/* -*- C++ -*-

 * lemon/floyd_warshall.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_FLOYD_WARSHALL_H

#define LEMON_FLOYD_WARSHALL_H

///\ingroup flowalgs

/// \file

/// \brief FloydWarshall algorithm.

///

/// \todo getPath() should be implemented! (also for BFS and DFS)

#include <lemon/list_graph.h>

#include <lemon/graph_utils.h>

#include <lemon/invalid.h>

#include <lemon/error.h>

#include <lemon/matrix_maps.h>

#include <lemon/maps.h>

#include <limits>

namespace lemon {

  /// \brief Default OperationTraits for the FloydWarshall algorithm class.

  ///  

  /// It defines all computational operations and constants which are

  /// used in the Floyd-Warshall algorithm. The default implementation

  /// is based on the numeric_limits class. If the numeric type does not

  /// have infinity value then the maximum value is used as extremal

  /// infinity value.

  template <

    typename Value, 

    bool has_infinity = std::numeric_limits<Value>::has_infinity>

  struct FloydWarshallDefaultOperationTraits {

    /// \brief Gives back the zero value of the type.

    static Value zero() {

      return static_cast<Value>(0);

    }

    /// \brief Gives back the positive infinity value of the type.

    static Value infinity() {

      return std::numeric_limits<Value>::infinity();

    }

    /// \brief Gives back the sum of the given two elements.

    static Value plus(const Value& left, const Value& right) {

      return left + right;

    }

    /// \brief Gives back true only if the first value less than the second.

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  template <typename Value>

  struct FloydWarshallDefaultOperationTraits<Value, false> {

    static Value zero() {

      return static_cast<Value>(0);

    }

    static Value infinity() {

      return std::numeric_limits<Value>::max();

    }

    static Value plus(const Value& left, const Value& right) {

      if (left == infinity() || right == infinity()) return infinity();

      return left + right;

    }

    static bool less(const Value& left, const Value& right) {

      return left < right;

    }

  };

  /// \brief Default traits class of FloydWarshall class.

  ///

  /// Default traits class of FloydWarshall class.

  /// \param _Graph Graph type.

  /// \param _LegthMap Type of length map.

  template<class _Graph, class _LengthMap>

  struct FloydWarshallDefaultTraits {

    /// The graph type the algorithm runs on. 

    typedef _Graph Graph;

    /// \brief 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 _LengthMap LengthMap;

    // The type of the length of the edges.

    typedef typename _LengthMap::Value Value;

    /// \brief Operation traits for belmann-ford algorithm.

    ///

    /// It defines the infinity type on the given Value type

    /// and the used operation.

    /// \see FloydWarshallDefaultOperationTraits

    typedef FloydWarshallDefaultOperationTraits<Value> OperationTraits;

    /// \brief The type of the matrix 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 be a matrix map with \c Graph::Edge value type.

    ///

    typedef DynamicMatrixMap<Graph, typename Graph::Node, 

			     typename Graph::Edge> PredMap;

    /// \brief 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 _Graph& graph) {

      return new PredMap(graph);

    }

    /// \brief 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::WriteMatrixMap "WriteMatrixMap" concept.

    ///

    typedef DynamicMatrixMap<Graph, typename Graph::Node, Value> DistMap;

    /// \brief 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 _Graph& graph) {

      return new DistMap(graph);

    }

  };

  /// \brief FloydWarshall algorithm class.

  ///

  /// \ingroup flowalgs

  /// This class provides an efficient implementation of \c FloydWarshall 

  /// 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 algorithm solves the shortest path problem for each pairs

  /// of node when the edges can have negative length but the graph should

  /// not contain circle with negative sum of length. If we can assume

  /// that all edge is non-negative in the graph then the dijkstra algorithm

  /// should be used from each node rather and if the graph is sparse and

  /// there are negative circles then the johson algorithm.

  ///

  /// The complexity of this algorithm is O(n^3 + e).

  ///

  /// The type of the length is determined by the

  /// \ref concept::ReadMap::Value "Value" of the length map.

  ///

  /// \param _Graph The graph type the algorithm runs on. The default value

  /// is \ref ListGraph. The value of _Graph is not used directly by

  /// FloydWarshall, it is only passed to \ref FloydWarshallDefaultTraits.

  /// \param _LengthMap 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 _LengthMap is not used directly by FloydWarshall, it is only passed 

  /// to \ref FloydWarshallDefaultTraits.  \param _Traits Traits class to set

  /// various data types used by the algorithm.  The default traits

  /// class is \ref FloydWarshallDefaultTraits

  /// "FloydWarshallDefaultTraits<_Graph,_LengthMap>".  See \ref

  /// FloydWarshallDefaultTraits for the documentation of a FloydWarshall 

  /// traits class.

