RhodeCode

/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_CONCEPT_MAPS_H

#define LEMON_CONCEPT_MAPS_H

#include <lemon/bits/utility.h>

#include <lemon/concept_check.h>

///\ingroup concept

///\file

///\brief Map concepts checking classes for testing and documenting.

namespace lemon {

  namespace concepts {

    /// \addtogroup concept

    /// @{

    /// Readable map concept

    /// Readable map concept.

    ///

    template<typename K, typename T>

    class ReadMap

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Returns the value associated with a key.

      /// Returns the value associated with a key.

      /// \bug Value shouldn't need to be default constructible.

      ///

      Value operator[](const Key &) const {return Value();}

      template<typename _ReadMap>

      struct Constraints {

	void constraints() {

	  Value val = m[key];

	  val = m[key];

	  typename _ReadMap::Value own_val = m[own_key]; 

	  own_val = m[own_key]; 

	  ignore_unused_variable_warning(val);

	  ignore_unused_variable_warning(own_val);

	  ignore_unused_variable_warning(key);

	}

	Key& key;

	typename _ReadMap::Key& own_key;

	_ReadMap& m;

      };

    };

    /// Writable map concept

    /// Writable map concept.

    ///

    template<typename K, typename T>

    class WriteMap

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Sets the value associated with a key.

      void set(const Key &,const Value &) {}

      ///Default constructor

      WriteMap() {}

      template <typename _WriteMap>

      struct Constraints {

	void constraints() {

	  // No constraints for constructor.

	  m.set(key, val);

	  m.set(own_key, own_val);

	  ignore_unused_variable_warning(key);

	  ignore_unused_variable_warning(val);

	  ignore_unused_variable_warning(own_key);

	  ignore_unused_variable_warning(own_val);

	}

	Value& val;

	typename _WriteMap::Value own_val;

	Key& key;

	typename _WriteMap::Key& own_key;

	_WriteMap& m;

      };

    };

    /// Read/writable map concept

    /// Read/writable map concept.

    ///

    template<typename K, typename T>

    class ReadWriteMap : public ReadMap<K,T>,

			 public WriteMap<K,T>

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Returns the value associated with a key.

      Value operator[](const Key &) const {return Value();}

      /// Sets the value associated with a key.

      void set(const Key & ,const Value &) {}

      template<typename _ReadWriteMap>

      struct Constraints {

	void constraints() {

	  checkConcept<ReadMap<K, T>, _ReadWriteMap >();

	  checkConcept<WriteMap<K, T>, _ReadWriteMap >();

	}

      };

    };

    /// Dereferable map concept

    /// Dereferable map concept.

    ///

    /// \todo Rethink this concept.

    template<typename K, typename T, typename R, typename CR>

    class ReferenceMap : public ReadWriteMap<K,T>

    {

    public:

      /// Tag for reference maps.

      typedef True ReferenceMapTag;

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// The reference type of the map.

      typedef R Reference;

      /// The const reference type of the map.

      typedef CR ConstReference;

    protected:

      Value tmp;

    public:

      ///Returns a reference to the value associated with a key.

      Reference operator[](const Key &) { return tmp; }

      ///Returns a const reference to the value associated with a key.

      ConstReference operator[](const Key &) const { return tmp; }

      /// Sets the value associated with a key.

      void set(const Key &k,const Value &t) { operator[](k)=t; }

      template<typename _ReferenceMap>

	void constraints() {

	  m[key] = val;

	  val  = m[key];

	  m[key] = ref;

	  ref = m[key];

	  m[own_key] = own_val;

	  own_val  = m[own_key];

	  m[own_key] = own_ref;

	  own_ref = m[own_key];	  	  

	}

	typename _ReferenceMap::Key& own_key;

	typename _ReferenceMap::Value& own_val;

	Key& key;

	Value& val;

	_ReferenceMap& m;

      };

    };

    // @}

  } //namespace concepts

} //namespace lemon

#endif // LEMON_CONCEPT_MAPS_H

/* -*- C++ -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library

 *

 * Copyright (C) 2003-2008

 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

 * (Egervary Research Group on Combinatorial Optimization, EGRES).

 *

 * Permission to use, modify and distribute this software is granted

 * provided that this copyright notice appears in all copies. For

 * precise terms see the accompanying LICENSE file.

 *

 * This software is provided "AS IS" with no warranty of any kind,

 * express or implied, and with no claim as to its suitability for any

 * purpose.

