/* -*- C++ -*-
 * src/lemon/dijkstra.h - Part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2004 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Combinatorial Optimization Research Group, 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_DIJKSTRA_H
#define LEMON_DIJKSTRA_H

///\ingroup flowalgs
///\file
///\brief Dijkstra algorithm.

#include <lemon/list_graph.h>
#include <lemon/bin_heap.h>
#include <lemon/invalid.h>
#include <lemon/error.h>
#include <lemon/maps.h>

namespace lemon {


  class UninitializedData : public LogicError {};


/// \addtogroup flowalgs
/// @{

  ///Default traits class of Dijkstra class.

  ///Default traits class of Dijkstra class.
  ///\param GR Graph type.
  ///\param LM Type of length map.
  template<class GR, class LM>
  struct DijkstraDefaultTraits
  {
    ///The graph type the algorithm runs on. 
    typedef GR Graph;
    ///The type of the map that stores the edge lengths.

    ///The type of the map that stores the edge lengths.
    ///It must meet the \ref concept::ReadMap "ReadMap" concept.
    typedef LM LengthMap;
    //The type of the length of the edges.
    typedef typename LM::Value Value;
    ///The heap type used by Dijkstra algorithm.

    ///The heap type used by Dijkstra algorithm.
    ///
    ///\sa BinHeap
    ///\sa Dijkstra
    typedef BinHeap<typename Graph::Node,
		    typename LM::Value,
		    typename GR::template NodeMap<int>,
		    std::less<Value> > Heap;

    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    /// 
    ///The type of the map that stores the last
    ///edges of the shortest paths.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///
    typedef typename Graph::template NodeMap<typename GR::Edge> PredMap;
    ///Instantiates a PredMap.
 
    ///This function instantiates a \ref PredMap. 
    ///\param G is the graph, to which we would like to define the PredMap.
    ///\todo The graph alone may be insufficient for the initialization
    static PredMap *createPredMap(const GR &G) 
    {
      return new PredMap(G);
    }
    ///\brief The type of the map that stores the last but one
    ///nodes of the shortest paths.
    ///
    ///The type of the map that stores the last but one
    ///nodes of the shortest paths.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///
    typedef typename Graph::template NodeMap<typename GR::Node> PredNodeMap;
    ///Instantiates a PredNodeMap.
 
    ///This function instantiates a \ref PredNodeMap. 
    ///\param G is the graph, to which we would like to define the \ref PredNodeMap
    static PredNodeMap *createPredNodeMap(const GR &G)
    {
      return new PredNodeMap(G);
    }

    ///The type of the map that stores whether a nodes is reached.
 
    ///The type of the map that stores whether a nodes is reached.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///By default it is a NullMap.
    ///\todo If it is set to a real map, Dijkstra::reached() should read this.
    ///\todo named parameter to set this type, function to read and write.
    typedef NullMap<typename Graph::Node,bool> ReachedMap;
    ///Instantiates a ReachedMap.
 
    ///This function instantiates a \ref ReachedMap. 
    ///\param G is the graph, to which we would like to define the \ref ReachedMap
    static ReachedMap *createReachedMap(const GR &G)
    {
      return new ReachedMap();
    }
    ///The type of the map that stores the dists of the nodes.
 
    ///The type of the map that stores the dists of the nodes.
    ///It must meet the \ref concept::WriteMap "WriteMap" concept.
    ///
    typedef typename Graph::template NodeMap<typename LM::Value> DistMap;
    ///Instantiates a DistMap.
 
    ///This function instantiates a \ref DistMap. 
    ///\param G is the graph, to which we would like to define the \ref DistMap
    static DistMap *createDistMap(const GR &G)
    {
      return new DistMap(G);
    }
  };
  
  ///%Dijkstra algorithm class.