  ///

  /// \author Balazs Dezso

#ifdef DOXYGEN

  template <typename _Graph, typename _LengthMap typename _Traits >

#else

  template <typename _Graph=ListGraph,

	    typename _LengthMap=typename _Graph::template EdgeMap<int>,

	    typename _Traits=FloydWarshallDefaultTraits<_Graph,_LengthMap> >

#endif

  class FloydWarshall {

  public:

    /// \brief \ref Exception for uninitialized parameters.

    ///

    /// This error represents problems in the initialization

    /// of the parameters of the algorithms.

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

      virtual const char* exceptionName() const {

	return "lemon::FloydWarshall::UninitializedParameter";

      }

    };

    typedef _Traits Traits;

    ///The type of the underlying graph.

    typedef typename _Traits::Graph Graph;

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::EdgeIt EdgeIt;

    /// \brief The type of the length of the edges.

    typedef typename _Traits::LengthMap::Value Value;

    /// \brief The type of the map that stores the edge lengths.

    typedef typename _Traits::LengthMap LengthMap;

    /// \brief The type of the map that stores the last

    /// edges of the shortest paths. The type of the PredMap

    /// is a matrix map for Edges

    typedef typename _Traits::PredMap PredMap;

    /// \brief The type of the map that stores the dists of the nodes.

    /// The type of the DistMap is a matrix map for Values

    typedef typename _Traits::DistMap DistMap;

    /// \brief The operation traits.

    typedef typename _Traits::OperationTraits OperationTraits;

  private:

    /// Pointer to the underlying graph.

    const Graph *graph;

    /// 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 distances.

    DistMap *_dist;

    ///Indicates if \ref _dist is locally allocated (\c true) or not.

    bool local_dist;

    /// Creates the maps if necessary.

    void create_maps() {

      if(!_pred) {

	local_pred = true;

	_pred = Traits::createPredMap(*graph);

      }

      if(!_dist) {

	local_dist = true;

	_dist = Traits::createDistMap(*graph);

      }

    }

  public :

    /// \name Named template parameters

    ///@{

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph& graph) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting PredMap 

    /// type

    /// \ref named-templ-param "Named parameter" for setting PredMap type

    ///

    template <class T>

    struct DefPredMap 

      : public FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > {

      typedef FloydWarshall< Graph, LengthMap, DefPredMapTraits<T> > Create;

    };

    template <class T>

    struct DefDistMapTraits : public Traits {

      typedef T DistMap;

      static DistMap *createDistMap(const Graph& graph) {

	throw UninitializedParameter();

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for setting DistMap 

    /// type

    ///

    /// \ref named-templ-param "Named parameter" for setting DistMap type

    ///

    template <class T>

    struct DefDistMap 

      : public FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > {

      typedef FloydWarshall< Graph, LengthMap, DefDistMapTraits<T> > Create;

    };

    template <class T>

    struct DefOperationTraitsTraits : public Traits {

      typedef T OperationTraits;

    };

    /// \brief \ref named-templ-param "Named parameter" for setting 

    /// OperationTraits type

    ///

    /// \ref named-templ-param "Named parameter" for setting PredMap type

    template <class T>

    struct DefOperationTraits

      : public FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> > {

      typedef FloydWarshall< Graph, LengthMap, DefOperationTraitsTraits<T> >

      Create;

    };

    ///@}

  protected:

    FloydWarshall() {}

  public:      

    typedef FloydWarshall Create;

    /// \brief Constructor.

    ///

    /// \param _graph the graph the algorithm will run on.

    /// \param _length the length map used by the algorithm.

    FloydWarshall(const Graph& _graph, const LengthMap& _length) :

      graph(&_graph), length(&_length),

      _pred(0), local_pred(false),

      _dist(0), local_dist(false) {}

    ///Destructor.

    ~FloydWarshall() {

      if(local_pred) delete _pred;

      if(local_dist) delete _dist;

    }

    /// \brief Sets the length map.

    ///

    /// Sets the length map.

    /// \return \c (*this)

    FloydWarshall &lengthMap(const LengthMap &m) {

      length = &m;

      return *this;

    }

    /// \brief 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 \c (*this)

    FloydWarshall &predMap(PredMap &m) {

      if(local_pred) {

	delete _pred;

	local_pred=false;

      }

      _pred = &m;

      return *this;

    }

    /// \brief 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 \c (*this)

    FloydWarshall &distMap(DistMap &m) {

      if(local_dist) {

	delete _dist;

	local_dist=false;

      }

      _dist = &m;

      return *this;

    }

    ///\name Execution control

    /// The simplest way to execute the algorithm is to use

    /// one of the member functions called \c run(...).

    /// \n

    /// If you need more control on the execution,

    /// Finally \ref start() will perform the actual path

    /// computation.

    ///@{

    /// \brief Initializes the internal data structures.

    /// 

    /// Initializes the internal data structures.

    void init() {

      create_maps();

      for (NodeIt it(*graph); it != INVALID; ++it) {

	for (NodeIt jt(*graph); jt != INVALID; ++jt) {

	  _pred->set(it, jt, INVALID);

	  _dist->set(it, jt, it == jt ? 