 *

 */

#ifndef LEMON_LIST_GRAPH_H

#define LEMON_LIST_GRAPH_H

///\ingroup graphs

///\file

///\brief ListDigraph, ListGraph classes.

#include <lemon/bits/graph_extender.h>

#include <vector>

#include <list>

namespace lemon {

  class ListDigraphBase {

  protected:

    struct NodeT {

      int first_in, first_out;

      int prev, next;

    };

    struct ArcT {

      int target, source;

      int prev_in, prev_out;

      int next_in, next_out;

    };

    std::vector<NodeT> nodes;

    int first_node;

    int first_free_node;

    std::vector<ArcT> arcs;

    int first_free_arc;

  public:

    typedef ListDigraphBase Digraph;

    class Node {

      friend class ListDigraphBase;

    protected:

      int id;

      explicit Node(int pid) { id = pid;}

    public:

      Node() {}

      Node (Invalid) { id = -1; }

      bool operator==(const Node& node) const {return id == node.id;}

      bool operator!=(const Node& node) const {return id != node.id;}

      bool operator<(const Node& node) const {return id < node.id;}

    };

    class Arc {

      friend class ListDigraphBase;

    protected:

      int id;

      explicit Arc(int pid) { id = pid;}

    public:

      Arc() {}

      Arc (Invalid) { id = -1; }

      bool operator==(const Arc& arc) const {return id == arc.id;}

      bool operator!=(const Arc& arc) const {return id != arc.id;}

      bool operator<(const Arc& arc) const {return id < arc.id;}

    };

    ListDigraphBase()

      : nodes(), first_node(-1),

	first_free_node(-1), arcs(), first_free_arc(-1) {}

    int maxNodeId() const { return nodes.size()-1; } 

    int maxArcId() const { return arcs.size()-1; }

    Node source(Arc e) const { return Node(arcs[e.id].source); }

    Node target(Arc e) const { return Node(arcs[e.id].target); }

    void first(Node& node) const { 

      node.id = first_node;

    }

    void next(Node& node) const {

      node.id = nodes[node.id].next;

    }

      int n;

      for(n = first_node; 

	  n!=-1 && nodes[n].first_in == -1; 

	  n = nodes[n].next);

    }

    void next(Arc& arc) const {

      if (arcs[arc.id].next_in != -1) {

	arc.id = arcs[arc.id].next_in;

      } else {

	int n;

	for(n = nodes[arcs[arc.id].target].next;

	  n!=-1 && nodes[n].first_in == -1; 

	  n = nodes[n].next);

	arc.id = (n == -1) ? -1 : nodes[n].first_in;

      }      

    }

    void firstOut(Arc &e, const Node& v) const {

      e.id = nodes[v.id].first_out;

    }

    void nextOut(Arc &e) const {

      e.id=arcs[e.id].next_out;

    }

    void firstIn(Arc &e, const Node& v) const {

      e.id = nodes[v.id].first_in;

    }

    void nextIn(Arc &e) const {

      e.id=arcs[e.id].next_in;

    }

    static int id(Node v) { return v.id; }

    static int id(Arc e) { return e.id; }

    static Node nodeFromId(int id) { return Node(id);}

    static Arc arcFromId(int id) { return Arc(id);}

    Node addNode() {     

      int n;

      if(first_free_node==-1) {

	n = nodes.size();

	nodes.push_back(NodeT());

      } else {

	n = first_free_node;

	first_free_node = nodes[n].next;

      }

      nodes[n].next = first_node;

      if(first_node != -1) nodes[first_node].prev = n;

      first_node = n;

      nodes[n].prev = -1;

      nodes[n].first_in = nodes[n].first_out = -1;

      return Node(n);

    }

    Arc addArc(Node u, Node v) {

      int n;      

      if (first_free_arc == -1) {

	n = arcs.size();

	arcs.push_back(ArcT());

      } else {

	n = first_free_arc;

	first_free_arc = arcs[n].next_in;

      }

      arcs[n].source = u.id; 

      arcs[n].target = v.id;

      arcs[n].next_out = nodes[u.id].first_out;

      if(nodes[u.id].first_out != -1) {

	arcs[nodes[u.id].first_out].prev_out = n;

      }

      arcs[n].next_in = nodes[v.id].first_in;

      if(nodes[v.id].first_in != -1) {

	arcs[nodes[v.id].first_in].prev_in = n;

