/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2010

  * 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_HAO_ORLIN_H

 #define LEMON_HAO_ORLIN_H

 #include <vector>

 #include <list>

 #include <limits>

 #include <lemon/maps.h>

 #include <lemon/core.h>

 #include <lemon/tolerance.h>

 /// \file

 /// \ingroup min_cut

 /// \brief Implementation of the Hao-Orlin algorithm.

 ///

 /// Implementation of the Hao-Orlin algorithm for finding a minimum cut

 /// in a digraph.

 namespace lemon {

   /// \ingroup min_cut

   ///

   /// \brief Hao-Orlin algorithm for finding a minimum cut in a digraph.

   ///

   /// This class implements the Hao-Orlin algorithm for finding a minimum

   /// value cut in a directed graph \f$D=(V,A)\f$.

   /// It takes a fixed node \f$ source \in V \f$ and

   /// consists of two phases: in the first phase it determines a

   /// minimum cut with \f$ source \f$ on the source-side (i.e. a set

   /// \f$ X\subsetneq V \f$ with \f$ source \in X \f$ and minimal outgoing

   /// capacity) and in the second phase it determines a minimum cut

   /// with \f$ source \f$ on the sink-side (i.e. a set

   /// \f$ X\subsetneq V \f$ with \f$ source \notin X \f$ and minimal outgoing

   /// capacity). Obviously, the smaller of these two cuts will be a

   /// minimum cut of \f$ D \f$. The algorithm is a modified

   /// preflow push-relabel algorithm. Our implementation calculates

   /// the minimum cut in \f$ O(n^2\sqrt{m}) \f$ time (we use the

   /// highest-label rule), or in \f$O(nm)\f$ for unit capacities. The

   /// purpose of such algorithm is e.g. testing network reliability.

   ///

   /// For an undirected graph you can run just the first phase of the

   /// algorithm or you can use the algorithm of Nagamochi and Ibaraki,

   /// which solves the undirected problem in \f$ O(nm + n^2 \log n) \f$

   /// time. It is implemented in the NagamochiIbaraki algorithm class.

   ///

   /// \tparam GR The type of the digraph the algorithm runs on.

   /// \tparam CAP The type of the arc map containing the capacities,

   /// which can be any numreric type. The default map type is

   /// \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".

   /// \tparam TOL Tolerance class for handling inexact computations. The

   /// default tolerance type is \ref Tolerance "Tolerance<CAP::Value>".

 #ifdef DOXYGEN

   template <typename GR, typename CAP, typename TOL>

 #else

   template <typename GR,

             typename CAP = typename GR::template ArcMap<int>,

             typename TOL = Tolerance<typename CAP::Value> >

 #endif

   class HaoOrlin {

   public:

     /// The digraph type of the algorithm

     typedef GR Digraph;

     /// The capacity map type of the algorithm

     typedef CAP CapacityMap;

     /// The tolerance type of the algorithm

     typedef TOL Tolerance;

   private:

     typedef typename CapacityMap::Value Value;

     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

     const Digraph& _graph;

     const CapacityMap* _capacity;

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

     FlowMap* _flow;

     Node _source;

     int _node_num;

     // Bucketing structure

     std::vector<Node> _first, _last;

     typename Digraph::template NodeMap<Node>* _next;

     typename Digraph::template NodeMap<Node>* _prev;

     typename Digraph::template NodeMap<bool>* _active;

     typename Digraph::template NodeMap<int>* _bucket;

     std::vector<bool> _dormant;

     std::list<std::list<int> > _sets;

     std::list<int>::iterator _highest;

     typedef typename Digraph::template NodeMap<Value> ExcessMap;

     ExcessMap* _excess;

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

     SourceSetMap* _source_set;

     Value _min_cut;

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

     MinCutMap* _min_cut_map;

     Tolerance _tolerance;

   public:

     /// \brief Constructor

     ///

     /// Constructor of the algorithm class.

