deba@433: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@433:  *
deba@433:  * This file is a part of LEMON, a generic C++ optimization library.
deba@433:  *
alpar@463:  * Copyright (C) 2003-2009
deba@433:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@433:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@433:  *
deba@433:  * Permission to use, modify and distribute this software is granted
deba@433:  * provided that this copyright notice appears in all copies. For
deba@433:  * precise terms see the accompanying LICENSE file.
deba@433:  *
deba@433:  * This software is provided "AS IS" with no warranty of any kind,
deba@433:  * express or implied, and with no claim as to its suitability for any
deba@433:  * purpose.
deba@433:  *
deba@433:  */
deba@433: 
deba@435: #ifndef LEMON_CONNECTIVITY_H
deba@435: #define LEMON_CONNECTIVITY_H
deba@433: 
deba@433: #include <lemon/dfs.h>
deba@433: #include <lemon/bfs.h>
deba@433: #include <lemon/core.h>
deba@433: #include <lemon/maps.h>
deba@433: #include <lemon/adaptors.h>
deba@433: 
deba@433: #include <lemon/concepts/digraph.h>
deba@433: #include <lemon/concepts/graph.h>
deba@433: #include <lemon/concept_check.h>
deba@433: 
deba@433: #include <stack>
deba@433: #include <functional>
deba@433: 
deba@433: /// \ingroup connectivity
deba@433: /// \file
deba@433: /// \brief Connectivity algorithms
deba@433: ///
deba@433: /// Connectivity algorithms
deba@433: 
deba@433: namespace lemon {
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check whether the given undirected graph is connected.
deba@433:   ///
deba@433:   /// Check whether the given undirected graph is connected.
deba@433:   /// \param graph The undirected graph.
kpeter@606:   /// \return \c true when there is path between any two nodes in the graph.
deba@433:   /// \note By definition, the empty graph is connected.
deba@433:   template <typename Graph>
deba@433:   bool connected(const Graph& graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     if (NodeIt(graph) == INVALID) return true;
deba@433:     Dfs<Graph> dfs(graph);
deba@433:     dfs.run(NodeIt(graph));
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         return false;
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Count the number of connected components of an undirected graph
deba@433:   ///
deba@433:   /// Count the number of connected components of an undirected graph
deba@433:   ///
deba@433:   /// \param graph The graph. It must be undirected.
deba@433:   /// \return The number of components
deba@433:   /// \note By definition, the empty graph consists
deba@433:   /// of zero connected components.
deba@433:   template <typename Graph>
deba@433:   int countConnectedComponents(const Graph &graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::Arc Arc;
deba@433: 
deba@433:     typedef NullMap<Node, Arc> PredMap;
deba@433:     typedef NullMap<Node, int> DistMap;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     typename Bfs<Graph>::
deba@433:       template SetPredMap<PredMap>::
deba@433:       template SetDistMap<DistMap>::
deba@433:       Create bfs(graph);
deba@433: 
deba@433:     PredMap predMap;
deba@433:     bfs.predMap(predMap);
deba@433: 
deba@433:     DistMap distMap;
deba@433:     bfs.distMap(distMap);
deba@433: 
deba@433:     bfs.init();
deba@433:     for(typename Graph::NodeIt n(graph); n != INVALID; ++n) {
deba@433:       if (!bfs.reached(n)) {
deba@433:         bfs.addSource(n);
deba@433:         bfs.start();
deba@433:         ++compNum;
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the connected components of an undirected graph
deba@433:   ///
deba@433:   /// Find the connected components of an undirected graph.
deba@433:   ///
deba@433:   /// \param graph The graph. It must be undirected.
deba@433:   /// \retval compMap A writable node map. The values will be set from 0 to
deba@433:   /// the number of the connected components minus one. Each values of the map
deba@433:   /// will be set exactly once, the values of a certain component will be
deba@433:   /// set continuously.
