Index: lemon/connectivity.h
===================================================================
 lemon/connectivity.h (revision 586)
+++ lemon/connectivity.h (revision 648)
@@ 43,10 +43,14 @@
/// \ingroup graph_properties
///
 /// \brief Check whether the given undirected graph is connected.
 ///
 /// Check whether the given undirected graph is connected.
 /// \param graph The undirected graph.
 /// \return \c true when there is path between any two nodes in the graph.
+ /// \brief Check whether an undirected graph is connected.
+ ///
+ /// This function checks whether the given undirected graph is connected,
+ /// i.e. there is a path between any two nodes in the graph.
+ ///
+ /// \return \c true if the graph is connected.
/// \note By definition, the empty graph is connected.
+ ///
+ /// \see countConnectedComponents(), connectedComponents()
+ /// \see stronglyConnected()
template
bool connected(const Graph& graph) {
@@ 68,10 +72,16 @@
/// \brief Count the number of connected components of an undirected graph
///
 /// Count the number of connected components of an undirected graph
 ///
 /// \param graph The graph. It must be undirected.
 /// \return The number of components
+ /// This function counts the number of connected components of the given
+ /// undirected graph.
+ ///
+ /// The connected components are the classes of an equivalence relation
+ /// on the nodes of an undirected graph. Two nodes are in the same class
+ /// if they are connected with a path.
+ ///
+ /// \return The number of connected components.
/// \note By definition, the empty graph consists
/// of zero connected components.
+ ///
+ /// \see connected(), connectedComponents()
template
int countConnectedComponents(const Graph &graph) {
@@ 110,15 +120,24 @@
/// \brief Find the connected components of an undirected graph
///
 /// Find the connected components of an undirected graph.
+ /// This function finds the connected components of the given undirected
+ /// graph.
+ ///
+ /// The connected components are the classes of an equivalence relation
+ /// on the nodes of an undirected graph. Two nodes are in the same class
+ /// if they are connected with a path.
///
/// \image html connected_components.png
/// \image latex connected_components.eps "Connected components" width=\textwidth
///
 /// \param graph The graph. It must be undirected.
+ /// \param graph The undirected graph.
/// \retval compMap A writable node map. The values will be set from 0 to
 /// the number of the connected components minus one. Each values of the map
 /// will be set exactly once, the values of a certain component will be
+ /// the number of the connected components minus one. Each value of the map
+ /// will be set exactly once, and the values of a certain component will be
/// set continuously.
 /// \return The number of components
+ /// \return The number of connected components.
+ /// \note By definition, the empty graph consists
+ /// of zero connected components.
+ ///
+ /// \see connected(), countConnectedComponents()
template
int connectedComponents(const Graph &graph, NodeMap &compMap) {
@@ 232,13 +251,15 @@
/// \ingroup graph_properties
///
 /// \brief Check whether the given directed graph is strongly connected.
 ///
 /// Check whether the given directed graph is strongly connected. The
 /// graph is strongly connected when any two nodes of the graph are
+ /// \brief Check whether a directed graph is strongly connected.
+ ///
+ /// This function checks whether the given directed graph is strongly
+ /// connected, i.e. any two nodes of the digraph are
/// connected with directed paths in both direction.
 /// \return \c false when the graph is not strongly connected.
 /// \see connected
 ///
 /// \note By definition, the empty graph is strongly connected.
+ ///
+ /// \return \c true if the digraph is strongly connected.
+ /// \note By definition, the empty digraph is strongly connected.
+ ///
+ /// \see countStronglyConnectedComponents(), stronglyConnectedComponents()
+ /// \see connected()
template
bool stronglyConnected(const Digraph& digraph) {
@@ 271,5 +292,5 @@
RDigraph rdigraph(digraph);
 typedef DfsVisitor RVisitor;
+ typedef DfsVisitor RVisitor;
RVisitor rvisitor;
@@ 290,16 +311,20 @@
/// \ingroup graph_properties
///
 /// \brief Count the strongly connected components of a directed graph
 ///
 /// Count the strongly connected components of a directed graph.
+ /// \brief Count the number of strongly connected components of a
+ /// directed graph
+ ///
+ /// This function counts the number of strongly connected components of
+ /// the given directed graph.
+ ///
/// The strongly connected components are the classes of an
 /// equivalence relation on the nodes of the graph. Two nodes are in
+ /// equivalence relation on the nodes of a digraph. Two nodes are in
/// the same class if they are connected with directed paths in both
/// direction.
///
 /// \param digraph The graph.
 /// \return The number of components
 /// \note By definition, the empty graph has zero
+ /// \return The number of strongly connected components.
+ /// \note By definition, the empty digraph has zero
/// strongly connected components.
+ ///
+ /// \see stronglyConnected(), stronglyConnectedComponents()
template
int countStronglyConnectedComponents(const Digraph& digraph) {
@@ 356,11 +381,13 @@
/// \brief Find the strongly connected components of a directed graph
///
 /// Find the strongly connected components of a directed graph. The
 /// strongly connected components are the classes of an equivalence
 /// relation on the nodes of the graph. Two nodes are in
 /// relationship when there are directed paths between them in both
 /// direction. In addition, the numbering of components will satisfy
 /// that there is no arc going from a higher numbered component to
 /// a lower.
+ /// This function finds the strongly connected components of the given
+ /// directed graph. In addition, the numbering of the components will
+ /// satisfy that there is no arc going from a higher numbered component
+ /// to a lower one (i.e. it provides a topological order of the components).
+ ///
+ /// The strongly connected components are the classes of an
+ /// equivalence relation on the nodes of a digraph. Two nodes are in
+ /// the same class if they are connected with directed paths in both
+ /// direction.
