/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

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

 *

 * Copyright (C) 2003-2013

 * 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_SMART_GRAPH_H

#define LEMON_SMART_GRAPH_H

///\ingroup graphs

///\file

///\brief SmartDigraph and SmartGraph classes.

#include <vector>

#include <lemon/core.h>

#include <lemon/error.h>

#include <lemon/bits/graph_extender.h>

namespace lemon {

  class SmartDigraph;

  class SmartDigraphBase {

  protected:

    struct NodeT

    {

      int first_in, first_out;

      NodeT() {}

    };

    struct ArcT

    {

      int target, source, next_in, next_out;

      ArcT() {}

    };

    std::vector<NodeT> _nodes;

    std::vector<ArcT> _arcs;

  public:

    typedef SmartDigraphBase Digraph;

    class Node;

    class Arc;

  public:

    SmartDigraphBase() : _nodes(), _arcs() { }

    SmartDigraphBase(const SmartDigraphBase &_g)

      : _nodes(_g._nodes), _arcs(_g._arcs) { }

    typedef True NodeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return _nodes.size(); }

    int arcNum() const { return _arcs.size(); }

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

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

    Node addNode() {

      int n = _nodes.size();

      _nodes.push_back(NodeT());

      _nodes[n].first_in = -1;

      _nodes[n].first_out = -1;

      return Node(n);

    }

    Arc addArc(Node u, Node v) {

      int n = _arcs.size();

      _arcs.push_back(ArcT());

      _arcs[n].source = u._id;

      _arcs[n].target = v._id;

      _arcs[n].next_out = _nodes[u._id].first_out;

      _arcs[n].next_in = _nodes[v._id].first_in;

      _nodes[u._id].first_out = _nodes[v._id].first_in = n;

      return Arc(n);

    }

    void clear() {

      _arcs.clear();

      _nodes.clear();

    }

    Node source(Arc a) const { return Node(_arcs[a._id].source); }

    Node target(Arc a) const { return Node(_arcs[a._id].target); }

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

    static int id(Arc a) { return a._id; }

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

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

    bool valid(Node n) const {

      return n._id >= 0 && n._id < static_cast<int>(_nodes.size());

    }

    bool valid(Arc a) const {

      return a._id >= 0 && a._id < static_cast<int>(_arcs.size());

    }

    class Node {

      friend class SmartDigraphBase;

      friend class SmartDigraph;

    protected:

      int _id;

      explicit Node(int id) : _id(id) {}

    public:

      Node() {}

      Node (Invalid) : _id(-1) {}

      bool operator==(const Node i) const {return _id == i._id;}

      bool operator!=(const Node i) const {return _id != i._id;}

      bool operator<(const Node i) const {return _id < i._id;}

    };

    class Arc {

      friend class SmartDigraphBase;

      friend class SmartDigraph;

    protected:

      int _id;

      explicit Arc(int id) : _id(id) {}

    public:

      Arc() { }

      Arc (Invalid) : _id(-1) {}

      bool operator==(const Arc i) const {return _id == i._id;}

      bool operator!=(const Arc i) const {return _id != i._id;}

      bool operator<(const Arc i) const {return _id < i._id;}

    };

    void first(Node& node) const {

      node._id = _nodes.size() - 1;

    }

    static void next(Node& node) {

      --node._id;

    }

    void first(Arc& arc) const {

      arc._id = _arcs.size() - 1;

    }

    static void next(Arc& arc) {

      --arc._id;

    }

    void firstOut(Arc& arc, const Node& node) const {

      arc._id = _nodes[node._id].first_out;

    }

    void nextOut(Arc& arc) const {

      arc._id = _arcs[arc._id].next_out;

    }

    void firstIn(Arc& arc, const Node& node) const {

      arc._id = _nodes[node._id].first_in;

    }

    void nextIn(Arc& arc) const {

      arc._id = _arcs[arc._id].next_in;

    }

  };

  typedef DigraphExtender<SmartDigraphBase> ExtendedSmartDigraphBase;

  ///\ingroup graphs

  ///

  ///\brief A smart directed graph class.

  ///

  ///\ref SmartDigraph is a simple and fast digraph implementation.

  ///It is also quite memory efficient but at the price

  ///that it does not support node and arc deletion

  ///(except for the Snapshot feature).

  ///

  ///This type fully conforms to the \ref concepts::Digraph "Digraph concept"

  ///and it also provides some additional functionalities.

  ///Most of its member functions and nested classes are documented

  ///only in the concept class.

  ///

  ///This class provides constant time counting for nodes and arcs.

