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[SVN r9444]
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Ralf W. Grosse-Kunstleve
2001-03-05 20:01:01 +00:00
parent 5b441d6110
commit 3ad17643b9
2 changed files with 63 additions and 41 deletions
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68
doc/adjacency_list.html
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@@ -38,7 +38,20 @@ best meets your needs. An <a
href="graph_theory_review.html#sec:adjacency-list-representation">adjacency-list</a>
is basically a two-dimensional structure, where each element of the
first dimension represents a vertex, and each of the vertices contains
a one-dimensional structure that is its edge list. The
a one-dimensional structure that is its edge list. <a
href="fig:adj-list-graph">Figure 1</a> shows an adjacency list
representation of a directed graph.
<P></P>
<DIV ALIGN="center"><A NAME="fig:adj-list-graph"></A><A NAME="1509"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG> Adjacency List Representation of a Directed Graph.</CAPTION>
<TR><TD><IMG SRC="./figs/adj-matrix-graph.gif" width="386" height="284"></TD>
<TD><IMG SRC="./figs/adj-list.gif" width="62" height="122"></TD></TR>
</TABLE>
</DIV><P></P>
The
<TT>VertexList</TT> template parameter of the <TT>adjacency_list</TT>
class controls what kind of container is used to represent the outer
two-dimensional container. The <TT>EdgeList</TT> template parameter
@@ -55,7 +68,18 @@ The <TT>Directed</TT> template parameter controls whether the graph is
directed, undirected, or directed with access to both the in-edges and
out-edges (which we call bidirectional). The bidirectional graph takes
up twice the space (per edge) of a directed graph since each edge will
appear in both an out-edge and in-edge list.
appear in both an out-edge and in-edge list. <a
href="fig:undir-adj-list-graph">Figure 2</a> shows an adjacency list
representation of an undirected graph.
<P></P>
<DIV ALIGN="center"><A NAME="fig:undir-adj-list-graph"></A><A NAME="1509"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG> Adjacency List Representation of an Undirected Graph.</CAPTION>
<TR><TD><IMG SRC="./figs/undir-adj-matrix-graph.gif" width="2573" height="60929"></TD>
<TD><IMG SRC="./figs/undir-adj-list.gif" width="62" height="122"></TD></TR>
</TABLE>
</DIV><P></P>
<P>
A tutorial on how to use the <TT>adjacency_list</TT> class is in
@@ -395,9 +419,9 @@ The type for the iterators returned by <TT>vertices()</TT>.
When <tt>VertexList=vecS</tt> then the <tt>vertex_iterator</tt> models
<a
href="http://www.sgi.com/Technology/STL/RandomAccessIterator.html">RandomAccessIterator</a>. Otherwise
href="http://www.sgi.com/tech/stl/RandomAccessIterator.html">RandomAccessIterator</a>. Otherwise
the <tt>vertex_iterator</tt> models <a
href="http://www.sgi.com/Technology/STL/BidirectionalIterator.html">BidirectionalIterator</a>.
href="http://www.sgi.com/tech/stl/BidirectionalIterator.html">BidirectionalIterator</a>.
<hr>
@@ -405,7 +429,7 @@ href="http://www.sgi.com/Technology/STL/BidirectionalIterator.html">Bidirectiona
<br><br>
The type for the iterators returned by <TT>edges()</TT>.
The <tt>edge_iterator</tt> models <a
href="http://www.sgi.com/Technology/STL/BidirectionalIterator.html">BidirectionalIterator</a>.
href="http://www.sgi.com/tech/stl/BidirectionalIterator.html">BidirectionalIterator</a>.
<hr>
@@ -416,13 +440,13 @@ href="http://www.sgi.com/Technology/STL/BidirectionalIterator.html">Bidirectiona
The type for the iterators returned by <TT>out_edges()</TT>.
