/* -*- C++ -*-

  * src/lemon/graph_utils.h - Part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2005 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_GRAPH_UTILS_H

 #define LEMON_GRAPH_UTILS_H

 #include <iterator>

 #include <vector>

 #include <map>

 #include <lemon/invalid.h>

 #include <lemon/utility.h>

 #include <lemon/maps.h>

 ///\ingroup gutils

 ///\file

 ///\brief Graph utilities.

 ///

 ///\todo Please

 ///revise the documentation.

 ///

 namespace lemon {

   /// \addtogroup gutils

   /// @{

   /// \brief Function to count the items in the graph.

   ///

   /// This function counts the items in the graph.

   /// The complexity of the function is O(n) because

   /// it iterates on all of the items.

   template <typename Graph, typename ItemIt>

   inline int countItems(const Graph& g) {

     int num = 0;

     for (ItemIt it(g); it != INVALID; ++it) {

       ++num;

     }

     return num;

   }

   // Node counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::NodeNumTag, int>::type

   _countNodes(const Graph &g) {

     return g.nodeNum();

   }

   template <typename Graph>

   inline int _countNodes(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::NodeIt>(w.value);

   }

   /// \brief Function to count the nodes in the graph.

   ///

   /// This function counts the nodes in the graph.

   /// The complexity of the function is O(n) but for some

   /// graph structure it is specialized to run in O(1).

   ///

   /// \todo refer how to specialize it

   template <typename Graph>

   inline int countNodes(const Graph& g) {

     return _countNodes<Graph>(g);

   }

   // Edge counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::EdgeNumTag, int>::type

   _countEdges(const Graph &g) {

     return g.edgeNum();

   }

   template <typename Graph>

   inline int _countEdges(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::EdgeIt>(w.value);

   }

   /// \brief Function to count the edges in the graph.

   ///

   /// This function counts the edges in the graph.

   /// The complexity of the function is O(e) but for some

   /// graph structure it is specialized to run in O(1).

   template <typename Graph>

   inline int countEdges(const Graph& g) {

     return _countEdges<Graph>(g);

   }

   // Undirected edge counting:

   template <typename Graph>

   inline

   typename enable_if<typename Graph::EdgeNumTag, int>::type

   _countUndirEdges(const Graph &g) {

     return g.undirEdgeNum();

   }

   template <typename Graph>

   inline int _countUndirEdges(Wrap<Graph> w) {

     return countItems<Graph, typename Graph::UndirEdgeIt>(w.value);

   }

   /// \brief Function to count the edges in the graph.

   ///

   /// This function counts the edges in the graph.

   /// The complexity of the function is O(e) but for some

   /// graph structure it is specialized to run in O(1).

   template <typename Graph>

   inline int countUndirEdges(const Graph& g) {

     return _countUndirEdges<Graph>(g);

   }

   template <typename Graph, typename DegIt>

   inline int countNodeDegree(const Graph& _g, const typename Graph::Node& _n) {

     int num = 0;

     for (DegIt it(_g, _n); it != INVALID; ++it) {

       ++num;

     }

     return num;

   }

   /// Finds an edge between two nodes of a graph.

   /// Finds an edge from node \c u to node \c v in graph \c g.

   ///

   /// If \c prev is \ref INVALID (this is the default value), then

   /// it finds the first edge from \c u to \c v. Otherwise it looks for

   /// the next edge from \c u to \c v after \c prev.

   /// \return The found edge or \ref INVALID if there is no such an edge.

   ///

   /// Thus you can iterate through each edge from \c u to \c v as it follows.

   /// \code

   /// for(Edge e=findEdge(g,u,v);e!=INVALID;e=findEdge(g,u,v,e)) {

   ///   ...

   /// }

   /// \endcode

   /// \todo We may want to use the \ref concept::GraphBase "GraphBase"

   /// interface here...

   /// \bug Untested ...

   template <typename Graph>

   typename Graph::Edge findEdge(const Graph &g,

 				typename Graph::Node u, typename Graph::Node v,

 				typename Graph::Edge prev = INVALID) 

   {

     typename Graph::OutEdgeIt e(g,prev);

     //    if(prev==INVALID) g.first(e,u);

     if(prev==INVALID) e=typename Graph::OutEdgeIt(g,u);

     else ++e;

     while(e!=INVALID && g.target(e)!=v) ++e;

     return e;

   }

   ///\e

   ///\todo Please document.