     HaoOrlin(const Digraph& graph, const CapacityMap& capacity,

              const Tolerance& tolerance = Tolerance()) :

       _graph(graph), _capacity(&capacity), _flow(0), _source(),

       _node_num(), _first(), _last(), _next(0), _prev(0),

       _active(0), _bucket(0), _dormant(), _sets(), _highest(),

       _excess(0), _source_set(0), _min_cut(), _min_cut_map(0),

       _tolerance(tolerance) {}

     ~HaoOrlin() {

       if (_min_cut_map) {

         delete _min_cut_map;

       }

       if (_source_set) {

         delete _source_set;

       }

       if (_excess) {

         delete _excess;

       }

       if (_next) {

         delete _next;

       }

       if (_prev) {

         delete _prev;

       }

       if (_active) {

         delete _active;

       }

       if (_bucket) {

         delete _bucket;

       }

       if (_flow) {

         delete _flow;

       }

     }

     /// \brief Set the tolerance used by the algorithm.

     ///

     /// This function sets the tolerance object used by the algorithm.

     /// \return <tt>(*this)</tt>

     HaoOrlin& tolerance(const Tolerance& tolerance) {

       _tolerance = tolerance;

       return *this;

     }

     /// \brief Returns a const reference to the tolerance.

     ///

     /// This function returns a const reference to the tolerance object

     /// used by the algorithm.

     const Tolerance& tolerance() const {

       return _tolerance;

     }

   private:

     void activate(const Node& i) {

       (*_active)[i] = true;

       int bucket = (*_bucket)[i];

       if ((*_prev)[i] == INVALID || (*_active)[(*_prev)[i]]) return;

       //unlace

       (*_next)[(*_prev)[i]] = (*_next)[i];

       if ((*_next)[i] != INVALID) {

         (*_prev)[(*_next)[i]] = (*_prev)[i];

       } else {

         _last[bucket] = (*_prev)[i];

       }

       //lace

       (*_next)[i] = _first[bucket];

       (*_prev)[_first[bucket]] = i;

       (*_prev)[i] = INVALID;

       _first[bucket] = i;

     }

     void deactivate(const Node& i) {

       (*_active)[i] = false;

       int bucket = (*_bucket)[i];

       if ((*_next)[i] == INVALID || !(*_active)[(*_next)[i]]) return;

       //unlace

       (*_prev)[(*_next)[i]] = (*_prev)[i];

       if ((*_prev)[i] != INVALID) {

         (*_next)[(*_prev)[i]] = (*_next)[i];

       } else {

         _first[bucket] = (*_next)[i];

       }

       //lace

       (*_prev)[i] = _last[bucket];

       (*_next)[_last[bucket]] = i;

       (*_next)[i] = INVALID;

       _last[bucket] = i;

     }

     void addItem(const Node& i, int bucket) {

       (*_bucket)[i] = bucket;

       if (_last[bucket] != INVALID) {

         (*_prev)[i] = _last[bucket];

         (*_next)[_last[bucket]] = i;

         (*_next)[i] = INVALID;

         _last[bucket] = i;

       } else {

         (*_prev)[i] = INVALID;

         _first[bucket] = i;

         (*_next)[i] = INVALID;

         _last[bucket] = i;

       }

     }

     void findMinCutOut() {

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

         (*_excess)[n] = 0;

         (*_source_set)[n] = false;

       }

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

         (*_flow)[a] = 0;

       }

       int bucket_num = 0;

       std::vector<Node> queue(_node_num);

       int qfirst = 0, qlast = 0, qsep = 0;

       {

         typename Digraph::template NodeMap<bool> reached(_graph, false);

         reached[_source] = true;

         bool first_set = true;

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

           if (reached[t]) continue;

           _sets.push_front(std::list<int>());

           queue[qlast++] = t;

           reached[t] = true;

           while (qfirst != qlast) {

             if (qsep == qfirst) {

               ++bucket_num;

               _sets.front().push_front(bucket_num);

               _dormant[bucket_num] = !first_set;

               _first[bucket_num] = _last[bucket_num] = INVALID;

               qsep = qlast;

             }

             Node n = queue[qfirst++];

             addItem(n, bucket_num);

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

               Node u = _graph.source(a);

               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {

                 reached[u] = true;

                 queue[qlast++] = u;

               }

             }

           }

           first_set = false;

         }

         ++bucket_num;