      }

      arcs[n].prev_in = arcs[n].prev_out = -1;

      nodes[u.id].first_out = nodes[v.id].first_in = n;

      return Arc(n);

    }

    void erase(const Node& node) {

      int n = node.id;

      if(nodes[n].next != -1) {

	nodes[nodes[n].next].prev = nodes[n].prev;

      }

      if(nodes[n].prev != -1) {

	nodes[nodes[n].prev].next = nodes[n].next;

      } else {

	first_node = nodes[n].next;

      }

      nodes[n].next = first_free_node;

      first_free_node = n;

    }

    void erase(const Arc& arc) {

      int n = arc.id;

      if(arcs[n].next_in!=-1) {

	arcs[arcs[n].next_in].prev_in = arcs[n].prev_in;

      }

      if(arcs[n].prev_in!=-1) {

	arcs[arcs[n].prev_in].next_in = arcs[n].next_in;

      } else {

	nodes[arcs[n].target].first_in = arcs[n].next_in;

      }

      if(arcs[n].next_out!=-1) {

	arcs[arcs[n].next_out].prev_out = arcs[n].prev_out;

      } 

      if(arcs[n].prev_out!=-1) {

	arcs[arcs[n].prev_out].next_out = arcs[n].next_out;

      } else {

	nodes[arcs[n].source].first_out = arcs[n].next_out;

      }

      arcs[n].next_in = first_free_arc;

      first_free_arc = n;      

    }

    void clear() {

      arcs.clear();

      nodes.clear();

      first_node = first_free_node = first_free_arc = -1;

    }

  protected:

    void changeTarget(Arc e, Node n) 

    {

      if(arcs[e.id].next_in != -1)

	arcs[arcs[e.id].next_in].prev_in = arcs[e.id].prev_in;

      if(arcs[e.id].prev_in != -1)

	arcs[arcs[e.id].prev_in].next_in = arcs[e.id].next_in;

      else nodes[arcs[e.id].target].first_in = arcs[e.id].next_in;

      if (nodes[n.id].first_in != -1) {

	arcs[nodes[n.id].first_in].prev_in = e.id;

      }

      arcs[e.id].target = n.id;

      arcs[e.id].prev_in = -1;

      arcs[e.id].next_in = nodes[n.id].first_in;

      nodes[n.id].first_in = e.id;

    }

    void changeSource(Arc e, Node n) 

    {

      if(arcs[e.id].next_out != -1)

	arcs[arcs[e.id].next_out].prev_out = arcs[e.id].prev_out;

      if(arcs[e.id].prev_out != -1)

	arcs[arcs[e.id].prev_out].next_out = arcs[e.id].next_out;

      else nodes[arcs[e.id].source].first_out = arcs[e.id].next_out;

      if (nodes[n.id].first_out != -1) {

	arcs[nodes[n.id].first_out].prev_out = e.id;

      }

      arcs[e.id].source = n.id;

      arcs[e.id].prev_out = -1;

      arcs[e.id].next_out = nodes[n.id].first_out;

      nodes[n.id].first_out = e.id;

    }

  };

  typedef DigraphExtender<ListDigraphBase> ExtendedListDigraphBase;

  /// @{

  ///

  ///It conforms to the \ref concepts::Digraph "Digraph concept" and it

  ///

  ///An important extra feature of this digraph implementation is that

  ///its maps are real \ref concepts::ReferenceMap "reference map"s.

  ///

  class ListDigraph : public ExtendedListDigraphBase {

  private:

    ///

    ListDigraph(const ListDigraph &) :ExtendedListDigraphBase() {};

    ///\brief Assignment of ListDigraph to another one is \e not allowed.

    ///Assignment of ListDigraph to another one is \e not allowed.

    void operator=(const ListDigraph &) {}

  public:

    typedef ExtendedListDigraphBase Parent;

    /// Constructor

    /// Constructor.

    ///

    ListDigraph() {}

    ///Add a new node to the digraph.

    /// \return the new node.

    Node addNode() { return Parent::addNode(); }

    ///Add a new arc to the digraph.

    ///Add a new arc to the digraph with source node \c s

    ///and target node \c t.

    ///\return the new arc.

    Arc addArc(const Node& s, const Node& t) { 

      return Parent::addArc(s, t); 

    }

    ///

    ///\note The <tt>ArcIt</tt>s and <tt>OutArcIt</tt>s referencing

    ///the changed arc remain valid. However <tt>InArcIt</tt>s are

    ///invalidated.