///
/// \image html strongly_connected_components.png
@@ 370,7 +397,11 @@
/// \retval compMap A writable node map. The values will be set from 0 to
/// the number of the strongly connected components minus one. Each value
 /// of the map will be set exactly once, the values of a certain component
 /// will be set continuously.
 /// \return The number of components
+ /// of the map will be set exactly once, and the values of a certain
+ /// component will be set continuously.
+ /// \return The number of strongly connected components.
+ /// \note By definition, the empty digraph has zero
+ /// strongly connected components.
+ ///
+ /// \see stronglyConnected(), countStronglyConnectedComponents()
template
int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) {
@@ 425,17 +456,22 @@
/// \brief Find the cut arcs of the strongly connected components.
///
 /// Find the cut arcs of the strongly connected components.
 /// The strongly connected components are the classes of an equivalence
 /// relation on the nodes of the graph. Two nodes are in relationship
 /// when there are directed paths between them in both direction.
+ /// This function finds the cut arcs of the strongly connected components
+ /// of the given digraph.
+ ///
+ /// The strongly connected components are the classes of an
+ /// equivalence relation on the nodes of a digraph. Two nodes are in
+ /// the same class if they are connected with directed paths in both
+ /// direction.
/// The strongly connected components are separated by the cut arcs.
///
 /// \param graph The graph.
 /// \retval cutMap A writable node map. The values will be set true when the
 /// arc is a cut arc.
 ///
 /// \return The number of cut arcs
+ /// \param digraph The digraph.
+ /// \retval cutMap A writable arc map. The values will be set to \c true
+ /// for the cut arcs (exactly once for each cut arc), and will not be
+ /// changed for other arcs.
+ /// \return The number of cut arcs.
+ ///
+ /// \see stronglyConnected(), stronglyConnectedComponents()
template
 int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) {
+ int stronglyConnectedCutArcs(const Digraph& digraph, ArcMap& cutMap) {
checkConcept();
typedef typename Digraph::Node Node;
@@ 449,11 +485,11 @@
typedef typename Container::iterator Iterator;
 Container nodes(countNodes(graph));
+ Container nodes(countNodes(digraph));
typedef LeaveOrderVisitor Visitor;
Visitor visitor(nodes.begin());
 DfsVisit dfs(graph, visitor);
+ DfsVisit dfs(digraph, visitor);
dfs.init();
 for (NodeIt it(graph); it != INVALID; ++it) {
+ for (NodeIt it(digraph); it != INVALID; ++it) {
if (!dfs.reached(it)) {
dfs.addSource(it);
@@ 465,12 +501,12 @@
typedef ReverseDigraph RDigraph;
 RDigraph rgraph(graph);
+ RDigraph rdigraph(digraph);
int cutNum = 0;
typedef StronglyConnectedCutArcsVisitor RVisitor;
 RVisitor rvisitor(rgraph, cutMap, cutNum);

 DfsVisit rdfs(rgraph, rvisitor);
+ RVisitor rvisitor(rdigraph, cutMap, cutNum);
+
+ DfsVisit rdfs(rdigraph, rvisitor);
rdfs.init();
@@ 707,12 +743,13 @@
/// \ingroup graph_properties
///
 /// \brief Checks the graph is binodeconnected.
 ///
 /// This function checks that the undirected graph is binodeconnected
 /// graph. The graph is binodeconnected if any two undirected edge is
 /// on same circle.
 ///
 /// \param graph The graph.
 /// \return \c true when the graph binodeconnected.
+ /// \brief Check whether an undirected graph is binodeconnected.
+ ///
+ /// This function checks whether the given undirected graph is
+ /// binodeconnected, i.e. any two edges are on same circle.
+ ///
+ /// \return \c true if the graph binodeconnected.
+ /// \note By definition, the empty graph is binodeconnected.
+ ///
+ /// \see countBiNodeConnectedComponents(), biNodeConnectedComponents()
template
bool biNodeConnected(const Graph& graph) {
@@ 722,13 +759,17 @@
/// \ingroup graph_properties
///
 /// \brief Count the biconnected components.
 ///
 /// This function finds the binodeconnected components in an undirected
 /// graph. The biconnected components are the classes of an equivalence
 /// relation on the undirected edges. Two undirected edge is in relationship
 /// when they are on same circle.
 ///
 /// \param graph The graph.
 /// \return The number of components.
+ /// \brief Count the number of binodeconnected components of an
+ /// undirected graph.
+ ///
+ /// This function counts the number of binodeconnected components of
+ /// the given undirected graph.
+ ///
+ /// The binodeconnected components are the classes of an equivalence
+ /// relation on the edges of a undirected graph. Two edges are in the
+ /// same class if they are on same circle.
+ ///
+ /// \return The number of binodeconnected components.
+ ///
+ /// \see biNodeConnected(), biNodeConnectedComponents()
template
int countBiNodeConnectedComponents(const Graph& graph) {
@@ 757,20 +798,24 @@
/// \ingroup graph_properties
///
 /// \brief Find the binodeconnected components.
 ///
 /// This function finds the binodeconnected components in an undirected
 /// graph. The binodeconnected components are the classes of an equivalence
 /// relation on the undirected edges. Two undirected edge are in relationship
 /// when they are on same circle.
+ /// \brief Find the binodeconnected components of an undirected graph.
+ ///
+ /// This function finds the binodeconnected components of the given
+ /// undirected graph.
+ ///
+ /// The binodeconnected components are the classes of an equivalence
+ /// relation on the edges of a undirected graph. Two edges are in the
+ /// same class if they are on same circle.
///
/// \image html node_biconnected_components.png
/// \image latex node_biconnected_components.eps "binodeconnected components" width=\textwidth
///
 /// \param graph The graph.
