/* -*- 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_HARTMANN_ORLIN_MMC_H

 #define LEMON_HARTMANN_ORLIN_MMC_H

 /// \ingroup min_mean_cycle

 ///

 /// \file

 /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.

 #include <vector>

 #include <limits>

 #include <lemon/core.h>

 #include <lemon/path.h>

 #include <lemon/tolerance.h>

 #include <lemon/connectivity.h>

 namespace lemon {

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

   ///

   /// Default traits class of HartmannOrlinMmc class.

   /// \tparam GR The type of the digraph.

   /// \tparam CM The type of the cost map.

   /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.

 #ifdef DOXYGEN

   template <typename GR, typename CM>

 #else

   template <typename GR, typename CM,

     bool integer = std::numeric_limits<typename CM::Value>::is_integer>

 #endif

   struct HartmannOrlinMmcDefaultTraits

   {

     /// The type of the digraph

     typedef GR Digraph;

     /// The type of the cost map

     typedef CM CostMap;

     /// The type of the arc costs

     typedef typename CostMap::Value Cost;

     /// \brief The large cost type used for internal computations

     ///

     /// The large cost type used for internal computations.

     /// It is \c long \c long if the \c Cost type is integer,

     /// otherwise it is \c double.

     /// \c Cost must be convertible to \c LargeCost.

     typedef double LargeCost;

     /// The tolerance type used for internal computations

     typedef lemon::Tolerance<LargeCost> Tolerance;

     /// \brief The path type of the found cycles

     ///

     /// The path type of the found cycles.

     /// It must conform to the \ref lemon::concepts::Path "Path" concept

     /// and it must have an \c addFront() function.

     typedef lemon::Path<Digraph> Path;

   };

   // Default traits class for integer cost types

   template <typename GR, typename CM>

   struct HartmannOrlinMmcDefaultTraits<GR, CM, true>

   {

     typedef GR Digraph;

     typedef CM CostMap;

     typedef typename CostMap::Value Cost;

 #ifdef LEMON_HAVE_LONG_LONG

     typedef long long LargeCost;

 #else

     typedef long LargeCost;

 #endif

     typedef lemon::Tolerance<LargeCost> Tolerance;

     typedef lemon::Path<Digraph> Path;

   };

   /// \addtogroup min_mean_cycle

   /// @{

   /// \brief Implementation of the Hartmann-Orlin algorithm for finding

   /// a minimum mean cycle.

   ///

   /// This class implements the Hartmann-Orlin algorithm for finding

   /// a directed cycle of minimum mean cost in a digraph

   /// \ref amo93networkflows, \ref dasdan98minmeancycle.

   /// It is an improved version of \ref Karp "Karp"'s original algorithm,

   /// it applies an efficient early termination scheme.

   /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e).

   ///

   /// \tparam GR The type of the digraph the algorithm runs on.

   /// \tparam CM The type of the cost map. The default

   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".

   /// \tparam TR The traits class that defines various types used by the

   /// algorithm. By default, it is \ref HartmannOrlinMmcDefaultTraits

   /// "HartmannOrlinMmcDefaultTraits<GR, CM>".

   /// In most cases, this parameter should not be set directly,

   /// consider to use the named template parameters instead.

 #ifdef DOXYGEN

   template <typename GR, typename CM, typename TR>

 #else

   template < typename GR,

              typename CM = typename GR::template ArcMap<int>,

              typename TR = HartmannOrlinMmcDefaultTraits<GR, CM> >

 #endif

   class HartmannOrlinMmc

   {

   public:

     /// The type of the digraph

     typedef typename TR::Digraph Digraph;

     /// The type of the cost map

     typedef typename TR::CostMap CostMap;

     /// The type of the arc costs

     typedef typename TR::Cost Cost;

     /// \brief The large cost type

     ///

     /// The large cost type used for internal computations.

     /// By default, it is \c long \c long if the \c Cost type is integer,

     /// otherwise it is \c double.

     typedef typename TR::LargeCost LargeCost;

     /// The tolerance type

     typedef typename TR::Tolerance Tolerance;

     /// \brief The path type of the found cycles

     ///

     /// The path type of the found cycles.

