/* -*- 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_CANCEL_AND_TIGHTEN_H

 #define LEMON_CANCEL_AND_TIGHTEN_H

 /// \ingroup min_cost_flow

 ///

 /// \file

 /// \brief Cancel and Tighten algorithm for finding a minimum cost flow.

 #include <vector>

 #include <lemon/circulation.h>

 #include <lemon/bellman_ford.h>

 #include <lemon/howard.h>

 #include <lemon/adaptors.h>

 #include <lemon/tolerance.h>

 #include <lemon/math.h>

 #include <lemon/static_graph.h>

 namespace lemon {

   /// \addtogroup min_cost_flow

   /// @{

   /// \brief Implementation of the Cancel and Tighten algorithm for

   /// finding a minimum cost flow.

   ///

   /// \ref CancelAndTighten implements the Cancel and Tighten algorithm for

   /// finding a minimum cost flow.

   ///

   /// \tparam Digraph The digraph type the algorithm runs on.

   /// \tparam LowerMap The type of the lower bound map.

   /// \tparam CapacityMap The type of the capacity (upper bound) map.

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

   /// \tparam SupplyMap The type of the supply map.

   ///

   /// \warning

   /// - Arc capacities and costs should be \e non-negative \e integers.

   /// - Supply values should be \e signed \e integers.

   /// - The value types of the maps should be convertible to each other.

   /// - \c CostMap::Value must be signed type.

   ///

   /// \author Peter Kovacs

   template < typename Digraph,

              typename LowerMap = typename Digraph::template ArcMap<int>,

              typename CapacityMap = typename Digraph::template ArcMap<int>,

              typename CostMap = typename Digraph::template ArcMap<int>,

              typename SupplyMap = typename Digraph::template NodeMap<int> >

   class CancelAndTighten

   {

     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

     typedef typename CapacityMap::Value Capacity;

     typedef typename CostMap::Value Cost;

     typedef typename SupplyMap::Value Supply;

     typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;

     typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;

     typedef ResidualDigraph< const Digraph,

       CapacityArcMap, CapacityArcMap > ResDigraph;

   public:

     /// The type of the flow map.

     typedef typename Digraph::template ArcMap<Capacity> FlowMap;

     /// The type of the potential map.

     typedef typename Digraph::template NodeMap<Cost> PotentialMap;

   private:

     /// \brief Map adaptor class for handling residual arc costs.

     ///

     /// Map adaptor class for handling residual arc costs.

     class ResidualCostMap : public MapBase<typename ResDigraph::Arc, Cost>

     {

       typedef typename ResDigraph::Arc Arc;

     private:

       const CostMap &_cost_map;

     public:

       ///\e

       ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}

       ///\e

       Cost operator[](const Arc &e) const {

         return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];

       }

     }; //class ResidualCostMap

     /// \brief Map adaptor class for handling reduced arc costs.

     ///

     /// Map adaptor class for handling reduced arc costs.

     class ReducedCostMap : public MapBase<Arc, Cost>

     {

     private:

       const Digraph &_gr;

       const CostMap &_cost_map;

       const PotentialMap &_pot_map;

     public:

       ///\e

       ReducedCostMap( const Digraph &gr,

                       const CostMap &cost_map,

                       const PotentialMap &pot_map ) :

         _gr(gr), _cost_map(cost_map), _pot_map(pot_map) {}

       ///\e

       inline Cost operator[](const Arc &e) const {

         return _cost_map[e] + _pot_map[_gr.source(e)]

                             - _pot_map[_gr.target(e)];

       }

     }; //class ReducedCostMap

     struct BFOperationTraits {

       static double zero() { return 0; }

       static double infinity() {

         return std::numeric_limits<double>::infinity();

       }

       static double plus(const double& left, const double& right) {

         return left + right;

       }

       static bool less(const double& left, const double& right) {

         return left + 1e-6 < right;

       }

     }; // class BFOperationTraits

   private:

     // The digraph the algorithm runs on

     const Digraph &_graph;