 /// \retval compMap A writable uedge map. The values will be set from 0
 /// to the number of the biconnected components minus one. Each values
 /// of the map will be set exactly once, the values of a certain component
 /// will be set continuously.
 /// \return The number of components.
+ /// \param graph The undirected graph.
+ /// \retval compMap A writable edge map. The values will be set from 0
+ /// to the number of the binodeconnected components minus one. Each
+ /// value of the map will be set exactly once, and the values of a
+ /// certain component will be set continuously.
+ /// \return The number of binodeconnected components.
+ ///
+ /// \see biNodeConnected(), countBiNodeConnectedComponents()
template
int biNodeConnectedComponents(const Graph& graph,
@@ 802,16 +847,23 @@
/// \ingroup graph_properties
///
 /// \brief Find the binodeconnected cut nodes.
 ///
 /// This function finds the binodeconnected cut nodes in an undirected
 /// graph. The binodeconnected components are the classes of an equivalence
 /// relation on the undirected edges. Two undirected edges are in
 /// relationship when they are on same circle. The biconnected components
 /// are separted by nodes which are the cut nodes of the components.
 ///
 /// \param graph The graph.
 /// \retval cutMap A writable edge map. The values will be set true when
 /// the node separate two or more components.
+ /// \brief Find the binodeconnected cut nodes in an undirected graph.
+ ///
+ /// This function finds the binodeconnected cut nodes in the given
+ /// undirected graph.
+ ///
+ /// The binodeconnected components are the classes of an equivalence
+ /// relation on the edges of a undirected graph. Two edges are in the
+ /// same class if they are on same circle.
+ /// The binodeconnected components are separted by the cut nodes of
+ /// the components.
+ ///
+ /// \param graph The undirected graph.
+ /// \retval cutMap A writable node map. The values will be set to
+ /// \c true for the nodes that separate two or more components
+ /// (exactly once for each cut node), and will not be changed for
+ /// other nodes.
/// \return The number of the cut nodes.
+ ///
+ /// \see biNodeConnected(), biNodeConnectedComponents()
template
int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) {
@@ 1032,12 +1084,14 @@
/// \ingroup graph_properties
///
 /// \brief Checks that the graph is biedgeconnected.
 ///
 /// This function checks that the graph is biedgeconnected. The undirected
 /// graph is biedgeconnected when any two nodes are connected with two
 /// edgedisjoint paths.
 ///
 /// \param graph The undirected graph.
 /// \return The number of components.
+ /// \brief Check whether an undirected graph is biedgeconnected.
+ ///
+ /// This function checks whether the given undirected graph is
+ /// biedgeconnected, i.e. any two nodes are connected with at least
+ /// two edgedisjoint paths.
+ ///
+ /// \return \c true if the graph is biedgeconnected.
+ /// \note By definition, the empty graph is biedgeconnected.
+ ///
+ /// \see countBiEdgeConnectedComponents(), biEdgeConnectedComponents()
template
bool biEdgeConnected(const Graph& graph) {
@@ 1047,13 +1101,18 @@
/// \ingroup graph_properties
///
 /// \brief Count the biedgeconnected components.
 ///
 /// This function count the biedgeconnected components in an undirected
 /// graph. The biedgeconnected components are the classes of an equivalence
 /// relation on the nodes. Two nodes are in relationship when they are
 /// connected with at least two edgedisjoint paths.
 ///
 /// \param graph The undirected graph.
 /// \return The number of components.
+ /// \brief Count the number of biedgeconnected components of an
+ /// undirected graph.
+ ///
+ /// This function counts the number of biedgeconnected components of
+ /// the given undirected graph.
+ ///
+ /// The biedgeconnected components are the classes of an equivalence
+ /// relation on the nodes of an undirected graph. Two nodes are in the
+ /// same class if they are connected with at least two edgedisjoint
+ /// paths.
+ ///
+ /// \return The number of biedgeconnected components.
+ ///
+ /// \see biEdgeConnected(), biEdgeConnectedComponents()
template
int countBiEdgeConnectedComponents(const Graph& graph) {
@@ 1082,20 +1141,25 @@
/// \ingroup graph_properties
///
 /// \brief Find the biedgeconnected components.
 ///
 /// This function finds the biedgeconnected components in an undirected
 /// graph. The biedgeconnected components are the classes of an equivalence
 /// relation on the nodes. Two nodes are in relationship when they are
 /// connected at least two edgedisjoint paths.
+ /// \brief Find the biedgeconnected components of an undirected graph.
+ ///
+ /// This function finds the biedgeconnected components of the given
+ /// undirected graph.
+ ///
+ /// The biedgeconnected components are the classes of an equivalence
+ /// relation on the nodes of an undirected graph. Two nodes are in the
+ /// same class if they are connected with at least two edgedisjoint
+ /// paths.
///
/// \image html edge_biconnected_components.png
/// \image latex edge_biconnected_components.eps "biedgeconnected components" width=\textwidth
///
 /// \param graph The graph.
+ /// \param graph The undirected graph.
/// \retval compMap A writable node map. The values will be set from 0 to
 /// the number of the biconnected components minus one. Each values
 /// of the map will be set exactly once, the values of a certain component
 /// will be set continuously.
 /// \return The number of components.
+ /// the number of the biedgeconnected components minus one. Each value
+ /// of the map will be set exactly once, and the values of a certain
+ /// component will be set continuously.
+ /// \return The number of biedgeconnected components.
+ ///
+ /// \see biEdgeConnected(), countBiEdgeConnectedComponents()
template
int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) {
@@ 1126,17 +1190,23 @@
/// \ingroup graph_properties
///
 /// \brief Find the biedgeconnected cut edges.