         (*_bucket)[_source] = 0;

         _dormant[0] = true;

       }

       (*_source_set)[_source] = true;

       Node target = _last[_sets.back().back()];

       {

         for (OutArcIt a(_graph, _source); a != INVALID; ++a) {

           if (_tolerance.positive((*_capacity)[a])) {

             Node u = _graph.target(a);

             (*_flow)[a] = (*_capacity)[a];

             (*_excess)[u] += (*_capacity)[a];

             if (!(*_active)[u] && u != _source) {

               activate(u);

             }

           }

         }

         if ((*_active)[target]) {

           deactivate(target);

         }

         _highest = _sets.back().begin();

         while (_highest != _sets.back().end() &&

                !(*_active)[_first[*_highest]]) {

           ++_highest;

         }

       }

       while (true) {

         while (_highest != _sets.back().end()) {

           Node n = _first[*_highest];

           Value excess = (*_excess)[n];

           int next_bucket = _node_num;

           int under_bucket;

           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {

             under_bucket = -1;

           } else {

             under_bucket = *(++std::list<int>::iterator(_highest));

           }

           for (OutArcIt a(_graph, n); a != INVALID; ++a) {

             Node v = _graph.target(a);

             if (_dormant[(*_bucket)[v]]) continue;

             Value rem = (*_capacity)[a] - (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             if ((*_bucket)[v] == under_bucket) {

               if (!(*_active)[v] && v != target) {

                 activate(v);

               }

               if (!_tolerance.less(rem, excess)) {

                 (*_flow)[a] += excess;

                 (*_excess)[v] += excess;

                 excess = 0;

                 goto no_more_push;

               } else {

                 excess -= rem;

                 (*_excess)[v] += rem;

                 (*_flow)[a] = (*_capacity)[a];

               }

             } else if (next_bucket > (*_bucket)[v]) {

               next_bucket = (*_bucket)[v];

             }

           }

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

             Node v = _graph.source(a);

             if (_dormant[(*_bucket)[v]]) continue;

             Value rem = (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             if ((*_bucket)[v] == under_bucket) {

               if (!(*_active)[v] && v != target) {

                 activate(v);

               }

               if (!_tolerance.less(rem, excess)) {

                 (*_flow)[a] -= excess;

                 (*_excess)[v] += excess;

                 excess = 0;

                 goto no_more_push;

               } else {

                 excess -= rem;

                 (*_excess)[v] += rem;

                 (*_flow)[a] = 0;

               }

             } else if (next_bucket > (*_bucket)[v]) {

               next_bucket = (*_bucket)[v];

             }

           }

         no_more_push:

           (*_excess)[n] = excess;

           if (excess != 0) {

             if ((*_next)[n] == INVALID) {

               typename std::list<std::list<int> >::iterator new_set =

                 _sets.insert(--_sets.end(), std::list<int>());

               new_set->splice(new_set->end(), _sets.back(),

                               _sets.back().begin(), ++_highest);

               for (std::list<int>::iterator it = new_set->begin();

                    it != new_set->end(); ++it) {

                 _dormant[*it] = true;

               }

               while (_highest != _sets.back().end() &&

                      !(*_active)[_first[*_highest]]) {

                 ++_highest;

               }

             } else if (next_bucket == _node_num) {

               _first[(*_bucket)[n]] = (*_next)[n];

               (*_prev)[(*_next)[n]] = INVALID;

               std::list<std::list<int> >::iterator new_set =

                 _sets.insert(--_sets.end(), std::list<int>());

               new_set->push_front(bucket_num);

               (*_bucket)[n] = bucket_num;

               _first[bucket_num] = _last[bucket_num] = n;

               (*_next)[n] = INVALID;

               (*_prev)[n] = INVALID;

               _dormant[bucket_num] = true;

               ++bucket_num;

               while (_highest != _sets.back().end() &&

                      !(*_active)[_first[*_highest]]) {

                 ++_highest;

               }

             } else {

               _first[*_highest] = (*_next)[n];

               (*_prev)[(*_next)[n]] = INVALID;

               while (next_bucket != *_highest) {

                 --_highest;

