/* -*- 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 ListGraph, ListUGraph classes.

#include <lemon/bits/base_extender.h>

#include <lemon/bits/graph_extender.h>

#include <lemon/error.h>

#include <vector>

#include <list>

namespace lemon {

  class ListGraphBase {

  protected:

    struct NodeT {

      int first_in, first_out;

      int prev, next;

    };

    struct EdgeT {

      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<EdgeT> edges;

    int first_free_edge;

  public:

    typedef ListGraphBase Graph;

    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; }

      bool operator==(const Edge& edge) const {return id == edge.id;}

      bool operator!=(const Edge& edge) const {return id != edge.id;}

      bool operator<(const Edge& edge) const {return id < edge.id;}

    };

    ListGraphBase()

      : nodes(), first_node(-1),

	first_free_node(-1), edges(), first_free_edge(-1) {}

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

    int maxEdgeId() const { return edges.size()-1; }

    Node source(Edge e) const { return Node(edges[e.id].source); }

    Node target(Edge e) const { return Node(edges[e.id].target); }

    void first(Node& node) const { 

      node.id = first_node;

    }

    void next(Node& node) const {

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

    }

    void first(Edge& e) const { 

      int n;

      for(n = first_node; 

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

	  n = nodes[n].next);

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

    }

    void next(Edge& edge) const {

      if (edges[edge.id].next_in != -1) {

	edge.id = edges[edge.id].next_in;

      } else {

	int n;

	for(n = nodes[edges[edge.id].target].next;

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

	  n = nodes[n].next);

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

      }      

    }

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

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

    }

    void nextOut(Edge &e) const {

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

    }

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

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

    }

    void nextIn(Edge &e) const {

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

    }

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

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

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

    static Edge edgeFromId(int id) { return Edge(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);

    }

    Edge addEdge(Node u, Node v) {

      int n;      

      if (first_free_edge == -1) {

	n = edges.size();

	edges.push_back(EdgeT());

      } else {

	n = first_free_edge;

	first_free_edge = edges[n].next_in;

      }

      edges[n].source = u.id; 

      edges[n].target = v.id;

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

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

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

      }

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

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

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

      }

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

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

      return Edge(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 Edge& edge) {

      int n = edge.id;

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

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

      }

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

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

      } else {

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

      }

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

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

      } 

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

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

      } else {

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

      }

      edges[n].next_in = first_free_edge;

      first_free_edge = n;      

    }

    void clear() {

      edges.clear();

      nodes.clear();

      first_node = first_free_node = first_free_edge = -1;

    }

  protected:

    void changeTarget(Edge e, Node n) 

    {

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

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

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

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

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

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

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

      }

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

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

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

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

    }

    void changeSource(Edge e, Node n) 

    {

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

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

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

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

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

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

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

      }

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

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

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

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

    }

  };

  typedef GraphExtender<ListGraphBase> ExtendedListGraphBase;

  /// \addtogroup graphs

  /// @{

  ///A list graph class.

  ///This is a simple and fast graph implementation.

  ///

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

  ///also provides several additional useful extra functionalities.

  ///The most of the member functions and nested classes are

  ///documented only in the concept class.

  ///

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

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

  ///

  ///\sa concepts::Graph.

  class ListGraph : public ExtendedListGraphBase {

  private:

    ///ListGraph is \e not copy constructible. Use GraphCopy() instead.

    ///ListGraph is \e not copy constructible. Use GraphCopy() instead.

    ///

    ListGraph(const ListGraph &) :ExtendedListGraphBase() {};

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

    ///Use GraphCopy() instead.

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

    ///Use GraphCopy() instead.

    void operator=(const ListGraph &) {}

  public:

    typedef ExtendedListGraphBase Parent;

    /// Constructor

    /// Constructor.

    ///

    ListGraph() {}

    ///Add a new node to the graph.

    /// \return the new node.

    ///

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

    ///Add a new edge to the graph.