deba@433:   /// \return The number of components
deba@433:   ///
deba@433:   template <class Graph, class NodeMap>
deba@433:   int connectedComponents(const Graph &graph, NodeMap &compMap) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::Arc Arc;
deba@433:     checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
deba@433: 
deba@433:     typedef NullMap<Node, Arc> PredMap;
deba@433:     typedef NullMap<Node, int> DistMap;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     typename Bfs<Graph>::
deba@433:       template SetPredMap<PredMap>::
deba@433:       template SetDistMap<DistMap>::
deba@433:       Create bfs(graph);
deba@433: 
deba@433:     PredMap predMap;
deba@433:     bfs.predMap(predMap);
deba@433: 
deba@433:     DistMap distMap;
deba@433:     bfs.distMap(distMap);
deba@433: 
deba@433:     bfs.init();
deba@433:     for(typename Graph::NodeIt n(graph); n != INVALID; ++n) {
deba@433:       if(!bfs.reached(n)) {
deba@433:         bfs.addSource(n);
deba@433:         while (!bfs.emptyQueue()) {
deba@433:           compMap.set(bfs.nextNode(), compNum);
deba@433:           bfs.processNextNode();
deba@433:         }
deba@433:         ++compNum;
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@435:   namespace _connectivity_bits {
deba@433: 
deba@433:     template <typename Digraph, typename Iterator >
deba@433:     struct LeaveOrderVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       LeaveOrderVisitor(Iterator it) : _it(it) {}
deba@433: 
deba@433:       void leave(const Node& node) {
deba@433:         *(_it++) = node;
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       Iterator _it;
deba@433:     };
deba@433: 
deba@433:     template <typename Digraph, typename Map>
deba@433:     struct FillMapVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Map::Value Value;
deba@433: 
deba@433:       FillMapVisitor(Map& map, Value& value)
deba@433:         : _map(map), _value(value) {}
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _map.set(node, _value);
deba@433:       }
deba@433:     private:
deba@433:       Map& _map;
deba@433:       Value& _value;
deba@433:     };
deba@433: 
deba@433:     template <typename Digraph, typename ArcMap>
deba@435:     struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433: 
deba@435:       StronglyConnectedCutArcsVisitor(const Digraph& digraph,
deba@435:                                       ArcMap& cutMap,
deba@435:                                       int& cutNum)
deba@433:         : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum),
deba@435:           _compMap(digraph, -1), _num(-1) {
deba@433:       }
deba@433: 
deba@435:       void start(const Node&) {
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _compMap.set(node, _num);
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& arc) {
deba@433:          if (_compMap[_digraph.source(arc)] !=
deba@433:              _compMap[_digraph.target(arc)]) {
deba@433:            _cutMap.set(arc, true);
deba@433:            ++_cutNum;
deba@433:          }
deba@433:       }
deba@433:     private:
deba@433:       const Digraph& _digraph;
deba@433:       ArcMap& _cutMap;
deba@433:       int& _cutNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _compMap;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433:   }
deba@433: 
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check whether the given directed graph is strongly connected.
deba@433:   ///
deba@433:   /// Check whether the given directed graph is strongly connected. The
deba@433:   /// graph is strongly connected when any two nodes of the graph are
deba@433:   /// connected with directed paths in both direction.
kpeter@606:   /// \return \c false when the graph is not strongly connected.
deba@433:   /// \see connected
deba@433:   ///
deba@433:   /// \note By definition, the empty graph is strongly connected.
deba@433:   template <typename Digraph>
deba@433:   bool stronglyConnected(const Digraph& digraph) {
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433: 
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433: 
deba@433:     typename Digraph::Node source = NodeIt(digraph);
deba@433:     if (source == INVALID) return true;
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef DfsVisitor<Digraph> Visitor;
deba@433:     Visitor visitor;
deba@433: 
deba@433:     DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
deba@433:     dfs.init();
deba@433:     dfs.addSource(source);
deba@433:     dfs.start();
deba@433: 
deba@433:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         return false;
deba@433:       }
deba@433:     }
deba@433: 
deba@433:     typedef ReverseDigraph<const Digraph> RDigraph;
deba@435:     typedef typename RDigraph::NodeIt RNodeIt;
deba@433:     RDigraph rdigraph(digraph);
deba@433: 
deba@433:     typedef DfsVisitor<Digraph> RVisitor;
deba@433:     RVisitor rvisitor;
deba@433: 
deba@433:     DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
deba@433:     rdfs.init();
deba@433:     rdfs.addSource(source);
deba@433:     rdfs.start();
deba@433: 
deba@435:     for (RNodeIt it(rdigraph); it != INVALID; ++it) {
deba@433:       if (!rdfs.reached(it)) {
deba@433:         return false;
deba@433:       }
deba@433:     }
deba@433: 
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Count the strongly connected components of a directed graph
deba@433:   ///
deba@433:   /// Count the strongly connected components of a directed graph.
deba@433:   /// The strongly connected components are the classes of an
deba@433:   /// equivalence relation on the nodes of the graph. Two nodes are in
deba@433:   /// the same class if they are connected with directed paths in both
deba@433:   /// direction.
deba@433:   ///
deba@444:   /// \param digraph The graph.
deba@433:   /// \return The number of components
deba@433:   /// \note By definition, the empty graph has zero
deba@433:   /// strongly connected components.
deba@433:   template <typename Digraph>
deba@433:   int countStronglyConnectedComponents(const Digraph& digraph) {
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::Arc Arc;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     typedef typename Digraph::ArcIt ArcIt;
deba@433: 
deba@433:     typedef std::vector<Node> Container;
deba@433:     typedef typename Container::iterator Iterator;
deba@433: 
deba@433:     Container nodes(countNodes(digraph));
deba@433:     typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
deba@433:     Visitor visitor(nodes.begin());
deba@433: 
deba@433:     DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
deba@433:     dfs.init();
deba@433:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433: 
deba@433:     typedef typename Container::reverse_iterator RIterator;
deba@433:     typedef ReverseDigraph<const Digraph> RDigraph;
deba@433: 
deba@433:     RDigraph rdigraph(digraph);
deba@433: 
deba@433:     typedef DfsVisitor<Digraph> RVisitor;
deba@433:     RVisitor rvisitor;
deba@433: 
deba@433:     DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
deba@433: 
deba@433:     int compNum = 0;
deba@433: 
deba@433:     rdfs.init();
deba@433:     for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
deba@433:       if (!rdfs.reached(*it)) {
deba@433:         rdfs.addSource(*it);
deba@433:         rdfs.start();
deba@433:         ++compNum;
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the strongly connected components of a directed graph
deba@433:   ///
deba@433:   /// Find the strongly connected components of a directed graph.  The
deba@433:   /// strongly connected components are the classes of an equivalence
deba@433:   /// relation on the nodes of the graph. Two nodes are in
deba@433:   /// relationship when there are directed paths between them in both
deba@433:   /// direction. In addition, the numbering of components will satisfy
deba@433:   /// that there is no arc going from a higher numbered component to
deba@433:   /// a lower.