               }

               if (_highest == _sets.back().begin()) {

                 _sets.back().push_front(bucket_num);

                 _dormant[bucket_num] = false;

                 _first[bucket_num] = _last[bucket_num] = INVALID;

                 ++bucket_num;

               }

               --_highest;

               (*_bucket)[n] = *_highest;

               (*_next)[n] = _first[*_highest];

               if (_first[*_highest] != INVALID) {

                 (*_prev)[_first[*_highest]] = n;

               } else {

                 _last[*_highest] = n;

               }

               _first[*_highest] = n;

             }

           } else {

             deactivate(n);

             if (!(*_active)[_first[*_highest]]) {

               ++_highest;

               if (_highest != _sets.back().end() &&

                   !(*_active)[_first[*_highest]]) {

                 _highest = _sets.back().end();

               }

             }

           }

         }

         if ((*_excess)[target] < _min_cut) {

           _min_cut = (*_excess)[target];

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

             (*_min_cut_map)[i] = true;

           }

           for (std::list<int>::iterator it = _sets.back().begin();

                it != _sets.back().end(); ++it) {

             Node n = _first[*it];

             while (n != INVALID) {

               (*_min_cut_map)[n] = false;

               n = (*_next)[n];

             }

           }

         }

         {

           Node new_target;

           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {

             if ((*_next)[target] == INVALID) {

               _last[(*_bucket)[target]] = (*_prev)[target];

               new_target = (*_prev)[target];

             } else {

               (*_prev)[(*_next)[target]] = (*_prev)[target];

               new_target = (*_next)[target];

             }

             if ((*_prev)[target] == INVALID) {

               _first[(*_bucket)[target]] = (*_next)[target];

             } else {

               (*_next)[(*_prev)[target]] = (*_next)[target];

             }

           } else {

             _sets.back().pop_back();

             if (_sets.back().empty()) {

               _sets.pop_back();

               if (_sets.empty())

                 break;

               for (std::list<int>::iterator it = _sets.back().begin();

                    it != _sets.back().end(); ++it) {

                 _dormant[*it] = false;

               }

             }

             new_target = _last[_sets.back().back()];

           }

           (*_bucket)[target] = 0;

           (*_source_set)[target] = true;

           for (OutArcIt a(_graph, target); a != INVALID; ++a) {

             Value rem = (*_capacity)[a] - (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             Node v = _graph.target(a);

             if (!(*_active)[v] && !(*_source_set)[v]) {

               activate(v);

             }

             (*_excess)[v] += rem;

             (*_flow)[a] = (*_capacity)[a];

           }

           for (InArcIt a(_graph, target); a != INVALID; ++a) {

             Value rem = (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             Node v = _graph.source(a);

             if (!(*_active)[v] && !(*_source_set)[v]) {

               activate(v);

             }

             (*_excess)[v] += rem;

             (*_flow)[a] = 0;

           }

           target = new_target;

           if ((*_active)[target]) {

             deactivate(target);

           }

           _highest = _sets.back().begin();

           while (_highest != _sets.back().end() &&

                  !(*_active)[_first[*_highest]]) {

             ++_highest;

           }

         }

       }

     }

     void findMinCutIn() {

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

         (*_excess)[n] = 0;

         (*_source_set)[n] = false;

       }

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

         (*_flow)[a] = 0;

       }

       int bucket_num = 0;

       std::vector<Node> queue(_node_num);

       int qfirst = 0, qlast = 0, qsep = 0;

       {

         typename Digraph::template NodeMap<bool> reached(_graph, false);

         reached[_source] = true;

         bool first_set = true;

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

           if (reached[t]) continue;

           _sets.push_front(std::list<int>());

           queue[qlast++] = t;

           reached[t] = true;

           while (qfirst != qlast) {

             if (qsep == qfirst) {

               ++bucket_num;

               _sets.front().push_front(bucket_num);

               _dormant[bucket_num] = !first_set;

               _first[bucket_num] = _last[bucket_num] = INVALID;

               qsep = qlast;