    ///\warning This functionality cannot be used together with the Snapshot

    ///feature.

    void changeTarget(Arc e, Node n) { 

      Parent::changeTarget(e,n); 

    }

    ///

    ///\note The <tt>ArcIt</tt>s and <tt>InArcIt</tt>s referencing

    ///the changed arc remain valid. However <tt>OutArcIt</tt>s are

    ///invalidated.

    ///\warning This functionality cannot be used together with the Snapshot

    ///feature.

    void changeSource(Arc e, Node n) { 

      Parent::changeSource(e,n);

    }

    /// Invert the direction of an arc.

    ///\note The <tt>ArcIt</tt>s referencing the changed arc remain

    ///valid. However <tt>OutArcIt</tt>s and <tt>InArcIt</tt>s are

    ///invalidated.

    ///\warning This functionality cannot be used together with the Snapshot

    ///feature.

    void reverseArc(Arc e) {

      Node t=target(e);

      changeTarget(e,source(e));

      changeSource(e,t);

    }

    /// allocation: if you know that the digraph you want to build will

    /// be very large (e.g. it will contain millions of nodes and/or arcs)

    /// then it is worth reserving space for this amount before starting

    /// to build the digraph.

    /// \sa reserveArc

    void reserveNode(int n) { nodes.reserve(n); };

    /// allocation: if you know that the digraph you want to build will

    /// be very large (e.g. it will contain millions of nodes and/or arcs)

    /// then it is worth reserving space for this amount before starting

    /// to build the digraph.

    /// \sa reserveNode

    void reserveArc(int m) { arcs.reserve(m); };

    ///Contract two nodes.

    ///This function contracts two nodes.

    ///Node \p b will be removed but instead of deleting

    ///incident arcs, they will be joined to \p a.

    ///The last parameter \p r controls whether to remove loops. \c true

    ///means that loops will be removed.

    ///

    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s

    ///may be invalidated.

    ///\warning This functionality cannot be used together with the Snapshot

    ///feature.

    void contract(Node a, Node b, bool r = true) 

    {

      for(OutArcIt e(*this,b);e!=INVALID;) {

	OutArcIt f=e;

	++f;

	if(r && target(e)==a) erase(e);

	else changeSource(e,a);

	e=f;

      }

      for(InArcIt e(*this,b);e!=INVALID;) {

	InArcIt f=e;

	++f;

	if(r && source(e)==a) erase(e);

	else changeTarget(e,a);

	e=f;

      }

      erase(b);

    }

    ///Split a node.

    ///This function splits a node. First a new node is added to the digraph,

    ///then the source of each outgoing arc of \c n is moved to this new node.

    ///If \c connect is \c true (this is the default value), then a new arc

    ///from \c n to the newly created node is also added.

    ///\return The newly created node.

    ///

    ///\note The <tt>ArcIt</tt>s referencing a moved arc remain

    ///valid. However <tt>InArcIt</tt>s and <tt>OutArcIt</tt>s may

    ///be invalidated.  

    ///

    ///\warning This functionality cannot be used together with the

    Node split(Node n, bool connect = true) {

      Node b = addNode();

      for(OutArcIt e(*this,n);e!=INVALID;) {

 	OutArcIt f=e;

	++f;

	changeSource(e,b);

	e=f;

      }

      if (connect) addArc(n,b);

      return b;

    }

    ///Split an arc.

    ///This function splits an arc. First a new node \c b is added to

    ///the digraph, then the original arc is re-targeted to \c

    ///b. Finally an arc from \c b to the original target is added.

    ///\return The newly created node.  

    Node split(Arc e) {

      Node b = addNode();

      addArc(b,target(e));

      changeTarget(e,b);

      return b;

    }

    /// \brief Class to make a snapshot of the digraph and restore

    ///

    ///

    /// The newly added nodes and arcs can be removed using the

    /// restore() function.