  ///This class provides an efficient implementation of %Dijkstra algorithm.
  ///The edge lengths are passed to the algorithm using a
  ///\ref concept::ReadMap "ReadMap",
  ///so it is easy to change it to any kind of length.
  ///
  ///The type of the length is determined by the
  ///\ref concept::ReadMap::Value "Value" of the length map.
  ///
  ///It is also possible to change the underlying priority heap.
  ///
  ///\param GR The graph type the algorithm runs on. The default value is
  ///\ref ListGraph. The value of GR is not used directly by Dijkstra, it
  ///is only passed to \ref DijkstraDefaultTraits.
  ///\param LM This read-only
  ///EdgeMap
  ///determines the
  ///lengths of the edges. It is read once for each edge, so the map
  ///may involve in relatively time consuming process to compute the edge
  ///length if it is necessary. The default map type is
  ///\ref concept::StaticGraph::EdgeMap "Graph::EdgeMap<int>".
  ///The value of LM is not used directly by Dijkstra, it
  ///is only passed to \ref DijkstraDefaultTraits.
  ///\param TR Traits class to set various data types used by the algorithm.
  ///The default traits class is
  ///\ref DijkstraDefaultTraits "DijkstraDefaultTraits<GR,LM>".
  ///See \ref DijkstraDefaultTraits for the documentation of
  ///a Dijkstra traits class.
  ///
  ///\author Jacint Szabo and Alpar Juttner
  ///\todo We need a typedef-names should be standardized. (-:

#ifdef DOXYGEN
  template <typename GR,
	    typename LM,
	    typename TR>
#else
  template <typename GR=ListGraph,
	    typename LM=typename GR::template EdgeMap<int>,
	    typename TR=DijkstraDefaultTraits<GR,LM> >
#endif
  class Dijkstra {
  public:
    ///Exception thrown by dijkstra.
    class UninitializedData : public lemon::UninitializedData {};

    typedef TR Traits;
    ///The type of the underlying graph.
    typedef typename TR::Graph Graph;
    ///\e
    typedef typename Graph::Node Node;
    ///\e
    typedef typename Graph::NodeIt NodeIt;
    ///\e
    typedef typename Graph::Edge Edge;
    ///\e
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    
    ///The type of the length of the edges.
    typedef typename TR::LengthMap::Value Value;
    ///The type of the map that stores the edge lengths.
    typedef typename TR::LengthMap LengthMap;
    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    typedef typename TR::PredMap PredMap;
    ///\brief The type of the map that stores the last but one
    ///nodes of the shortest paths.
    typedef typename TR::PredNodeMap PredNodeMap;
    ///The type of the map indicating if a node is reached.
    typedef typename TR::ReachedMap ReachedMap;
    ///The type of the map that stores the dists of the nodes.
    typedef typename TR::DistMap DistMap;
    ///The heap type used by the dijkstra algorithm.
    typedef typename TR::Heap Heap;
  private:
    /// Pointer to the underlying graph.
    const Graph *G;
    /// Pointer to the length map
    const LengthMap *length;
    ///Pointer to the map of predecessors edges.
    PredMap *_pred;
    ///Indicates if \ref _pred is locally allocated (\c true) or not.
    bool local_pred;
    ///Pointer to the map of predecessors nodes.
    PredNodeMap *pred_node;
    ///Indicates if \ref pred_node is locally allocated (\c true) or not.
    bool local_pred_node;
    ///Pointer to the map of distances.
    DistMap *distance;
    ///Indicates if \ref distance is locally allocated (\c true) or not.
    bool local_distance;
    ///Pointer to the map of reached status of the nodes.
    ReachedMap *_reached;
    ///Indicates if \ref _reached is locally allocated (\c true) or not.
    bool local_reached;

    ///The source node of the last execution.
    Node source;

    ///Initializes the maps.
    
