lemon/topology.h
changeset 1913 49fe71fce7fb
parent 1875 98698b69a902
child 1956 a055123339d5
equal deleted inserted replaced
12:a9c0b95504f6 13:29e4b2ec1169
    22 #include <lemon/graph_utils.h>
    22 #include <lemon/graph_utils.h>
    23 #include <lemon/graph_adaptor.h>
    23 #include <lemon/graph_adaptor.h>
    24 #include <lemon/maps.h>
    24 #include <lemon/maps.h>
    25 
    25 
    26 #include <lemon/concept/graph.h>
    26 #include <lemon/concept/graph.h>
    27 #include <lemon/concept/undir_graph.h>
    27 #include <lemon/concept/ugraph.h>
    28 #include <lemon/concept_check.h>
    28 #include <lemon/concept_check.h>
    29 
    29 
    30 #include <lemon/bin_heap.h>
    30 #include <lemon/bin_heap.h>
    31 #include <lemon/linear_heap.h>
    31 #include <lemon/linear_heap.h>
    32 
    32 
    47   ///
    47   ///
    48   /// Check that the given undirected graph connected.
    48   /// Check that the given undirected graph connected.
    49   /// \param graph The undirected graph.
    49   /// \param graph The undirected graph.
    50   /// \return %True when there is path between any two nodes in the graph.
    50   /// \return %True when there is path between any two nodes in the graph.
    51   /// \note By definition, the empty graph is connected.
    51   /// \note By definition, the empty graph is connected.
    52   template <typename UndirGraph>
    52   template <typename UGraph>
    53   bool connected(const UndirGraph& graph) {
    53   bool connected(const UGraph& graph) {
    54     checkConcept<concept::UndirGraph, UndirGraph>();
    54     checkConcept<concept::UGraph, UGraph>();
    55     typedef typename UndirGraph::NodeIt NodeIt;
    55     typedef typename UGraph::NodeIt NodeIt;
    56     if (NodeIt(graph) == INVALID) return true;
    56     if (NodeIt(graph) == INVALID) return true;
    57     Dfs<UndirGraph> dfs(graph);
    57     Dfs<UGraph> dfs(graph);
    58     dfs.run(NodeIt(graph));
    58     dfs.run(NodeIt(graph));
    59     for (NodeIt it(graph); it != INVALID; ++it) {
    59     for (NodeIt it(graph); it != INVALID; ++it) {
    60       if (!dfs.reached(it)) {
    60       if (!dfs.reached(it)) {
    61 	return false;
    61 	return false;
    62       }
    62       }
    72   ///
    72   ///
    73   /// \param graph The graph. It should be undirected.
    73   /// \param graph The graph. It should be undirected.
    74   /// \return The number of components
    74   /// \return The number of components
    75   /// \note By definition, the empty graph consists
    75   /// \note By definition, the empty graph consists
    76   /// of zero connected components.
    76   /// of zero connected components.
    77   template <typename UndirGraph>
    77   template <typename UGraph>
    78   int countConnectedComponents(const UndirGraph &graph) {
    78   int countConnectedComponents(const UGraph &graph) {
    79     checkConcept<concept::UndirGraph, UndirGraph>();
    79     checkConcept<concept::UGraph, UGraph>();
    80     typedef typename UndirGraph::Node Node;
    80     typedef typename UGraph::Node Node;
    81     typedef typename UndirGraph::Edge Edge;
    81     typedef typename UGraph::Edge Edge;
    82 
    82 
    83     typedef NullMap<Node, Edge> PredMap;
    83     typedef NullMap<Node, Edge> PredMap;
    84     typedef NullMap<Node, int> DistMap;
    84     typedef NullMap<Node, int> DistMap;
    85 
    85 
    86     int compNum = 0;
    86     int compNum = 0;
    87     typename Bfs<UndirGraph>::
    87     typename Bfs<UGraph>::
    88       template DefPredMap<PredMap>::
    88       template DefPredMap<PredMap>::
    89       template DefDistMap<DistMap>::
    89       template DefDistMap<DistMap>::
    90       Create bfs(graph);
    90       Create bfs(graph);
    91 
    91 
    92     PredMap predMap;
    92     PredMap predMap;
    94 
    94 
    95     DistMap distMap;
    95     DistMap distMap;
    96     bfs.distMap(distMap);
    96     bfs.distMap(distMap);
    97 
    97 
    98     bfs.init();
    98     bfs.init();
    99     for(typename UndirGraph::NodeIt n(graph); n != INVALID; ++n) {
    99     for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) {
   100       if (!bfs.reached(n)) {
   100       if (!bfs.reached(n)) {
   101 	bfs.addSource(n);
   101 	bfs.addSource(n);
   102 	bfs.start();
   102 	bfs.start();
   103 	++compNum;
   103 	++compNum;
   104       }
   104       }
   120   /// the number of the connected components minus one. Each values of the map
   120   /// the number of the connected components minus one. Each values of the map
   121   /// will be set exactly once, the values of a certain component will be
   121   /// will be set exactly once, the values of a certain component will be
   122   /// set continuously.