    ///Add a new edge to the graph with source node \c s

    ///and target node \c t.

    ///\return the new edge.

    Edge addEdge(const Node& s, const Node& t) { 

      return Parent::addEdge(s, t); 

    }

    /// Changes the target of \c e to \c n

    /// Changes the target of \c e to \c n

    ///

    ///\note The <tt>EdgeIt</tt>s and <tt>OutEdgeIt</tt>s referencing

    ///the changed edge remain valid. However <tt>InEdgeIt</tt>s are

    ///invalidated.

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

    ///feature.

    void changeTarget(Edge e, Node n) { 

      Parent::changeTarget(e,n); 

    }

    /// Changes the source of \c e to \c n

    /// Changes the source of \c e to \c n

    ///

    ///\note The <tt>EdgeIt</tt>s and <tt>InEdgeIt</tt>s referencing

    ///the changed edge remain valid. However <tt>OutEdgeIt</tt>s are

    ///invalidated.

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

    ///feature.

    void changeSource(Edge e, Node n) { 

      Parent::changeSource(e,n);

    }

    /// Invert the direction of an edge.

    ///\note The <tt>EdgeIt</tt>s referencing the changed edge remain

    ///valid. However <tt>OutEdgeIt</tt>s and <tt>InEdgeIt</tt>s are

    ///invalidated.

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

    ///feature.

    void reverseEdge(Edge e) {

      Node t=target(e);

      changeTarget(e,source(e));

      changeSource(e,t);

    }

    /// Using this it is possible to avoid the superfluous memory

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

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

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

    /// to build the graph.

    /// \sa reserveEdge

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

    /// \brief Using this it is possible to avoid the superfluous memory

    /// allocation.

    /// Using this it is possible to avoid the superfluous memory

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

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

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

    /// to build the graph.

    /// \sa reserveNode

    void reserveEdge(int m) { edges.reserve(m); };

    ///Contract two nodes.

    ///This function contracts two nodes.

    ///

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

    ///incident edges, 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.

    ///

    ///\note The <tt>EdgeIt</tt>s

    ///referencing a moved edge remain

    ///valid. However <tt>InEdgeIt</tt>s and <tt>OutEdgeIt</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(OutEdgeIt e(*this,b);e!=INVALID;) {

	OutEdgeIt f=e;

	++f;

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

	else changeSource(e,a);

	e=f;

      }

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

	InEdgeIt 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 graph,

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

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

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

    ///\return The newly created node.

    ///

    ///\note The <tt>EdgeIt</tt>s referencing a moved edge remain

    ///valid. However <tt>InEdgeIt</tt>s and <tt>OutEdgeIt</tt>s may

    ///be invalidated.  

    ///

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

    ///Snapshot feature.  \todo It could be implemented in a bit

    ///faster way.

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

      Node b = addNode();

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

 	OutEdgeIt f=e;

	++f;

	changeSource(e,b);

	e=f;

      }

      if (connect) addEdge(n,b);

      return b;

    }

    ///Split an edge.

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

    ///the graph, then the original edge is re-targeted to \c

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

    ///\return The newly created node.  

    ///\warning This functionality

    ///cannot be used together with the Snapshot feature.

    Node split(Edge e) {

      Node b = addNode();

      addEdge(b,target(e));

      changeTarget(e,b);

      return b;

    }

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

    /// to it later.

    ///

    /// Class to make a snapshot of the graph and to restore it

    /// later.

    ///

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

    /// restore() function.

    ///

    /// \warning Edge and node deletions cannot be restored. This

    /// events invalidate the snapshot. 