    ///\todo Error if \c G or are \c NULL. What about \c length?
    ///\todo Better memory allocation (instead of new).
    void init_maps() 
    {
      if(!_pred) {
	local_pred = true;
	_pred = Traits::createPredMap(*G);
      }
      if(!pred_node) {
	local_pred_node = true;
	pred_node = Traits::createPredNodeMap(*G);
      }
      if(!distance) {
	local_distance = true;
	distance = Traits::createDistMap(*G);
      }
      if(!_reached) {
	local_reached = true;
	_reached = Traits::createReachedMap(*G);
      }
    }
    
  public :
 
    template <class T>
    struct DefPredMapTraits : public Traits {
      typedef T PredMap;
      ///\todo An exception should be thrown.
      ///
      static PredMap *createPredMap(const Graph &G) 
      {
	throw UninitializedData();
      }
    };
    ///\ref named-templ-param "Named parameter" for setting PredMap type

    ///\ref named-templ-param "Named parameter" for setting PredMap type
    ///
    template <class T>
    class DefPredMap : public Dijkstra< Graph,
					LengthMap,
					DefPredMapTraits<T> > { };
    
    template <class T>
    struct DefPredNodeMapTraits : public Traits {
      typedef T PredNodeMap;
      ///\todo An exception should be thrown.
      ///
      static PredNodeMap *createPredNodeMap(const Graph &G) 
      {
	throw UninitializedData();
      }
    };
    ///\ref named-templ-param "Named parameter" for setting PredNodeMap type

    ///\ref named-templ-param "Named parameter" for setting PredNodeMap type
    ///
    template <class T>
    class DefPredNodeMap : public Dijkstra< Graph,
					    LengthMap,
					    DefPredNodeMapTraits<T> > { };
    
    template <class T>
    struct DefDistMapTraits : public Traits {
      typedef T DistMap;
      ///\todo An exception should be thrown.
      ///
      static DistMap *createDistMap(const Graph &G) 
      {
	throw UninitializedData();
      }
    };
    ///\ref named-templ-param "Named parameter" for setting DistMap type

    ///\ref named-templ-param "Named parameter" for setting DistMap type
    ///
    template <class T>
    class DefDistMap : public Dijkstra< Graph,
					LengthMap,
					DefDistMapTraits<T> > { };
    
    ///Constructor.
    
    ///\param _G the graph the algorithm will run on.
    ///\param _length the length map used by the algorithm.
    Dijkstra(const Graph& _G, const LengthMap& _length) :
      G(&_G), length(&_length),
      _pred(NULL), local_pred(false),
      pred_node(NULL), local_pred_node(false),
      distance(NULL), local_distance(false),
      _reached(NULL), local_reached(false)
    { }
    
    ///Destructor.
    ~Dijkstra() 
    {
      if(local_pred) delete _pred;
      if(local_pred_node) delete pred_node;
      if(local_distance) delete distance;
      if(local_reached) delete _reached;
    }

    ///Sets the length map.

    ///Sets the length map.
    ///\return <tt> (*this) </tt>
    Dijkstra &lengthMap(const LengthMap &m) 
    {
      length = &m;
      return *this;
    }

    ///Sets the map storing the predecessor edges.

    ///Sets the map storing the predecessor edges.
    ///If you don't use this function before calling \ref run(),
    ///it will allocate one. The destuctor deallocates this
    ///automatically allocated map, of course.
    ///\return <tt> (*this) </tt>
    Dijkstra &predMap(PredMap &m) 
    {
      if(local_pred) {
	delete _pred;
	local_pred=false;
      }
      _pred = &m;
      return *this;
    }

    ///Sets the map storing the predecessor nodes.

    ///Sets the map storing the predecessor nodes.
    ///If you don't use this function before calling \ref run(),
    ///it will allocate one. The destuctor deallocates this
    ///automatically allocated map, of course.
    ///\return <tt> (*this) </tt>
    Dijkstra &predNodeMap(PredNodeMap &m) 
    {
      if(local_pred_node) {
	delete pred_node;
	local_pred_node=false;
      }
      pred_node = &m;
      return *this;
    }

    ///Sets the map storing the distances calculated by the algorithm.

