/* -*- 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