  ///

  ///\sa concepts::Digraph

  ///\sa SmartGraph

  class SmartDigraph : public ExtendedSmartDigraphBase {

    typedef ExtendedSmartDigraphBase Parent;

  private:

    /// Digraphs are \e not copy constructible. Use DigraphCopy instead.

    SmartDigraph(const SmartDigraph &) : ExtendedSmartDigraphBase() {};

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

    /// Use DigraphCopy instead.

    void operator=(const SmartDigraph &) {}

  public:

    /// Constructor

    /// Constructor.

    ///

    SmartDigraph() {};

    ///Add a new node to the digraph.

    ///This function adds a new node to the digraph.

    ///\return The new node.

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

    ///Add a new arc to the digraph.

    ///This function adds a new arc to the digraph with source node \c s

    ///and target node \c t.

    ///\return The new arc.

    Arc addArc(Node s, Node t) {

      return Parent::addArc(s, t);

    }

    /// \brief Node validity check

    ///

    /// This function gives back \c true if the given node is valid,

    /// i.e. it is a real node of the digraph.

    ///

    /// \warning A removed node (using Snapshot) could become valid again

    /// if new nodes are added to the digraph.

    bool valid(Node n) const { return Parent::valid(n); }

    /// \brief Arc validity check

    ///

    /// This function gives back \c true if the given arc is valid,

    /// i.e. it is a real arc of the digraph.

    ///

    /// \warning A removed arc (using Snapshot) could become valid again

    /// if new arcs are added to the graph.

    bool valid(Arc a) const { return Parent::valid(a); }

    ///Split a node.

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

    ///to the digraph, then the source of each outgoing arc of node \c n

    ///is moved to this new node.

    ///If the second parameter \c connect is \c true (this is the default

    ///value), then a new arc from node \c n to the newly created node

    ///is also added.

    ///\return The newly created node.

    ///

    ///\note All iterators remain valid.

    ///

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

    ///feature.

    Node split(Node n, bool connect = true)

    {

      Node b = addNode();

      _nodes[b._id].first_out=_nodes[n._id].first_out;

      _nodes[n._id].first_out=-1;

      for(int i=_nodes[b._id].first_out; i!=-1; i=_arcs[i].next_out) {

        _arcs[i].source=b._id;

      }

      if(connect) addArc(n,b);

      return b;

    }

    ///Clear the digraph.

    ///This function erases all nodes and arcs from the digraph.

    ///

    void clear() {

      Parent::clear();

    }

    /// Reserve memory for nodes.

    /// Using this function, it is possible to avoid superfluous memory

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

    /// be 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); };

    /// Reserve memory for arcs.

    /// Using this function, it is possible to avoid superfluous memory

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

    /// be 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); };

  public:

    class Snapshot;

  protected:

    void restoreSnapshot(const Snapshot &s)

    {

      while(s.arc_num<_arcs.size()) {

        Arc arc = arcFromId(_arcs.size()-1);

        Parent::notifier(Arc()).erase(arc);

        _nodes[_arcs.back().source].first_out=_arcs.back().next_out;

        _nodes[_arcs.back().target].first_in=_arcs.back().next_in;

        _arcs.pop_back();

      }

      while(s.node_num<_nodes.size()) {

        Node node = nodeFromId(_nodes.size()-1);

        Parent::notifier(Node()).erase(node);

        _nodes.pop_back();

      }

    }

  public:

    ///Class to make a snapshot of the digraph and to restore it later.

    ///Class to make a snapshot of the digraph and to restore it later.

    ///

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

    ///restore() function. This is the only way for deleting nodes and/or

    ///arcs from a SmartDigraph structure.

    ///

    ///\note After a state is restored, you cannot restore a later state,

    ///i.e. you cannot add the removed nodes and arcs again using

    ///another Snapshot instance.

    ///

    ///\warning Node splitting cannot be restored.

    ///\warning The validity of the snapshot is not stored due to

    ///performance reasons. If you do not use the snapshot correctly,

    ///it can cause broken program, invalid or not restored state of

    ///the digraph or no change.

    class Snapshot

    {

      SmartDigraph *_graph;

    protected:

      friend class SmartDigraph;

      unsigned int node_num;

      unsigned int arc_num;

    public:

      ///Default constructor.

      ///Default constructor.

      ///You have to call save() to actually make a snapshot.

      Snapshot() : _graph(0) {}

      ///Constructor that immediately makes a snapshot

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

      ///

      Snapshot(SmartDigraph &gr) : _graph(&gr) {

        node_num=_graph->_nodes.size();

        arc_num=_graph->_arcs.size();

      }

      ///Make a snapshot.