   122   /// set continuously.
   123   /// \return The number of components
   123   /// \return The number of components
   124   ///
   124   ///
   125   template <class UndirGraph, class NodeMap>
   125   template <class UGraph, class NodeMap>
   126   int connectedComponents(const UndirGraph &graph, NodeMap &compMap) {
   126   int connectedComponents(const UGraph &graph, NodeMap &compMap) {
   127     checkConcept<concept::UndirGraph, UndirGraph>();
   127     checkConcept<concept::UGraph, UGraph>();
   128     typedef typename UndirGraph::Node Node;
   128     typedef typename UGraph::Node Node;
   129     typedef typename UndirGraph::Edge Edge;
   129     typedef typename UGraph::Edge Edge;
   130     checkConcept<concept::WriteMap<Node, int>, NodeMap>();
   130     checkConcept<concept::WriteMap<Node, int>, NodeMap>();
   131 
   131 
   132     typedef NullMap<Node, Edge> PredMap;
   132     typedef NullMap<Node, Edge> PredMap;
   133     typedef NullMap<Node, int> DistMap;
   133     typedef NullMap<Node, int> DistMap;
   134 
   134 
   135     int compNum = 0;
   135     int compNum = 0;
   136     typename Bfs<UndirGraph>::
   136     typename Bfs<UGraph>::
   137       template DefPredMap<PredMap>::
   137       template DefPredMap<PredMap>::
   138       template DefDistMap<DistMap>::
   138       template DefDistMap<DistMap>::
   139       Create bfs(graph);
   139       Create bfs(graph);
   140 
   140 
   141     PredMap predMap;
   141     PredMap predMap;
   143 
   143 
   144     DistMap distMap;
   144     DistMap distMap;
   145     bfs.distMap(distMap);
   145     bfs.distMap(distMap);
   146     
   146     
   147     bfs.init();
   147     bfs.init();
   148     for(typename UndirGraph::NodeIt n(graph); n != INVALID; ++n) {
   148     for(typename UGraph::NodeIt n(graph); n != INVALID; ++n) {
   149       if(!bfs.reached(n)) {
   149       if(!bfs.reached(n)) {
   150 	bfs.addSource(n);
   150 	bfs.addSource(n);
   151 	while (!bfs.emptyQueue()) {
   151 	while (!bfs.emptyQueue()) {
   152 	  compMap.set(bfs.nextNode(), compNum);
   152 	  compMap.set(bfs.nextNode(), compNum);
   153 	  bfs.processNextNode();
   153 	  bfs.processNextNode();
   482     template <typename Graph>
   482     template <typename Graph>
   483     class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   483     class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   484     public:
   484     public:
   485       typedef typename Graph::Node Node;
   485       typedef typename Graph::Node Node;
   486       typedef typename Graph::Edge Edge;
   486       typedef typename Graph::Edge Edge;
   487       typedef typename Graph::UndirEdge UndirEdge;
   487       typedef typename Graph::UEdge UEdge;
   488 
   488 
   489       CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) 
   489       CountBiNodeConnectedComponentsVisitor(const Graph& graph, int &compNum) 
   490 	: _graph(graph), _compNum(compNum), 
   490 	: _graph(graph), _compNum(compNum), 
   491 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   491 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   492 
   492 
   540     template <typename Graph, typename EdgeMap>
   540     template <typename Graph, typename EdgeMap>
   541     class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   541     class BiNodeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   542     public:
   542     public:
   543       typedef typename Graph::Node Node;
   543       typedef typename Graph::Node Node;
   544       typedef typename Graph::Edge Edge;
   544       typedef typename Graph::Edge Edge;
   545       typedef typename Graph::UndirEdge UndirEdge;
   545       typedef typename Graph::UEdge UEdge;
   546 
   546 
   547       BiNodeConnectedComponentsVisitor(const Graph& graph, 
   547       BiNodeConnectedComponentsVisitor(const Graph& graph, 
   548 				       EdgeMap& compMap, int &compNum) 
   548 				       EdgeMap& compMap, int &compNum) 
   549 	: _graph(graph), _compMap(compMap), _compNum(compNum), 
   549 	: _graph(graph), _compMap(compMap), _compNum(compNum), 
   550 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   550 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   610       int& _compNum; 
   610       int& _compNum; 
   611 
   611 
   612       typename Graph::template NodeMap<int> _numMap;
   612       typename Graph::template NodeMap<int> _numMap;
   613       typename Graph::template NodeMap<int> _retMap;
   613       typename Graph::template NodeMap<int> _retMap;
   614       typename Graph::template NodeMap<Edge> _predMap;
   614       typename Graph::template NodeMap<Edge> _predMap;
   615       std::stack<UndirEdge> _edgeStack;
   615       std::stack<UEdge> _edgeStack;
   616       int _num;
   616       int _num;
   617     };
   617     };
   618 
   618 
   619 
   619 
   620     template <typename Graph, typename NodeMap>
   620     template <typename Graph, typename NodeMap>