    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 EdgeObserverProxy : public EdgeNotifier::ObserverBase {

      public:

        EdgeObserverProxy(Snapshot& _snapshot)

          : snapshot(_snapshot) {}

        using EdgeNotifier::ObserverBase::attach;

        using EdgeNotifier::ObserverBase::detach;

        using EdgeNotifier::ObserverBase::attached;

      protected:

        virtual void add(const Edge& edge) {

          snapshot.addEdge(edge);

        }

        virtual void add(const std::vector<Edge>& edges) {

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

            snapshot.addEdge(edges[i]);

          }

        }

        virtual void erase(const Edge& edge) {

          snapshot.eraseEdge(edge);

        }

        virtual void erase(const std::vector<Edge>& edges) {

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

            snapshot.eraseEdge(edges[i]);

          }

        }

        virtual void build() {

          Edge edge;

          std::vector<Edge> edges;

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

               notifier()->next(edge)) {

            edges.push_back(edge);

          }

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

            snapshot.addEdge(edges[i]);

          }

        }

        virtual void clear() {

          Edge edge;

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

               notifier()->next(edge)) {

            snapshot.eraseEdge(edge);

          }

        }

        Snapshot& snapshot;

      };

      ListGraph *graph;

      NodeObserverProxy node_observer_proxy;

      EdgeObserverProxy edge_observer_proxy;

      std::list<Node> added_nodes;

      std::list<Edge> added_edges;

      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();

          edge_observer_proxy.detach();

          throw NodeNotifier::ImmediateDetach();

        } else {

          added_nodes.erase(it);

        }

      }

      void addEdge(const Edge& edge) {

        added_edges.push_front(edge);        

      }

      void eraseEdge(const Edge& edge) {

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

          std::find(added_edges.begin(), added_edges.end(), edge);

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

          clear();

          node_observer_proxy.detach(); 

          throw EdgeNotifier::ImmediateDetach();

        } else {

          added_edges.erase(it);

        }        

      }

      void attach(ListGraph &_graph) {

	graph = &_graph;

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

        edge_observer_proxy.attach(graph->notifier(Edge()));

      }

      void detach() {

	node_observer_proxy.detach();

	edge_observer_proxy.detach();

      }

      bool attached() const {

        return node_observer_proxy.attached();

      }

      void clear() {

        added_nodes.clear();

        added_edges.clear();        

      }

    public:

      /// \brief Default constructor.

      ///

      /// Default constructor.

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

      Snapshot() 

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

          edge_observer_proxy(*this) {}

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

      ///      

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

      /// \param _graph The graph we make a snapshot of.

      Snapshot(ListGraph &_graph) 

        : node_observer_proxy(*this), 

          edge_observer_proxy(*this) {

	attach(_graph);

      }

      /// \brief Make a snapshot.

      ///

      /// Make a snapshot of the graph.

      ///

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

      /// call, the previous snapshot gets lost.

      /// \param _graph The graph we make the snapshot of.

      void save(ListGraph &_graph) {

        if (attached()) {

          detach();

          clear();

        }

        attach(_graph);

      }

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

      // 

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

      void restore() {

	detach();

	for(std::list<Edge>::iterator it = added_edges.begin(); 

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

	  graph->erase(*it);

	}

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

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

	  graph->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 ListUGraphBase {

  protected:

    struct NodeT {

      int first_out;

      int prev, next;

    };

    struct EdgeT {

      int target;

      int prev_out, next_out;

    };

    std::vector<NodeT> nodes;

    int first_node;

    int first_free_node;

    std::vector<EdgeT> edges;

    int first_free_edge;

  public:

    typedef ListUGraphBase Graph;

    class Node;

    class Edge;

    class UEdge;

    class Node {

      friend class ListUGraphBase;

    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 UEdge {

      friend class ListUGraphBase;

    protected:

      int id;

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

    public:

      UEdge() {}

      UEdge (Invalid) { id = -1; }

      bool operator==(const UEdge& edge) const {return id == edge.id;}

      bool operator!=(const UEdge& edge) const {return id != edge.id;}

      bool operator<(const UEdge& edge) const {return id < edge.id;}

    };

    class Edge {

      friend class ListUGraphBase;

    protected:

      int id;