     /// Using the \ref HartmannOrlinMmcDefaultTraits "default traits class",

     /// it is \ref lemon::Path "Path<Digraph>".

     typedef typename TR::Path Path;

     /// The \ref HartmannOrlinMmcDefaultTraits "traits class" of the algorithm

     typedef TR Traits;

   private:

     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

     // Data sturcture for path data

     struct PathData

     {

       LargeCost dist;

       Arc pred;

       PathData(LargeCost d, Arc p = INVALID) :

         dist(d), pred(p) {}

     };

     typedef typename Digraph::template NodeMap<std::vector<PathData> >

       PathDataNodeMap;

   private:

     // The digraph the algorithm runs on

     const Digraph &_gr;

     // The cost of the arcs

     const CostMap &_cost;

     // Data for storing the strongly connected components

     int _comp_num;

     typename Digraph::template NodeMap<int> _comp;

     std::vector<std::vector<Node> > _comp_nodes;

     std::vector<Node>* _nodes;

     typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;

     // Data for the found cycles

     bool _curr_found, _best_found;

     LargeCost _curr_cost, _best_cost;

     int _curr_size, _best_size;

     Node _curr_node, _best_node;

     int _curr_level, _best_level;

     Path *_cycle_path;

     bool _local_path;

     // Node map for storing path data

     PathDataNodeMap _data;

     // The processed nodes in the last round

     std::vector<Node> _process;

     Tolerance _tolerance;

     // Infinite constant

     const LargeCost INF;

   public:

     /// \name Named Template Parameters

     /// @{

     template <typename T>

     struct SetLargeCostTraits : public Traits {

       typedef T LargeCost;

       typedef lemon::Tolerance<T> Tolerance;

     };

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

     /// \c LargeCost type.

     ///

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

     /// type. It is used for internal computations in the algorithm.

     template <typename T>

     struct SetLargeCost

       : public HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > {

       typedef HartmannOrlinMmc<GR, CM, SetLargeCostTraits<T> > Create;

     };

     template <typename T>

     struct SetPathTraits : public Traits {

       typedef T Path;

     };

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

     /// \c %Path type.

     ///

     /// \ref named-templ-param "Named parameter" for setting the \c %Path

     /// type of the found cycles.

     /// It must conform to the \ref lemon::concepts::Path "Path" concept

     /// and it must have an \c addFront() function.

     template <typename T>

     struct SetPath

       : public HartmannOrlinMmc<GR, CM, SetPathTraits<T> > {

       typedef HartmannOrlinMmc<GR, CM, SetPathTraits<T> > Create;

     };

     /// @}

   protected:

     HartmannOrlinMmc() {}

   public:

     /// \brief Constructor.

     ///

     /// The constructor of the class.

     ///

     /// \param digraph The digraph the algorithm runs on.

     /// \param cost The costs of the arcs.

     HartmannOrlinMmc( const Digraph &digraph,

                       const CostMap &cost ) :

       _gr(digraph), _cost(cost), _comp(digraph), _out_arcs(digraph),

       _best_found(false), _best_cost(0), _best_size(1),

       _cycle_path(NULL), _local_path(false), _data(digraph),

       INF(std::numeric_limits<LargeCost>::has_infinity ?

           std::numeric_limits<LargeCost>::infinity() :

           std::numeric_limits<LargeCost>::max())

     {}

     /// Destructor.

     ~HartmannOrlinMmc() {

       if (_local_path) delete _cycle_path;

     }

     /// \brief Set the path structure for storing the found cycle.

     ///

     /// This function sets an external path structure for storing the

     /// found cycle.

     ///

     /// If you don't call this function before calling \ref run() or

     /// \ref findCycleMean(), it will allocate a local \ref Path "path"

     /// structure. The destuctor deallocates this automatically

     /// allocated object, of course.

     ///

     /// \note The algorithm calls only the \ref lemon::Path::addFront()

     /// "addFront()" function of the given path structure.

     ///

     /// \return <tt>(*this)</tt>

     HartmannOrlinMmc& cycle(Path &path) {

       if (_local_path) {

         delete _cycle_path;

         _local_path = false;

       }

       _cycle_path = &path;

       return *this;

     }

     /// \brief Set the tolerance used by the algorithm.

     ///

     /// This function sets the tolerance object used by the algorithm.

     ///

     /// \return <tt>(*this)</tt>

     HartmannOrlinMmc& tolerance(const Tolerance& tolerance) {

       _tolerance = tolerance;

       return *this;

     }

     /// \brief Return a const reference to the tolerance.

     ///

     /// This function returns a const reference to the tolerance object

     /// used by the algorithm.

     const Tolerance& tolerance() const {

       return _tolerance;

     }

     /// \name Execution control

     /// The simplest way to execute the algorithm is to call the \ref run()

     /// function.\n

     /// If you only need the minimum mean cost, you may call

     /// \ref findCycleMean().

     /// @{

     /// \brief Run the algorithm.

     ///

     /// This function runs the algorithm.

     /// It can be called more than once (e.g. if the underlying digraph

     /// and/or the arc costs have been modified).

     ///

     /// \return \c true if a directed cycle exists in the digraph.

