kpeter@758: /* -*- C++ -*-
kpeter@758:  *
kpeter@758:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@758:  *
kpeter@758:  * Copyright (C) 2003-2008
kpeter@758:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@758:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@758:  *
kpeter@758:  * Permission to use, modify and distribute this software is granted
kpeter@758:  * provided that this copyright notice appears in all copies. For
kpeter@758:  * precise terms see the accompanying LICENSE file.
kpeter@758:  *
kpeter@758:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@758:  * express or implied, and with no claim as to its suitability for any
kpeter@758:  * purpose.
kpeter@758:  *
kpeter@758:  */
kpeter@758: 
kpeter@764: #ifndef LEMON_HOWARD_H
kpeter@764: #define LEMON_HOWARD_H
kpeter@758: 
kpeter@768: /// \ingroup min_mean_cycle
kpeter@758: ///
kpeter@758: /// \file
kpeter@758: /// \brief Howard's algorithm for finding a minimum mean cycle.
kpeter@758: 
kpeter@758: #include <vector>
kpeter@763: #include <limits>
kpeter@758: #include <lemon/core.h>
kpeter@758: #include <lemon/path.h>
kpeter@758: #include <lemon/tolerance.h>
kpeter@758: #include <lemon/connectivity.h>
kpeter@758: 
kpeter@758: namespace lemon {
kpeter@758: 
kpeter@764:   /// \brief Default traits class of Howard class.
kpeter@761:   ///
kpeter@764:   /// Default traits class of Howard class.
kpeter@761:   /// \tparam GR The type of the digraph.
kpeter@761:   /// \tparam LEN The type of the length map.
kpeter@761:   /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.
kpeter@761: #ifdef DOXYGEN
kpeter@761:   template <typename GR, typename LEN>
kpeter@761: #else
kpeter@761:   template <typename GR, typename LEN,
kpeter@761:     bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
kpeter@761: #endif
kpeter@764:   struct HowardDefaultTraits
kpeter@761:   {
kpeter@761:     /// The type of the digraph
kpeter@761:     typedef GR Digraph;
kpeter@761:     /// The type of the length map
kpeter@761:     typedef LEN LengthMap;
kpeter@761:     /// The type of the arc lengths
kpeter@761:     typedef typename LengthMap::Value Value;
kpeter@761: 
kpeter@761:     /// \brief The large value type used for internal computations
kpeter@761:     ///
kpeter@761:     /// The large value type used for internal computations.
kpeter@761:     /// It is \c long \c long if the \c Value type is integer,
kpeter@761:     /// otherwise it is \c double.
kpeter@761:     /// \c Value must be convertible to \c LargeValue.
kpeter@761:     typedef double LargeValue;
kpeter@761: 
kpeter@761:     /// The tolerance type used for internal computations
kpeter@761:     typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@761: 
kpeter@761:     /// \brief The path type of the found cycles
kpeter@761:     ///
kpeter@761:     /// The path type of the found cycles.
kpeter@761:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@761:     /// and it must have an \c addBack() function.
kpeter@761:     typedef lemon::Path<Digraph> Path;
kpeter@761:   };
kpeter@761: 
kpeter@761:   // Default traits class for integer value types
kpeter@761:   template <typename GR, typename LEN>
kpeter@764:   struct HowardDefaultTraits<GR, LEN, true>
kpeter@761:   {
kpeter@761:     typedef GR Digraph;
kpeter@761:     typedef LEN LengthMap;
kpeter@761:     typedef typename LengthMap::Value Value;
kpeter@761: #ifdef LEMON_HAVE_LONG_LONG
kpeter@761:     typedef long long LargeValue;
kpeter@761: #else
kpeter@761:     typedef long LargeValue;
kpeter@761: #endif
kpeter@761:     typedef lemon::Tolerance<LargeValue> Tolerance;
kpeter@761:     typedef lemon::Path<Digraph> Path;
kpeter@761:   };
kpeter@761: 
kpeter@761: 
kpeter@768:   /// \addtogroup min_mean_cycle
kpeter@758:   /// @{
kpeter@758: 
kpeter@758:   /// \brief Implementation of Howard's algorithm for finding a minimum
kpeter@758:   /// mean cycle.