      ///This function makes a snapshot of the given digraph.

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

      ///call, the previous snapshot gets lost.

      void save(SmartDigraph &gr) {

        _graph=&gr;

        node_num=_graph->_nodes.size();

        arc_num=_graph->_arcs.size();

      }

      ///Undo the changes until a snapshot.

      ///This function undos the changes until the last snapshot

      ///created by save() or Snapshot(SmartDigraph&).

      void restore()

      {

        _graph->restoreSnapshot(*this);

      }

    };

  };

  class SmartGraphBase {

  protected:

    struct NodeT {

      int first_out;

    };

    struct ArcT {

      int target;

      int next_out;

    };

    std::vector<NodeT> _nodes;

    std::vector<ArcT> _arcs;

  public:

    typedef SmartGraphBase Graph;

    class Node;

    class Arc;

    class Edge;

    class Node {

      friend class SmartGraphBase;

    protected:

      int _id;

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

    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 SmartGraphBase;

    protected:

      int _id;

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

    public:

      Edge() {}

      Edge (Invalid) { _id = -1; }

      bool operator==(const Edge& arc) const {return _id == arc._id;}

      bool operator!=(const Edge& arc) const {return _id != arc._id;}

      bool operator<(const Edge& arc) const {return _id < arc._id;}

    };

    class Arc {

      friend class SmartGraphBase;

    protected:

      int _id;

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

    public:

      operator Edge() const {

        return _id != -1 ? edgeFromId(_id / 2) : INVALID;

      }

      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;}

    };

    SmartGraphBase()

      : _nodes(), _arcs() {}

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return _nodes.size(); }

    int edgeNum() const { return _arcs.size() / 2; }

    int arcNum() const { return _arcs.size(); }

    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 = _nodes.size() - 1;

    }

    static void next(Node& node) {

      --node._id;

    }

    void first(Arc& arc) const {

      arc._id = _arcs.size() - 1;

    }

    static void next(Arc& arc) {

      --arc._id;

    }

    void first(Edge& arc) const {

      arc._id = _arcs.size() / 2 - 1;

    }

    static void next(Edge& arc) {

      --arc._id;

    }

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

      arc._id = _nodes[v._id].first_out;

    }

    void nextOut(Arc &arc) const {

      arc._id = _arcs[arc._id].next_out;

    }

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

      arc._id = ((_nodes[v._id].first_out) ^ 1);

      if (arc._id == -2) arc._id = -1;

    }

    void nextIn(Arc &arc) const {

      arc._id = ((_arcs[arc._id ^ 1].next_out) ^ 1);

      if (arc._id == -2) arc._id = -1;

    }

    void firstInc(Edge &arc, bool& d, const Node& v) const {

      int de = _nodes[v._id].first_out;

      if (de != -1) {

        arc._id = de / 2;

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

      } else {

        arc._id = -1;

        d = true;

      }

    }

    void nextInc(Edge &arc, bool& d) const {

      int de = (_arcs[(arc._id * 2) | (d ? 1 : 0)].next_out);

      if (de != -1) {

        arc._id = de / 2;

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

      } else {

        arc._id = -1;

        d = true;

      }

    }

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

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

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

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

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

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

    bool valid(Node n) const {

      return n._id >= 0 && n._id < static_cast<int>(_nodes.size());

    }

    bool valid(Arc a) const {

      return a._id >= 0 && a._id < static_cast<int>(_arcs.size());

    }

    bool valid(Edge e) const {

      return e._id >= 0 && 2 * e._id < static_cast<int>(_arcs.size());

    }

    Node addNode() {

      int n = _nodes.size();

      _nodes.push_back(NodeT());

      _nodes[n].first_out = -1;

      return Node(n);

    }

    Edge addEdge(Node u, Node v) {

      int n = _arcs.size();

      _arcs.push_back(ArcT());

      _arcs.push_back(ArcT());

      _arcs[n].target = u._id;

      _arcs[n | 1].target = v._id;

      _arcs[n].next_out = _nodes[v._id].first_out;

      _nodes[v._id].first_out = n;

      _arcs[n | 1].next_out = _nodes[u._id].first_out;

      _nodes[u._id].first_out = (n | 1);

      return Edge(n / 2);

    }

    void clear() {

      _arcs.clear();

      _nodes.clear();

    }

  };

  typedef GraphExtender<SmartGraphBase> ExtendedSmartGraphBase;

  /// \ingroup graphs

  ///

  /// \brief A smart undirected graph class.