   621     class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> {
   621     class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Graph> {
   622     public:
   622     public:
   623       typedef typename Graph::Node Node;
   623       typedef typename Graph::Node Node;
   624       typedef typename Graph::Edge Edge;
   624       typedef typename Graph::Edge Edge;
   625       typedef typename Graph::UndirEdge UndirEdge;
   625       typedef typename Graph::UEdge UEdge;
   626 
   626 
   627       BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap,
   627       BiNodeConnectedCutNodesVisitor(const Graph& graph, NodeMap& cutMap,
   628 				     int& cutNum) 
   628 				     int& cutNum) 
   629 	: _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
   629 	: _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
   630 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   630 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   686       int& _cutNum; 
   686       int& _cutNum; 
   687 
   687 
   688       typename Graph::template NodeMap<int> _numMap;
   688       typename Graph::template NodeMap<int> _numMap;
   689       typename Graph::template NodeMap<int> _retMap;
   689       typename Graph::template NodeMap<int> _retMap;
   690       typename Graph::template NodeMap<Node> _predMap;
   690       typename Graph::template NodeMap<Node> _predMap;
   691       std::stack<UndirEdge> _edgeStack;
   691       std::stack<UEdge> _edgeStack;
   692       int _num;
   692       int _num;
   693       bool rootCut;
   693       bool rootCut;
   694     };
   694     };
   695 
   695 
   696   }
   696   }
   697 
   697 
   698   template <typename UndirGraph>
   698   template <typename UGraph>
   699   int countBiNodeConnectedComponents(const UndirGraph& graph);
   699   int countBiNodeConnectedComponents(const UGraph& graph);
   700 
   700 
   701   /// \ingroup topology
   701   /// \ingroup topology
   702   ///
   702   ///
   703   /// \brief Checks the graph is bi-node-connected.
   703   /// \brief Checks the graph is bi-node-connected.
   704   ///
   704   ///
   707   /// on same circle.
   707   /// on same circle.
   708   ///
   708   ///
   709   /// \param graph The graph.
   709   /// \param graph The graph.
   710   /// \return %True when the graph bi-node-connected.
   710   /// \return %True when the graph bi-node-connected.
   711   /// \todo Make it faster.
   711   /// \todo Make it faster.
   712   template <typename UndirGraph>
   712   template <typename UGraph>
   713   bool biNodeConnected(const UndirGraph& graph) {
   713   bool biNodeConnected(const UGraph& graph) {
   714     return countBiNodeConnectedComponents(graph) == 1;
   714     return countBiNodeConnectedComponents(graph) == 1;
   715   }
   715   }
   716 
   716 
   717   /// \ingroup topology
   717   /// \ingroup topology
   718   ///
   718   ///
   723   /// relation on the undirected edges. Two undirected edge is in relationship
   723   /// relation on the undirected edges. Two undirected edge is in relationship
   724   /// when they are on same circle.
   724   /// when they are on same circle.
   725   ///
   725   ///
   726   /// \param graph The graph.
   726   /// \param graph The graph.
   727   /// \return The number of components.
   727   /// \return The number of components.
   728   template <typename UndirGraph>
   728   template <typename UGraph>
   729   int countBiNodeConnectedComponents(const UndirGraph& graph) {
   729   int countBiNodeConnectedComponents(const UGraph& graph) {
   730     checkConcept<concept::UndirGraph, UndirGraph>();
   730     checkConcept<concept::UGraph, UGraph>();
   731     typedef typename UndirGraph::NodeIt NodeIt;
   731     typedef typename UGraph::NodeIt NodeIt;
   732 
   732 
   733     using namespace _topology_bits;
   733     using namespace _topology_bits;
   734 
   734 
   735     typedef CountBiNodeConnectedComponentsVisitor<UndirGraph> Visitor;
   735     typedef CountBiNodeConnectedComponentsVisitor<UGraph> Visitor;
   736 
   736 
   737     int compNum = 0;
   737     int compNum = 0;
   738     Visitor visitor(graph, compNum);
   738     Visitor visitor(graph, compNum);
   739 
   739 
   740     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
   740     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
   741     dfs.init();
   741     dfs.init();
   742     
   742     
   743     for (NodeIt it(graph); it != INVALID; ++it) {
   743     for (NodeIt it(graph); it != INVALID; ++it) {
   744       if (!dfs.reached(it)) {
   744       if (!dfs.reached(it)) {
   745 	dfs.addSource(it);
   745 	dfs.addSource(it);
   760   ///
   760   ///
   761   /// \image html node_biconnected_components.png
   761   /// \image html node_biconnected_components.png
   762   /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth
   762   /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth
   763   ///
   763   ///
   764   /// \param graph The graph.