kpeter@758:   ///
kpeter@764:   /// This class implements Howard's policy iteration algorithm for finding
kpeter@771:   /// a directed cycle of minimum mean length (cost) in a digraph
kpeter@771:   /// \ref amo93networkflows, \ref dasdan98minmeancycle.
kpeter@768:   /// This class provides the most efficient algorithm for the
kpeter@768:   /// minimum mean cycle problem, though the best known theoretical
kpeter@768:   /// bound on its running time is exponential.
kpeter@758:   ///
kpeter@758:   /// \tparam GR The type of the digraph the algorithm runs on.
kpeter@758:   /// \tparam LEN The type of the length map. The default
kpeter@758:   /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
kpeter@825:   /// \tparam TR The traits class that defines various types used by the
kpeter@825:   /// algorithm. By default, it is \ref HowardDefaultTraits
kpeter@825:   /// "HowardDefaultTraits<GR, LEN>".
kpeter@825:   /// In most cases, this parameter should not be set directly,
kpeter@825:   /// consider to use the named template parameters instead.
kpeter@758: #ifdef DOXYGEN
kpeter@761:   template <typename GR, typename LEN, typename TR>
kpeter@758: #else
kpeter@758:   template < typename GR,
kpeter@761:              typename LEN = typename GR::template ArcMap<int>,
kpeter@764:              typename TR = HowardDefaultTraits<GR, LEN> >
kpeter@758: #endif
kpeter@764:   class Howard
kpeter@758:   {
kpeter@758:   public:
kpeter@758:   
kpeter@761:     /// The type of the digraph
kpeter@761:     typedef typename TR::Digraph Digraph;
kpeter@758:     /// The type of the length map
kpeter@761:     typedef typename TR::LengthMap LengthMap;
kpeter@758:     /// The type of the arc lengths
kpeter@761:     typedef typename TR::Value Value;
kpeter@761: 
kpeter@761:     /// \brief The large value type
kpeter@761:     ///
kpeter@761:     /// The large value type used for internal computations.
kpeter@825:     /// By default, it is \c long \c long if the \c Value type is integer,
kpeter@761:     /// otherwise it is \c double.
kpeter@761:     typedef typename TR::LargeValue LargeValue;
kpeter@761: 
kpeter@761:     /// The tolerance type
kpeter@761:     typedef typename TR::Tolerance Tolerance;
kpeter@761: 
kpeter@761:     /// \brief The path type of the found cycles
kpeter@761:     ///
kpeter@761:     /// The path type of the found cycles.
kpeter@764:     /// Using the \ref HowardDefaultTraits "default traits class",
kpeter@761:     /// it is \ref lemon::Path "Path<Digraph>".
kpeter@761:     typedef typename TR::Path Path;
kpeter@761: 
kpeter@764:     /// The \ref HowardDefaultTraits "traits class" of the algorithm
kpeter@761:     typedef TR Traits;
kpeter@758: 
kpeter@758:   private:
kpeter@758: 
kpeter@758:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@758:   
kpeter@758:     // The digraph the algorithm runs on
kpeter@758:     const Digraph &_gr;
kpeter@758:     // The length of the arcs
kpeter@758:     const LengthMap &_length;
kpeter@758: 
kpeter@760:     // Data for the found cycles
kpeter@760:     bool _curr_found, _best_found;
kpeter@761:     LargeValue _curr_length, _best_length;
kpeter@760:     int _curr_size, _best_size;
kpeter@760:     Node _curr_node, _best_node;
kpeter@760: 
kpeter@758:     Path *_cycle_path;
kpeter@760:     bool _local_path;
kpeter@758: 
kpeter@760:     // Internal data used by the algorithm
kpeter@760:     typename Digraph::template NodeMap<Arc> _policy;
kpeter@760:     typename Digraph::template NodeMap<bool> _reached;
kpeter@760:     typename Digraph::template NodeMap<int> _level;
kpeter@761:     typename Digraph::template NodeMap<LargeValue> _dist;
kpeter@758: 
kpeter@760:     // Data for storing the strongly connected components
kpeter@760:     int _comp_num;
kpeter@758:     typename Digraph::template NodeMap<int> _comp;
kpeter@760:     std::vector<std::vector<Node> > _comp_nodes;
kpeter@760:     std::vector<Node>* _nodes;
kpeter@760:     typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;
kpeter@760:     
kpeter@760:     // Queue used for BFS search
kpeter@760:     std::vector<Node> _queue;
kpeter@760:     int _qfront, _qback;
kpeter@761: 
kpeter@761:     Tolerance _tolerance;
kpeter@761:   
kpeter@767:     // Infinite constant
kpeter@767:     const LargeValue INF;
kpeter@767: 
kpeter@761:   public:
kpeter@761:   
kpeter@761:     /// \name Named Template Parameters
kpeter@761:     /// @{
kpeter@761: 
kpeter@761:     template <typename T>
kpeter@761:     struct SetLargeValueTraits : public Traits {
kpeter@761:       typedef T LargeValue;
kpeter@761:       typedef lemon::Tolerance<T> Tolerance;
kpeter@761:     };
kpeter@761: 
kpeter@761:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@761:     /// \c LargeValue type.