  ///

  /// \ref SmartGraph is a simple and fast graph implementation.

  /// It is also quite memory efficient but at the price

  /// that it does not support node and edge deletion

  /// (except for the Snapshot feature).

  ///

  /// This type fully conforms to the \ref concepts::Graph "Graph concept"

  /// and it also provides some additional functionalities.

  /// Most of its member functions and nested classes are documented

  /// only in the concept class.

  ///

  /// This class provides constant time counting for nodes, edges and arcs.

  ///

  /// \sa concepts::Graph

  /// \sa SmartDigraph

  class SmartGraph : public ExtendedSmartGraphBase {

    typedef ExtendedSmartGraphBase Parent;

  private:

    /// Graphs are \e not copy constructible. Use GraphCopy instead.

    SmartGraph(const SmartGraph &) : ExtendedSmartGraphBase() {};

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

    /// Use GraphCopy instead.

    void operator=(const SmartGraph &) {}

  public:

    /// Constructor

    /// Constructor.

    ///

    SmartGraph() {}

    /// \brief Add a new node to the graph.

    ///

    /// This function adds a new node to the graph.

    /// \return The new node.

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

    /// \brief Add a new edge to the graph.

    ///

    /// This function adds a new edge to the graph between nodes

    /// \c u and \c v with inherent orientation from node \c u to

    /// node \c v.

    /// \return The new edge.

    Edge addEdge(Node u, Node v) {

      return Parent::addEdge(u, v);

    }

    /// \brief Node validity check

    ///

    /// This function gives back \c true if the given node is valid,

    /// i.e. it is a real node of the graph.

    ///

    /// \warning A removed node (using Snapshot) could become valid again

    /// if new nodes are added to the graph.

    bool valid(Node n) const { return Parent::valid(n); }

    /// \brief Edge validity check

    ///

    /// This function gives back \c true if the given edge is valid,

    /// i.e. it is a real edge of the graph.

    ///

    /// \warning A removed edge (using Snapshot) could become valid again

    /// if new edges are added to the graph.

    bool valid(Edge e) const { return Parent::valid(e); }

    /// \brief Arc validity check

    ///

    /// This function gives back \c true if the given arc is valid,

    /// i.e. it is a real arc of the graph.

    ///

    /// \warning A removed arc (using Snapshot) could become valid again

    /// if new edges are added to the graph.

    bool valid(Arc a) const { return Parent::valid(a); }

    ///Clear the graph.

    ///This function erases all nodes and arcs from the graph.

    ///

    void clear() {

      Parent::clear();

    }

    /// Reserve memory for nodes.

    /// Using this function, it is possible to avoid superfluous memory

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

    /// be 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); };

    /// Reserve memory for edges.

    /// Using this function, it is possible to avoid superfluous memory

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

    /// be 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) { _arcs.reserve(2 * m); };

  public:

    class Snapshot;

  protected:

    void saveSnapshot(Snapshot &s)

    {

      s._graph = this;

      s.node_num = _nodes.size();

      s.arc_num = _arcs.size();

    }

    void restoreSnapshot(const Snapshot &s)

    {

      while(s.arc_num<_arcs.size()) {

        int n=_arcs.size()-1;

        Edge arc=edgeFromId(n/2);

        Parent::notifier(Edge()).erase(arc);

        std::vector<Arc> dir;

        dir.push_back(arcFromId(n));

        dir.push_back(arcFromId(n-1));

        Parent::notifier(Arc()).erase(dir);

        _nodes[_arcs[n-1].target].first_out=_arcs[n].next_out;

        _nodes[_arcs[n].target].first_out=_arcs[n-1].next_out;

        _arcs.pop_back();

        _arcs.pop_back();

      }

      while(s.node_num<_nodes.size()) {

        int n=_nodes.size()-1;

        Node node = nodeFromId(n);

        Parent::notifier(Node()).erase(node);

        _nodes.pop_back();

      }

    }

  public:

    ///Class to make a snapshot of the graph and to restore 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. This is the only way for deleting nodes and/or

    ///edges from a SmartGraph structure.

    ///

    ///\note After a state is restored, you cannot restore a later state,

    ///i.e. you cannot add the removed nodes and edges again using

    ///another Snapshot instance.

    ///

    ///\warning The validity of the snapshot is not stored due to

    ///performance reasons. If you do not use the snapshot correctly,

    ///it can cause broken program, invalid or not restored state of

    ///the graph or no change.

    class Snapshot

    {

      SmartGraph *_graph;

    protected:

      friend class SmartGraph;

      unsigned int node_num;

      unsigned int arc_num;

    public:

      ///Default constructor.