   764   /// \param graph The graph.
   765   /// \retval compMap A writable undir edge map. The values will be set from 0
   765   /// \retval compMap A writable uedge map. The values will be set from 0
   766   /// to the number of the biconnected components minus one. Each values 
   766   /// to the number of the biconnected components minus one. Each values 
   767   /// of the map will be set exactly once, the values of a certain component 
   767   /// of the map will be set exactly once, the values of a certain component 
   768   /// will be set continuously.
   768   /// will be set continuously.
   769   /// \return The number of components.
   769   /// \return The number of components.
   770   ///
   770   ///
   771   template <typename UndirGraph, typename UndirEdgeMap>
   771   template <typename UGraph, typename UEdgeMap>
   772   int biNodeConnectedComponents(const UndirGraph& graph, 
   772   int biNodeConnectedComponents(const UGraph& graph, 
   773 				UndirEdgeMap& compMap) {
   773 				UEdgeMap& compMap) {
   774     checkConcept<concept::UndirGraph, UndirGraph>();
   774     checkConcept<concept::UGraph, UGraph>();
   775     typedef typename UndirGraph::NodeIt NodeIt;
   775     typedef typename UGraph::NodeIt NodeIt;
   776     typedef typename UndirGraph::UndirEdge UndirEdge;
   776     typedef typename UGraph::UEdge UEdge;
   777     checkConcept<concept::WriteMap<UndirEdge, int>, UndirEdgeMap>();
   777     checkConcept<concept::WriteMap<UEdge, int>, UEdgeMap>();
   778 
   778 
   779     using namespace _topology_bits;
   779     using namespace _topology_bits;
   780 
   780 
   781     typedef BiNodeConnectedComponentsVisitor<UndirGraph, UndirEdgeMap> Visitor;
   781     typedef BiNodeConnectedComponentsVisitor<UGraph, UEdgeMap> Visitor;
   782     
   782     
   783     int compNum = 0;
   783     int compNum = 0;
   784     Visitor visitor(graph, compMap, compNum);
   784     Visitor visitor(graph, compMap, compNum);
   785 
   785 
   786     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
   786     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
   787     dfs.init();
   787     dfs.init();
   788     
   788     
   789     for (NodeIt it(graph); it != INVALID; ++it) {
   789     for (NodeIt it(graph); it != INVALID; ++it) {
   790       if (!dfs.reached(it)) {
   790       if (!dfs.reached(it)) {
   791 	dfs.addSource(it);
   791 	dfs.addSource(it);
   807   ///
   807   ///
   808   /// \param graph The graph.
   808   /// \param graph The graph.
   809   /// \retval cutMap A writable edge map. The values will be set true when
   809   /// \retval cutMap A writable edge map. The values will be set true when
   810   /// the node separate two or more components.
   810   /// the node separate two or more components.
   811   /// \return The number of the cut nodes.
   811   /// \return The number of the cut nodes.
