiB |
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user