kpeter@761:     ///
kpeter@761:     /// \ref named-templ-param "Named parameter" for setting \c LargeValue
kpeter@761:     /// type. It is used for internal computations in the algorithm.
kpeter@761:     template <typename T>
kpeter@761:     struct SetLargeValue
kpeter@764:       : public Howard<GR, LEN, SetLargeValueTraits<T> > {
kpeter@764:       typedef Howard<GR, LEN, SetLargeValueTraits<T> > Create;
kpeter@761:     };
kpeter@761: 
kpeter@761:     template <typename T>
kpeter@761:     struct SetPathTraits : public Traits {
kpeter@761:       typedef T Path;
kpeter@761:     };
kpeter@761: 
kpeter@761:     /// \brief \ref named-templ-param "Named parameter" for setting
kpeter@761:     /// \c %Path type.
kpeter@761:     ///
kpeter@761:     /// \ref named-templ-param "Named parameter" for setting the \c %Path
kpeter@761:     /// type of the found cycles.
kpeter@761:     /// It must conform to the \ref lemon::concepts::Path "Path" concept
kpeter@761:     /// and it must have an \c addBack() function.
kpeter@761:     template <typename T>
kpeter@761:     struct SetPath
kpeter@764:       : public Howard<GR, LEN, SetPathTraits<T> > {
kpeter@764:       typedef Howard<GR, LEN, SetPathTraits<T> > Create;
kpeter@761:     };
kpeter@760:     
kpeter@761:     /// @}
kpeter@758: 
kpeter@758:   public:
kpeter@758: 
kpeter@758:     /// \brief Constructor.
kpeter@758:     ///
kpeter@758:     /// The constructor of the class.
kpeter@758:     ///
kpeter@758:     /// \param digraph The digraph the algorithm runs on.
kpeter@758:     /// \param length The lengths (costs) of the arcs.
kpeter@764:     Howard( const Digraph &digraph,
kpeter@764:             const LengthMap &length ) :
kpeter@767:       _gr(digraph), _length(length), _best_found(false),
kpeter@767:       _best_length(0), _best_size(1), _cycle_path(NULL), _local_path(false),
kpeter@760:       _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),
kpeter@767:       _comp(digraph), _in_arcs(digraph),
kpeter@767:       INF(std::numeric_limits<LargeValue>::has_infinity ?
kpeter@767:           std::numeric_limits<LargeValue>::infinity() :
kpeter@767:           std::numeric_limits<LargeValue>::max())
kpeter@758:     {}
kpeter@758: 
kpeter@758:     /// Destructor.
kpeter@764:     ~Howard() {
kpeter@758:       if (_local_path) delete _cycle_path;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Set the path structure for storing the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function sets an external path structure for storing the
kpeter@758:     /// found cycle.
kpeter@758:     ///
kpeter@758:     /// If you don't call this function before calling \ref run() or
kpeter@759:     /// \ref findMinMean(), it will allocate a local \ref Path "path"
kpeter@758:     /// structure. The destuctor deallocates this automatically
kpeter@758:     /// allocated object, of course.
kpeter@758:     ///
kpeter@758:     /// \note The algorithm calls only the \ref lemon::Path::addBack()
kpeter@758:     /// "addBack()" function of the given path structure.
kpeter@758:     ///
kpeter@758:     /// \return <tt>(*this)</tt>
kpeter@764:     Howard& cycle(Path &path) {
kpeter@758:       if (_local_path) {
kpeter@758:         delete _cycle_path;
kpeter@758:         _local_path = false;
kpeter@758:       }
kpeter@758:       _cycle_path = &path;
kpeter@758:       return *this;
kpeter@758:     }
kpeter@758: 
kpeter@769:     /// \brief Set the tolerance used by the algorithm.