deba@433:   ///
deba@433:   /// \param digraph The digraph.
deba@433:   /// \retval compMap A writable node map. The values will be set from 0 to
deba@433:   /// the number of the strongly connected components minus one. Each value
deba@433:   /// of the map will be set exactly once, the values of a certain component
deba@433:   /// will be set continuously.
deba@433:   /// \return The number of components
deba@433:   ///
deba@433:   template <typename Digraph, typename NodeMap>
deba@433:   int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) {
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef std::vector<Node> Container;
deba@433:     typedef typename Container::iterator Iterator;
deba@433: 
deba@433:     Container nodes(countNodes(digraph));
deba@433:     typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
deba@433:     Visitor visitor(nodes.begin());
deba@433: 
deba@433:     DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
deba@433:     dfs.init();
deba@433:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433: 
deba@433:     typedef typename Container::reverse_iterator RIterator;
deba@433:     typedef ReverseDigraph<const Digraph> RDigraph;
deba@433: 
deba@433:     RDigraph rdigraph(digraph);
deba@433: 
deba@433:     int compNum = 0;
deba@433: 
deba@433:     typedef FillMapVisitor<RDigraph, NodeMap> RVisitor;
deba@433:     RVisitor rvisitor(compMap, compNum);
deba@433: 
deba@433:     DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
deba@433: 
deba@433:     rdfs.init();
deba@433:     for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
deba@433:       if (!rdfs.reached(*it)) {
deba@433:         rdfs.addSource(*it);
deba@433:         rdfs.start();
deba@433:         ++compNum;
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the cut arcs of the strongly connected components.
deba@433:   ///
deba@433:   /// Find the cut arcs of the strongly connected components.
deba@433:   /// The strongly connected components are the classes of an equivalence
deba@433:   /// relation on the nodes of the graph. Two nodes are in relationship
deba@433:   /// when there are directed paths between them in both direction.
deba@433:   /// The strongly connected components are separated by the cut arcs.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \retval cutMap A writable node map. The values will be set true when the
deba@433:   /// arc is a cut arc.
deba@433:   ///
deba@433:   /// \return The number of cut arcs
deba@433:   template <typename Digraph, typename ArcMap>
deba@433:   int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) {
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::Arc Arc;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef std::vector<Node> Container;
deba@433:     typedef typename Container::iterator Iterator;
deba@433: 
deba@433:     Container nodes(countNodes(graph));
deba@433:     typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
deba@433:     Visitor visitor(nodes.begin());
deba@433: 
deba@433:     DfsVisit<Digraph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433: 
deba@433:     typedef typename Container::reverse_iterator RIterator;
deba@433:     typedef ReverseDigraph<const Digraph> RDigraph;
deba@433: 
deba@433:     RDigraph rgraph(graph);
deba@433: 
deba@433:     int cutNum = 0;
deba@433: 
deba@435:     typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor;
deba@433:     RVisitor rvisitor(rgraph, cutMap, cutNum);
deba@433: 
deba@433:     DfsVisit<RDigraph, RVisitor> rdfs(rgraph, rvisitor);
deba@433: 
deba@433:     rdfs.init();
deba@433:     for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
deba@433:       if (!rdfs.reached(*it)) {
deba@433:         rdfs.addSource(*it);
deba@433:         rdfs.start();
deba@433:       }
deba@433:     }
deba@433:     return cutNum;
deba@433:   }
deba@433: 
deba@435:   namespace _connectivity_bits {
deba@433: 
deba@433:     template <typename Digraph>
deba@433:     class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum)
deba@433:         : _graph(graph), _compNum(compNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap.set(node, INVALID);
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         _predMap.set(_graph.target(edge), _graph.source(edge));
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         if (_graph.source(edge) == _graph.target(edge) &&
deba@433:             _graph.direction(edge)) {
deba@433:           ++_compNum;
deba@433:           return;
deba@433:         }
deba@433:         if (_predMap[_graph.source(edge)] == _graph.target(edge)) {
deba@433:           return;
deba@433:         }
deba@433:         if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:         if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) {
deba@433:           ++_compNum;
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       int& _compNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Node> _predMap;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433:     template <typename Digraph, typename ArcMap>
deba@433:     class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       BiNodeConnectedComponentsVisitor(const Digraph& graph,
deba@433:                                        ArcMap& compMap, int &compNum)
deba@433:         : _graph(graph), _compMap(compMap), _compNum(compNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap.set(node, INVALID);
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         Node target = _graph.target(edge);
deba@433:         _predMap.set(target, edge);
deba@433:         _edgeStack.push(edge);
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         Node source = _graph.source(edge);
deba@433:         Node target = _graph.target(edge);
deba@433:         if (source == target && _graph.direction(edge)) {
deba@433:           _compMap.set(edge, _compNum);
deba@433:           ++_compNum;
deba@433:           return;
deba@433:         }
deba@433:         if (_numMap[target] < _numMap[source]) {
deba@433:           if (_predMap[source] != _graph.oppositeArc(edge)) {
deba@433:             _edgeStack.push(edge);
deba@433:           }
deba@433:         }
deba@433:         if (_predMap[source] != INVALID &&
deba@433:             target == _graph.source(_predMap[source])) {