     ///

     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.

     /// \code

     ///   return mmc.findCycleMean() && mmc.findCycle();

     /// \endcode

     bool run() {

       return findCycleMean() && findCycle();

     }

     /// \brief Find the minimum cycle mean.

     ///

     /// This function finds the minimum mean cost of the directed

     /// cycles in the digraph.

     ///

     /// \return \c true if a directed cycle exists in the digraph.

     bool findCycleMean() {

       // Initialization and find strongly connected components

       init();

       findComponents();

       // Find the minimum cycle mean in the components

       for (int comp = 0; comp < _comp_num; ++comp) {

         if (!initComponent(comp)) continue;

         processRounds();

         // Update the best cycle (global minimum mean cycle)

         if ( _curr_found && (!_best_found || 

              _curr_cost * _best_size < _best_cost * _curr_size) ) {

           _best_found = true;

           _best_cost = _curr_cost;

           _best_size = _curr_size;

           _best_node = _curr_node;

           _best_level = _curr_level;

         }

       }

       return _best_found;

     }

     /// \brief Find a minimum mean directed cycle.

     ///

     /// This function finds a directed cycle of minimum mean cost

     /// in the digraph using the data computed by findCycleMean().

     ///

     /// \return \c true if a directed cycle exists in the digraph.

     ///

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

     bool findCycle() {

       if (!_best_found) return false;

       IntNodeMap reached(_gr, -1);

       int r = _best_level + 1;

       Node u = _best_node;

       while (reached[u] < 0) {

         reached[u] = --r;

         u = _gr.source(_data[u][r].pred);

       }

       r = reached[u];

       Arc e = _data[u][r].pred;

       _cycle_path->addFront(e);

       _best_cost = _cost[e];

       _best_size = 1;

       Node v;

       while ((v = _gr.source(e)) != u) {

         e = _data[v][--r].pred;

         _cycle_path->addFront(e);

         _best_cost += _cost[e];

         ++_best_size;

       }

       return true;

     }

     /// @}

     /// \name Query Functions

     /// The results of the algorithm can be obtained using these

     /// functions.\n

     /// The algorithm should be executed before using them.

     /// @{

     /// \brief Return the total cost of the found cycle.

     ///

     /// This function returns the total cost of the found cycle.

     ///

     /// \pre \ref run() or \ref findCycleMean() must be called before

     /// using this function.

     Cost cycleCost() const {

       return static_cast<Cost>(_best_cost);

     }

     /// \brief Return the number of arcs on the found cycle.

     ///

     /// This function returns the number of arcs on the found cycle.

     ///

     /// \pre \ref run() or \ref findCycleMean() must be called before

     /// using this function.

     int cycleSize() const {

       return _best_size;

     }

     /// \brief Return the mean cost of the found cycle.

     ///

     /// This function returns the mean cost of the found cycle.

     ///

     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the

     /// following code.

     /// \code

     ///   return static_cast<double>(alg.cycleCost()) / alg.cycleSize();

     /// \endcode

     ///

     /// \pre \ref run() or \ref findCycleMean() must be called before

     /// using this function.

     double cycleMean() const {

       return static_cast<double>(_best_cost) / _best_size;

     }

     /// \brief Return the found cycle.

     ///

     /// This function returns a const reference to the path structure

     /// storing the found cycle.

     ///

     /// \pre \ref run() or \ref findCycle() must be called before using

     /// this function.

     const Path& cycle() const {

       return *_cycle_path;

     }

     ///@}

   private:

     // Initialization

     void init() {

       if (!_cycle_path) {

         _local_path = true;

         _cycle_path = new Path;

       }

       _cycle_path->clear();

       _best_found = false;

       _best_cost = 0;

       _best_size = 1;

       _cycle_path->clear();

       for (NodeIt u(_gr); u != INVALID; ++u)

         _data[u].clear();

     }

     // Find strongly connected components and initialize _comp_nodes

     // and _out_arcs

     void findComponents() {

       _comp_num = stronglyConnectedComponents(_gr, _comp);

       _comp_nodes.resize(_comp_num);

       if (_comp_num == 1) {

         _comp_nodes[0].clear();

         for (NodeIt n(_gr); n != INVALID; ++n) {

           _comp_nodes[0].push_back(n);

           _out_arcs[n].clear();

           for (OutArcIt a(_gr, n); a != INVALID; ++a) {

             _out_arcs[n].push_back(a);

           }

         }

       } else {

         for (int i = 0; i < _comp_num; ++i)

           _comp_nodes[i].clear();

         for (NodeIt n(_gr); n != INVALID; ++n) {

           int k = _comp[n];

           _comp_nodes[k].push_back(n);

           _out_arcs[n].clear();

           for (OutArcIt a(_gr, n); a != INVALID; ++a) {

             if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);

           }

         }

       }

     }

     // Initialize path data for the current component

     bool initComponent(int comp) {

       _nodes = &(_comp_nodes[comp]);

       int n = _nodes->size();

       if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {

         return false;

       }      

       for (int i = 0; i < n; ++i) {

         _data[(*_nodes)[i]].resize(n + 1, PathData(INF));

       }

       return true;

     }

     // Process all rounds of computing path data for the current component.