When <tt>EdgeList=vecS</tt> then the <tt>out_edge_iterator</tt> models
<a href="http://www.sgi.com/Technology/STL/RandomAccessIterator.html">
<a href="http://www.sgi.com/tech/stl/RandomAccessIterator.html">
RandomAccessIterator</a>. When <tt>EdgeList=slistS</tt> then the
<tt>out_edge_iterator</tt> models <a
href="http://www.sgi.com/Technology/STL/ForwardIterator.html">
href="http://www.sgi.com/tech/stl/ForwardIterator.html">
ForwardIterator</a>. Otherwise the <tt>out_edge_iterator</tt> models
<a
href="http://www.sgi.com/Technology/STL/BidirectionalIterator.html">
href="http://www.sgi.com/tech/stl/BidirectionalIterator.html">
BidirectionalIterator</a>.
<hr>
@@ -540,7 +564,7 @@ adjacency_list(vertices_size_type&nbsp;n,
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>.
The <tt>EdgeIterator</tt> must be a model of <a
href="http://www.sgi.com/Technology/STL/InputIterator.html">InputIterator</a>.
href="http://www.sgi.com/tech/stl/InputIterator.html">InputIterator</a>.
The value type of the <TT>EdgeIterator</TT> must be a
<TT>std::pair</TT>, where the type in the pair is an integer type. The
integers will correspond to vertices, and they must all fall in the
@@ -560,7 +584,7 @@ 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>.
The <tt>EdgeIterator</tt> and <tt>EdgePropertyIterator</tt> must be a
model of <a
href="http://www.sgi.com/Technology/STL/InputIterator.html">InputIterator</a>.
href="http://www.sgi.com/tech/stl/InputIterator.html">InputIterator</a>.
The value type of the <TT>EdgeIterator</TT> must be a
<TT>std::pair</TT>, where the type in the pair is an integer type. The
integers will correspond to vertices, and they must all fall in the
@@ -612,22 +636,24 @@ Returns an iterator-range providing access to the edge set of graph
<pre>
std::pair&lt;adjacency_iterator,&nbsp;adjacency_iterator&gt;
adjacent_vertices(vertex_descriptor&nbsp;v, const&nbsp;adjacency_list&amp;&nbsp;g)
adjacent_vertices(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns an iterator-range providing access to the vertices adjacent to
vertex <tt>v</tt> in graph <tt>g</tt>.
vertex <tt>u</tt> in graph <tt>g</tt>.
<hr>
<pre>
std::pair&lt;out_edge_iterator,&nbsp;out_edge_iterator&gt;
out_edges(vertex_descriptor&nbsp;v, const&nbsp;adjacency_list&amp;&nbsp;g)
out_edges(vertex_descriptor&nbsp;u, const&nbsp;adjacency_list&amp;&nbsp;g)
</pre>
Returns an iterator-range providing access to the out-edges of vertex
<tt>v</tt> in graph <tt>g</tt>. If the graph is undirected, this
iterator-range provides access to all edge incident on vertex
<tt>v</tt>.
<tt>u</tt> in graph <tt>g</tt>. If the graph is undirected, this
iterator-range provides access to all edges incident on vertex
<tt>u</tt>. For both directed and undirected graphs, for an out-edge
<tt>e</tt>, <tt>source(e, g) == u</tt> and <tt>target(e, g) == v</tt>
where <tt>v</tt> is a vertex adjacent to <tt>u</tt>.
<hr>
@@ -638,7 +664,9 @@ in_edges(vertex_descriptor&nbsp;v, const&nbsp;adjacency_list&amp;&nbsp;g)
Returns an iterator-range providing access to the in-edges of vertex
<tt>v</tt> in graph <tt>g</tt>. This operation is only available if
<TT>bidirectionalS</TT> was specified for the <TT>Directed</TT>
template parameter.
template parameter. For an in-edge <tt>e</tt>, <tt>target(e, g) == v</tt>
and <tt>source(e, g) == u</tt> for some vertex <tt>u</tt> that is
adjacent to <tt>v</tt>, whether the graph is directed or undirected.
<hr>
@@ -827,7 +855,7 @@ has time complexity <i>O(E/V)</i>.