deba@433:           return;
deba@433:         }
deba@433:         if (_retMap[source] > _numMap[target]) {
deba@433:           _retMap.set(source, _numMap[target]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         Node source = _graph.source(edge);
deba@433:         Node target = _graph.target(edge);
deba@433:         if (_retMap[source] > _retMap[target]) {
deba@433:           _retMap.set(source, _retMap[target]);
deba@433:         }
deba@433:         if (_numMap[source] <= _retMap[target]) {
deba@433:           while (_edgeStack.top() != edge) {
deba@433:             _compMap.set(_edgeStack.top(), _compNum);
deba@433:             _edgeStack.pop();
deba@433:           }
deba@433:           _compMap.set(edge, _compNum);
deba@433:           _edgeStack.pop();
deba@433:           ++_compNum;
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       ArcMap& _compMap;
deba@433:       int& _compNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Arc> _predMap;
deba@433:       std::stack<Edge> _edgeStack;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433: 
deba@433:     template <typename Digraph, typename NodeMap>
deba@433:     class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap,
deba@433:                                      int& cutNum)
deba@433:         : _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap.set(node, INVALID);
deba@433:         rootCut = false;
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         _predMap.set(_graph.target(edge), _graph.source(edge));
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         if (_graph.source(edge) == _graph.target(edge) &&
deba@433:             _graph.direction(edge)) {
deba@433:           if (!_cutMap[_graph.source(edge)]) {
deba@433:             _cutMap.set(_graph.source(edge), true);
deba@433:             ++_cutNum;
deba@433:           }
deba@433:           return;
deba@433:         }
deba@433:         if (_predMap[_graph.source(edge)] == _graph.target(edge)) return;
deba@433:         if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:         if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) {
deba@433:           if (_predMap[_graph.source(edge)] != INVALID) {
deba@433:             if (!_cutMap[_graph.source(edge)]) {
deba@433:               _cutMap.set(_graph.source(edge), true);
deba@433:               ++_cutNum;
deba@433:             }
deba@433:           } else if (rootCut) {
deba@433:             if (!_cutMap[_graph.source(edge)]) {
deba@433:               _cutMap.set(_graph.source(edge), true);
deba@433:               ++_cutNum;
deba@433:             }
deba@433:           } else {
deba@433:             rootCut = true;
deba@433:           }
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       NodeMap& _cutMap;
deba@433:       int& _cutNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Node> _predMap;
deba@433:       std::stack<Edge> _edgeStack;
deba@433:       int _num;
deba@433:       bool rootCut;
deba@433:     };
deba@433: 
deba@433:   }
deba@433: 
deba@433:   template <typename Graph>
deba@433:   int countBiNodeConnectedComponents(const Graph& graph);
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Checks the graph is bi-node-connected.
deba@433:   ///
deba@433:   /// This function checks that the undirected graph is bi-node-connected
deba@433:   /// graph. The graph is bi-node-connected if any two undirected edge is
deba@433:   /// on same circle.
deba@433:   ///
deba@433:   /// \param graph The graph.
kpeter@606:   /// \return \c true when the graph bi-node-connected.
deba@433:   template <typename Graph>
deba@433:   bool biNodeConnected(const Graph& graph) {
deba@433:     return countBiNodeConnectedComponents(graph) <= 1;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Count the biconnected components.
deba@433:   ///
deba@433:   /// This function finds the bi-node-connected components in an undirected
deba@433:   /// graph. The biconnected components are the classes of an equivalence
deba@433:   /// relation on the undirected edges. Two undirected edge is in relationship
deba@433:   /// when they are on same circle.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \return The number of components.
deba@433:   template <typename Graph>
deba@433:   int countBiNodeConnectedComponents(const Graph& graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     Visitor visitor(graph, compNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the bi-node-connected components.
deba@433:   ///
deba@433:   /// This function finds the bi-node-connected components in an undirected
deba@433:   /// graph. The bi-node-connected components are the classes of an equivalence
deba@433:   /// relation on the undirected edges. Two undirected edge are in relationship
deba@433:   /// when they are on same circle.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \retval compMap A writable uedge map. The values will be set from 0
deba@433:   /// to the number of the biconnected components minus one. Each values
deba@433:   /// of the map will be set exactly once, the values of a certain component
deba@433:   /// will be set continuously.
deba@433:   /// \return The number of components.
deba@433:   ///
deba@433:   template <typename Graph, typename EdgeMap>
deba@433:   int biNodeConnectedComponents(const Graph& graph,
deba@433:                                 EdgeMap& compMap) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::Edge Edge;
deba@433:     checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     Visitor visitor(graph, compMap, compNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the bi-node-connected cut nodes.
deba@433:   ///
deba@433:   /// This function finds the bi-node-connected cut nodes in an undirected
deba@433:   /// graph. The bi-node-connected components are the classes of an equivalence
deba@433:   /// relation on the undirected edges. Two undirected edges are in
deba@433:   /// relationship when they are on same circle. The biconnected components
deba@433:   /// are separted by nodes which are the cut nodes of the components.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \retval cutMap A writable edge map. The values will be set true when
deba@433:   /// the node separate two or more components.