kpeter@769:     ///
kpeter@769:     /// This function sets the tolerance object used by the algorithm.
kpeter@769:     ///
kpeter@769:     /// \return <tt>(*this)</tt>
kpeter@769:     Howard& tolerance(const Tolerance& tolerance) {
kpeter@769:       _tolerance = tolerance;
kpeter@769:       return *this;
kpeter@769:     }
kpeter@769: 
kpeter@769:     /// \brief Return a const reference to the tolerance.
kpeter@769:     ///
kpeter@769:     /// This function returns a const reference to the tolerance object
kpeter@769:     /// used by the algorithm.
kpeter@769:     const Tolerance& tolerance() const {
kpeter@769:       return _tolerance;
kpeter@769:     }
kpeter@769: 
kpeter@758:     /// \name Execution control
kpeter@758:     /// The simplest way to execute the algorithm is to call the \ref run()
kpeter@758:     /// function.\n
kpeter@759:     /// If you only need the minimum mean length, you may call
kpeter@759:     /// \ref findMinMean().
kpeter@758: 
kpeter@758:     /// @{
kpeter@758: 
kpeter@758:     /// \brief Run the algorithm.
kpeter@758:     ///
kpeter@758:     /// This function runs the algorithm.
kpeter@759:     /// It can be called more than once (e.g. if the underlying digraph
kpeter@759:     /// and/or the arc lengths have been modified).
kpeter@758:     ///
kpeter@758:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@758:     ///
kpeter@759:     /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
kpeter@758:     /// \code
kpeter@759:     ///   return mmc.findMinMean() && mmc.findCycle();
kpeter@758:     /// \endcode
kpeter@758:     bool run() {
kpeter@758:       return findMinMean() && findCycle();
kpeter@758:     }
kpeter@758: 
kpeter@759:     /// \brief Find the minimum cycle mean.
kpeter@758:     ///
kpeter@759:     /// This function finds the minimum mean length of the directed
kpeter@759:     /// cycles in the digraph.
kpeter@758:     ///
kpeter@759:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@759:     bool findMinMean() {
kpeter@760:       // Initialize and find strongly connected components
kpeter@760:       init();
kpeter@760:       findComponents();
kpeter@760:       
kpeter@759:       // Find the minimum cycle mean in the components
kpeter@758:       for (int comp = 0; comp < _comp_num; ++comp) {
kpeter@760:         // Find the minimum mean cycle in the current component
kpeter@760:         if (!buildPolicyGraph(comp)) continue;
kpeter@758:         while (true) {
kpeter@760:           findPolicyCycle();
kpeter@758:           if (!computeNodeDistances()) break;
kpeter@758:         }
kpeter@760:         // Update the best cycle (global minimum mean cycle)
kpeter@767:         if ( _curr_found && (!_best_found ||
kpeter@760:              _curr_length * _best_size < _best_length * _curr_size) ) {
kpeter@760:           _best_found = true;
kpeter@760:           _best_length = _curr_length;
kpeter@760:           _best_size = _curr_size;
kpeter@760:           _best_node = _curr_node;
kpeter@760:         }
kpeter@758:       }
kpeter@760:       return _best_found;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Find a minimum mean directed cycle.
kpeter@758:     ///
kpeter@758:     /// This function finds a directed cycle of minimum mean length
kpeter@758:     /// in the digraph using the data computed by findMinMean().
kpeter@758:     ///
kpeter@758:     /// \return \c true if a directed cycle exists in the digraph.
kpeter@758:     ///
kpeter@759:     /// \pre \ref findMinMean() must be called before using this function.
kpeter@758:     bool findCycle() {
kpeter@760:       if (!_best_found) return false;
kpeter@760:       _cycle_path->addBack(_policy[_best_node]);
kpeter@760:       for ( Node v = _best_node;
kpeter@760:             (v = _gr.target(_policy[v])) != _best_node; ) {
kpeter@758:         _cycle_path->addBack(_policy[v]);
kpeter@758:       }
kpeter@758:       return true;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// @}
kpeter@758: 
kpeter@758:     /// \name Query Functions
kpeter@759:     /// The results of the algorithm can be obtained using these
kpeter@758:     /// functions.\n
kpeter@758:     /// The algorithm should be executed before using them.