      ///Default constructor.

      ///You have to call save() to actually make a snapshot.

      Snapshot() : _graph(0) {}

      ///Constructor that immediately makes a snapshot

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

      ///

      Snapshot(SmartGraph &gr) {

        gr.saveSnapshot(*this);

      }

      ///Make a snapshot.

      ///This function makes a snapshot of the given graph.

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

      ///call, the previous snapshot gets lost.

      void save(SmartGraph &gr)

      {

        gr.saveSnapshot(*this);

      }

      ///Undo the changes until the last snapshot.

      ///This function undos the changes until the last snapshot

      ///created by save() or Snapshot(SmartGraph&).

      void restore()

      {

        _graph->restoreSnapshot(*this);

      }

    };

  };

  class SmartBpGraphBase {

  protected:

    struct NodeT {

      int first_out;

      int partition_next;

      int partition_index;

      bool red;

    };

    struct ArcT {

      int target;

      int next_out;

    };

    std::vector<NodeT> _nodes;

    std::vector<ArcT> _arcs;

    int first_red, first_blue;

    int max_red, max_blue;

  public:

    typedef SmartBpGraphBase Graph;

    class Node;

    class Arc;

    class Edge;

    class Node {

      friend class SmartBpGraphBase;

    protected:

      int _id;

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

    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 RedNode : public Node {

      friend class SmartBpGraphBase;

    protected:

      explicit RedNode(int pid) : Node(pid) {}

    public:

      RedNode() {}

      RedNode(const RedNode& node) : Node(node) {}

      RedNode(Invalid) : Node(INVALID){}

    };

    class BlueNode : public Node {

      friend class SmartBpGraphBase;

    protected:

      explicit BlueNode(int pid) : Node(pid) {}

    public:

      BlueNode() {}

      BlueNode(const BlueNode& node) : Node(node) {}

      BlueNode(Invalid) : Node(INVALID){}

    };

    class Edge {

      friend class SmartBpGraphBase;

    protected:

      int _id;

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

    public:

      Edge() {}

      Edge (Invalid) { _id = -1; }

      bool operator==(const Edge& arc) const {return _id == arc._id;}

      bool operator!=(const Edge& arc) const {return _id != arc._id;}

      bool operator<(const Edge& arc) const {return _id < arc._id;}

    };

    class Arc {

      friend class SmartBpGraphBase;

    protected:

      int _id;

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

    public:

      operator Edge() const {

        return _id != -1 ? edgeFromId(_id / 2) : INVALID;

      }

      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;}

    };

    SmartBpGraphBase()

      : _nodes(), _arcs(), first_red(-1), first_blue(-1),

        max_red(-1), max_blue(-1) {}

    typedef True NodeNumTag;

    typedef True EdgeNumTag;

    typedef True ArcNumTag;

    int nodeNum() const { return _nodes.size(); }

    int redNum() const { return max_red + 1; }

    int blueNum() const { return max_blue + 1; }

    int edgeNum() const { return _arcs.size() / 2; }

    int arcNum() const { return _arcs.size(); }

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

    int maxRedId() const { return max_red; }

    int maxBlueId() const { return max_blue; }

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

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

    bool red(Node n) const { return _nodes[n._id].red; }

    bool blue(Node n) const { return !_nodes[n._id].red; }

    static RedNode asRedNodeUnsafe(Node n) { return RedNode(n._id); }

    static BlueNode asBlueNodeUnsafe(Node n) { return BlueNode(n._id); }

    Node source(Arc a) const { return Node(_arcs[a._id ^ 1].target); }

    Node target(Arc a) const { return Node(_arcs[a._id].target); }

    RedNode redNode(Edge e) const {

      return RedNode(_arcs[2 * e._id].target);

    }

    BlueNode blueNode(Edge e) const {

      return BlueNode(_arcs[2 * e._id + 1].target);

    }

    static bool direction(Arc a) {

      return (a._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 = _nodes.size() - 1;

    }

    static void next(Node& node) {

      --node._id;

    }

    void first(RedNode& node) const {

      node._id = first_red;

    }

    void next(RedNode& node) const {

      node._id = _nodes[node._id].partition_next;

    }

    void first(BlueNode& node) const {

      node._id = first_blue;

    }

    void next(BlueNode& node) const {

      node._id = _nodes[node._id].partition_next;

    }

    void first(Arc& arc) const {

      arc._id = _arcs.size() - 1;

    }

    static void next(Arc& arc) {

      --arc._id;

    }

    void first(Edge& arc) const {