deba@433:   /// \return The number of the cut nodes.
deba@433:   template <typename Graph, typename NodeMap>
deba@433:   int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     checkConcept<concepts::WriteMap<Node, bool>, NodeMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor;
deba@433: 
deba@433:     int cutNum = 0;
deba@433:     Visitor visitor(graph, cutMap, cutNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return cutNum;
deba@433:   }
deba@433: 
deba@435:   namespace _connectivity_bits {
deba@433: 
deba@433:     template <typename Digraph>
deba@433:     class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum)
deba@433:         : _graph(graph), _compNum(compNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap.set(node, INVALID);
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void leave(const Node& node) {
deba@433:         if (_numMap[node] <= _retMap[node]) {
deba@433:           ++_compNum;
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         _predMap.set(_graph.target(edge), edge);
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) {
deba@433:           return;
deba@433:         }
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       int& _compNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Arc> _predMap;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433:     template <typename Digraph, typename NodeMap>
deba@433:     class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       BiEdgeConnectedComponentsVisitor(const Digraph& graph,
deba@433:                                        NodeMap& compMap, int &compNum)
deba@433:         : _graph(graph), _compMap(compMap), _compNum(compNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap.set(node, INVALID);
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         _nodeStack.push(node);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void leave(const Node& node) {
deba@433:         if (_numMap[node] <= _retMap[node]) {
deba@433:           while (_nodeStack.top() != node) {
deba@433:             _compMap.set(_nodeStack.top(), _compNum);
deba@433:             _nodeStack.pop();
deba@433:           }
deba@433:           _compMap.set(node, _compNum);
deba@433:           _nodeStack.pop();
deba@433:           ++_compNum;
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         _predMap.set(_graph.target(edge), edge);
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) {
deba@433:           return;
deba@433:         }
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       NodeMap& _compMap;
deba@433:       int& _compNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Arc> _predMap;
deba@433:       std::stack<Node> _nodeStack;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433: 
deba@433:     template <typename Digraph, typename ArcMap>
deba@433:     class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Edge Edge;
deba@433: 
deba@433:       BiEdgeConnectedCutEdgesVisitor(const Digraph& graph,
deba@433:                                      ArcMap& cutMap, int &cutNum)
deba@433:         : _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
deba@433:           _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _predMap[node] = INVALID;
deba@433:       }
deba@433: 
deba@433:       void reach(const Node& node) {
deba@433:         _numMap.set(node, _num);
deba@433:         _retMap.set(node, _num);
deba@433:         ++_num;
deba@433:       }
deba@433: 
deba@433:       void leave(const Node& node) {
deba@433:         if (_numMap[node] <= _retMap[node]) {
deba@433:           if (_predMap[node] != INVALID) {
deba@433:             _cutMap.set(_predMap[node], true);
deba@433:             ++_cutNum;
deba@433:           }
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void discover(const Arc& edge) {
deba@433:         _predMap.set(_graph.target(edge), edge);
deba@433:       }
deba@433: 
deba@433:       void examine(const Arc& edge) {
deba@433:         if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) {
deba@433:           return;
deba@433:         }
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:       void backtrack(const Arc& edge) {
deba@433:         if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
deba@433:           _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
deba@433:         }
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       const Digraph& _graph;
deba@433:       ArcMap& _cutMap;
deba@433:       int& _cutNum;
deba@433: 
deba@433:       typename Digraph::template NodeMap<int> _numMap;
deba@433:       typename Digraph::template NodeMap<int> _retMap;
deba@433:       typename Digraph::template NodeMap<Arc> _predMap;
deba@433:       int _num;
deba@433:     };
deba@433:   }
deba@433: 
deba@433:   template <typename Graph>
deba@433:   int countBiEdgeConnectedComponents(const Graph& graph);
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Checks that the graph is bi-edge-connected.
deba@433:   ///
deba@433:   /// This function checks that the graph is bi-edge-connected. The undirected
deba@433:   /// graph is bi-edge-connected when any two nodes are connected with two
deba@433:   /// edge-disjoint paths.
deba@433:   ///
deba@433:   /// \param graph The undirected graph.
deba@433:   /// \return The number of components.
deba@433:   template <typename Graph>
deba@433:   bool biEdgeConnected(const Graph& graph) {
deba@433:     return countBiEdgeConnectedComponents(graph) <= 1;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Count the bi-edge-connected components.
deba@433:   ///
deba@433:   /// This function count the bi-edge-connected components in an undirected
deba@433:   /// graph. The bi-edge-connected components are the classes of an equivalence
deba@433:   /// relation on the nodes. Two nodes are in relationship when they are
deba@433:   /// connected with at least two edge-disjoint paths.
deba@433:   ///
deba@433:   /// \param graph The undirected graph.
deba@433:   /// \return The number of components.
deba@433:   template <typename Graph>
deba@433:   int countBiEdgeConnectedComponents(const Graph& graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     Visitor visitor(graph, compNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the bi-edge-connected components.