   ///

   template <typename Graph>

   inline int countOutEdges(const Graph& _g,  const typename Graph::Node& _n) {

     return countNodeDegree<Graph, typename Graph::OutEdgeIt>(_g, _n);

   }

   ///\e

   ///\todo Please document.

   ///

   template <typename Graph>

   inline int countInEdges(const Graph& _g,  const typename Graph::Node& _n) {

     return countNodeDegree<Graph, typename Graph::InEdgeIt>(_g, _n);

   }

   // graph copy

   template <

     typename DestinationGraph, 

     typename SourceGraph, 

     typename NodeBijection>

   void copyNodes(DestinationGraph& _d, const SourceGraph& _s, 

 		 NodeBijection& _nb) {    

     for (typename SourceGraph::NodeIt it(_s); it != INVALID; ++it) {

       _nb[it] = _d.addNode();

     }

   }

   template <

     typename DestinationGraph, 

     typename SourceGraph, 

     typename NodeBijection,

     typename EdgeBijection>

   void copyEdges(DestinationGraph& _d, const SourceGraph& _s,

 		 const NodeBijection& _nb, EdgeBijection& _eb) {    

     for (typename SourceGraph::EdgeIt it(_s); it != INVALID; ++it) {

       _eb[it] = _d.addEdge(_nb[_s.source(it)], _nb[_s.target(it)]);

     }

   }

   template <

     typename DestinationGraph, 

     typename SourceGraph, 

     typename NodeBijection,

     typename EdgeBijection>

   void copyGraph(DestinationGraph& _d, const SourceGraph& _s, 

 		 NodeBijection& _nb, EdgeBijection& _eb) {

     nodeCopy(_d, _s, _nb);

     edgeCopy(_d, _s, _nb, _eb);

   }

   template <

     typename _DestinationGraph, 

     typename _SourceGraph, 

     typename _NodeBijection 

     =typename _SourceGraph::template NodeMap<typename _DestinationGraph::Node>,

     typename _EdgeBijection 

     = typename _SourceGraph::template EdgeMap<typename _DestinationGraph::Edge>

   >

   class GraphCopy {

   public:

     typedef _DestinationGraph DestinationGraph;

     typedef _SourceGraph SourceGraph;

     typedef _NodeBijection NodeBijection;

     typedef _EdgeBijection EdgeBijection;

   protected:          

     NodeBijection node_bijection;

     EdgeBijection edge_bijection;     

   public:

     GraphCopy(DestinationGraph& _d, const SourceGraph& _s) {

       copyGraph(_d, _s, node_bijection, edge_bijection);

     }

     const NodeBijection& getNodeBijection() const {

       return node_bijection;

     }

     const EdgeBijection& getEdgeBijection() const {

       return edge_bijection;

     }

   };

   template <typename _Graph, typename _Item>

   class ItemSetTraits {};

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::Node> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Node Item;

     typedef typename Graph::NodeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template NodeMap<_Value> {

     public:

       typedef typename Graph::template NodeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::Edge> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::Edge Item;

     typedef typename Graph::EdgeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template EdgeMap<_Value> {

     public:

       typedef typename Graph::template EdgeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   template <typename _Graph>

   class ItemSetTraits<_Graph, typename _Graph::UndirEdge> {

   public:

     typedef _Graph Graph;

     typedef typename Graph::UndirEdge Item;

     typedef typename Graph::UndirEdgeIt ItemIt;

     template <typename _Value>

     class Map : public Graph::template UndirEdgeMap<_Value> {

     public:

       typedef typename Graph::template UndirEdgeMap<_Value> Parent; 

       typedef typename Parent::Value Value;

       Map(const Graph& _graph) : Parent(_graph) {}

       Map(const Graph& _graph, const Value& _value) 

 	: Parent(_graph, _value) {}

     };

   };

   /// @}

   /// \addtogroup graph_maps

   /// @{

   template <typename Map, typename Enable = void>

   struct ReferenceMapTraits {

     typedef typename Map::Value Value;

     typedef typename Map::Value& Reference;

     typedef const typename Map::Value& ConstReference;

     typedef typename Map::Value* Pointer;

     typedef const typename Map::Value* ConstPointer;

   };

   template <typename Map>

   struct ReferenceMapTraits<

     Map, 

     typename enable_if<typename Map::FullTypeTag, void>::type

   > {

     typedef typename Map::Value Value;

     typedef typename Map::Reference Reference;

     typedef typename Map::ConstReference ConstReference;

     typedef typename Map::Pointer Pointer;

     typedef typename Map::ConstPointer ConstPointer;

   };

   /// Provides an immutable and unique id for each item in the graph.