     // _data[v][k] is the cost of a shortest directed walk from the root

     // node to node v containing exactly k arcs.

     void processRounds() {

       Node start = (*_nodes)[0];

       _data[start][0] = PathData(0);

       _process.clear();

       _process.push_back(start);

       int k, n = _nodes->size();

       int next_check = 4;

       bool terminate = false;

       for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {

         processNextBuildRound(k);

         if (k == next_check || k == n) {

           terminate = checkTermination(k);

           next_check = next_check * 3 / 2;

         }

       }

       for ( ; k <= n && !terminate; ++k) {

         processNextFullRound(k);

         if (k == next_check || k == n) {

           terminate = checkTermination(k);

           next_check = next_check * 3 / 2;

         }

       }

     }

     // Process one round and rebuild _process

     void processNextBuildRound(int k) {

       std::vector<Node> next;

       Node u, v;

       Arc e;

       LargeCost d;

       for (int i = 0; i < int(_process.size()); ++i) {

         u = _process[i];

         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {

           e = _out_arcs[u][j];

           v = _gr.target(e);

           d = _data[u][k-1].dist + _cost[e];

           if (_tolerance.less(d, _data[v][k].dist)) {

             if (_data[v][k].dist == INF) next.push_back(v);

             _data[v][k] = PathData(d, e);

           }

         }

       }

       _process.swap(next);

     }

     // Process one round using _nodes instead of _process

     void processNextFullRound(int k) {

       Node u, v;

       Arc e;

       LargeCost d;

       for (int i = 0; i < int(_nodes->size()); ++i) {

         u = (*_nodes)[i];

         for (int j = 0; j < int(_out_arcs[u].size()); ++j) {

           e = _out_arcs[u][j];

           v = _gr.target(e);

           d = _data[u][k-1].dist + _cost[e];

           if (_tolerance.less(d, _data[v][k].dist)) {

             _data[v][k] = PathData(d, e);

           }

         }

       }

     }

     // Check early termination

     bool checkTermination(int k) {

       typedef std::pair<int, int> Pair;

       typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));

       typename GR::template NodeMap<LargeCost> pi(_gr);

       int n = _nodes->size();

       LargeCost cost;

       int size;

       Node u;

       // Search for cycles that are already found

       _curr_found = false;

       for (int i = 0; i < n; ++i) {

         u = (*_nodes)[i];

         if (_data[u][k].dist == INF) continue;

         for (int j = k; j >= 0; --j) {

           if (level[u].first == i && level[u].second > 0) {

             // A cycle is found

             cost = _data[u][level[u].second].dist - _data[u][j].dist;

             size = level[u].second - j;

             if (!_curr_found || cost * _curr_size < _curr_cost * size) {

               _curr_cost = cost;

               _curr_size = size;

               _curr_node = u;

               _curr_level = level[u].second;

               _curr_found = true;

             }

           }

           level[u] = Pair(i, j);

           if (j != 0) {

 	    u = _gr.source(_data[u][j].pred);

 	  }

         }

       }

       // If at least one cycle is found, check the optimality condition

       LargeCost d;

       if (_curr_found && k < n) {

         // Find node potentials

         for (int i = 0; i < n; ++i) {

           u = (*_nodes)[i];

           pi[u] = INF;

           for (int j = 0; j <= k; ++j) {

             if (_data[u][j].dist < INF) {

               d = _data[u][j].dist * _curr_size - j * _curr_cost;

               if (_tolerance.less(d, pi[u])) pi[u] = d;

             }

           }

         }

         // Check the optimality condition for all arcs

         bool done = true;

         for (ArcIt a(_gr); a != INVALID; ++a) {

           if (_tolerance.less(_cost[a] * _curr_size - _curr_cost,

                               pi[_gr.target(a)] - pi[_gr.source(a)]) ) {

             done = false;

             break;

           }

         }

         return done;

       }

       return (k == n);

     }

   }; //class HartmannOrlinMmc

   ///@}

 } //namespace lemon

 #endif //LEMON_HARTMANN_ORLIN_MMC_H