/* -*- 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_MIN_MEAN_CYCLE_H

#define LEMON_MIN_MEAN_CYCLE_H

/// \ingroup shortest_path

///

/// \file

/// \brief Howard's algorithm for finding a minimum mean cycle.

#include <vector>

#include <lemon/core.h>

#include <lemon/path.h>

#include <lemon/tolerance.h>

#include <lemon/connectivity.h>

namespace lemon {

  /// \addtogroup shortest_path

  /// @{

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

  /// mean cycle.

  ///

  /// \ref MinMeanCycle implements Howard's algorithm for finding a

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

  ///

  /// \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>".

  ///

  /// \warning \c LEN::Value must be convertible to \c double.

#ifdef DOXYGEN

  template <typename GR, typename LEN>

#else

  template < typename GR,

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

#endif

  class MinMeanCycle

  {

  public:

    /// The type of the digraph the algorithm runs on

    typedef GR Digraph;

    /// The type of the length map

    typedef LEN LengthMap;

    /// The type of the arc lengths

    typedef typename LengthMap::Value Value;

    /// The type of the paths

    typedef lemon::Path<Digraph> Path;

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

    // The digraph the algorithm runs on

    const Digraph &_gr;

    // The length of the arcs

    const LengthMap &_length;

    // The total length of the found cycle

    Value _cycle_length;

    // The number of arcs on the found cycle

    int _cycle_size;

    // The found cycle

    Path *_cycle_path;

    bool _local_path;

    bool _cycle_found;

    Node _cycle_node;

    typename Digraph::template NodeMap<bool> _reached;

    typename Digraph::template NodeMap<double> _dist;

    typename Digraph::template NodeMap<Arc> _policy;

    typename Digraph::template NodeMap<int> _comp;

    int _comp_num;

    std::vector<Node> _nodes;

    std::vector<Arc> _arcs;

    Tolerance<double> _tol;

  public:

    /// \brief Constructor.

    ///

    /// The constructor of the class.

    ///

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

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

    MinMeanCycle( const Digraph &digraph,

                  const LengthMap &length ) :

      _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),

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

      _dist(digraph), _policy(digraph), _comp(digraph)

    {}

    /// Destructor.

    ~MinMeanCycle() {

      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 init(), 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::addBack()

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

    ///

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

    ///

    /// \sa cycle()

    MinMeanCycle& cyclePath(Path &path) {

      if (_local_path) {

        delete _cycle_path;

        _local_path = false;

      }

      _cycle_path = &path;

      return *this;

    }

    /// \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 init()

    /// and \ref findMinMean().

    /// If you would like to run the algorithm again (e.g. the underlying

    /// digraph and/or the arc lengths has been modified), you may not

    /// create a new instance of the class, rather call \ref reset(),

    /// \ref findMinMean() and \ref findCycle() instead.

    /// @{

    /// \brief Run the algorithm.

    ///

    /// This function runs the algorithm.

    ///

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

    ///

    /// \note Apart from the return value, <tt>mmc.run()</tt> is just a

    /// shortcut of the following code.

    /// \code

    ///   mmc.init();

    ///   mmc.findMinMean();

    ///   mmc.findCycle();

    /// \endcode

    bool run() {

      init();

      return findMinMean() && findCycle();

    }

    /// \brief Initialize the internal data structures.

    ///

    /// This function initializes the internal data structures.

    ///

    /// \sa reset()

    void init() {

      _tol.epsilon(1e-6);

      if (!_cycle_path) {

        _local_path = true;

        _cycle_path = new Path;

      }

      _cycle_found = false;

      _comp_num = stronglyConnectedComponents(_gr, _comp);

    }

    /// \brief Reset the internal data structures.

    ///

    /// This function resets the internal data structures so that

    /// findMinMean() and findCycle() can be called again (e.g. when the

    /// underlying digraph and/or the arc lengths has been modified).

    ///

    /// \sa init()

    void reset() {

      if (_cycle_path) _cycle_path->clear();

      _cycle_found = false;

      _comp_num = stronglyConnectedComponents(_gr, _comp);

    }

    /// \brief Find the minimum cycle mean.

    ///

    /// This function computes all the required data and finds the

    /// minimum mean length of the directed cycles in the digraph.

    ///

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

    ///

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

    bool findMinMean() {

      // Find the minimum cycle mean in the components

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

        if (!initCurrentComponent(comp)) continue;

        while (true) {

          if (!findPolicyCycles()) break;

          contractPolicyGraph(comp);

          if (!computeNodeDistances()) break;

        }

      }

      return _cycle_found;

    }

    /// \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 init() and \ref findMinMean() must be called before

    /// using this function.

    bool findCycle() {

      if (!_cycle_found) return false;

      _cycle_path->addBack(_policy[_cycle_node]);

      for ( Node v = _cycle_node;

            (v = _gr.target(_policy[v])) != _cycle_node; ) {

        _cycle_path->addBack(_policy[v]);

      }

      return true;

    }

    /// @}

    /// \name Query Functions

    /// The result 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 findCycle() must be called before

    /// using this function.

    Value 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 findCycle() 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>mmc.cycleMean()</tt> is just a shortcut of the

    /// following code.

    /// \code

    ///   return double(mmc.cycleLength()) / mmc.cycleArcNum();

    /// \endcode

    ///

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

    /// using this function.

    double cycleMean() const {

      return 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.