<hr>
<pre>
template &lt;class <a href="http://www.sgi.com/Technology/STL/Predicate.html">Predicate</a>&gt;
template &lt;class <a href="http://www.sgi.com/tech/stl/Predicate.html">Predicate</a>&gt;
void remove_out_edge_if(vertex_descriptor u, Predicate predicate,
adjacency_list&amp; g)
</pre>
@@ -842,7 +870,7 @@ invoking <tt>remove_edge()</tt> on each of the removed edges.
<pre>
template &lt;class <a
href="http://www.sgi.com/Technology/STL/Predicate.html">Predicate</a>&gt;
href="http://www.sgi.com/tech/stl/Predicate.html">Predicate</a>&gt;
void remove_in_edge_if(vertex_descriptor v, Predicate predicate,
adjacency_list&amp; g)
</pre>
@@ -860,7 +888,7 @@ This operation is available for undirected and bidirectional
<hr>
<pre>
template &lt;class <a href="http://www.sgi.com/Technology/STL/Predicate.html">Predicate</a>&gt;
template &lt;class <a href="http://www.sgi.com/tech/stl/Predicate.html">Predicate</a>&gt;
void remove_edge_if(Predicate predicate, adjacency_list&amp; g)
</pre>
Removes all edges from the graph that satisfy

36
example/girth.cpp
View File

@@ -49,19 +49,13 @@ typedef Traits::vertex_iterator vertex_iterator;
std::vector<std::size_t> distance_list;
typedef boost::v_property<long> dist_t;
boost::property_map<Graph*, dist_t>::type distance;
boost::property_map<Graph*, dist_t>::type distance_map;
typedef boost::u_property<vertex_descriptor> pred_t;
boost::property_map<Graph*, pred_t>::type predecessor;
boost::property_map<Graph*, pred_t>::type predecessor_map;
typedef boost::w_property<long> color_t;
boost::property_map<Graph*, color_t>::type color;
namespace boost {
long white(long) { return 0; } // "unseen"
long gray(long) { return 2; } // "seen"
long black(long) { return 1; } // "known"
}
boost::property_map<Graph*, color_t>::type color_map;
class diameter_and_girth_visitor : public boost::bfs_visitor<>
{
@@ -71,16 +65,16 @@ public:
void tree_edge(edge_descriptor e, Graph* g) {
vertex_descriptor u = source(e, g), v = target(e, g);
k = distance[u] + 1;
distance[v] = k;
k = distance_map[u] + 1;
distance_map[v] = k;
++distance_list[k];
predecessor[v] = u;
predecessor_map[v] = u;
}
void cycle_edge(edge_descriptor e, Graph* g) {
void non_tree_edge(edge_descriptor e, Graph* g) {
vertex_descriptor u = source(e, g), v = target(e, g);
k = distance[u] + 1;
if (distance[v] + k < girth && v != predecessor[u])
girth = distance[v]+ k;
k = distance_map[u] + 1;
if (distance_map[v] + k < girth && v != predecessor_map[u])
girth = distance_map[v]+ k;
}
private:
std::size_t& k;
@@ -127,13 +121,13 @@ main()
distance_list.resize(boost::num_vertices(g), 0);
// obtain property maps
distance = get(dist_t(), g);
predecessor = get(pred_t(), g);
color = get(color_t(), g);
distance_map = get(dist_t(), g);
predecessor_map = get(pred_t(), g);
color_map = get(color_t(), g);
vertex_iterator i, end;
for (boost::tie(i, end) = boost::vertices(g); i != end; ++i)
distance[*i] = 0;
distance_map[*i] = 0;
std::size_t k = 0;
std::size_t girth = std::numeric_limits<std::size_t>::max();
@@ -142,7 +136,7 @@ main()
vertex_descriptor s = *boost::vertices(g).first;
// Call Variant 2 of BFS
boost::breadth_first_search(g, s, visitor, color);
boost::breadth_first_search(g, s, visitor, color_map);
std::cout << "Starting at any given vertex, there are" << std::endl;