 ///
 /// This function finds the biedgeconnected components in an undirected
 /// graph. The biedgeconnected components are the classes of an equivalence
 /// relation on the nodes. Two nodes are in relationship when they are
 /// connected with at least two edgedisjoint paths. The biedgeconnected
 /// components are separted by edges which are the cut edges of the
 /// components.
 ///
 /// \param graph The graph.
 /// \retval cutMap A writable node map. The values will be set true when the
 /// edge is a cut edge.
+ /// \brief Find the biedgeconnected cut edges in an undirected graph.
+ ///
+ /// This function finds the biedgeconnected cut edges in the given
+ /// undirected graph.
+ ///
+ /// The biedgeconnected components are the classes of an equivalence
+ /// relation on the nodes of an undirected graph. Two nodes are in the
+ /// same class if they are connected with at least two edgedisjoint
+ /// paths.
+ /// The biedgeconnected components are separted by the cut edges of
+ /// the components.
+ ///
+ /// \param graph The undirected graph.
+ /// \retval cutMap A writable edge map. The values will be set to \c true
+ /// for the cut edges (exactly once for each cut edge), and will not be
+ /// changed for other edges.
/// \return The number of cut edges.
+ ///
+ /// \see biEdgeConnected(), biEdgeConnectedComponents()
template
int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) {
@@ 1190,21 +1260,14 @@
/// \ingroup graph_properties
///
 /// \brief Sort the nodes of a DAG into topolgical order.
 ///
 /// Sort the nodes of a DAG into topolgical order.
 ///
 /// \param graph The graph. It must be directed and acyclic.
 /// \retval order A writable node map. The values will be set from 0 to
 /// the number of the nodes in the graph minus one. Each values of the map
 /// will be set exactly once, the values will be set descending order.
 ///
 /// \see checkedTopologicalSort
 /// \see dag
 template
 void topologicalSort(const Digraph& graph, NodeMap& order) {
 using namespace _connectivity_bits;
+ /// \brief Check whether a digraph is DAG.
+ ///
+ /// This function checks whether the given digraph is DAG, i.e.
+ /// \e Directed \e Acyclic \e Graph.
+ /// \return \c true if there is no directed cycle in the digraph.
+ /// \see acyclic()
+ template
+ bool dag(const Digraph& digraph) {
checkConcept();
 checkConcept, NodeMap>();
typedef typename Digraph::Node Node;
@@ 1212,12 +1275,62 @@
typedef typename Digraph::Arc Arc;
+ typedef typename Digraph::template NodeMap ProcessedMap;
+
+ typename Dfs::template SetProcessedMap::
+ Create dfs(digraph);
+
+ ProcessedMap processed(digraph);
+ dfs.processedMap(processed);
+
+ dfs.init();
+ for (NodeIt it(digraph); it != INVALID; ++it) {
+ if (!dfs.reached(it)) {
+ dfs.addSource(it);
+ while (!dfs.emptyQueue()) {
+ Arc arc = dfs.nextArc();
+ Node target = digraph.target(arc);
+ if (dfs.reached(target) && !processed[target]) {
+ return false;
+ }
+ dfs.processNextArc();
+ }
+ }
+ }
+ return true;
+ }
+
+ /// \ingroup graph_properties
+ ///
+ /// \brief Sort the nodes of a DAG into topolgical order.
+ ///
+ /// This function sorts the nodes of the given acyclic digraph (DAG)
+ /// into topolgical order.
+ ///
+ /// \param digraph The digraph, which must be DAG.
+ /// \retval order A writable node map. The values will be set from 0 to
+ /// the number of the nodes in the digraph minus one. Each value of the
+ /// map will be set exactly once, and the values will be set descending
+ /// order.
+ ///
+ /// \see dag(), checkedTopologicalSort()
+ template
+ void topologicalSort(const Digraph& digraph, NodeMap& order) {
+ using namespace _connectivity_bits;
+
+ checkConcept();
+ checkConcept, NodeMap>();
+
+ typedef typename Digraph::Node Node;
+ typedef typename Digraph::NodeIt NodeIt;
+ typedef typename Digraph::Arc Arc;
+
TopologicalSortVisitor
 visitor(order, countNodes(graph));
+ visitor(order, countNodes(digraph));
DfsVisit >
 dfs(graph, visitor);
+ dfs(digraph, visitor);
dfs.init();
 for (NodeIt it(graph); it != INVALID; ++it) {
+ for (NodeIt it(digraph); it != INVALID; ++it) {
if (!dfs.reached(it)) {
dfs.addSource(it);
@@ 1231,16 +1344,16 @@
/// \brief Sort the nodes of a DAG into topolgical order.
///
 /// Sort the nodes of a DAG into topolgical order. It also checks
 /// that the given graph is DAG.
 ///
 /// \param digraph The graph. It must be directed and acyclic.
 /// \retval order A readable  writable node map. The values will be set
 /// from 0 to the number of the nodes in the graph minus one. Each values
 /// of the map will be set exactly once, the values will be set descending
 /// order.
 /// \return \c false when the graph is not DAG.
 ///
 /// \see topologicalSort
 /// \see dag
+ /// This function sorts the nodes of the given acyclic digraph (DAG)
+ /// into topolgical order and also checks whether the given digraph
+ /// is DAG.
+ ///
+ /// \param digraph The digraph.
+ /// \retval order A readable and writable node map. The values will be
+ /// set from 0 to the number of the nodes in the digraph minus one.
+ /// Each value of the map will be set exactly once, and the values will
+ /// be set descending order.
+ /// \return \c false if the digraph is not DAG.