    ///

    class Snapshot {

    protected:

      typedef Parent::NodeNotifier NodeNotifier;

      class NodeObserverProxy : public NodeNotifier::ObserverBase {

      public:

        NodeObserverProxy(Snapshot& _snapshot)

          : snapshot(_snapshot) {}

        using NodeNotifier::ObserverBase::attach;

        using NodeNotifier::ObserverBase::detach;

        using NodeNotifier::ObserverBase::attached;

      protected:

        virtual void add(const Node& node) {

          snapshot.addNode(node);

        }

        virtual void add(const std::vector<Node>& nodes) {

          for (int i = nodes.size() - 1; i >= 0; ++i) {

            snapshot.addNode(nodes[i]);

          }

        }

        virtual void erase(const Node& node) {

          snapshot.eraseNode(node);

        }

        virtual void erase(const std::vector<Node>& nodes) {

          for (int i = 0; i < int(nodes.size()); ++i) {

            snapshot.eraseNode(nodes[i]);

          }

        }

        virtual void build() {

          Node node;

          std::vector<Node> nodes;

          for (notifier()->first(node); node != INVALID; 

               notifier()->next(node)) {

            nodes.push_back(node);

          }

          for (int i = nodes.size() - 1; i >= 0; --i) {

            snapshot.addNode(nodes[i]);

          }

        }

        virtual void clear() {

          Node node;

          for (notifier()->first(node); node != INVALID; 

               notifier()->next(node)) {

            snapshot.eraseNode(node);

          }

        }

        Snapshot& snapshot;

      };

      class ArcObserverProxy : public ArcNotifier::ObserverBase {

      public:

        ArcObserverProxy(Snapshot& _snapshot)

          : snapshot(_snapshot) {}

        using ArcNotifier::ObserverBase::attach;

        using ArcNotifier::ObserverBase::detach;

        using ArcNotifier::ObserverBase::attached;

      protected:

        virtual void add(const Arc& arc) {

          snapshot.addArc(arc);

        }

        virtual void add(const std::vector<Arc>& arcs) {

          for (int i = arcs.size() - 1; i >= 0; ++i) {

            snapshot.addArc(arcs[i]);

          }

        }

        virtual void erase(const Arc& arc) {

          snapshot.eraseArc(arc);

        }

        virtual void erase(const std::vector<Arc>& arcs) {

          for (int i = 0; i < int(arcs.size()); ++i) {

            snapshot.eraseArc(arcs[i]);

          }

        }

        virtual void build() {

          Arc arc;

          std::vector<Arc> arcs;

          for (notifier()->first(arc); arc != INVALID; 

               notifier()->next(arc)) {

            arcs.push_back(arc);

          }

          for (int i = arcs.size() - 1; i >= 0; --i) {

            snapshot.addArc(arcs[i]);

          }

        }

        virtual void clear() {

          Arc arc;

          for (notifier()->first(arc); arc != INVALID; 

               notifier()->next(arc)) {

            snapshot.eraseArc(arc);

          }

        }

        Snapshot& snapshot;

      };

      ListDigraph *digraph;

      NodeObserverProxy node_observer_proxy;

      ArcObserverProxy arc_observer_proxy;

      std::list<Node> added_nodes;

      std::list<Arc> added_arcs;

      void addNode(const Node& node) {

        added_nodes.push_front(node);        

      }

      void eraseNode(const Node& node) {

        std::list<Node>::iterator it = 

          std::find(added_nodes.begin(), added_nodes.end(), node);

        if (it == added_nodes.end()) {

          clear();

          arc_observer_proxy.detach();

          throw NodeNotifier::ImmediateDetach();

        } else {

          added_nodes.erase(it);

        }

      }

      void addArc(const Arc& arc) {

        added_arcs.push_front(arc);        

      }

      void eraseArc(const Arc& arc) {

        std::list<Arc>::iterator it = 

          std::find(added_arcs.begin(), added_arcs.end(), arc);

        if (it == added_arcs.end()) {

          clear();

          node_observer_proxy.detach(); 

          throw ArcNotifier::ImmediateDetach();

        } else {

          added_arcs.erase(it);

        }        

      }

      void attach(ListDigraph &_digraph) {

	digraph = &_digraph;

	node_observer_proxy.attach(digraph->notifier(Node()));

        arc_observer_proxy.attach(digraph->notifier(Arc()));

      }

      void detach() {

	node_observer_proxy.detach();

	arc_observer_proxy.detach();

      }

      bool attached() const {

        return node_observer_proxy.attached();

      }

      void clear() {

        added_nodes.clear();

        added_arcs.clear();        

      }

    public:

      /// \brief Default constructor.

      ///

      /// Default constructor.

      /// To actually make a snapshot you must call save().

      Snapshot() 

        : digraph(0), node_observer_proxy(*this), 

          arc_observer_proxy(*this) {}

      /// \brief Constructor that immediately makes a snapshot.