     // The original lower bound map

     const LowerMap *_lower;

     // The modified capacity map

     CapacityArcMap _capacity;

     // The original cost map

     const CostMap &_cost;

     // The modified supply map

     SupplyNodeMap _supply;

     bool _valid_supply;

     // Arc map of the current flow

     FlowMap *_flow;

     bool _local_flow;

     // Node map of the current potentials

     PotentialMap *_potential;

     bool _local_potential;

     // The residual digraph

     ResDigraph *_res_graph;

     // The residual cost map

     ResidualCostMap _res_cost;

   public:

     /// \brief General constructor (with lower bounds).

     ///

     /// General constructor (with lower bounds).

     ///

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

     /// \param lower The lower bounds of the arcs.

     /// \param capacity The capacities (upper bounds) of the arcs.

     /// \param cost The cost (length) values of the arcs.

     /// \param supply The supply values of the nodes (signed).

     CancelAndTighten( const Digraph &digraph,

                       const LowerMap &lower,

                       const CapacityMap &capacity,

                       const CostMap &cost,

                       const SupplyMap &supply ) :

       _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),

       _supply(digraph), _flow(NULL), _local_flow(false),

       _potential(NULL), _local_potential(false),

       _res_graph(NULL), _res_cost(_cost)

     {

       // Check the sum of supply values

       Supply sum = 0;

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

         _supply[n] = supply[n];

         sum += _supply[n];

       }

       _valid_supply = sum == 0;

       // Remove non-zero lower bounds

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

         _capacity[e] = capacity[e];

         if (lower[e] != 0) {

           _capacity[e] -= lower[e];

           _supply[_graph.source(e)] -= lower[e];

           _supply[_graph.target(e)] += lower[e];

         }

       }

     }

 /*

     /// \brief General constructor (without lower bounds).

     ///

     /// General constructor (without lower bounds).

     ///

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

     /// \param capacity The capacities (upper bounds) of the arcs.

     /// \param cost The cost (length) values of the arcs.

     /// \param supply The supply values of the nodes (signed).

     CancelAndTighten( const Digraph &digraph,

                       const CapacityMap &capacity,

                       const CostMap &cost,

                       const SupplyMap &supply ) :

       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),

       _supply(supply), _flow(NULL), _local_flow(false),

       _potential(NULL), _local_potential(false),

       _res_graph(NULL), _res_cost(_cost)

     {

       // Check the sum of supply values

       Supply sum = 0;

       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];

       _valid_supply = sum == 0;

     }

     /// \brief Simple constructor (with lower bounds).

     ///

     /// Simple constructor (with lower bounds).

     ///

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

     /// \param lower The lower bounds of the arcs.

     /// \param capacity The capacities (upper bounds) of the arcs.

     /// \param cost The cost (length) values of the arcs.

     /// \param s The source node.

     /// \param t The target node.

     /// \param flow_value The required amount of flow from node \c s

     /// to node \c t (i.e. the supply of \c s and the demand of \c t).

     CancelAndTighten( const Digraph &digraph,

                       const LowerMap &lower,

                       const CapacityMap &capacity,

                       const CostMap &cost,

                       Node s, Node t,

                       Supply flow_value ) :

       _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),

       _supply(digraph, 0), _flow(NULL), _local_flow(false),

       _potential(NULL), _local_potential(false),

       _res_graph(NULL), _res_cost(_cost)

     {

       // Remove non-zero lower bounds

       _supply[s] =  flow_value;

       _supply[t] = -flow_value;

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

         if (lower[e] != 0) {

           _capacity[e] -= lower[e];

           _supply[_graph.source(e)] -= lower[e];

           _supply[_graph.target(e)] += lower[e];

         }

       }

       _valid_supply = true;

     }

     /// \brief Simple constructor (without lower bounds).

     ///

     /// Simple constructor (without lower bounds).

     ///

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

     /// \param capacity The capacities (upper bounds) of the arcs.