+ ///
+ /// \see dag(), topologicalSort()
template
bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) {
@@ 1284,52 +1397,9 @@
/// \ingroup graph_properties
///
 /// \brief Check that the given directed graph is a DAG.
 ///
 /// Check that the given directed graph is a DAG. The DAG is
 /// an Directed Acyclic Digraph.
 /// \return \c false when the graph is not DAG.
 /// \see acyclic
 template
 bool dag(const Digraph& digraph) {

 checkConcept();

 typedef typename Digraph::Node Node;
 typedef typename Digraph::NodeIt NodeIt;
 typedef typename Digraph::Arc Arc;

 typedef typename Digraph::template NodeMap ProcessedMap;

 typename Dfs::template SetProcessedMap::
 Create dfs(digraph);

 ProcessedMap processed(digraph);
 dfs.processedMap(processed);

 dfs.init();
 for (NodeIt it(digraph); it != INVALID; ++it) {
 if (!dfs.reached(it)) {
 dfs.addSource(it);
 while (!dfs.emptyQueue()) {
 Arc edge = dfs.nextArc();
 Node target = digraph.target(edge);
 if (dfs.reached(target) && !processed[target]) {
 return false;
 }
 dfs.processNextArc();
 }
 }
 }
 return true;
 }

 /// \ingroup graph_properties
 ///
 /// \brief Check that the given undirected graph is acyclic.
 ///
 /// Check that the given undirected graph acyclic.
 /// \param graph The undirected graph.
 /// \return \c true when there is no circle in the graph.
 /// \see dag
+ /// \brief Check whether an undirected graph is acyclic.
+ ///
+ /// This function checks whether the given undirected graph is acyclic.
+ /// \return \c true if there is no cycle in the graph.
+ /// \see dag()
template
bool acyclic(const Graph& graph) {
@@ 1344,9 +1414,9 @@
dfs.addSource(it);
while (!dfs.emptyQueue()) {
 Arc edge = dfs.nextArc();
 Node source = graph.source(edge);
 Node target = graph.target(edge);
+ Arc arc = dfs.nextArc();
+ Node source = graph.source(arc);
+ Node target = graph.target(arc);
if (dfs.reached(target) &&
 dfs.predArc(source) != graph.oppositeArc(edge)) {
+ dfs.predArc(source) != graph.oppositeArc(arc)) {
return false;
}
@@ 1360,9 +1430,9 @@
/// \ingroup graph_properties
///
 /// \brief Check that the given undirected graph is tree.
 ///
 /// Check that the given undirected graph is tree.
 /// \param graph The undirected graph.
 /// \return \c true when the graph is acyclic and connected.
+ /// \brief Check whether an undirected graph is tree.
+ ///
+ /// This function checks whether the given undirected graph is tree.
+ /// \return \c true if the graph is acyclic and connected.
+ /// \see acyclic(), connected()
template
bool tree(const Graph& graph) {
@@ 1371,13 +1441,14 @@
typedef typename Graph::NodeIt NodeIt;
typedef typename Graph::Arc Arc;
+ if (NodeIt(graph) == INVALID) return true;
Dfs dfs(graph);
dfs.init();
dfs.addSource(NodeIt(graph));
while (!dfs.emptyQueue()) {
 Arc edge = dfs.nextArc();
 Node source = graph.source(edge);
 Node target = graph.target(edge);
+ Arc arc = dfs.nextArc();
+ Node source = graph.source(arc);
+ Node target = graph.target(arc);
if (dfs.reached(target) &&
 dfs.predArc(source) != graph.oppositeArc(edge)) {
+ dfs.predArc(source) != graph.oppositeArc(arc)) {
return false;
}
@@ 1452,13 +1523,12 @@
/// \ingroup graph_properties
///
 /// \brief Check if the given undirected graph is bipartite or not
 ///
 /// The function checks if the given undirected \c graph graph is bipartite
 /// or not. The \ref Bfs algorithm is used to calculate the result.
 /// \param graph The undirected graph.
 /// \return \c true if \c graph is bipartite, \c false otherwise.
 /// \sa bipartitePartitions
+ /// \brief Check whether an undirected graph is bipartite.
+ ///
+ /// The function checks whether the given undirected graph is bipartite.
+ /// \return \c true if the graph is bipartite.
+ ///
+ /// \see bipartitePartitions()
template
 inline bool bipartite(const Graph &graph){
+ bool bipartite(const Graph &graph){
using namespace _connectivity_bits;
@@ 1489,10 +1559,8 @@
/// \ingroup graph_properties
///
 /// \brief Check if the given undirected graph is bipartite or not
 ///
 /// The function checks if the given undirected graph is bipartite
 /// or not. The \ref Bfs algorithm is used to calculate the result.
 /// During the execution, the \c partMap will be set as the two
 /// partitions of the graph.
+ /// \brief Find the bipartite partitions of an undirected graph.
+ ///
+ /// This function checks whether the given undirected graph is bipartite
+ /// and gives back the bipartite partitions.
///
/// \image html bipartite_partitions.png
@@ 1500,12 +1568,16 @@
///
/// \param graph The undirected graph.
 /// \retval partMap A writable bool map of nodes. It will be set as the
 /// two partitions of the graph.
 /// \return \c true if \c graph is bipartite, \c false otherwise.
+ /// \retval partMap A writable node map of \c bool (or convertible) value
+ /// type. The values will be set to \c true for one component and
+ /// \c false for the other one.
+ /// \return \c true if the graph is bipartite, \c false otherwise.