deba@433:   ///
deba@433:   /// This function finds the bi-edge-connected components in an undirected
deba@433:   /// graph. The bi-edge-connected components are the classes of an equivalence
deba@433:   /// relation on the nodes. Two nodes are in relationship when they are
deba@433:   /// connected at least two edge-disjoint paths.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \retval compMap A writable node map. The values will be set from 0 to
deba@433:   /// the number of the biconnected components minus one. Each values
deba@433:   /// of the map will be set exactly once, the values of a certain component
deba@433:   /// will be set continuously.
deba@433:   /// \return The number of components.
deba@433:   ///
deba@433:   template <typename Graph, typename NodeMap>
deba@433:   int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::Node Node;
deba@433:     checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor;
deba@433: 
deba@433:     int compNum = 0;
deba@433:     Visitor visitor(graph, compMap, compNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return compNum;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Find the bi-edge-connected cut edges.
deba@433:   ///
deba@433:   /// This function finds the bi-edge-connected components in an undirected
deba@433:   /// graph. The bi-edge-connected components are the classes of an equivalence
deba@433:   /// relation on the nodes. Two nodes are in relationship when they are
deba@433:   /// connected with at least two edge-disjoint paths. The bi-edge-connected
deba@433:   /// components are separted by edges which are the cut edges of the
deba@433:   /// components.
deba@433:   ///
deba@433:   /// \param graph The graph.
deba@433:   /// \retval cutMap A writable node map. The values will be set true when the
deba@433:   /// edge is a cut edge.
deba@433:   /// \return The number of cut edges.
deba@433:   template <typename Graph, typename EdgeMap>
deba@433:   int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::Edge Edge;
deba@433:     checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>();
deba@433: 
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor;
deba@433: 
deba@433:     int cutNum = 0;
deba@433:     Visitor visitor(graph, cutMap, cutNum);
deba@433: 
deba@433:     DfsVisit<Graph, Visitor> dfs(graph, visitor);
deba@433:     dfs.init();
deba@433: 
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:     return cutNum;
deba@433:   }
deba@433: 
deba@433: 
deba@435:   namespace _connectivity_bits {
deba@433: 
deba@433:     template <typename Digraph, typename IntNodeMap>
deba@433:     class TopologicalSortVisitor : public DfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Node Node;
deba@433:       typedef typename Digraph::Arc edge;
deba@433: 
deba@433:       TopologicalSortVisitor(IntNodeMap& order, int num)
deba@433:         : _order(order), _num(num) {}
deba@433: 
deba@433:       void leave(const Node& node) {
deba@433:         _order.set(node, --_num);
deba@433:       }
deba@433: 
deba@433:     private:
deba@433:       IntNodeMap& _order;
deba@433:       int _num;
deba@433:     };
deba@433: 
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Sort the nodes of a DAG into topolgical order.
deba@433:   ///
deba@433:   /// Sort the nodes of a DAG into topolgical order.
deba@433:   ///
deba@433:   /// \param graph The graph. It must be directed and acyclic.
deba@433:   /// \retval order A writable node map. The values will be set from 0 to
deba@433:   /// the number of the nodes in the graph minus one. Each values of the map
deba@433:   /// will be set exactly once, the values  will be set descending order.
deba@433:   ///
deba@433:   /// \see checkedTopologicalSort
deba@433:   /// \see dag
deba@433:   template <typename Digraph, typename NodeMap>
deba@433:   void topologicalSort(const Digraph& graph, NodeMap& order) {
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433:     checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>();
deba@433: 
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     typedef typename Digraph::Arc Arc;
deba@433: 
deba@433:     TopologicalSortVisitor<Digraph, NodeMap>
deba@433:       visitor(order, countNodes(graph));
deba@433: 
deba@433:     DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> >
deba@433:       dfs(graph, visitor);
deba@433: 
deba@433:     dfs.init();
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         dfs.start();
deba@433:       }
deba@433:     }
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Sort the nodes of a DAG into topolgical order.
deba@433:   ///
deba@433:   /// Sort the nodes of a DAG into topolgical order. It also checks
deba@433:   /// that the given graph is DAG.
deba@433:   ///
deba@444:   /// \param digraph The graph. It must be directed and acyclic.
deba@433:   /// \retval order A readable - writable node map. The values will be set
deba@433:   /// from 0 to the number of the nodes in the graph minus one. Each values
deba@433:   /// of the map will be set exactly once, the values will be set descending
deba@433:   /// order.
kpeter@606:   /// \return \c false when the graph is not DAG.
deba@433:   ///
deba@433:   /// \see topologicalSort
deba@433:   /// \see dag
deba@433:   template <typename Digraph, typename NodeMap>
deba@435:   bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) {
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433:     checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>,
deba@433:       NodeMap>();
deba@433: 
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     typedef typename Digraph::Arc Arc;
deba@433: 
deba@435:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@435:       order.set(it, -1);
deba@435:     }
deba@433: 
deba@433:     TopologicalSortVisitor<Digraph, NodeMap>
deba@435:       visitor(order, countNodes(digraph));
deba@433: 
deba@433:     DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> >
deba@435:       dfs(digraph, visitor);
deba@433: 
deba@433:     dfs.init();
deba@435:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         while (!dfs.emptyQueue()) {
deba@435:            Arc arc = dfs.nextArc();
deba@435:            Node target = digraph.target(arc);
deba@433:            if (dfs.reached(target) && order[target] == -1) {
deba@433:              return false;
deba@433:            }
deba@433:            dfs.processNextArc();
deba@433:          }
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check that the given directed graph is a DAG.