    ///Sets the map storing the distances calculated by the algorithm.
    ///If you don't use this function before calling \ref run(),
    ///it will allocate one. The destuctor deallocates this
    ///automatically allocated map, of course.
    ///\return <tt> (*this) </tt>
    Dijkstra &distMap(DistMap &m) 
    {
      if(local_distance) {
	delete distance;
	local_distance=false;
      }
      distance = &m;
      return *this;
    }
    
  ///Runs %Dijkstra algorithm from node \c s.

  ///This method runs the %Dijkstra algorithm from a root node \c s
  ///in order to
  ///compute the
  ///shortest path to each node. The algorithm computes
  ///- The shortest path tree.
  ///- The distance of each node from the root.
  ///\todo heap_map's type could also be in the traits class.
    void run(Node s) {
      
      init_maps();
      
      source = s;
      
      for ( NodeIt u(*G) ; u!=INVALID ; ++u ) {
	_pred->set(u,INVALID);
	pred_node->set(u,INVALID);
	///\todo *_reached is not set to false.
      }
      
      typename Graph::template NodeMap<int> heap_map(*G,-1);
      
      Heap heap(heap_map);
      
      heap.push(s,0); 
      
      while ( !heap.empty() ) {
	
	Node v=heap.top(); 
	_reached->set(v,true);
	Value oldvalue=heap[v];
	heap.pop();
	distance->set(v, oldvalue);
	
	
	for(OutEdgeIt e(*G,v); e!=INVALID; ++e) {
	  Node w=G->target(e); 
	  switch(heap.state(w)) {
	  case Heap::PRE_HEAP:
	    heap.push(w,oldvalue+(*length)[e]); 
	    _pred->set(w,e);
	    pred_node->set(w,v);
	    break;
	  case Heap::IN_HEAP:
	    if ( oldvalue+(*length)[e] < heap[w] ) {
	      heap.decrease(w, oldvalue+(*length)[e]); 
	      _pred->set(w,e);
	      pred_node->set(w,v);
	    }
	    break;
	  case Heap::POST_HEAP:
	    break;
	  }
	}
      }
    }
    
    ///The distance of a node from the root.

    ///Returns the distance of a node from the root.
    ///\pre \ref run() must be called before using this function.
    ///\warning If node \c v in unreachable from the root the return value
    ///of this funcion is undefined.
    Value dist(Node v) const { return (*distance)[v]; }

    ///Returns the 'previous edge' of the shortest path tree.

    ///For a node \c v it returns the 'previous edge' of the shortest path tree,
    ///i.e. it returns the last edge of a shortest path from the root to \c
    ///v. It is \ref INVALID
    ///if \c v is unreachable from the root or if \c v=s. The
    ///shortest path tree used here is equal to the shortest path tree used in
    ///\ref predNode(Node v).  \pre \ref run() must be called before using
    ///this function.
    ///\todo predEdge could be a better name.
    Edge pred(Node v) const { return (*_pred)[v]; }

    ///Returns the 'previous node' of the shortest path tree.

    ///For a node \c v it returns the 'previous node' of the shortest path tree,
    ///i.e. it returns the last but one node from a shortest path from the
    ///root to \c /v. It is INVALID if \c v is unreachable from the root or if
    ///\c v=s. The shortest path tree used here is equal to the shortest path
    ///tree used in \ref pred(Node v).  \pre \ref run() must be called before
    ///using this function.
    Node predNode(Node v) const { return (*pred_node)[v]; }
    
    ///Returns a reference to the NodeMap of distances.

    ///Returns a reference to the NodeMap of distances. \pre \ref run() must
    ///be called before using this function.
    const DistMap &distMap() const { return *distance;}
 
    ///Returns a reference to the shortest path tree map.

    ///Returns a reference to the NodeMap of the edges of the
    ///shortest path tree.
    ///\pre \ref run() must be called before using this function.
    const PredMap &predMap() const { return *_pred;}
 
    ///Returns a reference to the map of nodes of shortest paths.