   812   template <typename UndirGraph, typename NodeMap>
   812   template <typename UGraph, typename NodeMap>
   813   int biNodeConnectedCutNodes(const UndirGraph& graph, NodeMap& cutMap) {
   813   int biNodeConnectedCutNodes(const UGraph& graph, NodeMap& cutMap) {
   814     checkConcept<concept::UndirGraph, UndirGraph>();
   814     checkConcept<concept::UGraph, UGraph>();
   815     typedef typename UndirGraph::Node Node;
   815     typedef typename UGraph::Node Node;
   816     typedef typename UndirGraph::NodeIt NodeIt;
   816     typedef typename UGraph::NodeIt NodeIt;
   817     checkConcept<concept::WriteMap<Node, bool>, NodeMap>();
   817     checkConcept<concept::WriteMap<Node, bool>, NodeMap>();
   818 
   818 
   819     using namespace _topology_bits;
   819     using namespace _topology_bits;
   820 
   820 
   821     typedef BiNodeConnectedCutNodesVisitor<UndirGraph, NodeMap> Visitor;
   821     typedef BiNodeConnectedCutNodesVisitor<UGraph, NodeMap> Visitor;
   822     
   822     
   823     int cutNum = 0;
   823     int cutNum = 0;
   824     Visitor visitor(graph, cutMap, cutNum);
   824     Visitor visitor(graph, cutMap, cutNum);
   825 
   825 
   826     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
   826     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
   827     dfs.init();
   827     dfs.init();
   828     
   828     
   829     for (NodeIt it(graph); it != INVALID; ++it) {
   829     for (NodeIt it(graph); it != INVALID; ++it) {
   830       if (!dfs.reached(it)) {
   830       if (!dfs.reached(it)) {
   831 	dfs.addSource(it);
   831 	dfs.addSource(it);
   840     template <typename Graph>
   840     template <typename Graph>
   841     class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   841     class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   842     public:
   842     public:
   843       typedef typename Graph::Node Node;
   843       typedef typename Graph::Node Node;
   844       typedef typename Graph::Edge Edge;
   844       typedef typename Graph::Edge Edge;
   845       typedef typename Graph::UndirEdge UndirEdge;
   845       typedef typename Graph::UEdge UEdge;
   846 
   846 
   847       CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) 
   847       CountBiEdgeConnectedComponentsVisitor(const Graph& graph, int &compNum) 
   848 	: _graph(graph), _compNum(compNum), 
   848 	: _graph(graph), _compNum(compNum), 
   849 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   849 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   850 
   850 
   896     template <typename Graph, typename NodeMap>
   896     template <typename Graph, typename NodeMap>
   897     class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   897     class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Graph> {
   898     public:
   898     public:
   899       typedef typename Graph::Node Node;
   899       typedef typename Graph::Node Node;
   900       typedef typename Graph::Edge Edge;
   900       typedef typename Graph::Edge Edge;
   901       typedef typename Graph::UndirEdge UndirEdge;
   901       typedef typename Graph::UEdge UEdge;
   902 
   902 
   903       BiEdgeConnectedComponentsVisitor(const Graph& graph, 
   903       BiEdgeConnectedComponentsVisitor(const Graph& graph, 
   904 				       NodeMap& compMap, int &compNum) 
   904 				       NodeMap& compMap, int &compNum) 
   905 	: _graph(graph), _compMap(compMap), _compNum(compNum), 
   905 	: _graph(graph), _compMap(compMap), _compNum(compNum), 
   906 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   906 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   963     template <typename Graph, typename EdgeMap>
   963     template <typename Graph, typename EdgeMap>
   964     class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> {
   964     class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Graph> {
   965     public:
   965     public:
   966       typedef typename Graph::Node Node;
   966       typedef typename Graph::Node Node;
   967       typedef typename Graph::Edge Edge;
   967       typedef typename Graph::Edge Edge;
   968       typedef typename Graph::UndirEdge UndirEdge;
   968       typedef typename Graph::UEdge UEdge;
   969 
   969 
   970       BiEdgeConnectedCutEdgesVisitor(const Graph& graph, 
   970       BiEdgeConnectedCutEdgesVisitor(const Graph& graph, 
   971 				     EdgeMap& cutMap, int &cutNum) 
   971 				     EdgeMap& cutMap, int &cutNum) 
   972 	: _graph(graph), _cutMap(cutMap), _cutNum(cutNum), 
   972 	: _graph(graph), _cutMap(cutMap), _cutNum(cutNum), 
   973 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
   973 	  _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
  1020       typename Graph::template NodeMap<Edge> _predMap;
  1020       typename Graph::template NodeMap<Edge> _predMap;
  1021       int _num;
  1021       int _num;
  1022     };
  1022     };
  1023   }
  1023   }
  1024 
  1024 
  1025   template <typename UndirGraph>
  1025   template <typename UGraph>
  1026   int countbiEdgeConnectedComponents(const UndirGraph& graph);
  1026   int countbiEdgeConnectedComponents(const UGraph& graph);
  1027 
  1027 
  1028   /// \ingroup topology
  1028   /// \ingroup topology
  1029   ///
  1029   ///
  1030   /// \brief Checks that the graph is bi-edge-connected.
  1030   /// \brief Checks that the graph is bi-edge-connected.
  1031   ///
  1031   ///
  1034   /// edge-disjoint paths.
  1034   /// edge-disjoint paths.
  1035   ///
  1035   ///
  1036   /// \param graph The undirected graph.
  1036   /// \param graph The undirected graph.
  1037   /// \return The number of components.
  1037   /// \return The number of components.
  1038   /// \todo Make it faster.
  1038   /// \todo Make it faster.
