// The total length of the found cycle

     // Data for the found cycles

     Value _cycle_length;

     bool _curr_found, _best_found;

     // The number of arcs on the found cycle

     Value _curr_length, _best_length;

     int _cycle_size;

     int _curr_size, _best_size;

     // The found cycle

     Node _curr_node, _best_node;

     bool _cycle_found;

     Node _cycle_node;

     // Internal data used by the algorithm

     typename Digraph::template NodeMap<Arc> _policy;

     typename Digraph::template NodeMap<Arc> _policy;

     // Data for storing the strongly connected components

     int _comp_num;

     int _comp_num;

     std::vector<std::vector<Node> > _comp_nodes;

     std::vector<Node>* _nodes;

     std::vector<Node> _nodes;

     typename Digraph::template NodeMap<std::vector<Arc> > _in_arcs;

     std::vector<Arc> _arcs;

     // Queue used for BFS search

     std::vector<Node> _queue;

     int _qfront, _qback;

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

       _gr(digraph), _length(length), _cycle_path(NULL), _local_path(false),

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

       _policy(digraph), _reached(digraph), _level(digraph), _dist(digraph),

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

       _comp(digraph), _in_arcs(digraph)

       // Initialize

       // Initialize and find strongly connected components

       init();

       findComponents();

       // Find the minimum cycle mean in the components

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

         // Find the minimum mean cycle in the current component

         if (!buildPolicyGraph(comp)) continue;

         while (true) {

           findPolicyCycle();

           if (!computeNodeDistances()) break;

         }

         // Update the best cycle (global minimum mean cycle)

         if ( !_best_found || (_curr_found &&

              _curr_length * _best_size < _best_length * _curr_size) ) {

           _best_found = true;

           _best_length = _curr_length;

           _best_size = _curr_size;

           _best_node = _curr_node;

         }

       }

       return _best_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 (!_best_found) return false;

       _cycle_path->addBack(_policy[_best_node]);

       for ( Node v = _best_node;

             (v = _gr.target(_policy[v])) != _best_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 findMinMean() must be called before

     /// using this function.

     Value cycleLength() const {

       return _best_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 _best_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>(_best_length) / _best_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

     void init() {

       _cycle_found = false;

     }

       // Find the minimum cycle mean in the components

     // Find strongly connected components and initialize _comp_nodes

     // and _in_arcs

     void findComponents() {

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

       _comp_nodes.resize(_comp_num);

         if (!initCurrentComponent(comp)) continue;

       if (_comp_num == 1) {

         while (true) {

         _comp_nodes[0].clear();

           if (!findPolicyCycles()) break;

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

           contractPolicyGraph(comp);

           _comp_nodes[0].push_back(n);

           if (!computeNodeDistances()) break;

           _in_arcs[n].clear();

         }

           for (InArcIt a(_gr, n); a != INVALID; ++a) {

       }

             _in_arcs[n].push_back(a);

       return _cycle_found;

           }

     }

         }

       } else {

     /// \brief Find a minimum mean directed cycle.

         for (int i = 0; i < _comp_num; ++i)

     ///

           _comp_nodes[i].clear();

     /// This function finds a directed cycle of minimum mean length

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

     /// in the digraph using the data computed by findMinMean().

           int k = _comp[n];

     ///

           _comp_nodes[k].push_back(n);

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

           _in_arcs[n].clear();

     ///

           for (InArcIt a(_gr, n); a != INVALID; ++a) {

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

             if (_comp[_gr.source(a)] == k) _in_arcs[n].push_back(a);

     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]);

     // Build the policy graph in the given strongly connected component

     // (the out-degree of every node is 1)

     bool buildPolicyGraph(int comp) {

       _nodes = &(_comp_nodes[comp]);

       if (_nodes->size() < 1 ||

           (_nodes->size() == 1 && _in_arcs[(*_nodes)[0]].size() == 0)) {

         return false;

       }

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

         _dist[(*_nodes)[i]] = std::numeric_limits<double>::max();