     /// \param cost The cost (length) values of the arcs.

     /// \param s The source node.

     /// \param t The target node.

     /// \param flow_value The required amount of flow from node \c s

     /// to node \c t (i.e. the supply of \c s and the demand of \c t).

     CancelAndTighten( const Digraph &digraph,

                       const CapacityMap &capacity,

                       const CostMap &cost,

                       Node s, Node t,

                       Supply flow_value ) :

       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),

       _supply(digraph, 0), _flow(NULL), _local_flow(false),

       _potential(NULL), _local_potential(false),

       _res_graph(NULL), _res_cost(_cost)

     {

       _supply[s] =  flow_value;

       _supply[t] = -flow_value;

       _valid_supply = true;

     }

 */

     /// Destructor.

     ~CancelAndTighten() {

       if (_local_flow) delete _flow;

       if (_local_potential) delete _potential;

       delete _res_graph;

     }

     /// \brief Set the flow map.

     ///

     /// Set the flow map.

     ///

     /// \return \c (*this)

     CancelAndTighten& flowMap(FlowMap &map) {

       if (_local_flow) {

         delete _flow;

         _local_flow = false;

       }

       _flow = ↦

       return *this;

     }

     /// \brief Set the potential map.

     ///

     /// Set the potential map.

     ///

     /// \return \c (*this)

     CancelAndTighten& potentialMap(PotentialMap &map) {

       if (_local_potential) {

         delete _potential;

         _local_potential = false;

       }

       _potential = ↦

       return *this;

     }

     /// \name Execution control

     /// @{

     /// \brief Run the algorithm.

     ///

     /// Run the algorithm.

     ///

     /// \return \c true if a feasible flow can be found.

     bool run() {

       return init() && start();

     }

     /// @}

     /// \name Query Functions

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

     /// functions.\n

     /// \ref lemon::CancelAndTighten::run() "run()" must be called before

     /// using them.

     /// @{

     /// \brief Return a const reference to the arc map storing the

     /// found flow.

     ///

     /// Return a const reference to the arc map storing the found flow.

     ///

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

     const FlowMap& flowMap() const {

       return *_flow;

     }

     /// \brief Return a const reference to the node map storing the

     /// found potentials (the dual solution).

     ///

     /// Return a const reference to the node map storing the found

     /// potentials (the dual solution).

     ///

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

     const PotentialMap& potentialMap() const {

       return *_potential;

     }

     /// \brief Return the flow on the given arc.

     ///

     /// Return the flow on the given arc.

     ///

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

     Capacity flow(const Arc& arc) const {

       return (*_flow)[arc];

     }

     /// \brief Return the potential of the given node.

     ///

     /// Return the potential of the given node.

     ///

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

     Cost potential(const Node& node) const {

       return (*_potential)[node];

     }

     /// \brief Return the total cost of the found flow.

     ///

     /// Return the total cost of the found flow. The complexity of the

     /// function is \f$ O(e) \f$.

     ///

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

     Cost totalCost() const {

       Cost c = 0;

       for (ArcIt e(_graph); e != INVALID; ++e)

         c += (*_flow)[e] * _cost[e];

       return c;

     }

     /// @}

   private:

     /// Initialize the algorithm.

     bool init() {

       if (!_valid_supply) return false;

       // Initialize flow and potential maps

       if (!_flow) {

         _flow = new FlowMap(_graph);

         _local_flow = true;

       }

       if (!_potential) {

         _potential = new PotentialMap(_graph);

         _local_potential = true;

       }

       _res_graph = new ResDigraph(_graph, _capacity, *_flow);

       // Find a feasible flow using Circulation

       Circulation< Digraph, ConstMap<Arc, Capacity>,

                    CapacityArcMap, SupplyMap >

         circulation( _graph, constMap<Arc>(Capacity(0)),

                      _capacity, _supply );

       return circulation.flowMap(*_flow).run();