  1039   template <typename UndirGraph>
  1039   template <typename UGraph>
  1040   bool biEdgeConnected(const UndirGraph& graph) { 
  1040   bool biEdgeConnected(const UGraph& graph) { 
  1041     return countBiEdgeConnectedComponents(graph) == 1;
  1041     return countBiEdgeConnectedComponents(graph) == 1;
  1042   }
  1042   }
  1043 
  1043 
  1044   /// \ingroup topology
  1044   /// \ingroup topology
  1045   ///
  1045   ///
  1050   /// relation on the nodes. Two nodes are in relationship when they are  
  1050   /// relation on the nodes. Two nodes are in relationship when they are  
  1051   /// connected with at least two edge-disjoint paths.
  1051   /// connected with at least two edge-disjoint paths.
  1052   ///
  1052   ///
  1053   /// \param graph The undirected graph.
  1053   /// \param graph The undirected graph.
  1054   /// \return The number of components.
  1054   /// \return The number of components.
  1055   template <typename UndirGraph>
  1055   template <typename UGraph>
  1056   int countBiEdgeConnectedComponents(const UndirGraph& graph) { 
  1056   int countBiEdgeConnectedComponents(const UGraph& graph) { 
  1057     checkConcept<concept::UndirGraph, UndirGraph>();
  1057     checkConcept<concept::UGraph, UGraph>();
  1058     typedef typename UndirGraph::NodeIt NodeIt;
  1058     typedef typename UGraph::NodeIt NodeIt;
  1059 
  1059 
  1060     using namespace _topology_bits;
  1060     using namespace _topology_bits;
  1061 
  1061 
  1062     typedef CountBiEdgeConnectedComponentsVisitor<UndirGraph> Visitor;
  1062     typedef CountBiEdgeConnectedComponentsVisitor<UGraph> Visitor;
  1063     
  1063     
  1064     int compNum = 0;
  1064     int compNum = 0;
  1065     Visitor visitor(graph, compNum);
  1065     Visitor visitor(graph, compNum);
  1066 
  1066 
  1067     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
  1067     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
  1068     dfs.init();
  1068     dfs.init();
  1069     
  1069     
  1070     for (NodeIt it(graph); it != INVALID; ++it) {
  1070     for (NodeIt it(graph); it != INVALID; ++it) {
  1071       if (!dfs.reached(it)) {
  1071       if (!dfs.reached(it)) {
  1072 	dfs.addSource(it);
  1072 	dfs.addSource(it);
  1093   /// the number of the biconnected components minus one. Each values 
  1093   /// the number of the biconnected components minus one. Each values 
  1094   /// of the map will be set exactly once, the values of a certain component 
  1094   /// of the map will be set exactly once, the values of a certain component 
  1095   /// will be set continuously.
  1095   /// will be set continuously.
  1096   /// \return The number of components.
  1096   /// \return The number of components.
  1097   ///
  1097   ///
  1098   template <typename UndirGraph, typename NodeMap>
  1098   template <typename UGraph, typename NodeMap>
  1099   int biEdgeConnectedComponents(const UndirGraph& graph, NodeMap& compMap) { 
  1099   int biEdgeConnectedComponents(const UGraph& graph, NodeMap& compMap) { 
  1100     checkConcept<concept::UndirGraph, UndirGraph>();
  1100     checkConcept<concept::UGraph, UGraph>();
  1101     typedef typename UndirGraph::NodeIt NodeIt;
  1101     typedef typename UGraph::NodeIt NodeIt;
  1102     typedef typename UndirGraph::Node Node;
  1102     typedef typename UGraph::Node Node;
  1103     checkConcept<concept::WriteMap<Node, int>, NodeMap>();
  1103     checkConcept<concept::WriteMap<Node, int>, NodeMap>();
  1104 
  1104 
  1105     using namespace _topology_bits;
  1105     using namespace _topology_bits;
  1106 
  1106 
  1107     typedef BiEdgeConnectedComponentsVisitor<UndirGraph, NodeMap> Visitor;
  1107     typedef BiEdgeConnectedComponentsVisitor<UGraph, NodeMap> Visitor;
  1108     
  1108     
  1109     int compNum = 0;
  1109     int compNum = 0;
  1110     Visitor visitor(graph, compMap, compNum);
  1110     Visitor visitor(graph, compMap, compNum);
  1111 
  1111 
  1112     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
  1112     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
  1113     dfs.init();
  1113     dfs.init();
  1114     
  1114     
  1115     for (NodeIt it(graph); it != INVALID; ++it) {
  1115     for (NodeIt it(graph); it != INVALID; ++it) {
  1116       if (!dfs.reached(it)) {
  1116       if (!dfs.reached(it)) {
  1117 	dfs.addSource(it);
  1117 	dfs.addSource(it);
  1134   ///
  1134   ///
  1135   /// \param graph The graph.