       }

       Node u, v;

       Arc e;

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

         v = (*_nodes)[i];

         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {

           e = _in_arcs[v][j];

           u = _gr.source(e);

           if (_length[e] < _dist[u]) {

             _dist[u] = _length[e];

             _policy[u] = e;

           }

         }

     /// @}

     // Find the minimum mean cycle in the policy graph

     void findPolicyCycle() {

     /// \name Query Functions

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

     /// The results of the algorithm can be obtained using these

         _level[(*_nodes)[i]] = -1;

     /// 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;

       // Searching for cycles

       _curr_found = false;

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

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

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

         u = (*_nodes)[i];

           u = _nodes[i];

         if (_level[u] >= 0) continue;

           level[u] = path_cnt;

         for (; _level[u] < 0; u = _gr.target(_policy[u])) {

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

           _level[u] = i;

             level[u] = path_cnt;

         }

           if (level[u] == path_cnt) {

         if (_level[u] == i) {

             // A cycle is found

           // A cycle is found

             curr_cycle_found = true;

           clength = _length[_policy[u]];

             clength = _length[_policy[u]];

           csize = 1;

             csize = 1;

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

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

             clength += _length[_policy[v]];

               clength += _length[_policy[v]];

             ++csize;

               ++csize;

           }

             }

           if ( !_curr_found ||

             if ( !_cycle_found ||

                (clength * _curr_size < _curr_length * csize) ) {

                  clength * _cycle_size < _cycle_length * csize ) {

             _curr_found = true;

               _cycle_found = true;

             _curr_length = clength;

               _cycle_length = clength;

             _curr_size = csize;

               _cycle_size = csize;

             _curr_node = u;

               _cycle_node = u;

           }

             }

         }

           }

       }

           ++path_cnt;

     }

         }

       }

     // Contract the policy graph and compute node distances

       return curr_cycle_found;

     bool computeNodeDistances() {

     }

       // Find the component of the main cycle and compute node distances

       // using reverse BFS

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

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

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

         _reached[(*_nodes)[i]] = false;

     void contractPolicyGraph(int comp) {

       }

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

       double curr_mean = double(_curr_length) / _curr_size;

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

       _qfront = _qback = 0;

       std::deque<Node> queue;

       _queue[0] = _curr_node;

       queue.push_back(_cycle_node);

       _reached[_curr_node] = true;

       found[_cycle_node] = true;

       _dist[_curr_node] = 0;

       while (!queue.empty()) {

       Arc e;

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

       while (_qfront <= _qback) {

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

         v = _queue[_qfront++];

         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {

           e = _in_arcs[v][j];

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

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

             found[u] = true;

             _reached[u] = true;

             queue.push_back(u);

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

           }

             _queue[++_qback] = u;

         }

           }

       }

         }

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

       }

       queue.clear();

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

       // Connect all other nodes to this component and compute node

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

       // distances using reverse BFS

       int found_cnt = queue.size();

       _qfront = 0;

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

       while (_qback < int(_nodes->size())-1) {

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

         v = _queue[_qfront++];

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

         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {

           e = _in_arcs[v][j];

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

           if (!_reached[u]) {

             found[u] = true;

             _reached[u] = true;

             ++found_cnt;

             queue.push_back(u);

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

           }

             _queue[++_qback] = u;

         }

           }

       }

         }

     }

       }

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

       // Improve node distances

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

       bool improved = false;

     bool computeNodeDistances() {

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

       // Compute node distances using reverse BFS search

         v = (*_nodes)[i];

       double cycle_mean = double(_cycle_length) / _cycle_size;

         for (int j = 0; j < int(_in_arcs[v].size()); ++j) {

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

           e = _in_arcs[v][j];

       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) {

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

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

             found[u] = true;

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

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

             _dist[u] = delta;

             queue.push_back(u);

             _policy[u] = e;

           }

             improved = true;

         }

           }

       }

       // 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;