    ///Returns a reference to the NodeMap of the last but one nodes of the
    ///shortest path tree.
    ///\pre \ref run() must be called before using this function.
    const PredNodeMap &predNodeMap() const { return *pred_node;}

    ///Checks if a node is reachable from the root.

    ///Returns \c true if \c v is reachable from the root.
    ///\note The root node is reported to be reached!
    ///\pre \ref run() must be called before using this function.
    ///
    bool reached(Node v) { return v==source || (*_pred)[v]!=INVALID; }
    
  };

  /// Default traits used by \ref DijkstraWizard

  /// To make it easier to use Dijkstra algorithm we have created a wizard class.
  /// This \ref DijkstraWizard class needs default traits, as well as the \ref Dijkstra class.
  /// The \ref DijkstraWizardBase is a class to be the default traits of the
  /// \ref DijkstraWizard class.
  template<class GR,class LM>
  class DijkstraWizardBase : public DijkstraDefaultTraits<GR,LM>
  {

    typedef DijkstraDefaultTraits<GR,LM> Base;
  protected:
    /// Pointer to the underlying graph.
    void *_g;
    /// Pointer to the length map
    void *_length;
    ///Pointer to the map of predecessors edges.
    void *_pred;
    ///Pointer to the map of predecessors nodes.
    void *_predNode;
    ///Pointer to the map of distances.
    void *_dist;
    ///Pointer to the source node.
    void *_source;

    /// Type of the nodes in the graph.
    typedef typename Base::Graph::Node Node;

    public:
    /// Constructor.
    
    /// This constructor does not require parameters, therefore it initiates
    /// all of the attributes to default values (0, INVALID).
    DijkstraWizardBase() : _g(0), _length(0), _pred(0), _predNode(0),
		       _dist(0), _source(INVALID) {}

    /// Constructor.
    
    /// This constructor requires some parameters, listed in the parameters list.
    /// Others are initiated to 0.
    /// \param g is the initial value of  \ref _g
    /// \param l is the initial value of  \ref _length
    /// \param s is the initial value of  \ref _source
    DijkstraWizardBase(const GR &g,const LM &l, Node s=INVALID) :
      _g((void *)&g), _length((void *)&l), _pred(0), _predNode(0),
		  _dist(0), _source((void *)&s) {}

  };
  
  /// A class to make easier the usage of Dijkstra algorithm

  /// This class is created to make it easier to use Dijkstra algorithm.
  /// It uses the functions and features of the plain \ref Dijkstra,
  /// but it is much more simple to use it.
  ///
  /// Simplicity means that the way to change the types defined
  /// in the traits class is based on functions that returns the new class
  /// and not on templatable built-in classes. When using the plain \ref Dijkstra
  /// the new class with the modified type comes from the original class by using the ::
  /// operator. In the case of \ref DijkstraWizard only a function have to be called and it will
  /// return the needed class.
  ///
  /// It does not have own \ref run method. When its \ref run method is called
  /// it initiates a plain \ref Dijkstra class, and calls the \ref Dijkstra::run
  /// method of it.
  template<class TR>
  class DijkstraWizard : public TR
  {
    typedef TR Base;

    ///The type of the underlying graph.
    typedef typename TR::Graph Graph;
    //\e
    typedef typename Graph::Node Node;
    //\e
    typedef typename Graph::NodeIt NodeIt;
    //\e
    typedef typename Graph::Edge Edge;
    //\e
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    
    ///The type of the map that stores the edge lengths.
    typedef typename TR::LengthMap LengthMap;
    ///The type of the length of the edges.
    typedef typename LengthMap::Value Value;
    ///\brief The type of the map that stores the last
    ///edges of the shortest paths.
    typedef typename TR::PredMap PredMap;
    ///\brief The type of the map that stores the last but one
    ///nodes of the shortest paths.
    typedef typename TR::PredNodeMap PredNodeMap;
    ///The type of the map that stores the dists of the nodes.
    typedef typename TR::DistMap DistMap;

    ///The heap type used by the dijkstra algorithm.
    typedef typename TR::Heap Heap;
public:
    /// Constructor.
    DijkstraWizard() : TR() {}

    /// Constructor that requires parameters.