  1135   /// \param graph The graph.
  1136   /// \retval cutMap A writable node map. The values will be set true when the
  1136   /// \retval cutMap A writable node map. The values will be set true when the
  1137   /// edge is a cut edge.
  1137   /// edge is a cut edge.
  1138   /// \return The number of cut edges.
  1138   /// \return The number of cut edges.
  1139   template <typename UndirGraph, typename UndirEdgeMap>
  1139   template <typename UGraph, typename UEdgeMap>
  1140   int biEdgeConnectedCutEdges(const UndirGraph& graph, UndirEdgeMap& cutMap) { 
  1140   int biEdgeConnectedCutEdges(const UGraph& graph, UEdgeMap& cutMap) { 
  1141     checkConcept<concept::UndirGraph, UndirGraph>();
  1141     checkConcept<concept::UGraph, UGraph>();
  1142     typedef typename UndirGraph::NodeIt NodeIt;
  1142     typedef typename UGraph::NodeIt NodeIt;
  1143     typedef typename UndirGraph::UndirEdge UndirEdge;
  1143     typedef typename UGraph::UEdge UEdge;
  1144     checkConcept<concept::WriteMap<UndirEdge, bool>, UndirEdgeMap>();
  1144     checkConcept<concept::WriteMap<UEdge, bool>, UEdgeMap>();
  1145 
  1145 
  1146     using namespace _topology_bits;
  1146     using namespace _topology_bits;
  1147 
  1147 
  1148     typedef BiEdgeConnectedCutEdgesVisitor<UndirGraph, UndirEdgeMap> Visitor;
  1148     typedef BiEdgeConnectedCutEdgesVisitor<UGraph, UEdgeMap> Visitor;
  1149     
  1149     
  1150     int cutNum = 0;
  1150     int cutNum = 0;
  1151     Visitor visitor(graph, cutMap, cutNum);
  1151     Visitor visitor(graph, cutMap, cutNum);
  1152 
  1152 
  1153     DfsVisit<UndirGraph, Visitor> dfs(graph, visitor);
  1153     DfsVisit<UGraph, Visitor> dfs(graph, visitor);
  1154     dfs.init();
  1154     dfs.init();
  1155     
  1155     
  1156     for (NodeIt it(graph); it != INVALID; ++it) {
  1156     for (NodeIt it(graph); it != INVALID; ++it) {
  1157       if (!dfs.reached(it)) {
  1157       if (!dfs.reached(it)) {
  1158 	dfs.addSource(it);
  1158 	dfs.addSource(it);
  1324   ///
  1324   ///
  1325   /// Check that the given undirected graph acyclic.
  1325   /// Check that the given undirected graph acyclic.
  1326   /// \param graph The undirected graph.
  1326   /// \param graph The undirected graph.
  1327   /// \return %True when there is no circle in the graph.
  1327   /// \return %True when there is no circle in the graph.
  1328   /// \see dag
  1328   /// \see dag
  1329   template <typename UndirGraph>
  1329   template <typename UGraph>
  1330   bool acyclic(const UndirGraph& graph) {
  1330   bool acyclic(const UGraph& graph) {
  1331     checkConcept<concept::UndirGraph, UndirGraph>();
  1331     checkConcept<concept::UGraph, UGraph>();
  1332     typedef typename UndirGraph::Node Node;
  1332     typedef typename UGraph::Node Node;
  1333     typedef typename UndirGraph::NodeIt NodeIt;
  1333     typedef typename UGraph::NodeIt NodeIt;
  1334     typedef typename UndirGraph::Edge Edge;
  1334     typedef typename UGraph::Edge Edge;
  1335     Dfs<UndirGraph> dfs(graph);
  1335     Dfs<UGraph> dfs(graph);
  1336     dfs.init();
  1336     dfs.init();
  1337     for (NodeIt it(graph); it != INVALID; ++it) {
  1337     for (NodeIt it(graph); it != INVALID; ++it) {
  1338       if (!dfs.reached(it)) {
  1338       if (!dfs.reached(it)) {
  1339 	dfs.addSource(it);
  1339 	dfs.addSource(it);
  1340 	while (!dfs.emptyQueue()) {
  1340 	while (!dfs.emptyQueue()) {
  1357   /// \brief Check that the given undirected graph is tree.
  1357   /// \brief Check that the given undirected graph is tree.
  1358   ///
  1358   ///
  1359   /// Check that the given undirected graph is tree.
  1359   /// Check that the given undirected graph is tree.
  1360   /// \param graph The undirected graph.
  1360   /// \param graph The undirected graph.
  1361   /// \return %True when the graph is acyclic and connected.
  1361   /// \return %True when the graph is acyclic and connected.