+ ///
+ /// \see bipartite()
template
 inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){
+ bool bipartitePartitions(const Graph &graph, NodeMap &partMap){
using namespace _connectivity_bits;
checkConcept();
+ checkConcept, NodeMap>();
typedef typename Graph::Node Node;
@@ 1532,51 +1604,57 @@
}
 /// \brief Returns true when there are not loop edges in the graph.
 ///
 /// Returns true when there are not loop edges in the graph.
 template
 bool loopFree(const Digraph& digraph) {
 for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) {
 if (digraph.source(it) == digraph.target(it)) return false;
+ /// \ingroup graph_properties
+ ///
+ /// \brief Check whether the given graph contains no loop arcs/edges.
+ ///
+ /// This function returns \c true if there are no loop arcs/edges in
+ /// the given graph. It works for both directed and undirected graphs.
+ template
+ bool loopFree(const Graph& graph) {
+ for (typename Graph::ArcIt it(graph); it != INVALID; ++it) {
+ if (graph.source(it) == graph.target(it)) return false;
}
return true;
}
 /// \brief Returns true when there are not parallel edges in the graph.
 ///
 /// Returns true when there are not parallel edges in the graph.
 template
 bool parallelFree(const Digraph& digraph) {
 typename Digraph::template NodeMap reached(digraph, false);
 for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
 for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 if (reached[digraph.target(a)]) return false;
 reached.set(digraph.target(a), true);
 }
 for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 reached.set(digraph.target(a), false);
 }
+ /// \ingroup graph_properties
+ ///
+ /// \brief Check whether the given graph contains no parallel arcs/edges.
+ ///
+ /// This function returns \c true if there are no parallel arcs/edges in
+ /// the given graph. It works for both directed and undirected graphs.
+ template
+ bool parallelFree(const Graph& graph) {
+ typename Graph::template NodeMap reached(graph, 0);
+ int cnt = 1;
+ for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
+ for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) {
+ if (reached[graph.target(a)] == cnt) return false;
+ reached[graph.target(a)] = cnt;
+ }
+ ++cnt;
}
return true;
}
 /// \brief Returns true when there are not loop edges and parallel
 /// edges in the graph.
 ///
 /// Returns true when there are not loop edges and parallel edges in
 /// the graph.
 template
 bool simpleDigraph(const Digraph& digraph) {
 typename Digraph::template NodeMap reached(digraph, false);
 for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
 reached.set(n, true);
 for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 if (reached[digraph.target(a)]) return false;
 reached.set(digraph.target(a), true);
 }
 for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 reached.set(digraph.target(a), false);
 }
 reached.set(n, false);
+ /// \ingroup graph_properties
+ ///
+ /// \brief Check whether the given graph is simple.
+ ///
+ /// This function returns \c true if the given graph is simple, i.e.
+ /// it contains no loop arcs/edges and no parallel arcs/edges.
+ /// The function works for both directed and undirected graphs.
+ /// \see loopFree(), parallelFree()
+ template
+ bool simpleGraph(const Graph& graph) {
+ typename Graph::template NodeMap reached(graph, 0);
+ int cnt = 1;
+ for (typename Graph::NodeIt n(graph); n != INVALID; ++n) {
+ reached[n] = cnt;
+ for (typename Graph::OutArcIt a(graph, n); a != INVALID; ++a) {
+ if (reached[graph.target(a)] == cnt) return false;
+ reached[graph.target(a)] = cnt;
+ }
+ ++cnt;
}
return true;
Index: lemon/euler.h
===================================================================
 lemon/euler.h (revision 592)
+++ lemon/euler.h (revision 648)
@@ 245,8 +245,8 @@
 ///Check if the given graph is \e Eulerian
+ ///Check if the given graph is Eulerian
/// \ingroup graph_properties
 ///This function checks if the given graph is \e Eulerian.
+ ///This function checks if the given graph is Eulerian.
///It works for both directed and undirected graphs.
///
Index: test/CMakeLists.txt
===================================================================
 test/CMakeLists.txt (revision 627)
+++ test/CMakeLists.txt (revision 649)
@@ 10,4 +10,5 @@
bfs_test
circulation_test
+ connectivity_test
counter_test
dfs_test
Index: test/Makefile.am
===================================================================
 test/Makefile.am (revision 611)
+++ test/Makefile.am (revision 649)
@@ 10,4 +10,5 @@
test/bfs_test \
test/circulation_test \
+ test/connectivity_test \
test/counter_test \
test/dfs_test \
@@ 55,4 +56,5 @@
test_circulation_test_SOURCES = test/circulation_test.cc
test_counter_test_SOURCES = test/counter_test.cc
+test_connectivity_test_SOURCES = test/connectivity_test.cc
test_dfs_test_SOURCES = test/dfs_test.cc