kpeter@758: 
kpeter@758:     /// @{
kpeter@758: 
kpeter@758:     /// \brief Return the total length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the total length of the found cycle.
kpeter@758:     ///
kpeter@760:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758:     /// using this function.
kpeter@761:     LargeValue cycleLength() const {
kpeter@760:       return _best_length;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the number of arcs on the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the number of arcs on the found cycle.
kpeter@758:     ///
kpeter@760:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758:     /// using this function.
kpeter@758:     int cycleArcNum() const {
kpeter@760:       return _best_size;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the mean length of the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns the mean length of the found cycle.
kpeter@758:     ///
kpeter@760:     /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
kpeter@758:     /// following code.
kpeter@758:     /// \code
kpeter@760:     ///   return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
kpeter@758:     /// \endcode
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findMinMean() must be called before
kpeter@758:     /// using this function.
kpeter@758:     double cycleMean() const {
kpeter@760:       return static_cast<double>(_best_length) / _best_size;
kpeter@758:     }
kpeter@758: 
kpeter@758:     /// \brief Return the found cycle.
kpeter@758:     ///
kpeter@758:     /// This function returns a const reference to the path structure
kpeter@758:     /// storing the found cycle.
kpeter@758:     ///
kpeter@758:     /// \pre \ref run() or \ref findCycle() must be called before using
kpeter@758:     /// this function.
kpeter@758:     const Path& cycle() const {
kpeter@758:       return *_cycle_path;
kpeter@758:     }
kpeter@758: 
kpeter@758:     ///@}
kpeter@758: 
kpeter@758:   private:
kpeter@758: 
kpeter@760:     // Initialize
kpeter@760:     void init() {
kpeter@760:       if (!_cycle_path) {
kpeter@760:         _local_path = true;
kpeter@760:         _cycle_path = new Path;
kpeter@758:       }
kpeter@760:       _queue.resize(countNodes(_gr));
kpeter@760:       _best_found = false;
kpeter@760:       _best_length = 0;
kpeter@760:       _best_size = 1;
kpeter@760:       _cycle_path->clear();
kpeter@760:     }
kpeter@760:     
kpeter@760:     // Find strongly connected components and initialize _comp_nodes
kpeter@760:     // and _in_arcs
kpeter@760:     void findComponents() {
kpeter@760:       _comp_num = stronglyConnectedComponents(_gr, _comp);
kpeter@760:       _comp_nodes.resize(_comp_num);
kpeter@760:       if (_comp_num == 1) {
kpeter@760:         _comp_nodes[0].clear();
kpeter@760:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760:           _comp_nodes[0].push_back(n);
kpeter@760:           _in_arcs[n].clear();
kpeter@760:           for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760:             _in_arcs[n].push_back(a);
kpeter@760:           }
kpeter@760:         }
kpeter@760:       } else {
kpeter@760:         for (int i = 0; i < _comp_num; ++i)
kpeter@760:           _comp_nodes[i].clear();
kpeter@760:         for (NodeIt n(_gr); n != INVALID; ++n) {
kpeter@760:           int k = _comp[n];
kpeter@760:           _comp_nodes[k].push_back(n);
kpeter@760:           _in_arcs[n].clear();
kpeter@760:           for (InArcIt a(_gr, n); a != INVALID; ++a) {
kpeter@760:             if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);
kpeter@760:           }
kpeter@760:         }
kpeter@758:       }
kpeter@760:     }
kpeter@760: 
kpeter@760:     // Build the policy graph in the given strongly connected component
kpeter@760:     // (the out-degree of every node is 1)
kpeter@760:     bool buildPolicyGraph(int comp) {
kpeter@760:       _nodes = &(_comp_nodes[comp]);
kpeter@760:       if (_nodes->size() < 1 ||
kpeter@760:           (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {
kpeter@760:         return false;
kpeter@758:       }
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@767:         _dist[(*_nodes)[i]] = INF;
kpeter@760:       }
kpeter@760:       Node u, v;
kpeter@760:       Arc e;
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760:         v = (*_nodes)[i];
kpeter@760:         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760:           e = _in_arcs[v][j];