    ///

    /// \sa cyclePath()

    const Path& cycle() const {

      return *_cycle_path;

    }

    ///@}

  private:

    // Initialize the internal data structures for the current strongly

    // connected component and create the policy graph.

    // The policy graph can be represented by the _policy map because

    // the out-degree of every node is 1.

    bool initCurrentComponent(int comp) {

      // Find the nodes of the current component

      _nodes.clear();

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

        if (_comp[n] == comp) _nodes.push_back(n);

      }

      if (_nodes.size() <= 1) return false;

      // Find the arcs of the current component

      _arcs.clear();

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

        if ( _comp[_gr.source(e)] == comp &&

             _comp[_gr.target(e)] == comp )

          _arcs.push_back(e);

      }

      // Initialize _reached, _dist, _policy maps

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

        _reached[_nodes[i]] = false;

        _policy[_nodes[i]] = INVALID;

      }

      Node u; Arc e;

      for (int j = 0; j < int(_arcs.size()); ++j) {

        e = _arcs[j];

        u = _gr.source(e);

        if (!_reached[u] || _length[e] < _dist[u]) {

          _dist[u] = _length[e];

          _policy[u] = e;

          _reached[u] = true;

        }

      }

      return true;

    }

    // Find all cycles in the policy graph.

    // Set _cycle_found to true if a cycle is found and set

    // _cycle_length, _cycle_size, _cycle_node to represent the minimum

    // mean cycle in the policy graph.

    bool findPolicyCycles() {

      typename Digraph::template NodeMap<int> level(_gr, -1);

      bool curr_cycle_found = false;

      Value clength;

      int csize;

      int path_cnt = 0;

      Node u, v;

      // Searching for cycles

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

        if (level[_nodes[i]] < 0) {

          u = _nodes[i];

          level[u] = path_cnt;

          while (level[u = _gr.target(_policy[u])] < 0)

            level[u] = path_cnt;

          if (level[u] == path_cnt) {

            // A cycle is found

            curr_cycle_found = true;

            clength = _length[_policy[u]];

            csize = 1;

            for (v = u; (v = _gr.target(_policy[v])) != u; ) {

              clength += _length[_policy[v]];

              ++csize;

            }

            if ( !_cycle_found ||

                 clength * _cycle_size < _cycle_length * csize ) {

              _cycle_found = true;

              _cycle_length = clength;

              _cycle_size = csize;

              _cycle_node = u;

            }

          }

          ++path_cnt;

        }

      }

      return curr_cycle_found;

    }

    // Contract the policy graph to be connected by cutting all cycles

    // except for the main cycle (i.e. the minimum mean cycle).

    void contractPolicyGraph(int comp) {

      // Find the component of the main cycle using reverse BFS search

      typename Digraph::template NodeMap<int> found(_gr, false);

      std::deque<Node> queue;

      queue.push_back(_cycle_node);

      found[_cycle_node] = true;

      Node u, v;

      while (!queue.empty()) {

        v = queue.front(); queue.pop_front();

        for (InArcIt e(_gr, v); e != INVALID; ++e) {

          u = _gr.source(e);

          if (_policy[u] == e && !found[u]) {

            found[u] = true;

            queue.push_back(u);

          }

        }

      }

      // Connect all other nodes to this component using reverse BFS search

      queue.clear();

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

        if (found[_nodes[i]]) queue.push_back(_nodes[i]);

      int found_cnt = queue.size();

      while (found_cnt < int(_nodes.size())) {

        v = queue.front(); queue.pop_front();

        for (InArcIt e(_gr, v); e != INVALID; ++e) {

          u = _gr.source(e);

          if (_comp[u] == comp && !found[u]) {

            found[u] = true;

            ++found_cnt;

            _policy[u] = e;

            queue.push_back(u);

          }

        }

      }

    }

    // Compute node distances in the policy graph and update the

    // policy graph if the node distances can be improved.

    bool computeNodeDistances() {

      // Compute node distances using reverse BFS search

      double cycle_mean = double(_cycle_length) / _cycle_size;

      typename Digraph::template NodeMap<int> found(_gr, false);

      std::deque<Node> queue;

      queue.push_back(_cycle_node);

      found[_cycle_node] = true;

      _dist[_cycle_node] = 0;

      Node u, v;

      while (!queue.empty()) {

        v = queue.front(); queue.pop_front();

        for (InArcIt e(_gr, v); e != INVALID; ++e) {

          u = _gr.source(e);

          if (_policy[u] == e && !found[u]) {

            found[u] = true;

            _dist[u] = _dist[v] + _length[e] - cycle_mean;

            queue.push_back(u);

          }

        }

      }

      // Improving node distances

      bool improved = false;

      for (int j = 0; j < int(_arcs.size()); ++j) {

        Arc e = _arcs[j];

        u = _gr.source(e); v = _gr.target(e);

        double delta = _dist[v] + _length[e] - cycle_mean;

        if (_tol.less(delta, _dist[u])) {

          improved = true;

          _dist[u] = delta;

          _policy[u] = e;

        }

      }

      return improved;

    }

  }; //class MinMeanCycle

  ///@}

} //namespace lemon

#endif //LEMON_MIN_MEAN_CYCLE_H