deba@433:   ///
deba@433:   /// Check that the given directed graph is a DAG. The DAG is
deba@433:   /// an Directed Acyclic Digraph.
kpeter@606:   /// \return \c false when the graph is not DAG.
deba@433:   /// \see acyclic
deba@433:   template <typename Digraph>
deba@435:   bool dag(const Digraph& digraph) {
deba@433: 
deba@433:     checkConcept<concepts::Digraph, Digraph>();
deba@433: 
deba@433:     typedef typename Digraph::Node Node;
deba@433:     typedef typename Digraph::NodeIt NodeIt;
deba@433:     typedef typename Digraph::Arc Arc;
deba@433: 
deba@433:     typedef typename Digraph::template NodeMap<bool> ProcessedMap;
deba@433: 
deba@433:     typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>::
deba@435:       Create dfs(digraph);
deba@433: 
deba@435:     ProcessedMap processed(digraph);
deba@433:     dfs.processedMap(processed);
deba@433: 
deba@433:     dfs.init();
deba@435:     for (NodeIt it(digraph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         while (!dfs.emptyQueue()) {
deba@433:           Arc edge = dfs.nextArc();
deba@435:           Node target = digraph.target(edge);
deba@433:           if (dfs.reached(target) && !processed[target]) {
deba@433:             return false;
deba@433:           }
deba@433:           dfs.processNextArc();
deba@433:         }
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check that the given undirected graph is acyclic.
deba@433:   ///
deba@433:   /// Check that the given undirected graph acyclic.
deba@433:   /// \param graph The undirected graph.
kpeter@606:   /// \return \c true when there is no circle in the graph.
deba@433:   /// \see dag
deba@433:   template <typename Graph>
deba@433:   bool acyclic(const Graph& graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::Arc Arc;
deba@433:     Dfs<Graph> dfs(graph);
deba@433:     dfs.init();
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         dfs.addSource(it);
deba@433:         while (!dfs.emptyQueue()) {
deba@433:           Arc edge = dfs.nextArc();
deba@433:           Node source = graph.source(edge);
deba@433:           Node target = graph.target(edge);
deba@433:           if (dfs.reached(target) &&
deba@433:               dfs.predArc(source) != graph.oppositeArc(edge)) {
deba@433:             return false;
deba@433:           }
deba@433:           dfs.processNextArc();
deba@433:         }
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check that the given undirected graph is tree.
deba@433:   ///
deba@433:   /// Check that the given undirected graph is tree.
deba@433:   /// \param graph The undirected graph.
kpeter@606:   /// \return \c true when the graph is acyclic and connected.
deba@433:   template <typename Graph>
deba@433:   bool tree(const Graph& graph) {
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::Arc Arc;
deba@433:     Dfs<Graph> dfs(graph);
deba@433:     dfs.init();
deba@433:     dfs.addSource(NodeIt(graph));
deba@433:     while (!dfs.emptyQueue()) {
deba@433:       Arc edge = dfs.nextArc();
deba@433:       Node source = graph.source(edge);
deba@433:       Node target = graph.target(edge);
deba@433:       if (dfs.reached(target) &&
deba@433:           dfs.predArc(source) != graph.oppositeArc(edge)) {
deba@433:         return false;
deba@433:       }
deba@433:       dfs.processNextArc();
deba@433:     }
deba@433:     for (NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if (!dfs.reached(it)) {
deba@433:         return false;
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@435:   namespace _connectivity_bits {
deba@433: 
deba@433:     template <typename Digraph>
deba@433:     class BipartiteVisitor : public BfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Node Node;
deba@433: 
deba@433:       BipartiteVisitor(const Digraph& graph, bool& bipartite)
deba@433:         : _graph(graph), _part(graph), _bipartite(bipartite) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _part[node] = true;
deba@433:       }
deba@433:       void discover(const Arc& edge) {
deba@433:         _part.set(_graph.target(edge), !_part[_graph.source(edge)]);
deba@433:       }
deba@433:       void examine(const Arc& edge) {
deba@433:         _bipartite = _bipartite &&
deba@433:           _part[_graph.target(edge)] != _part[_graph.source(edge)];
deba@433:       }
deba@433: 
deba@433:     private:
deba@433: 
deba@433:       const Digraph& _graph;
deba@433:       typename Digraph::template NodeMap<bool> _part;
deba@433:       bool& _bipartite;
deba@433:     };
deba@433: 
deba@433:     template <typename Digraph, typename PartMap>
deba@433:     class BipartitePartitionsVisitor : public BfsVisitor<Digraph> {
deba@433:     public:
deba@433:       typedef typename Digraph::Arc Arc;
deba@433:       typedef typename Digraph::Node Node;
deba@433: 
deba@433:       BipartitePartitionsVisitor(const Digraph& graph,
deba@433:                                  PartMap& part, bool& bipartite)
deba@433:         : _graph(graph), _part(part), _bipartite(bipartite) {}
deba@433: 
deba@433:       void start(const Node& node) {
deba@433:         _part.set(node, true);
deba@433:       }
deba@433:       void discover(const Arc& edge) {
deba@433:         _part.set(_graph.target(edge), !_part[_graph.source(edge)]);
deba@433:       }
deba@433:       void examine(const Arc& edge) {
deba@433:         _bipartite = _bipartite &&
deba@433:           _part[_graph.target(edge)] != _part[_graph.source(edge)];
deba@433:       }
deba@433: 
deba@433:     private:
deba@433: 
deba@433:       const Digraph& _graph;
deba@433:       PartMap& _part;
deba@433:       bool& _bipartite;
deba@433:     };
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check if the given undirected graph is bipartite or not
deba@433:   ///
deba@433:   /// The function checks if the given undirected \c graph graph is bipartite
deba@433:   /// or not. The \ref Bfs algorithm is used to calculate the result.