		     OperationTraits::zero() : OperationTraits::infinity());

	}

      }

      for (EdgeIt it(*graph); it != INVALID; ++it) {

	Node source = graph->source(it);

	Node target = graph->target(it);	

	if (OperationTraits::less((*length)[it], (*_dist)(source, target))) {

	  _dist->set(source, target, (*length)[it]);

	  _pred->set(source, target, it);

	}

      }

    }

    /// \brief Executes the algorithm.

    ///

    /// This method runs the %FloydWarshall algorithm in order to compute 

    /// the shortest path to each node pairs. The algorithm 

    /// computes 

    /// - The shortest path tree for each node.

    /// - The distance between each node pairs.

    void start() {

      for (NodeIt kt(*graph); kt != INVALID; ++kt) {

	for (NodeIt it(*graph); it != INVALID; ++it) {

	  for (NodeIt jt(*graph); jt != INVALID; ++jt) {

	    Value relaxed = OperationTraits::plus((*_dist)(it, kt),

						  (*_dist)(kt, jt));

	    if (OperationTraits::less(relaxed, (*_dist)(it, jt))) {

	      _dist->set(it, jt, relaxed);

	      _pred->set(it, jt, (*_pred)(kt, jt));

	    }

	  }

	}

      }

    }

    /// \brief Runs %FloydWarshall algorithm.

    ///    

    /// This method runs the %FloydWarshall algorithm from a each node

    /// in order to compute the shortest path to each node pairs. 

    /// The algorithm computes

    /// - The shortest path tree for each node.

    /// - The distance between each node pairs.

    ///

    /// \note d.run(s) is just a shortcut of the following code.

    /// \code

    ///  d.init();

    ///  d.start();

    /// \endcode

    void run() {

      init();

      start();

    }

    ///@}

    /// \name Query Functions

    /// The result of the %FloydWarshall algorithm can be obtained using these

    /// functions.\n

    /// Before the use of these functions,

    /// either run() or start() must be called.

    ///@{

    /// \brief Copies the shortest path to \c t into \c p

    ///    

    /// This function copies the shortest path to \c t into \c p.

    /// If it \c t is a source itself or unreachable, then it does not

    /// alter \c p.

    /// \todo Is it the right way to handle unreachable nodes?

    /// \return Returns \c true if a path to \c t was actually copied to \c p,

    /// \c false otherwise.

    /// \sa DirPath

    template <typename Path>

    bool getPath(Path &p, Node source, Node target) {

      if (connected(source, target)) {

	p.clear();

	typename Path::Builder b(target);

	for(b.setStartNode(target); pred(source, target) != INVALID;

	    target = predNode(target)) {

	  b.pushFront(pred(source, target));

	}

	b.commit();

	return true;

      }

      return false;

    }

    /// \brief The distance between two nodes.

    ///

    /// Returns the distance between two nodes.

    /// \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 source, Node target) const { 

      return (*_dist)(source, target); 

    }

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

    ///

    /// For the node \c node it returns the 'previous edge' of the shortest 

    /// path tree to direction of the node \c root 

    /// i.e. it returns the last edge of a shortest path from the node \c root 

    /// to \c node. It is \ref INVALID if \c node is unreachable from the root

    /// or if \c node=root. The shortest path tree used here is equal to the 

    /// shortest path tree used in \ref predNode(). 

    /// \pre \ref run() must be called before using this function.

    /// \todo predEdge could be a better name.

    Edge pred(Node root, Node node) const { 

      return (*_pred)(root, node); 

    }

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

    ///

    /// For a node \c node it returns the 'previous node' of the shortest path 

    /// tree to direction of the node \c root, i.e. it returns the last but 

    /// one node from a shortest path from the \c root to \c node. It is 

    /// INVALID if \c node is unreachable from the root or if \c node=root. 

    /// The shortest path tree used here is equal to the 

    /// shortest path tree used in \ref pred().  

    /// \pre \ref run() must be called before using this function.

    Node predNode(Node root, Node node) const { 

      return (*_pred)(root, node) == INVALID ? 

      INVALID : graph->source((*_pred)(root, node)); 

    }

    /// \brief Returns a reference to the matrix node map of distances.

    ///

    /// Returns a reference to the matrix node map of distances. 

    ///

    /// \pre \ref run() must be called before using this function.

    const DistMap &distMap() const { return *_dist;}

    /// \brief Returns a reference to the shortest path tree map.

    ///

    /// Returns a reference to the matrix node map of the edges of the

    /// shortest path tree.

    /// \pre \ref run() must be called before using this function.

    const PredMap &predMap() const { return *_pred;}

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

    ///

    /// Returns \c true if \c v is reachable from the root.

    /// \pre \ref run() must be called before using this function.

    ///

    bool connected(Node source, Node target) { 

      return (*_dist)(source, target) != OperationTraits::infinity(); 

    }

    ///@}

  };

} //END OF NAMESPACE LEMON

#endif