    /// Constructor that requires parameters.
    /// These parameters will be the default values for the traits class.
    DijkstraWizard(const Graph &g,const LengthMap &l, Node s=INVALID) :
      TR(g,l,s) {}

    ///Copy constructor
    DijkstraWizard(const TR &b) : TR(b) {}

    ~DijkstraWizard() {}

    ///Runs Dijkstra algorithm from a given node.
    
    ///Runs Dijkstra algorithm from a given node.
    ///The node can be given by the \ref source function.
    void run()
    {
      if(_source==0) throw UninitializedData();
      Dijkstra<Graph,LengthMap,TR> Dij(*(Graph*)_g,*(LengthMap*)_length);
      if(_pred) Dij.predMap(*(PredMap*)_pred);
      if(_predNode) Dij.predNodeMap(*(PredNodeMap*)_predNode);
      if(_dist) Dij.distMap(*(DistMap*)_dist);
      Dij.run(*(Node*)_source);
    }

    ///Runs Dijkstra algorithm from the given node.

    ///Runs Dijkstra algorithm from the given node.
    ///\param s is the given source.
    void run(Node s)
    {
      _source=(void *)&s;
      run();
    }

    template<class T>
    struct DefPredMapBase : public Base {
      typedef T PredMap;
      static PredMap *createPredMap(const Graph &G) { return 0; };
      DefPredMapBase(const Base &b) : Base(b) {}
    };
    
    /// \ref named-templ-param "Named parameter" function for setting PredMap type

    /// \ref named-templ-param "Named parameter" function for setting PredMap type
    ///
    template<class T>
    DijkstraWizard<DefPredMapBase<T> > predMap(const T &t) 
    {
      _pred=(void *)&t;
      return DijkstraWizard<DefPredMapBase<T> >(*this);
    }
    

    template<class T>
    struct DefPredNodeMapBase : public Base {
      typedef T PredNodeMap;
      static PredNodeMap *createPredNodeMap(const Graph &G) { return 0; };
      DefPredNodeMapBase(const Base &b) : Base(b) {}
    };
    
    /// \ref named-templ-param "Named parameter" function for setting PredNodeMap type

    /// \ref named-templ-param "Named parameter" function for setting PredNodeMap type
    ///
    template<class T>
    DijkstraWizard<DefPredNodeMapBase<T> > predNodeMap(const T &t) 
    {
      _predNode=(void *)&t;
      return DijkstraWizard<DefPredNodeMapBase<T> >(*this);
    }
   
    template<class T>
    struct DefDistMapBase : public Base {
      typedef T DistMap;
      static DistMap *createDistMap(const Graph &G) { return 0; };
      DefDistMapBase(const Base &b) : Base(b) {}
    };
    
    /// \ref named-templ-param "Named parameter" function for setting DistMap type

    /// \ref named-templ-param "Named parameter" function for setting DistMap type
    ///
    template<class T>
    DijkstraWizard<DefDistMapBase<T> > distMap(const T &t) 
    {
      _dist=(void *)&t;
      return DijkstraWizard<DefDistMapBase<T> >(*this);
    }
    
    /// Sets the source node, from which the Dijkstra algorithm runs.

    /// Sets the source node, from which the Dijkstra algorithm runs.
    /// \param s is the source node.
    DijkstraWizard<TR> &source(Node s) 
    {
      source=(void *)&s;
      return *this;
    }
    
  };
  
  ///\e

  ///\todo Please document...
  ///
  template<class GR, class LM>
  DijkstraWizard<DijkstraWizardBase<GR,LM> >
  dijkstra(const GR &g,const LM &l,typename GR::Node s=INVALID)
  {
    return DijkstraWizard<DijkstraWizardBase<GR,LM> >(g,l,s);
  }

/// @}
  
} //END OF NAMESPACE LEMON

#endif