/* -*- 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_SMART_GRAPH_H

 #define LEMON_SMART_GRAPH_H

 ///\ingroup graphs

 ///\file

 ///\brief SmartDigraph and SmartGraph classes.

 #include <vector>

 #include <lemon/bits/invalid.h>

 #include <lemon/bits/base_extender.h>

 #include <lemon/bits/graph_extender.h>

 #include <lemon/bits/utility.h>

 #include <lemon/error.h>

 #include <lemon/bits/graph_extender.h>

 namespace lemon {

   class SmartDigraph;

   ///Base of SmartDigraph

   ///Base of 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 Graph;

     class Node;

     class Arc;

   public:

     SmartDigraphBase() : nodes(), arcs() { }

     SmartDigraphBase(const SmartDigraphBase &_g) 

       : nodes(_g.nodes), arcs(_g.arcs) { }

     typedef True NodeNumTag;

     typedef True EdgeNumTag;

     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.

   ///

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

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

   ///that <b> it does support only limited (only stack-like)

   ///node and arc deletions</b>.

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

   ///an important extra feature that its maps are real \ref

   ///concepts::ReferenceMap "reference map"s.

   ///

   ///\sa concepts::Digraph.

   class SmartDigraph : public ExtendedSmartDigraphBase {

   public:

     typedef ExtendedSmartDigraphBase Parent;

   private:

     ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.

     ///SmartDigraph is \e not copy constructible. Use DigraphCopy() instead.

     ///

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

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

     ///Use DigraphCopy() instead.

     ///Assignment of SmartDigraph 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.

     /// \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); 

     }

     /// \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 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); };

     /// \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 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); };

     /// \brief Node validity check

     ///

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

     /// ie. it is a real node of the graph.  

     ///

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

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

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

     /// \brief Arc validity check

     ///

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

     /// ie. it is a real arc of the graph.  

     ///

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

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

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

     ///Clear the digraph.

     ///Erase all the nodes and arcs from the digraph.

     ///

     void clear() {

       Parent::clear();

     }

     ///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>Arc</tt>s

     ///referencing a moved arc remain

     ///valid. However <tt>InArc</tt>'s and <tt>OutArc</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();

       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].source=b._id;

       if(connect) addArc(n,b);

       return b;

     }

   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 restrore to it later.

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

     ///

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

     ///restore() function.

     ///\note After you restore a state, you cannot restore

     ///a later state, in other word you cannot add again the arcs deleted

     ///by restore() using another one Snapshot instance.

     ///

     ///\warning If you do not use correctly the snapshot that can cause

     ///either broken program, invalid state of the digraph, valid but

     ///not the restored digraph or no change. Because the runtime performance

     ///the validity of the snapshot is not stored.

     class Snapshot 

     {

       SmartDigraph *_graph;

     protected:

       friend class SmartDigraph;

       unsigned int node_num;

       unsigned int arc_num;

     public:

       ///Default constructor.

       ///Default constructor.

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

       ///

       Snapshot() : _graph(0) {}

       ///Constructor that immediately makes a snapshot

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

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

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

 	node_num=_graph->nodes.size();

 	arc_num=_graph->arcs.size();

       }

       ///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 _g The digraph we make the snapshot of.

       void save(SmartDigraph &graph) 

       {

 	_graph=&graph;

 	node_num=_graph->nodes.size();

 	arc_num=_graph->arcs.size();

       }

       ///Undo the changes until a snapshot.

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

       ///

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

       ///a later state, in other word you cannot add again the arcs deleted

       ///by restore().

       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;

     int first_free_arc;

   public:

     typedef SmartGraphBase Digraph;

     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 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;}

     };

     SmartGraphBase()

       : nodes(), arcs() {}

     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;

     }

     void next(Node& node) const {

       --node._id;

     }

     void first(Arc& arc) const { 

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

     }

     void next(Arc& arc) const {

       --arc._id;

     }

     void first(Edge& arc) const { 

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

     }

     void next(Edge& arc) const {

       --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.

   ///

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

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

   /// that <b> it does support only limited (only stack-like)

   /// node and arc deletions</b>.

   /// Except from this it conforms to 

   /// the \ref concepts::Graph "Graph concept".

   ///

   /// It also has an

   /// important extra feature that

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

   ///

   /// \sa concepts::Graph.

   ///

   class SmartGraph : public ExtendedSmartGraphBase {

   private:

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

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

     ///

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

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

     ///Use GraphCopy() instead.

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

     ///Use GraphCopy() instead.

     void operator=(const SmartGraph &) {}

   public:

     typedef ExtendedSmartGraphBase Parent;

     /// Constructor

     /// Constructor.

     ///

     SmartGraph() {}

     ///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 node \c s

     ///and \c t.

     ///\return the new edge.

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

       return Parent::addEdge(s, t); 

     }

     /// \brief Node validity check

     ///

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

     /// ie. it is a real node of the graph.  

     ///

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

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

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

     /// \brief Arc validity check

     ///

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

     /// ie. it is a real arc of the graph.  

     ///

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

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

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

     /// \brief Edge validity check

     ///

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

     /// ie. it is a real edge of the graph.  

     ///

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

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

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

     ///Clear the graph.

     ///Erase all the nodes and edges from the graph.

     ///

     void clear() {

       Parent::clear();

     }

   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].target].first_out=arcs[n].next_out;

 	nodes[arcs[n-1].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 digraph and to restrore to it later.

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

     ///

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

     ///restore() function.

     ///

     ///\note After you restore a state, you cannot restore

     ///a later state, in other word you cannot add again the arcs deleted

     ///by restore() using another one Snapshot instance.

     ///

     ///\warning If you do not use correctly the snapshot that can cause

     ///either broken program, invalid state of the digraph, valid but

     ///not the restored digraph or no change. Because the runtime performance

     ///the validity of the snapshot is not stored.

     class Snapshot 

     {

       SmartGraph *_graph;

     protected:

       friend class SmartGraph;

       unsigned int node_num;

       unsigned int arc_num;

     public:

       ///Default constructor.

       ///Default constructor.

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

       ///

       Snapshot() : _graph(0) {}

       ///Constructor that immediately makes a snapshot

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

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

       Snapshot(SmartGraph &graph) {

         graph.saveSnapshot(*this);

       }

       ///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 g The digraph we make the snapshot of.

       void save(SmartGraph &graph) 

       {

         graph.saveSnapshot(*this);

       }

       ///Undo the changes until a snapshot.

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

       ///

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

       ///a later state, in other word you cannot add again the arcs deleted

       ///by restore().

       void restore()

       {

         _graph->restoreSnapshot(*this);

       }

     };

   };

 } //namespace lemon

 #endif //LEMON_SMART_GRAPH_H