      ///      

      /// This constructor immediately makes a snapshot of the digraph.

      /// \param _digraph The digraph we make a snapshot of.

      Snapshot(ListDigraph &_digraph) 

        : node_observer_proxy(*this), 

          arc_observer_proxy(*this) {

	attach(_digraph);

      }

      /// \brief Make a snapshot.

      ///

      /// Make a snapshot of the digraph.

      ///

      /// This function can be called more than once. In case of a repeated

      /// call, the previous snapshot gets lost.

      /// \param _digraph The digraph we make the snapshot of.

      void save(ListDigraph &_digraph) {

        if (attached()) {

          detach();

          clear();

        }

        attach(_digraph);

      }

      /// \brief Undo the changes until the last snapshot.

      // 

      /// Undo the changes until the last snapshot created by save().

      void restore() {

	detach();

	for(std::list<Arc>::iterator it = added_arcs.begin(); 

            it != added_arcs.end(); ++it) {

	  digraph->erase(*it);

	}

	for(std::list<Node>::iterator it = added_nodes.begin(); 

            it != added_nodes.end(); ++it) {

	  digraph->erase(*it);

	}

        clear();

      }

      /// \brief Gives back true when the snapshot is valid.

      ///

      /// Gives back true when the snapshot is valid.

      bool valid() const {

        return attached();

      }

    };

  };

  ///@}

  class ListGraphBase {

  protected:

    struct NodeT {

      int first_out;

      int prev, next;

    };

    struct ArcT {

      int target;

      int prev_out, next_out;

    };

    std::vector<NodeT> nodes;

    int first_node;

    int first_free_node;

    std::vector<ArcT> arcs;

    int first_free_arc;

  public:

    typedef ListGraphBase Digraph;

    class Node;

    class Arc;

    class Edge;

    class Node {

      friend class ListGraphBase;

    protected:

      int id;

      explicit Node(int pid) { id = pid;}

    public:

      Node() {}

      Node (Invalid) { id = -1; }

      bool operator==(const Node& node) const {return id == node.id;}

      bool operator!=(const Node& node) const {return id != node.id;}

      bool operator<(const Node& node) const {return id < node.id;}

    };

    class Edge {

      friend class ListGraphBase;

    protected:

      int id;

      explicit Edge(int pid) { id = pid;}

    public:

      Edge() {}

      Edge (Invalid) { id = -1; }

    };

    class Arc {

      friend class ListGraphBase;

    protected:

      int id;

      explicit Arc(int pid) { id = pid;}

    public:

      operator Edge() const { return edgeFromId(id / 2); }

      Arc() {}

      Arc (Invalid) { id = -1; }

      bool operator==(const Arc& arc) const {return id == arc.id;}

      bool operator!=(const Arc& arc) const {return id != arc.id;}

      bool operator<(const Arc& arc) const {return id < arc.id;}

    };

    ListGraphBase()

      : nodes(), first_node(-1),

	first_free_node(-1), arcs(), first_free_arc(-1) {}

    int maxNodeId() const { return nodes.size()-1; } 

    int maxEdgeId() const { return arcs.size() / 2 - 1; }

    int maxArcId() const { return arcs.size()-1; }

    Node source(Arc e) const { return Node(arcs[e.id ^ 1].target); }

    Node target(Arc e) const { return Node(arcs[e.id].target); }

    Node u(Edge e) const { return Node(arcs[2 * e.id].target); }

    Node v(Edge e) const { return Node(arcs[2 * e.id + 1].target); }

    static bool direction(Arc e) {

      return (e.id & 1) == 1;

    }

    static Arc direct(Edge e, bool d) {

      return Arc(e.id * 2 + (d ? 1 : 0));

    }

    void first(Node& node) const { 

      node.id = first_node;

    }

    void next(Node& node) const {

      node.id = nodes[node.id].next;

    }

    void first(Arc& e) const { 

      int n = first_node;

      while (n != -1 && nodes[n].first_out == -1) {

        n = nodes[n].next;

      }

      e.id = (n == -1) ? -1 : nodes[n].first_out;

    }

    void next(Arc& e) const {

      if (arcs[e.id].next_out != -1) {

	e.id = arcs[e.id].next_out;

      } else {

	int n = nodes[arcs[e.id ^ 1].target].next;

        while(n != -1 && nodes[n].first_out == -1) {

          n = nodes[n].next;