/* -*- 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 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::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 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() {

       // Initialize

       _tol.epsilon(1e-6);

       if (!_cycle_path) {

         _local_path = true;

         _cycle_path = new Path;

       }

       _cycle_path->clear();

       _cycle_found = false;

       // Find the minimum cycle mean in the components

       _comp_num = stronglyConnectedComponents(_gr, _comp);

       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 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 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 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