   /// The IdMap class provides an unique and immutable mapping for each item

   /// in the graph.

   ///

   template <typename _Graph, typename _Item>

   class IdMap {

   public:

     typedef _Graph Graph;

     typedef int Value;

     typedef _Item Item;

     typedef _Item Key;

     typedef True NeedCopy;

     /// \brief Constructor.

     ///

     /// Constructor for creating id map.

     IdMap(const Graph& _graph) : graph(&_graph) {}

     /// \brief Gives back the \e id of the item.

     ///

     /// Gives back the immutable and unique \e id of the map.

     int operator[](const Item& item) const { return graph->id(item);}

   private:

     const Graph* graph;

   public:

     /// \brief The class represents the inverse of the map.

     ///

     /// The class represents the inverse of the map.

     /// \see inverse()

     class InverseMap {

     public:

       typedef True NeedCopy;

       /// \brief Constructor.

       ///

       /// Constructor for creating an id-to-item map.

       InverseMap(const Graph& _graph) : graph(&_graph) {}

       /// \brief Constructor.

       ///

       /// Constructor for creating an id-to-item map.

       InverseMap(const IdMap& idMap) : graph(idMap.graph) {}

       /// \brief Gives back the given item from its id.

       ///

       /// Gives back the given item from its id.

       /// 

       Item operator[](int id) const { return graph->fromId(id, Item());}

     private:

       const Graph* graph;

     };

     /// \brief Gives back the inverse of the map.

     ///

     /// Gives back the inverse of the map.

     InverseMap inverse() const { return InverseMap(*graph);} 

   };

   /// \brief General inversable graph-map type.

   /// This type provides simple inversable map functions. 

   /// The InversableMap wraps an arbitrary ReadWriteMap 

   /// and if a key is setted to a new value then store it

   /// in the inverse map.

   /// \param _Graph The graph type.

   /// \param _Map The map to extend with inversable functionality. 

   template <

     typename _Graph,

     typename _Item, 

     typename _Value,

     typename _Map 

     = typename ItemSetTraits<_Graph, _Item>::template Map<_Value>::Parent 

   >

   class InvertableMap : protected _Map {

   public:

     typedef _Map Map;

     typedef _Graph Graph;

     /// The key type of InvertableMap (Node, Edge, UndirEdge).

     typedef typename _Map::Key Key;

     /// The value type of the InvertableMap.

     typedef typename _Map::Value Value;

     /// \brief Constructor.

     ///

     /// Construct a new InvertableMap for the graph.

     ///

     InvertableMap(const Graph& graph) : Map(graph) {} 

     /// \brief The setter function of the map.

     ///

     /// Sets the mapped value.

     void set(const Key& key, const Value& val) {

       Value oldval = Map::operator[](key);

       typename Container::iterator it = invMap.find(oldval);

       if (it != invMap.end() && it->second == key) {

 	invMap.erase(it);

       }      

       invMap.insert(make_pair(val, key));

       Map::set(key, val);

     }

     /// \brief The getter function of the map.

     ///

     /// It gives back the value associated with the key.

     const Value operator[](const Key& key) const {

       return Map::operator[](key);

     }

     /// \brief Add a new key to the map.

     ///

     /// Add a new key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void add(const Key& key) {

       Map::add(key);

     }

     /// \brief Erase the key from the map.

     ///

     /// Erase the key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void erase(const Key& key) {

       Value val = Map::operator[](key);

       typename Container::iterator it = invMap.find(val);

       if (it != invMap.end() && it->second == key) {

 	invMap.erase(it);

       }

       Map::erase(key);

     }

     /// \brief Clear the keys from the map and inverse map.