deba@433:   /// \param graph The undirected graph.
kpeter@606:   /// \return \c true if \c graph is bipartite, \c false otherwise.
deba@433:   /// \sa bipartitePartitions
deba@433:   template<typename Graph>
deba@433:   inline bool bipartite(const Graph &graph){
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433: 
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::ArcIt ArcIt;
deba@433: 
deba@433:     bool bipartite = true;
deba@433: 
deba@433:     BipartiteVisitor<Graph>
deba@433:       visitor(graph, bipartite);
deba@433:     BfsVisit<Graph, BipartiteVisitor<Graph> >
deba@433:       bfs(graph, visitor);
deba@433:     bfs.init();
deba@433:     for(NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if(!bfs.reached(it)){
deba@433:         bfs.addSource(it);
deba@433:         while (!bfs.emptyQueue()) {
deba@433:           bfs.processNextNode();
deba@433:           if (!bipartite) return false;
deba@433:         }
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \ingroup connectivity
deba@433:   ///
deba@433:   /// \brief Check if the given undirected graph is bipartite or not
deba@433:   ///
deba@433:   /// The function checks if the given undirected graph is bipartite
deba@433:   /// or not. The  \ref  Bfs  algorithm  is   used  to  calculate the result.
deba@433:   /// During the execution, the \c partMap will be set as the two
deba@433:   /// partitions of the graph.
deba@433:   /// \param graph The undirected graph.
deba@433:   /// \retval partMap A writable bool map of nodes. It will be set as the
deba@433:   /// two partitions of the graph.
kpeter@606:   /// \return \c true if \c graph is bipartite, \c false otherwise.
deba@433:   template<typename Graph, typename NodeMap>
deba@433:   inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){
deba@435:     using namespace _connectivity_bits;
deba@433: 
deba@433:     checkConcept<concepts::Graph, Graph>();
deba@433: 
deba@433:     typedef typename Graph::Node Node;
deba@433:     typedef typename Graph::NodeIt NodeIt;
deba@433:     typedef typename Graph::ArcIt ArcIt;
deba@433: 
deba@433:     bool bipartite = true;
deba@433: 
deba@433:     BipartitePartitionsVisitor<Graph, NodeMap>
deba@433:       visitor(graph, partMap, bipartite);
deba@433:     BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> >
deba@433:       bfs(graph, visitor);
deba@433:     bfs.init();
deba@433:     for(NodeIt it(graph); it != INVALID; ++it) {
deba@433:       if(!bfs.reached(it)){
deba@433:         bfs.addSource(it);
deba@433:         while (!bfs.emptyQueue()) {
deba@433:           bfs.processNextNode();
deba@433:           if (!bipartite) return false;
deba@433:         }
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \brief Returns true when there are not loop edges in the graph.
deba@433:   ///
deba@433:   /// Returns true when there are not loop edges in the graph.
deba@433:   template <typename Digraph>
deba@435:   bool loopFree(const Digraph& digraph) {
deba@435:     for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) {
deba@435:       if (digraph.source(it) == digraph.target(it)) return false;
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \brief Returns true when there are not parallel edges in the graph.
deba@433:   ///
deba@433:   /// Returns true when there are not parallel edges in the graph.
deba@433:   template <typename Digraph>
deba@435:   bool parallelFree(const Digraph& digraph) {
deba@435:     typename Digraph::template NodeMap<bool> reached(digraph, false);
deba@435:     for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
deba@435:       for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
deba@435:         if (reached[digraph.target(a)]) return false;
deba@435:         reached.set(digraph.target(a), true);
deba@433:       }
deba@435:       for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
deba@435:         reached.set(digraph.target(a), false);
deba@433:       }
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433:   /// \brief Returns true when there are not loop edges and parallel
deba@433:   /// edges in the graph.
deba@433:   ///
deba@433:   /// Returns true when there are not loop edges and parallel edges in
deba@433:   /// the graph.
deba@433:   template <typename Digraph>
deba@435:   bool simpleDigraph(const Digraph& digraph) {
deba@435:     typename Digraph::template NodeMap<bool> reached(digraph, false);
deba@435:     for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
deba@433:       reached.set(n, true);
deba@435:       for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
deba@435:         if (reached[digraph.target(a)]) return false;
deba@435:         reached.set(digraph.target(a), true);
deba@433:       }
deba@435:       for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
deba@435:         reached.set(digraph.target(a), false);
deba@433:       }
deba@433:       reached.set(n, false);
deba@433:     }
deba@433:     return true;
deba@433:   }
deba@433: 
deba@433: } //namespace lemon
deba@433: 
deba@435: #endif //LEMON_CONNECTIVITY_H