     }

     bool start() {

       const double LIMIT_FACTOR = 0.01;

       const int MIN_LIMIT = 3;

       typedef typename Digraph::template NodeMap<double> FloatPotentialMap;

       typedef typename Digraph::template NodeMap<int> LevelMap;

       typedef typename Digraph::template NodeMap<bool> BoolNodeMap;

       typedef typename Digraph::template NodeMap<Node> PredNodeMap;

       typedef typename Digraph::template NodeMap<Arc> PredArcMap;

       typedef typename ResDigraph::template ArcMap<double> ResShiftCostMap;

       FloatPotentialMap pi(_graph);

       LevelMap level(_graph);

       BoolNodeMap reached(_graph);

       BoolNodeMap processed(_graph);

       PredNodeMap pred_node(_graph);

       PredArcMap pred_arc(_graph);

       int node_num = countNodes(_graph);

       typedef std::pair<Arc, bool> pair;

       std::vector<pair> stack(node_num);

       std::vector<Node> proc_vector(node_num);

       ResShiftCostMap shift_cost(*_res_graph);

       Tolerance<double> tol;

       tol.epsilon(1e-6);

       Timer t1, t2, t3;

       t1.reset();

       t2.reset();

       t3.reset();

       // Initialize epsilon and the node potentials

       double epsilon = 0;

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

         if (_capacity[e] - (*_flow)[e] > 0 && _cost[e] < -epsilon)

           epsilon = -_cost[e];

         else if ((*_flow)[e] > 0 && _cost[e] > epsilon)

           epsilon = _cost[e];

       }

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

         pi[v] = 0;

       }

       // Start phases

       int limit = int(LIMIT_FACTOR * node_num);

       if (limit < MIN_LIMIT) limit = MIN_LIMIT;

       int iter = limit;

       while (epsilon * node_num >= 1) {

         t1.start();

         // Find and cancel cycles in the admissible digraph using DFS

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

           reached[n] = false;

           processed[n] = false;

         }

         int stack_head = -1;

         int proc_head = -1;

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

           if (reached[start]) continue;

           // New start node

           reached[start] = true;

           pred_arc[start] = INVALID;

           pred_node[start] = INVALID;

           // Find the first admissible residual outgoing arc

           double p = pi[start];

           Arc e;

           _graph.firstOut(e, start);

           while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||

                   !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )

             _graph.nextOut(e);

           if (e != INVALID) {

             stack[++stack_head] = pair(e, true);

             goto next_step_1;

           }

           _graph.firstIn(e, start);

           while ( e != INVALID && ((*_flow)[e] == 0 ||

                   !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )

             _graph.nextIn(e);

           if (e != INVALID) {

             stack[++stack_head] = pair(e, false);

             goto next_step_1;

           }

           processed[start] = true;

           proc_vector[++proc_head] = start;

           continue;

         next_step_1:

           while (stack_head >= 0) {

             Arc se = stack[stack_head].first;

             bool sf = stack[stack_head].second;

             Node u, v;

             if (sf) {

               u = _graph.source(se);

               v = _graph.target(se);

             } else {

               u = _graph.target(se);

               v = _graph.source(se);

             }

             if (!reached[v]) {

               // A new node is reached

               reached[v] = true;

               pred_node[v] = u;

               pred_arc[v] = se;

               // Find the first admissible residual outgoing arc

               double p = pi[v];

               Arc e;

               _graph.firstOut(e, v);

               while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||

                       !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )

                 _graph.nextOut(e);

               if (e != INVALID) {

                 stack[++stack_head] = pair(e, true);

                 goto next_step_2;

               }

               _graph.firstIn(e, v);

               while ( e != INVALID && ((*_flow)[e] == 0 ||

                       !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )

                 _graph.nextIn(e);

               stack[++stack_head] = pair(e, false);

             next_step_2: ;

             } else {

               if (!processed[v]) {

                 // A cycle is found

                 Node n, w = u;

                 Capacity d, delta = sf ? _capacity[se] - (*_flow)[se] :

                                          (*_flow)[se];

                 for (n = u; n != v; n = pred_node[n]) {

                   d = _graph.target(pred_arc[n]) == n ?