kpeter@760:           u = _gr.source(e);
kpeter@760:           if (_length[e] < _dist[u]) {
kpeter@760:             _dist[u] = _length[e];
kpeter@760:             _policy[u] = e;
kpeter@760:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return true;
kpeter@758:     }
kpeter@758: 
kpeter@760:     // Find the minimum mean cycle in the policy graph
kpeter@760:     void findPolicyCycle() {
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760:         _level[(*_nodes)[i]] = -1;
kpeter@760:       }
kpeter@761:       LargeValue clength;
kpeter@758:       int csize;
kpeter@758:       Node u, v;
kpeter@760:       _curr_found = false;
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760:         u = (*_nodes)[i];
kpeter@760:         if (_level[u] >= 0) continue;
kpeter@760:         for (; _level[u] < 0; u = _gr.target(_policy[u])) {
kpeter@760:           _level[u] = i;
kpeter@760:         }
kpeter@760:         if (_level[u] == i) {
kpeter@760:           // A cycle is found
kpeter@760:           clength = _length[_policy[u]];
kpeter@760:           csize = 1;
kpeter@760:           for (v = u; (v = _gr.target(_policy[v])) != u; ) {
kpeter@760:             clength += _length[_policy[v]];
kpeter@760:             ++csize;
kpeter@758:           }
kpeter@760:           if ( !_curr_found ||
kpeter@760:                (clength * _curr_size < _curr_length * csize) ) {
kpeter@760:             _curr_found = true;
kpeter@760:             _curr_length = clength;
kpeter@760:             _curr_size = csize;
kpeter@760:             _curr_node = u;
kpeter@758:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:     }
kpeter@758: 
kpeter@760:     // Contract the policy graph and compute node distances
kpeter@758:     bool computeNodeDistances() {
kpeter@760:       // Find the component of the main cycle and compute node distances
kpeter@760:       // using reverse BFS
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760:         _reached[(*_nodes)[i]] = false;
kpeter@760:       }
kpeter@760:       _qfront = _qback = 0;
kpeter@760:       _queue[0] = _curr_node;
kpeter@760:       _reached[_curr_node] = true;
kpeter@760:       _dist[_curr_node] = 0;
kpeter@758:       Node u, v;
kpeter@760:       Arc e;
kpeter@760:       while (_qfront <= _qback) {
kpeter@760:         v = _queue[_qfront++];
kpeter@760:         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760:           e = _in_arcs[v][j];
kpeter@758:           u = _gr.source(e);
kpeter@760:           if (_policy[u] == e && !_reached[u]) {
kpeter@760:             _reached[u] = true;
kpeter@761:             _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@760:             _queue[++_qback] = u;
kpeter@758:           }
kpeter@758:         }
kpeter@758:       }
kpeter@760: 
kpeter@760:       // Connect all other nodes to this component and compute node
kpeter@760:       // distances using reverse BFS
kpeter@760:       _qfront = 0;
kpeter@760:       while (_qback < int(_nodes->size())-1) {
kpeter@760:         v = _queue[_qfront++];
kpeter@760:         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760:           e = _in_arcs[v][j];
kpeter@760:           u = _gr.source(e);
kpeter@760:           if (!_reached[u]) {
kpeter@760:             _reached[u] = true;
kpeter@760:             _policy[u] = e;
kpeter@761:             _dist[u] = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@760:             _queue[++_qback] = u;
kpeter@760:           }
kpeter@760:         }
kpeter@760:       }
kpeter@760: 
kpeter@760:       // Improve node distances
kpeter@758:       bool improved = false;
kpeter@760:       for (int i = 0; i < int(_nodes->size()); ++i) {
kpeter@760:         v = (*_nodes)[i];
kpeter@760:         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {
kpeter@760:           e = _in_arcs[v][j];
kpeter@760:           u = _gr.source(e);
kpeter@761:           LargeValue delta = _dist[v] + _length[e] * _curr_size - _curr_length;
kpeter@761:           if (_tolerance.less(delta, _dist[u])) {
kpeter@760:             _dist[u] = delta;
kpeter@760:             _policy[u] = e;
kpeter@760:             improved = true;
kpeter@760:           }
kpeter@758:         }
kpeter@758:       }
kpeter@758:       return improved;
kpeter@758:     }
kpeter@758: 
kpeter@764:   }; //class Howard
kpeter@758: 
kpeter@758:   ///@}
kpeter@758: 
kpeter@758: } //namespace lemon
kpeter@758: 
kpeter@764: #endif //LEMON_HOWARD_H