     ///

     /// Clear the keys from the map and inverse map. It is called by the

     /// \c AlterationNotifier.

     virtual void clear() {

       invMap.clear();

       Map::clear();

     }

   private:

     typedef std::map<Value, Key> Container;

     Container invMap;    

   public:

     /// \brief The inverse map type.

     ///

     /// The inverse of this map. The subscript operator of the map

     /// gives back always the item what was last assigned to the value. 

     class InverseMap {

     public:

       /// \brief Constructor of the InverseMap.

       ///

       /// Constructor of the InverseMap.

       InverseMap(const InvertableMap& _inverted) : inverted(_inverted) {}

       /// The value type of the InverseMap.

       typedef typename InvertableMap::Key Value;

       /// The key type of the InverseMap.

       typedef typename InvertableMap::Value Key; 

       /// \brief Subscript operator. 

       ///

       /// Subscript operator. It gives back always the item 

       /// what was last assigned to the value.

       Value operator[](const Key& key) const {

 	typename Container::const_iterator it = inverted.invMap.find(key);

 	return it->second;

       }

     private:

       const InvertableMap& inverted;

     };

     /// \brief It gives back the just readeable inverse map.

     ///

     /// It gives back the just readeable inverse map.

     InverseMap inverse() const {

       return InverseMap(*this);

     } 

   };

   /// \brief Provides a mutable, continuous and unique descriptor for each 

   /// item in the graph.

   ///

   /// The DescriptorMap class provides a mutable, continuous and immutable

   /// mapping for each item in the graph. The value for an item may mutated

   /// on each operation when the an item erased or added to graph.

   ///

   /// \param _Graph The graph class the \c DescriptorMap belongs to.

   /// \param _Item The Item is the Key of the Map. It may be Node, Edge or 

   /// UndirEdge.

   /// \param _Map A ReadWriteMap mapping from the item type to integer.

   template <

     typename _Graph,   

     typename _Item,

     typename _Map 

     = typename ItemSetTraits<_Graph, _Item>::template Map<int>::Parent

   >

   class DescriptorMap : protected _Map {

     typedef _Item Item;

     typedef _Map Map;

   public:

     /// The graph class of DescriptorMap.

     typedef _Graph Graph;

     /// The key type of DescriptorMap (Node, Edge, UndirEdge).

     typedef typename _Map::Key Key;

     /// The value type of DescriptorMap.

     typedef typename _Map::Value Value;

     /// \brief Constructor.

     ///

     /// Constructor for descriptor map.

     DescriptorMap(const Graph& _graph) : Map(_graph) {

       build();

     }

     /// \brief Add a new key to the map.

     ///

     /// Add a new key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void add(const Item& item) {

       Map::add(item);

       Map::set(item, invMap.size());

       invMap.push_back(item);

     }

     /// \brief Erase the key from the map.

     ///

     /// Erase the key to the map. It is called by the

     /// \c AlterationNotifier.

     virtual void erase(const Item& item) {

       Map::set(invMap.back(), Map::operator[](item));

       invMap[Map::operator[](item)] = invMap.back();

       invMap.pop_back();

       Map::erase(item);

     }

     /// \brief Build the unique map.

     ///

     /// Build the unique map. It is called by the

     /// \c AlterationNotifier.

     virtual void build() {

       Map::build();

       Item it;

       const typename Map::Graph* graph = Map::getGraph(); 

       for (graph->first(it); it != INVALID; graph->next(it)) {

 	Map::set(it, invMap.size());

 	invMap.push_back(it);	

       }      

     }

     /// \brief Clear the keys from the map.

     ///

     /// Clear the keys from the map. It is called by the

     /// \c AlterationNotifier.

     virtual void clear() {

       invMap.clear();

       Map::clear();

     }

     /// \brief Gives back the \e descriptor of the item.

     ///

     /// Gives back the mutable and unique \e descriptor of the map.

     int operator[](const Item& item) const {

       return Map::operator[](item);

     }

   private:

     typedef std::vector<Item> Container;

     Container invMap;

   public:

     /// \brief The inverse map type.

     ///

     /// The inverse map type.

     class InverseMap {

     public:

       /// \brief Constructor of the InverseMap.