  1362   template <typename UndirGraph>
  1362   template <typename UGraph>
  1363   bool tree(const UndirGraph& graph) {
  1363   bool tree(const UGraph& graph) {
  1364     checkConcept<concept::UndirGraph, UndirGraph>();
  1364     checkConcept<concept::UGraph, UGraph>();
  1365     typedef typename UndirGraph::Node Node;
  1365     typedef typename UGraph::Node Node;
  1366     typedef typename UndirGraph::NodeIt NodeIt;
  1366     typedef typename UGraph::NodeIt NodeIt;
  1367     typedef typename UndirGraph::Edge Edge;
  1367     typedef typename UGraph::Edge Edge;
  1368     Dfs<UndirGraph> dfs(graph);
  1368     Dfs<UGraph> dfs(graph);
  1369     dfs.init();
  1369     dfs.init();
  1370     dfs.addSource(NodeIt(graph));
  1370     dfs.addSource(NodeIt(graph));
  1371     while (!dfs.emptyQueue()) {
  1371     while (!dfs.emptyQueue()) {
  1372       Edge edge = dfs.nextEdge();
  1372       Edge edge = dfs.nextEdge();
  1373       Node source = graph.source(edge);
  1373       Node source = graph.source(edge);
  1395   /// \param graph The undirected graph.
  1395   /// \param graph The undirected graph.
  1396   /// \return %True if \c graph is bipartite, %false otherwise.
  1396   /// \return %True if \c graph is bipartite, %false otherwise.
  1397   /// \sa bipartitePartitions
  1397   /// \sa bipartitePartitions
  1398   ///
  1398   ///
  1399   /// \author Balazs Attila Mihaly  
  1399   /// \author Balazs Attila Mihaly  
  1400   template<typename UndirGraph>
  1400   template<typename UGraph>
  1401   inline bool bipartite(const UndirGraph &graph){
  1401   inline bool bipartite(const UGraph &graph){
  1402     checkConcept<concept::UndirGraph, UndirGraph>();
  1402     checkConcept<concept::UGraph, UGraph>();
  1403     
  1403     
  1404     typedef typename UndirGraph::NodeIt NodeIt;
  1404     typedef typename UGraph::NodeIt NodeIt;
  1405     typedef typename UndirGraph::EdgeIt EdgeIt;
  1405     typedef typename UGraph::EdgeIt EdgeIt;
  1406     
  1406     
  1407     Bfs<UndirGraph> bfs(graph);
  1407     Bfs<UGraph> bfs(graph);
  1408     bfs.init();
  1408     bfs.init();
  1409     for(NodeIt i(graph);i!=INVALID;++i){
  1409     for(NodeIt i(graph);i!=INVALID;++i){
  1410       if(!bfs.reached(i)){
  1410       if(!bfs.reached(i)){
  1411 	bfs.run(i);
  1411 	bfs.run(i);
  1412       }
  1412       }
  1432   ///
  1432   ///
  1433   /// \author Balazs Attila Mihaly  
  1433   /// \author Balazs Attila Mihaly  
  1434   ///
  1434   ///
  1435   /// \image html bipartite_partitions.png
  1435   /// \image html bipartite_partitions.png
  1436   /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth
  1436   /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth
  1437   template<typename UndirGraph, typename NodeMap>
  1437   template<typename UGraph, typename NodeMap>
  1438   inline bool bipartitePartitions(const UndirGraph &graph, NodeMap &partMap){
  1438   inline bool bipartitePartitions(const UGraph &graph, NodeMap &partMap){
  1439     checkConcept<concept::UndirGraph, UndirGraph>();
  1439     checkConcept<concept::UGraph, UGraph>();
  1440     
  1440     
  1441     typedef typename UndirGraph::Node Node;
  1441     typedef typename UGraph::Node Node;
  1442     typedef typename UndirGraph::NodeIt NodeIt;
  1442     typedef typename UGraph::NodeIt NodeIt;
  1443     typedef typename UndirGraph::EdgeIt EdgeIt;
  1443     typedef typename UGraph::EdgeIt EdgeIt;
  1444   
  1444   
  1445     Bfs<UndirGraph> bfs(graph);
  1445     Bfs<UGraph> bfs(graph);
  1446     bfs.init();
  1446     bfs.init();
  1447     for(NodeIt i(graph);i!=INVALID;++i){
  1447     for(NodeIt i(graph);i!=INVALID;++i){
  1448       if(!bfs.reached(i)){
  1448       if(!bfs.reached(i)){
  1449 	bfs.addSource(i);
  1449 	bfs.addSource(i);
  1450 	for(Node j=bfs.processNextNode();!bfs.emptyQueue();
  1450 	for(Node j=bfs.processNextNode();!bfs.emptyQueue();