             }

             Node n = queue[qfirst++];

             addItem(n, bucket_num);

             for (OutArcIt a(_graph, n); a != INVALID; ++a) {

               Node u = _graph.target(a);

               if (!reached[u] && _tolerance.positive((*_capacity)[a])) {

                 reached[u] = true;

                 queue[qlast++] = u;

               }

             }

           }

           first_set = false;

         }

         ++bucket_num;

         (*_bucket)[_source] = 0;

         _dormant[0] = true;

       }

       (*_source_set)[_source] = true;

       Node target = _last[_sets.back().back()];

       {

         for (InArcIt a(_graph, _source); a != INVALID; ++a) {

           if (_tolerance.positive((*_capacity)[a])) {

             Node u = _graph.source(a);

             (*_flow)[a] = (*_capacity)[a];

             (*_excess)[u] += (*_capacity)[a];

             if (!(*_active)[u] && u != _source) {

               activate(u);

             }

           }

         }

         if ((*_active)[target]) {

           deactivate(target);

         }

         _highest = _sets.back().begin();

         while (_highest != _sets.back().end() &&

                !(*_active)[_first[*_highest]]) {

           ++_highest;

         }

       }

       while (true) {

         while (_highest != _sets.back().end()) {

           Node n = _first[*_highest];

           Value excess = (*_excess)[n];

           int next_bucket = _node_num;

           int under_bucket;

           if (++std::list<int>::iterator(_highest) == _sets.back().end()) {

             under_bucket = -1;

           } else {

             under_bucket = *(++std::list<int>::iterator(_highest));

           }

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

             Node v = _graph.source(a);

             if (_dormant[(*_bucket)[v]]) continue;

             Value rem = (*_capacity)[a] - (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             if ((*_bucket)[v] == under_bucket) {

               if (!(*_active)[v] && v != target) {

                 activate(v);

               }

               if (!_tolerance.less(rem, excess)) {

                 (*_flow)[a] += excess;

                 (*_excess)[v] += excess;

                 excess = 0;

                 goto no_more_push;

               } else {

                 excess -= rem;

                 (*_excess)[v] += rem;

                 (*_flow)[a] = (*_capacity)[a];

               }

             } else if (next_bucket > (*_bucket)[v]) {

               next_bucket = (*_bucket)[v];

             }

           }

           for (OutArcIt a(_graph, n); a != INVALID; ++a) {

             Node v = _graph.target(a);

             if (_dormant[(*_bucket)[v]]) continue;

             Value rem = (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             if ((*_bucket)[v] == under_bucket) {

               if (!(*_active)[v] && v != target) {

                 activate(v);

               }

               if (!_tolerance.less(rem, excess)) {

                 (*_flow)[a] -= excess;

                 (*_excess)[v] += excess;

                 excess = 0;

                 goto no_more_push;

               } else {

                 excess -= rem;

                 (*_excess)[v] += rem;

                 (*_flow)[a] = 0;

               }

             } else if (next_bucket > (*_bucket)[v]) {

               next_bucket = (*_bucket)[v];

             }

           }

         no_more_push:

           (*_excess)[n] = excess;

           if (excess != 0) {

             if ((*_next)[n] == INVALID) {

               typename std::list<std::list<int> >::iterator new_set =

                 _sets.insert(--_sets.end(), std::list<int>());

               new_set->splice(new_set->end(), _sets.back(),

                               _sets.back().begin(), ++_highest);

               for (std::list<int>::iterator it = new_set->begin();

                    it != new_set->end(); ++it) {

                 _dormant[*it] = true;

               }

               while (_highest != _sets.back().end() &&

                      !(*_active)[_first[*_highest]]) {

                 ++_highest;

               }

             } else if (next_bucket == _node_num) {

               _first[(*_bucket)[n]] = (*_next)[n];

               (*_prev)[(*_next)[n]] = INVALID;

               std::list<std::list<int> >::iterator new_set =

                 _sets.insert(--_sets.end(), std::list<int>());

               new_set->push_front(bucket_num);

               (*_bucket)[n] = bucket_num;

               _first[bucket_num] = _last[bucket_num] = n;

               (*_next)[n] = INVALID;

               (*_prev)[n] = INVALID;

               _dormant[bucket_num] = true;

