/* -*- 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 directed cycle.

 #include <vector>

 #include <lemon/graph_utils.h>

 #include <lemon/path.h>

 #include <lemon/tolerance.h>

 #include <lemon/topology.h>

 namespace lemon {

   /// \addtogroup shortest_path

   /// @{

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

   /// mean directed cycle.

   ///

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

   /// minimum mean directed cycle.

   ///

   /// \tparam Graph The directed graph type the algorithm runs on.

   /// \tparam LengthMap The type of the length (cost) map.

   ///

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

   ///

   /// \author Peter Kovacs

   template < typename Graph,

              typename LengthMap = typename Graph::template EdgeMap<int> >

   class MinMeanCycle

   {

     GRAPH_TYPEDEFS(typename Graph);

     typedef typename LengthMap::Value Length;

     typedef lemon::Path<Graph> Path;

   private:

     // The directed graph the algorithm runs on

     const Graph &_graph;

     // The length of the edges

     const LengthMap &_length;

     // The total length of the found cycle

     Length _cycle_length;

     // The number of edges on the found cycle

     int _cycle_size;

     // The found cycle

     Path *_cycle_path;

     bool _local_path;

     bool _cycle_found;

     Node _cycle_node;

     typename Graph::template NodeMap<bool> _reached;

     typename Graph::template NodeMap<double> _dist;

     typename Graph::template NodeMap<Edge> _policy;

     typename Graph::template NodeMap<int> _component;

     int _component_num;

     std::vector<Node> _nodes;

     std::vector<Edge> _edges;

     Tolerance<double> _tolerance;

   public:

     /// \brief The constructor of the class.

     ///

     /// The constructor of the class.

     ///

     /// \param graph The directed graph the algorithm runs on.

     /// \param length The length (cost) of the edges.

     MinMeanCycle( const Graph &graph,

                   const LengthMap &length ) :

       _graph(graph), _length(length), _cycle_length(0), _cycle_size(-1),

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

       _dist(graph), _policy(graph), _component(graph)

     {}

     /// The destructor of the class.

     ~MinMeanCycle() {

       if (_local_path) delete _cycle_path;

     }

     /// \brief Sets the \ref Path "path" structure for storing the found

     /// cycle.

     ///

     /// Sets an external \ref Path "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 map,

     /// of course.

     ///

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

     /// "addBack()" function of the given \ref Path "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 run()

     /// function.

     /// \n

     /// If you only need the minimum mean value, you may call init()

     /// and findMinMean().

     /// \n

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

     /// underlaying graph and/or the edge costs were modified), you may

     /// not create a new instance of the class, rather call reset(),

     /// findMinMean(), and findCycle() instead.

     /// @{

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm.

     ///

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

     ///

     /// \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 Initializes the internal data structures.

     ///

     /// Initializes the internal data structures.

     ///

     /// \sa reset()

     void init() {

       _tolerance.epsilon(1e-6);

       if (!_cycle_path) {

         _local_path = true;

         _cycle_path = new Path;

       }

       _cycle_found = false;

       _component_num = stronglyConnectedComponents(_graph, _component);

     }

     /// \brief Resets the internal data structures.

     ///

     /// Resets the internal data structures so that \ref findMinMean()

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

     /// underlaying graph has been modified).

     ///

     /// \sa init()

     void reset() {

       if (_cycle_path) _cycle_path->clear();

       _cycle_found = false;

       _component_num = stronglyConnectedComponents(_graph, _component);

     }

     /// \brief Finds the minimum cycle mean length in the graph.

     ///

     /// Computes all the required data and finds the minimum cycle mean

     /// length in the graph.

     ///

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

     ///

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

     bool findMinMean() {

       // Finding the minimum mean cycle in the components

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

         if (!initCurrentComponent(comp)) continue;

         while (true) {

           if (!findPolicyCycles()) break;

           contractPolicyGraph(comp);

           if (!computeNodeDistances(comp)) break;

         }

       }

       return _cycle_found;

     }

     /// \brief Finds a critical (minimum mean) directed cycle.

     ///

     /// Finds a critical (minimum mean) directed cycle using the data

     /// computed in the \ref findMinMean() function.

     ///

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

     ///

     /// \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 = _graph.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 Returns the total length of the found cycle.

     ///

     /// Returns the total length of the found cycle.

     ///

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

     /// using this function.

     Length cycleLength() const {

       return _cycle_length;

     }

     /// \brief Returns the number of edges on the found cycle.

     ///

     /// Returns the number of edges on the found cycle.

     ///

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

     /// using this function.

     int cycleEdgeNum() const {

       return _cycle_size;

     }

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

     ///

     /// Returns the mean length of the found cycle.

     ///

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

     /// using this function.

     ///

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

     /// following code.

     /// \code

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

     /// \endcode

     double cycleMean() const {

       return double(_cycle_length) / _cycle_size;

     }

     /// \brief Returns a const reference to the \ref Path "path"

     /// structure storing the found cycle.

     ///

     /// Returns a const reference to the \ref Path "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:

     // Initializes the internal data structures for the current strongly

     // connected component and creating 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) {

       // Finding the nodes of the current component

       _nodes.clear();

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

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

       }

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

       // Finding the edges of the current component

       _edges.clear();

       for (EdgeIt e(_graph); e != INVALID; ++e) {

         if ( _component[_graph.source(e)] == comp &&

              _component[_graph.target(e)] == comp )

           _edges.push_back(e);

       }

       // Initializing _reached, _dist, _policy maps

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

         _reached[_nodes[i]] = false;

         _policy[_nodes[i]] = INVALID;

       }

       Node u; Edge e;

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

         e = _edges[j];

         u = _graph.source(e);

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

           _dist[u] = _length[e];

           _policy[u] = e;

           _reached[u] = true;

         }

       }

       return true;

     }

     // Finds all cycles in the policy graph.

     // Sets _cycle_found to true if a cycle is found and sets

     // _cycle_length, _cycle_size, _cycle_node to represent the minimum

     // mean cycle in the policy graph.

     bool findPolicyCycles() {

       typename Graph::template NodeMap<int> level(_graph, -1);

       bool curr_cycle_found = false;

       Length 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 = _graph.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 = _graph.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;

     }

     // Contracts 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) {

       // Finding the component of the main cycle using

       // reverse BFS search

       typename Graph::template NodeMap<int> found(_graph, 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 (InEdgeIt e(_graph, v); e != INVALID; ++e) {

           u = _graph.source(e);

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

             found[u] = true;

             queue.push_back(u);

           }

         }

       }

       // Connecting 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()) && !queue.empty()) {

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

         for (InEdgeIt e(_graph, v); e != INVALID; ++e) {

           u = _graph.source(e);

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

             found[u] = true;

             ++found_cnt;

             _policy[u] = e;

             queue.push_back(u);

           }

         }

       }

     }

     // Computes node distances in the policy graph and updates the

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

     bool computeNodeDistances(int comp) {

       // Computing node distances using reverse BFS search

       double cycle_mean = double(_cycle_length) / _cycle_size;

       typename Graph::template NodeMap<int> found(_graph, 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 (InEdgeIt e(_graph, v); e != INVALID; ++e) {

           u = _graph.source(e);

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

             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(_edges.size()); ++j) {

         Edge e = _edges[j];

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

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

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

           improved = true;

           _dist[u] = delta;

           _policy[u] = e;

         }

       }

       return improved;

     }

   }; //class MinMeanCycle

   ///@}

 } //namespace lemon

 #endif //LEMON_MIN_MEAN_CYCLE_H