                       _capacity[pred_arc[n]] - (*_flow)[pred_arc[n]] :

                       (*_flow)[pred_arc[n]];

                   if (d <= delta) {

                     delta = d;

                     w = pred_node[n];

                   }

                 }

 /*

                 std::cout << "CYCLE FOUND: ";

                 if (sf)

                   std::cout << _cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)];

                 else

                   std::cout << _graph.id(se) << ":" << -(_cost[se] + pi[_graph.source(se)] - pi[_graph.target(se)]);

                 for (n = u; n != v; n = pred_node[n]) {

                   if (_graph.target(pred_arc[n]) == n)

                     std::cout << " " << _cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])];

                   else

                     std::cout << " " << -(_cost[pred_arc[n]] + pi[_graph.source(pred_arc[n])] - pi[_graph.target(pred_arc[n])]);

                 }

                 std::cout << "\n";

 */

                 // Augment along the cycle

                 (*_flow)[se] = sf ? (*_flow)[se] + delta :

                                     (*_flow)[se] - delta;

                 for (n = u; n != v; n = pred_node[n]) {

                   if (_graph.target(pred_arc[n]) == n)

                     (*_flow)[pred_arc[n]] += delta;

                   else

                     (*_flow)[pred_arc[n]] -= delta;

                 }

                 for (n = u; stack_head > 0 && n != w; n = pred_node[n]) {

                   --stack_head;

                   reached[n] = false;

                 }

                 u = w;

               }

               v = u;

               // Find the next admissible residual outgoing arc

               double p = pi[v];

               Arc e = stack[stack_head].first;

               if (!stack[stack_head].second) {

                 _graph.nextIn(e);

                 goto in_arc_3;

               }

               _graph.nextOut(e);

               while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||

                       !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )

                 _graph.nextOut(e);

               if (e != INVALID) {

                 stack[stack_head] = pair(e, true);

                 goto next_step_3;

               }

               _graph.firstIn(e, v);

             in_arc_3:

               while ( e != INVALID && ((*_flow)[e] == 0 ||

                       !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )

                 _graph.nextIn(e);

               stack[stack_head] = pair(e, false);

             next_step_3: ;

             }

             while (stack_head >= 0 && stack[stack_head].first == INVALID) {

               processed[v] = true;

               proc_vector[++proc_head] = v;

               if (--stack_head >= 0) {

                 v = stack[stack_head].second ?

                     _graph.source(stack[stack_head].first) :

                     _graph.target(stack[stack_head].first);

                 // Find the next admissible residual outgoing arc

                 double p = pi[v];

                 Arc e = stack[stack_head].first;

                 if (!stack[stack_head].second) {

                   _graph.nextIn(e);

                   goto in_arc_4;

                 }

                 _graph.nextOut(e);

                 while ( e != INVALID && (_capacity[e] - (*_flow)[e] == 0 ||

                         !tol.negative(_cost[e] + p - pi[_graph.target(e)])) )

                   _graph.nextOut(e);

                 if (e != INVALID) {

                   stack[stack_head] = pair(e, true);

                   goto next_step_4;

                 }

                 _graph.firstIn(e, v);

               in_arc_4:

                 while ( e != INVALID && ((*_flow)[e] == 0 ||

                         !tol.negative(-_cost[e] + p - pi[_graph.source(e)])) )

                   _graph.nextIn(e);

                 stack[stack_head] = pair(e, false);

               next_step_4: ;

               }

             }

           }

         }

         t1.stop();

         // Tighten potentials and epsilon

         if (--iter > 0) {

           // Compute levels

           t2.start();

           for (int i = proc_head; i >= 0; --i) {

             Node v = proc_vector[i];

             double p = pi[v];

             int l = 0;

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

               Node u = _graph.source(e);

               if ( _capacity[e] - (*_flow)[e] > 0 &&

                    tol.negative(_cost[e] + pi[u] - p) &&

                    level[u] + 1 > l ) l = level[u] + 1;