               ++bucket_num;

               while (_highest != _sets.back().end() &&

                      !(*_active)[_first[*_highest]]) {

                 ++_highest;

               }

             } else {

               _first[*_highest] = (*_next)[n];

               (*_prev)[(*_next)[n]] = INVALID;

               while (next_bucket != *_highest) {

                 --_highest;

               }

               if (_highest == _sets.back().begin()) {

                 _sets.back().push_front(bucket_num);

                 _dormant[bucket_num] = false;

                 _first[bucket_num] = _last[bucket_num] = INVALID;

                 ++bucket_num;

               }

               --_highest;

               (*_bucket)[n] = *_highest;

               (*_next)[n] = _first[*_highest];

               if (_first[*_highest] != INVALID) {

                 (*_prev)[_first[*_highest]] = n;

               } else {

                 _last[*_highest] = n;

               }

               _first[*_highest] = n;

             }

           } else {

             deactivate(n);

             if (!(*_active)[_first[*_highest]]) {

               ++_highest;

               if (_highest != _sets.back().end() &&

                   !(*_active)[_first[*_highest]]) {

                 _highest = _sets.back().end();

               }

             }

           }

         }

         if ((*_excess)[target] < _min_cut) {

           _min_cut = (*_excess)[target];

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

             (*_min_cut_map)[i] = false;

           }

           for (std::list<int>::iterator it = _sets.back().begin();

                it != _sets.back().end(); ++it) {

             Node n = _first[*it];

             while (n != INVALID) {

               (*_min_cut_map)[n] = true;

               n = (*_next)[n];

             }

           }

         }

         {

           Node new_target;

           if ((*_prev)[target] != INVALID || (*_next)[target] != INVALID) {

             if ((*_next)[target] == INVALID) {

               _last[(*_bucket)[target]] = (*_prev)[target];

               new_target = (*_prev)[target];

             } else {

               (*_prev)[(*_next)[target]] = (*_prev)[target];

               new_target = (*_next)[target];

             }

             if ((*_prev)[target] == INVALID) {

               _first[(*_bucket)[target]] = (*_next)[target];

             } else {

               (*_next)[(*_prev)[target]] = (*_next)[target];

             }

           } else {

             _sets.back().pop_back();

             if (_sets.back().empty()) {

               _sets.pop_back();

               if (_sets.empty())

                 break;

               for (std::list<int>::iterator it = _sets.back().begin();

                    it != _sets.back().end(); ++it) {

                 _dormant[*it] = false;

               }

             }

             new_target = _last[_sets.back().back()];

           }

           (*_bucket)[target] = 0;

           (*_source_set)[target] = true;

           for (InArcIt a(_graph, target); a != INVALID; ++a) {

             Value rem = (*_capacity)[a] - (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             Node v = _graph.source(a);

             if (!(*_active)[v] && !(*_source_set)[v]) {

               activate(v);

             }

             (*_excess)[v] += rem;

             (*_flow)[a] = (*_capacity)[a];

           }

           for (OutArcIt a(_graph, target); a != INVALID; ++a) {

             Value rem = (*_flow)[a];

             if (!_tolerance.positive(rem)) continue;

             Node v = _graph.target(a);

             if (!(*_active)[v] && !(*_source_set)[v]) {

               activate(v);

             }

             (*_excess)[v] += rem;

             (*_flow)[a] = 0;

           }

           target = new_target;

           if ((*_active)[target]) {

             deactivate(target);

           }

           _highest = _sets.back().begin();

           while (_highest != _sets.back().end() &&

                  !(*_active)[_first[*_highest]]) {

             ++_highest;

           }

         }

       }

     }

   public:

     /// \name Execution Control

     /// The simplest way to execute the algorithm is to use

     /// one of the member functions called \ref run().

     /// \n

     /// If you need better control on the execution,

     /// you have to call one of the \ref init() functions first, then

     /// \ref calculateOut() and/or \ref calculateIn().

     /// @{

     /// \brief Initialize the internal data structures.

     ///

     /// This function initializes the internal data structures. It creates

     /// the maps and some bucket structures for the algorithm.