test_digraph_test_SOURCES = test/digraph_test.cc
Index: test/connectivity_test.cc
===================================================================
 test/connectivity_test.cc (revision 649)
+++ test/connectivity_test.cc (revision 649)
@@ 0,0 +1,297 @@
+/* * mode: C++; indenttabsmode: nil; *
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 20032009
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#include
+#include
+#include
+
+#include "test_tools.h"
+
+using namespace lemon;
+
+
+int main()
+{
+ typedef ListDigraph Digraph;
+ typedef Undirector Graph;
+
+ {
+ Digraph d;
+ Digraph::NodeMap order(d);
+ Graph g(d);
+
+ check(stronglyConnected(d), "The empty digraph is strongly connected");
+ check(countStronglyConnectedComponents(d) == 0,
+ "The empty digraph has 0 strongly connected component");
+ check(connected(g), "The empty graph is connected");
+ check(countConnectedComponents(g) == 0,
+ "The empty graph has 0 connected component");
+
+ check(biNodeConnected(g), "The empty graph is binodeconnected");
+ check(countBiNodeConnectedComponents(g) == 0,
+ "The empty graph has 0 binodeconnected component");
+ check(biEdgeConnected(g), "The empty graph is biedgeconnected");
+ check(countBiEdgeConnectedComponents(g) == 0,
+ "The empty graph has 0 biedgeconnected component");
+
+ check(dag(d), "The empty digraph is DAG.");
+ check(checkedTopologicalSort(d, order), "The empty digraph is DAG.");
+ check(loopFree(d), "The empty digraph is loopfree.");
+ check(parallelFree(d), "The empty digraph is parallelfree.");
+ check(simpleGraph(d), "The empty digraph is simple.");
+
+ check(acyclic(g), "The empty graph is acyclic.");
+ check(tree(g), "The empty graph is tree.");
+ check(bipartite(g), "The empty graph is bipartite.");
+ check(loopFree(g), "The empty graph is loopfree.");
+ check(parallelFree(g), "The empty graph is parallelfree.");
+ check(simpleGraph(g), "The empty graph is simple.");
+ }
+
+ {
+ Digraph d;
+ Digraph::NodeMap order(d);
+ Graph g(d);
+ Digraph::Node n = d.addNode();
+
+ check(stronglyConnected(d), "This digraph is strongly connected");
+ check(countStronglyConnectedComponents(d) == 1,
+ "This digraph has 1 strongly connected component");
+ check(connected(g), "This graph is connected");
+ check(countConnectedComponents(g) == 1,
+ "This graph has 1 connected component");
+
+ check(biNodeConnected(g), "This graph is binodeconnected");
+ check(countBiNodeConnectedComponents(g) == 0,
+ "This graph has 0 binodeconnected component");
+ check(biEdgeConnected(g), "This graph is biedgeconnected");
+ check(countBiEdgeConnectedComponents(g) == 1,
+ "This graph has 1 biedgeconnected component");
+
+ check(dag(d), "This digraph is DAG.");
+ check(checkedTopologicalSort(d, order), "This digraph is DAG.");
+ check(loopFree(d), "This digraph is loopfree.");
+ check(parallelFree(d), "This digraph is parallelfree.");
+ check(simpleGraph(d), "This digraph is simple.");
+
+ check(acyclic(g), "This graph is acyclic.");
+ check(tree(g), "This graph is tree.");
+ check(bipartite(g), "This graph is bipartite.");
+ check(loopFree(g), "This graph is loopfree.");
+ check(parallelFree(g), "This graph is parallelfree.");
+ check(simpleGraph(g), "This graph is simple.");
+ }
+
+ {
+ Digraph d;
+ Digraph::NodeMap order(d);
+ Graph g(d);
+
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+ Digraph::Node n4 = d.addNode();
+ Digraph::Node n5 = d.addNode();
+ Digraph::Node n6 = d.addNode();
+
+ d.addArc(n1, n3);
+ d.addArc(n3, n2);
+ d.addArc(n2, n1);
+ d.addArc(n4, n2);
+ d.addArc(n4, n3);
+ d.addArc(n5, n6);
+ d.addArc(n6, n5);
+
+ check(!stronglyConnected(d), "This digraph is not strongly connected");
+ check(countStronglyConnectedComponents(d) == 3,
+ "This digraph has 3 strongly connected components");
+ check(!connected(g), "This graph is not connected");
+ check(countConnectedComponents(g) == 2,
+ "This graph has 2 connected components");
+
+ check(!dag(d), "This digraph is not DAG.");
+ check(!checkedTopologicalSort(d, order), "This digraph is not DAG.");
+ check(loopFree(d), "This digraph is loopfree.");
+ check(parallelFree(d), "This digraph is parallelfree.");
+ check(simpleGraph(d), "This digraph is simple.");
+
+ check(!acyclic(g), "This graph is not acyclic.");
+ check(!tree(g), "This graph is not tree.");
+ check(!bipartite(g), "This graph is not bipartite.");
+ check(loopFree(g), "This graph is loopfree.");
+ check(!parallelFree(g), "This graph is not parallelfree.");
+ check(!simpleGraph(g), "This graph is not simple.");
+
+ d.addArc(n3, n3);
+
+ check(!loopFree(d), "This digraph is not loopfree.");
+ check(!loopFree(g), "This graph is not loopfree.");
+ check(!simpleGraph(d), "This digraph is not simple.");
+
+ d.addArc(n3, n2);
+
+ check(!parallelFree(d), "This digraph is not parallelfree.");
+ }
+
+ {
+ Digraph d;
