/* -*- 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_KARP_H

 #define LEMON_KARP_H

 /// \ingroup min_mean_cycle

 ///

 /// \file

 /// \brief Karp'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 Karp algorithm.

   ///

   /// Default traits class of Karp algorithm.

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

   /// \tparam LEN The type of the length map.

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

 #ifdef DOXYGEN

   template <typename GR, typename LEN>

 #else

   template <typename GR, typename LEN,

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

 #endif

   struct KarpDefaultTraits

   {

     /// The type of the digraph

     typedef GR Digraph;

     /// The type of the length map

     typedef LEN LengthMap;

     /// The type of the arc lengths

     typedef typename LengthMap::Value Value;

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

     ///

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

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

     /// otherwise it is \c double.

     /// \c Value must be convertible to \c LargeValue.

     typedef double LargeValue;

     /// The tolerance type used for internal computations

     typedef lemon::Tolerance<LargeValue> 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 value types

   template <typename GR, typename LEN>

   struct KarpDefaultTraits<GR, LEN, true>

   {

     typedef GR Digraph;

     typedef LEN LengthMap;

     typedef typename LengthMap::Value Value;

 #ifdef LEMON_HAVE_LONG_LONG

     typedef long long LargeValue;

 #else

     typedef long LargeValue;

 #endif

     typedef lemon::Tolerance<LargeValue> Tolerance;

     typedef lemon::Path<Digraph> Path;

   };

   /// \addtogroup min_mean_cycle

   /// @{

   /// \brief Implementation of Karp's algorithm for finding a minimum

   /// mean cycle.

   ///

   /// This class implements Karp's algorithm for finding a directed

   /// cycle of minimum mean length (cost) in a digraph

   /// \ref amo93networkflows, \ref dasdan98minmeancycle.

   /// 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 LEN The type of the length 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 KarpDefaultTraits

   /// "KarpDefaultTraits<GR, LEN>".

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

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

 #ifdef DOXYGEN

   template <typename GR, typename LEN, typename TR>

 #else

   template < typename GR,

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

              typename TR = KarpDefaultTraits<GR, LEN> >

 #endif

   class Karp

   {

   public:

     /// The type of the digraph

     typedef typename TR::Digraph Digraph;

     /// The type of the length map

     typedef typename TR::LengthMap LengthMap;

     /// The type of the arc lengths

     typedef typename TR::Value Value;

     /// \brief The large value type

     ///

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

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

     /// otherwise it is \c double.

     typedef typename TR::LargeValue LargeValue;

     /// 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 KarpDefaultTraits "default traits class",

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

     typedef typename TR::Path Path;

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

     typedef TR Traits;

   private:

     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

     // Data sturcture for path data

     struct PathData

     {

       LargeValue dist;

       Arc pred;

       PathData(LargeValue 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 length of the arcs

     const LengthMap &_length;

     // 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 cycle

     LargeValue _cycle_length;

     int _cycle_size;

     Node _cycle_node;

     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 LargeValue INF;

   public:

     /// \name Named Template Parameters

     /// @{

     template <typename T>

     struct SetLargeValueTraits : public Traits {

       typedef T LargeValue;

       typedef lemon::Tolerance<T> Tolerance;

     };

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

     /// \c LargeValue type.

     ///

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

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

     template <typename T>

     struct SetLargeValue

       : public Karp<GR, LEN, SetLargeValueTraits<T> > {

       typedef Karp<GR, LEN, SetLargeValueTraits<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 Karp<GR, LEN, SetPathTraits<T> > {

       typedef Karp<GR, LEN, SetPathTraits<T> > Create;

     };

     /// @}

   public:

     /// \brief Constructor.

     ///

     /// The constructor of the class.

     ///

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

     /// \param length The lengths (costs) of the arcs.

     Karp( const Digraph &digraph,

           const LengthMap &length ) :

       _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),

       _cycle_length(0), _cycle_size(1), _cycle_node(INVALID),

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

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

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

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

     {}

     /// Destructor.

     ~Karp() {

       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 findMinMean(), 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>

     Karp& 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>

     Karp& 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 length, you may call

     /// \ref findMinMean().

     /// @{

     /// \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 lengths 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.findMinMean() && mmc.findCycle();

     /// \endcode

     bool run() {

       return findMinMean() && findCycle();

     }

     /// \brief Find the minimum cycle mean.

     ///

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

     /// cycles in the digraph.

     ///

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

     bool findMinMean() {

       // 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();

         updateMinMean();

       }

       return (_cycle_node != INVALID);

     }

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

     ///

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

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

     ///

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

     ///

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

     bool findCycle() {

       if (_cycle_node == INVALID) return false;

       IntNodeMap reached(_gr, -1);

       int r = _data[_cycle_node].size();

       Node u = _cycle_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);

       _cycle_length = _length[e];

       _cycle_size = 1;

       Node v;

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

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

         _cycle_path->addFront(e);

         _cycle_length += _length[e];

         ++_cycle_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 length of the found cycle.

     ///

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

     ///

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

     /// using this function.

     LargeValue cycleLength() const {

       return _cycle_length;

     }

     /// \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 findMinMean() must be called before

     /// using this function.

     int cycleArcNum() const {

       return _cycle_size;

     }

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

     ///

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

     ///

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

     /// following code.

     /// \code

     ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();

     /// \endcode

     ///

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

     /// using this function.

     double cycleMean() const {

       return static_cast<double>(_cycle_length) / _cycle_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();

       _cycle_length = 0;

       _cycle_size = 1;

       _cycle_node = INVALID;

       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 length 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();

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

         processNextBuildRound(k);

       }

       for ( ; k <= n; ++k) {

         processNextFullRound(k);

       }

     }

     // Process one round and rebuild _process

     void processNextBuildRound(int k) {

       std::vector<Node> next;

       Node u, v;

       Arc e;

       LargeValue 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 + _length[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;

       LargeValue 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 + _length[e];

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

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

           }

         }

       }

     }

     // Update the minimum cycle mean

     void updateMinMean() {

       int n = _nodes->size();

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

         Node u = (*_nodes)[i];

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

         LargeValue length, max_length = 0;

         int size, max_size = 1;

         bool found_curr = false;

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

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

           length = _data[u][n].dist - _data[u][k].dist;

           size = n - k;

           if (!found_curr || length * max_size > max_length * size) {

             found_curr = true;

             max_length = length;

             max_size = size;

           }

         }

         if ( found_curr && (_cycle_node == INVALID ||

              max_length * _cycle_size < _cycle_length * max_size) ) {

           _cycle_length = max_length;

           _cycle_size = max_size;

           _cycle_node = u;

         }

       }

     }

   }; //class Karp

   ///@}

 } //namespace lemon

 #endif //LEMON_KARP_H