             }

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

               Node u = _graph.target(e);

               if ( (*_flow)[e] > 0 &&

                    tol.negative(-_cost[e] + pi[u] - p) &&

                    level[u] + 1 > l ) l = level[u] + 1;

             }

             level[v] = l;

           }

           // Modify potentials

           double p, q = -1;

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

             Node u = _graph.source(e);

             Node v = _graph.target(e);

             if (_capacity[e] - (*_flow)[e] > 0 && level[u] - level[v] > 0) {

               p = (_cost[e] + pi[u] - pi[v] + epsilon) /

                   (level[u] - level[v] + 1);

               if (q < 0 || p < q) q = p;

             }

             else if ((*_flow)[e] > 0 && level[v] - level[u] > 0) {

               p = (-_cost[e] - pi[u] + pi[v] + epsilon) /

                   (level[v] - level[u] + 1);

               if (q < 0 || p < q) q = p;

             }

           }

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

             pi[v] -= q * level[v];

           }

           // Modify epsilon

           epsilon = 0;

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

             double curr = _cost[e] + pi[_graph.source(e)]

                                    - pi[_graph.target(e)];

             if (_capacity[e] - (*_flow)[e] > 0 && curr < -epsilon)

               epsilon = -curr;

             else if ((*_flow)[e] > 0 && curr > epsilon)

               epsilon = curr;

           }

           t2.stop();

         } else {

           // Set epsilon to the minimum cycle mean

           t3.start();

 /**/

           StaticDigraph static_graph;

           typename ResDigraph::template NodeMap<typename StaticDigraph::Node> node_ref(*_res_graph);

           typename ResDigraph::template ArcMap<typename StaticDigraph::Arc> arc_ref(*_res_graph);

           static_graph.build(*_res_graph, node_ref, arc_ref);

           typename StaticDigraph::template NodeMap<double> static_pi(static_graph);

           typename StaticDigraph::template ArcMap<double> static_cost(static_graph);

           for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)

             static_cost[arc_ref[e]] = _res_cost[e];

           Howard<StaticDigraph, typename StaticDigraph::template ArcMap<double> >

             mmc(static_graph, static_cost);

           mmc.findMinMean();

           epsilon = -mmc.cycleMean();

 /**/

 /*

           Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);

           mmc.findMinMean();

           epsilon = -mmc.cycleMean();

 */

           // Compute feasible potentials for the current epsilon

           for (typename StaticDigraph::ArcIt e(static_graph); e != INVALID; ++e)

             static_cost[e] += epsilon;

           typename BellmanFord<StaticDigraph, typename StaticDigraph::template ArcMap<double> >::

             template SetDistMap<typename StaticDigraph::template NodeMap<double> >::

             template SetOperationTraits<BFOperationTraits>::Create

               bf(static_graph, static_cost);

           bf.distMap(static_pi).init(0);

           bf.start();

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

             pi[n] = static_pi[node_ref[n]];

 /*

           for (typename ResDigraph::ArcIt e(*_res_graph); e != INVALID; ++e)

             shift_cost[e] = _res_cost[e] + epsilon;

           typename BellmanFord<ResDigraph, ResShiftCostMap>::

             template SetDistMap<FloatPotentialMap>::

             template SetOperationTraits<BFOperationTraits>::Create

               bf(*_res_graph, shift_cost);

           bf.distMap(pi).init(0);

           bf.start();

 */

           iter = limit;

           t3.stop();

         }

       }

 //      std::cout << t1.realTime() << " " << t2.realTime() << " " << t3.realTime() << "\n";

       // Handle non-zero lower bounds

       if (_lower) {

         for (ArcIt e(_graph); e != INVALID; ++e)

           (*_flow)[e] += (*_lower)[e];

       }

       return true;

     }

   }; //class CancelAndTighten

   ///@}

 } //namespace lemon

 #endif //LEMON_CANCEL_AND_TIGHTEN_H