+ Digraph::ArcMap cutarcs(d, false);
+ Graph g(d);
+
+ Digraph::Node n1 = d.addNode();
+ Digraph::Node n2 = d.addNode();
+ Digraph::Node n3 = d.addNode();
+ Digraph::Node n4 = d.addNode();
+ Digraph::Node n5 = d.addNode();
+ Digraph::Node n6 = d.addNode();
+ Digraph::Node n7 = d.addNode();
+ Digraph::Node n8 = d.addNode();
+
+ d.addArc(n1, n2);
+ d.addArc(n5, n1);
+ d.addArc(n2, n8);
+ d.addArc(n8, n5);
+ d.addArc(n6, n4);
+ d.addArc(n4, n6);
+ d.addArc(n2, n5);
+ d.addArc(n1, n8);
+ d.addArc(n6, n7);
+ d.addArc(n7, n6);
+
+ check(!stronglyConnected(d), "This digraph is not strongly connected");
+ check(countStronglyConnectedComponents(d) == 3,
+ "This digraph has 3 strongly connected components");
+ Digraph::NodeMap scomp1(d);
+ check(stronglyConnectedComponents(d, scomp1) == 3,
+ "This digraph has 3 strongly connected components");
+ check(scomp1[n1] != scomp1[n3] && scomp1[n1] != scomp1[n4] &&
+ scomp1[n3] != scomp1[n4], "Wrong stronglyConnectedComponents()");
+ check(scomp1[n1] == scomp1[n2] && scomp1[n1] == scomp1[n5] &&
+ scomp1[n1] == scomp1[n8], "Wrong stronglyConnectedComponents()");
+ check(scomp1[n4] == scomp1[n6] && scomp1[n4] == scomp1[n7],
+ "Wrong stronglyConnectedComponents()");
+ Digraph::ArcMap scut1(d, false);
+ check(stronglyConnectedCutArcs(d, scut1) == 0,
+ "This digraph has 0 strongly connected cut arc.");
+ for (Digraph::ArcIt a(d); a != INVALID; ++a) {
+ check(!scut1[a], "Wrong stronglyConnectedCutArcs()");
+ }
+
+ check(!connected(g), "This graph is not connected");
+ check(countConnectedComponents(g) == 3,
+ "This graph has 3 connected components");
+ Graph::NodeMap comp(g);
+ check(connectedComponents(g, comp) == 3,
+ "This graph has 3 connected components");
+ check(comp[n1] != comp[n3] && comp[n1] != comp[n4] &&
+ comp[n3] != comp[n4], "Wrong connectedComponents()");
+ check(comp[n1] == comp[n2] && comp[n1] == comp[n5] &&
+ comp[n1] == comp[n8], "Wrong connectedComponents()");
+ check(comp[n4] == comp[n6] && comp[n4] == comp[n7],
+ "Wrong connectedComponents()");
+
+ cutarcs[d.addArc(n3, n1)] = true;
+ cutarcs[d.addArc(n3, n5)] = true;
+ cutarcs[d.addArc(n3, n8)] = true;
+ cutarcs[d.addArc(n8, n6)] = true;
+ cutarcs[d.addArc(n8, n7)] = true;
+
+ check(!stronglyConnected(d), "This digraph is not strongly connected");
+ check(countStronglyConnectedComponents(d) == 3,
+ "This digraph has 3 strongly connected components");
+ Digraph::NodeMap scomp2(d);
+ check(stronglyConnectedComponents(d, scomp2) == 3,
+ "This digraph has 3 strongly connected components");
+ check(scomp2[n3] == 0, "Wrong stronglyConnectedComponents()");
+ check(scomp2[n1] == 1 && scomp2[n2] == 1 && scomp2[n5] == 1 &&
+ scomp2[n8] == 1, "Wrong stronglyConnectedComponents()");
+ check(scomp2[n4] == 2 && scomp2[n6] == 2 && scomp2[n7] == 2,
+ "Wrong stronglyConnectedComponents()");
+ Digraph::ArcMap scut2(d, false);
+ check(stronglyConnectedCutArcs(d, scut2) == 5,
+ "This digraph has 5 strongly connected cut arcs.");
+ for (Digraph::ArcIt a(d); a != INVALID; ++a) {
+ check(scut2[a] == cutarcs[a], "Wrong stronglyConnectedCutArcs()");
+ }
+ }
+
+ {
+ // DAG example for topological sort from the book New Algorithms
+ // (T. H. Cormen, C. E. Leiserson, R. L. Rivest, C. Stein)
+ Digraph d;
+ Digraph::NodeMap order(d);
+
+ Digraph::Node belt = d.addNode();
+ Digraph::Node trousers = d.addNode();
+ Digraph::Node necktie = d.addNode();
+ Digraph::Node coat = d.addNode();
+ Digraph::Node socks = d.addNode();
+ Digraph::Node shirt = d.addNode();
+ Digraph::Node shoe = d.addNode();
+ Digraph::Node watch = d.addNode();
+ Digraph::Node pants = d.addNode();
+
+ d.addArc(socks, shoe);
+ d.addArc(pants, shoe);
+ d.addArc(pants, trousers);
+ d.addArc(trousers, shoe);
+ d.addArc(trousers, belt);
+ d.addArc(belt, coat);
+ d.addArc(shirt, belt);
+ d.addArc(shirt, necktie);
+ d.addArc(necktie, coat);
+
+ check(dag(d), "This digraph is DAG.");
+ topologicalSort(d, order);
+ for (Digraph::ArcIt a(d); a != INVALID; ++a) {
+ check(order[d.source(a)] < order[d.target(a)],
+ "Wrong topologicalSort()");
+ }
+ }
+
+ {
+ ListGraph g;
+ ListGraph::NodeMap map(g);
+
+ ListGraph::Node n1 = g.addNode();
+ ListGraph::Node n2 = g.addNode();
+ ListGraph::Node n3 = g.addNode();
+ ListGraph::Node n4 = g.addNode();
+ ListGraph::Node n5 = g.addNode();
+ ListGraph::Node n6 = g.addNode();
+ ListGraph::Node n7 = g.addNode();
+
+ g.addEdge(n1, n3);
+ g.addEdge(n1, n4);
+ g.addEdge(n2, n5);
+ g.addEdge(n3, n6);
+ g.addEdge(n4, n6);
+ g.addEdge(n4, n7);
+ g.addEdge(n5, n7);
+
+ check(bipartite(g), "This graph is bipartite");
+ check(bipartitePartitions(g, map), "This graph is bipartite");
+
+ check(map[n1] == map[n2] && map[n1] == map[n6] && map[n1] == map[n7],
+ "Wrong bipartitePartitions()");
+ check(map[n3] == map[n4] && map[n3] == map[n5],
+ "Wrong bipartitePartitions()");
+ }
+
+ return 0;
+}