     /// The first node is used as the source node for the push-relabel

     /// algorithm.

     void init() {

       init(NodeIt(_graph));

     }

     /// \brief Initialize the internal data structures.

     ///

     /// This function initializes the internal data structures. It creates

     /// the maps and some bucket structures for the algorithm.

     /// The given node is used as the source node for the push-relabel

     /// algorithm.

     void init(const Node& source) {

       _source = source;

       _node_num = countNodes(_graph);

       _first.resize(_node_num);

       _last.resize(_node_num);

       _dormant.resize(_node_num);

       if (!_flow) {

         _flow = new FlowMap(_graph);

       }

       if (!_next) {

         _next = new typename Digraph::template NodeMap<Node>(_graph);

       }

       if (!_prev) {

         _prev = new typename Digraph::template NodeMap<Node>(_graph);

       }

       if (!_active) {

         _active = new typename Digraph::template NodeMap<bool>(_graph);

       }

       if (!_bucket) {

         _bucket = new typename Digraph::template NodeMap<int>(_graph);

       }

       if (!_excess) {

         _excess = new ExcessMap(_graph);

       }

       if (!_source_set) {

         _source_set = new SourceSetMap(_graph);

       }

       if (!_min_cut_map) {

         _min_cut_map = new MinCutMap(_graph);

       }

       _min_cut = std::numeric_limits<Value>::max();

     }

     /// \brief Calculate a minimum cut with \f$ source \f$ on the

     /// source-side.

     ///

     /// This function calculates a minimum cut with \f$ source \f$ on the

     /// source-side (i.e. a set \f$ X\subsetneq V \f$ with

     /// \f$ source \in X \f$ and minimal outgoing capacity).

     ///

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

     void calculateOut() {

       findMinCutOut();

     }

     /// \brief Calculate a minimum cut with \f$ source \f$ on the

     /// sink-side.

     ///

     /// This function calculates a minimum cut with \f$ source \f$ on the

     /// sink-side (i.e. a set \f$ X\subsetneq V \f$ with

     /// \f$ source \notin X \f$ and minimal outgoing capacity).

     ///

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

     void calculateIn() {

       findMinCutIn();

     }

     /// \brief Run the algorithm.

     ///

     /// This function runs the algorithm. It finds nodes \c source and

     /// \c target arbitrarily and then calls \ref init(), \ref calculateOut()

     /// and \ref calculateIn().

     void run() {

       init();

       calculateOut();

       calculateIn();

     }

     /// \brief Run the algorithm.

     ///

     /// This function runs the algorithm. It uses the given \c source node,

     /// finds a proper \c target node and then calls the \ref init(),

     /// \ref calculateOut() and \ref calculateIn().

     void run(const Node& s) {

       init(s);

       calculateOut();

       calculateIn();

     }

     /// @}

     /// \name Query Functions

     /// The result of the %HaoOrlin algorithm

     /// can be obtained using these functions.\n

     /// \ref run(), \ref calculateOut() or \ref calculateIn()

     /// should be called before using them.

     /// @{

     /// \brief Return the value of the minimum cut.

     ///

     /// This function returns the value of the minimum cut.

     ///

     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()

     /// must be called before using this function.

     Value minCutValue() const {

       return _min_cut;

     }

     /// \brief Return a minimum cut.

     ///

     /// This function sets \c cutMap to the characteristic vector of a

     /// minimum value cut: it will give a non-empty set \f$ X\subsetneq V \f$

     /// with minimal outgoing capacity (i.e. \c cutMap will be \c true exactly

     /// for the nodes of \f$ X \f$).

     ///

     /// \param cutMap A \ref concepts::WriteMap "writable" node map with

     /// \c bool (or convertible) value type.

     ///

     /// \return The value of the minimum cut.

     ///

     /// \pre \ref run(), \ref calculateOut() or \ref calculateIn()

     /// must be called before using this function.

     template <typename CutMap>

     Value minCutMap(CutMap& cutMap) const {

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

         cutMap.set(it, (*_min_cut_map)[it]);

       }

       return _min_cut;

     }

     /// @}

   }; //class HaoOrlin

 } //namespace lemon

 #endif //LEMON_HAO_ORLIN_H