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

    public:

      operator UEdge() const { return uEdgeFromId(id / 2); }

      Edge() {}

      Edge (Invalid) { id = -1; }

      bool operator==(const Edge& edge) const {return id == edge.id;}

      bool operator!=(const Edge& edge) const {return id != edge.id;}

      bool operator<(const Edge& edge) const {return id < edge.id;}

    };

    ListUGraphBase()

      : nodes(), first_node(-1),

	first_free_node(-1), edges(), first_free_edge(-1) {}

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

    int maxUEdgeId() const { return edges.size() / 2 - 1; }

    int maxEdgeId() const { return edges.size()-1; }

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

    Node target(Edge e) const { return Node(edges[e.id].target); }

    Node source(UEdge e) const { return Node(edges[2 * e.id].target); }

    Node target(UEdge e) const { return Node(edges[2 * e.id + 1].target); }

    static bool direction(Edge e) {

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

    }

    static Edge direct(UEdge e, bool d) {

      return Edge(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(Edge& 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(Edge& e) const {

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

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

      } else {

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

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

          n = nodes[n].next;

        }

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

      }      

    }

    void first(UEdge& e) const { 

      int n = first_node;

      while (n != -1) {

        e.id = nodes[n].first_out;

        while ((e.id & 1) != 1) {

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

        }

        if (e.id != -1) {

          e.id /= 2;

          return;

        } 

        n = nodes[n].next;

      }

      e.id = -1;

    }

    void next(UEdge& e) const {

      int n = edges[e.id * 2].target;

      e.id = edges[(e.id * 2) | 1].next_out;

      while ((e.id & 1) != 1) {

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

      }

      if (e.id != -1) {

        e.id /= 2;

        return;

      } 

      n = nodes[n].next;

      while (n != -1) {

        e.id = nodes[n].first_out;

        while ((e.id & 1) != 1) {

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

        }

        if (e.id != -1) {

          e.id /= 2;

          return;

        } 

        n = nodes[n].next;

      }

      e.id = -1;

    }

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

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

    }

    void nextOut(Edge &e) const {

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

    }

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

      e.id = ((nodes[v.id].first_out) ^ 1);

      if (e.id == -2) e.id = -1;

    }

    void nextIn(Edge &e) const {

      e.id = ((edges[e.id ^ 1].next_out) ^ 1);

      if (e.id == -2) e.id = -1;

    }

    void firstInc(UEdge &e, bool& d, const Node& v) const {

      int de = nodes[v.id].first_out;

      if (de != -1 ) {

        e.id = de / 2;

        d = ((de & 1) == 1);

      } else {

        e.id = -1;

        d = true;

      }

    }

    void nextInc(UEdge &e, bool& d) const {

      int de = (edges[(e.id * 2) | (d ? 1 : 0)].next_out);

      if (de != -1 ) {

        e.id = de / 2;

        d = ((de & 1) == 1);

      } else {

        e.id = -1;

        d = true;

      }

    }

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

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

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

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

    static Edge edgeFromId(int id) { return Edge(id);}

    static UEdge uEdgeFromId(int id) { return UEdge(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_out = -1;

      return Node(n);

    }

    UEdge addEdge(Node u, Node v) {

      int n;      

      if (first_free_edge == -1) {

	n = edges.size();

	edges.push_back(EdgeT());

	edges.push_back(EdgeT());

      } else {

	n = first_free_edge;

	first_free_edge = edges[n].next_out;

      }

      edges[n].target = u.id;

      edges[n | 1].target = v.id;

      edges[n].next_out = nodes[v.id].first_out;

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

	edges[nodes[v.id].first_out].prev_out = n;

      }      

      edges[n].prev_out = -1;

      nodes[v.id].first_out = n;

      edges[n | 1].next_out = nodes[u.id].first_out;

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

	edges[nodes[u.id].first_out].prev_out = (n | 1);

      }

      edges[n | 1].prev_out = -1;      

      nodes[u.id].first_out = (n | 1);

      return UEdge(n / 2);