       ///

       /// Constructor of the InverseMap.

       InverseMap(const DescriptorMap& _inverted) 

 	: inverted(_inverted) {}

       /// The value type of the InverseMap.

       typedef typename DescriptorMap::Key Value;

       /// The key type of the InverseMap.

       typedef typename DescriptorMap::Value Key; 

       /// \brief Subscript operator. 

       ///

       /// Subscript operator. It gives back the item 

       /// that the descriptor belongs to currently.

       Value operator[](const Key& key) const {

 	return inverted.invMap[key];

       }

     private:

       const DescriptorMap& inverted;

     };

     /// \brief Gives back the inverse of the map.

     ///

     /// Gives back the inverse of the map.

     const InverseMap inverse() const {

       return InverseMap(*this);

     }

   };

   /// \brief Returns the source of the given edge.

   ///

   /// The SourceMap gives back the source Node of the given edge. 

   /// \author Balazs Dezso

   template <typename Graph>

   class SourceMap {

   public:

     typedef True NeedCopy;

     typedef typename Graph::Node Value;

     typedef typename Graph::Edge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     SourceMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param edge The edge 

     /// \return The source of the edge 

     Value operator[](const Key& edge) {

       return graph.source(edge);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref SourceMap class

   ///

   /// This function just returns an \ref SourceMap class.

   /// \relates SourceMap

   template <typename Graph>

   inline SourceMap<Graph> sourceMap(const Graph& graph) {

     return SourceMap<Graph>(graph);

   } 

   /// \brief Returns the target of the given edge.

   ///

   /// The TargetMap gives back the target Node of the given edge. 

   /// \author Balazs Dezso

   template <typename Graph>

   class TargetMap {

   public:

     typedef True NeedCopy;

     typedef typename Graph::Node Value;

     typedef typename Graph::Edge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     TargetMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param edge The edge 

     /// \return The target of the edge 

     Value operator[](const Key& key) {

       return graph.target(key);

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref TargetMap class

   /// This function just returns an \ref TargetMap class.

   /// \relates TargetMap

   template <typename Graph>

   inline TargetMap<Graph> targetMap(const Graph& graph) {

     return TargetMap<Graph>(graph);

   }

   /// \brief Returns the "forward" directed edge view of undirected edge.

   ///

   /// Returns the "forward" directed edge view of undirected edge.

   /// \author Balazs Dezso

   template <typename Graph>

   class ForwardMap {

   public:

     typedef True NeedCopy;

     typedef typename Graph::Edge Value;

     typedef typename Graph::UndirEdge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     ForwardMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param key An undirected edge 

     /// \return The "forward" directed edge view of undirected edge 

     Value operator[](const Key& key) const {

       return graph.edgeWithSource(key, graph.source(key));

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref ForwardMap class

   /// This function just returns an \ref ForwardMap class.

   /// \relates ForwardMap

   template <typename Graph>

   inline ForwardMap<Graph> forwardMap(const Graph& graph) {

     return ForwardMap<Graph>(graph);

   }

   /// \brief Returns the "backward" directed edge view of undirected edge.

   ///

   /// Returns the "backward" directed edge view of undirected edge.

   /// \author Balazs Dezso

   template <typename Graph>

   class BackwardMap {

   public:

     typedef True NeedCopy;

     typedef typename Graph::Edge Value;

     typedef typename Graph::UndirEdge Key;

     /// \brief Constructor

     ///

     /// Constructor

     /// \param _graph The graph that the map belongs to.

     BackwardMap(const Graph& _graph) : graph(_graph) {}

     /// \brief The subscript operator.

     ///

     /// The subscript operator.

     /// \param key An undirected edge 

     /// \return The "backward" directed edge view of undirected edge 

     Value operator[](const Key& key) const {

       return graph.edgeWithSource(key, graph.target(key));

     }

   private:

     const Graph& graph;

   };

   /// \brief Returns a \ref BackwardMap class

   /// This function just returns an \ref BackwardMap class.

   /// \relates BackwardMap

   template <typename Graph>

   inline BackwardMap<Graph> backwardMap(const Graph& graph) {

     return BackwardMap<Graph>(graph);

   }

   /// @}

 } //END OF NAMESPACE LEMON

 #endif