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

 *

 * 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_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 class for testing network

/// reliability.

namespace lemon {

  /// \ingroup min_cut

  ///

  /// \brief %Hao-Orlin algorithm to find a minimum cut in directed graphs.

  ///

  /// Hao-Orlin calculates a minimum 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

  /// out-degree) 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

  /// out-degree). Obviously, the smaller of these two cuts will be a

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

  /// push-relabel preflow algorithm and 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 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.

  ///

  /// \param _Digraph is the graph type of the algorithm.

  /// \param _CapacityMap is an edge map of capacities which should

  /// be any numreric type. The default type is _Digraph::ArcMap<int>.

  /// \param _Tolerance is the handler of the inexact computation. The

  /// default type for this is Tolerance<CapacityMap::Value>.

#ifdef DOXYGEN

  template <typename _Digraph, typename _CapacityMap, typename _Tolerance>

#else

  template <typename _Digraph,

            typename _CapacityMap = typename _Digraph::template ArcMap<int>,

            typename _Tolerance = Tolerance<typename _CapacityMap::Value> >

#endif

  class HaoOrlin {

  private:

    typedef _Digraph Digraph;

    typedef _CapacityMap CapacityMap;

    typedef _Tolerance Tolerance;

    typedef typename CapacityMap::Value Value;

    TEMPLATE_GRAPH_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;

      }

    }

  private:

    void activate(const Node& i) {

      _active->set(i, true);

      int bucket = (*_bucket)[i];

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

      //unlace

      _next->set((*_prev)[i], (*_next)[i]);

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

        _prev->set((*_next)[i], (*_prev)[i]);

      } else {

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

      }

      //lace

      _next->set(i, _first[bucket]);

      _prev->set(_first[bucket], i);

      _prev->set(i, INVALID);

      _first[bucket] = i;

    }

    void deactivate(const Node& i) {

      _active->set(i, false);

      int bucket = (*_bucket)[i];

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

      //unlace

      _prev->set((*_next)[i], (*_prev)[i]);

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

        _next->set((*_prev)[i], (*_next)[i]);

      } else {

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

      }

      //lace

      _prev->set(i, _last[bucket]);

      _next->set(_last[bucket], i);

      _next->set(i, INVALID);

      _last[bucket] = i;

    }

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

      (*_bucket)[i] = bucket;

      if (_last[bucket] != INVALID) {

        _prev->set(i, _last[bucket]);

        _next->set(_last[bucket], i);

        _next->set(i, INVALID);

        _last[bucket] = i;

      } else {

        _prev->set(i, INVALID);

        _first[bucket] = i;

        _next->set(i, INVALID);

        _last[bucket] = i;

      }

    }

    void findMinCutOut() {

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

        _excess->set(n, 0);

      }

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

        _flow->set(a, 0);

      }

      int bucket_num = 1;

      {

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

        reached.set(_source, true);

        bool first_set = true;

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

          if (reached[t]) continue;

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

          _sets.front().push_front(bucket_num);

          _dormant[bucket_num] = !first_set;

          _bucket->set(t, bucket_num);

          _first[bucket_num] = _last[bucket_num] = t;

          _next->set(t, INVALID);

          _prev->set(t, INVALID);

          ++bucket_num;

          std::vector<Node> queue;

          queue.push_back(t);

          reached.set(t, true);

          while (!queue.empty()) {

            _sets.front().push_front(bucket_num);

            _dormant[bucket_num] = !first_set;

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

            std::vector<Node> nqueue;

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

              Node n = queue[i];

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

                Node u = _graph.source(a);

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

                  reached.set(u, true);

                  addItem(u, bucket_num);

                  nqueue.push_back(u);

                }

              }

            }

            queue.swap(nqueue);

            ++bucket_num;

          }

          _sets.front().pop_front();

          --bucket_num;

          first_set = false;

        }

        _bucket->set(_source, 0);

        _dormant[0] = true;

      }

      _source_set->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->set(a, (*_capacity)[a]);

            _excess->set(u, (*_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->set(a, (*_flow)[a] + excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(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->set(a, (*_flow)[a] - excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(a, 0);

              }

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

              next_bucket = (*_bucket)[v];

            }

          }

        no_more_push:

          _excess->set(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->set((*_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->set(n, bucket_num);

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

              _next->set(n, INVALID);

              _prev->set(n, INVALID);

              _dormant[bucket_num] = true;

              ++bucket_num;

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

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

                ++_highest;

              }

            } else {

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

              _prev->set((*_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->set(n, *_highest);

              _next->set(n, _first[*_highest]);

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

                _prev->set(_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->set(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->set(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->set((*_next)[target], (*_prev)[target]);

              new_target = (*_next)[target];

            }

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

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

            } else {

              _next->set((*_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->set(target, 0);

          _source_set->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->set(v, (*_excess)[v] + rem);

            _flow->set(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->set(v, (*_excess)[v] + rem);

            _flow->set(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->set(n, 0);

      }

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

        _flow->set(a, 0);

      }

      int bucket_num = 1;

      {

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

        reached.set(_source, true);

        bool first_set = true;

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

          if (reached[t]) continue;

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

          _sets.front().push_front(bucket_num);

          _dormant[bucket_num] = !first_set;

          _bucket->set(t, bucket_num);

          _first[bucket_num] = _last[bucket_num] = t;

          _next->set(t, INVALID);

          _prev->set(t, INVALID);

          ++bucket_num;

          std::vector<Node> queue;

          queue.push_back(t);

          reached.set(t, true);

          while (!queue.empty()) {

            _sets.front().push_front(bucket_num);

            _dormant[bucket_num] = !first_set;

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

            std::vector<Node> nqueue;

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

              Node n = queue[i];

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

                Node u = _graph.target(a);

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

                  reached.set(u, true);

                  addItem(u, bucket_num);

                  nqueue.push_back(u);

                }

              }

            }

            queue.swap(nqueue);

            ++bucket_num;

          }

          _sets.front().pop_front();

          --bucket_num;

          first_set = false;

        }

        _bucket->set(_source, 0);

        _dormant[0] = true;

      }

      _source_set->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->set(a, (*_capacity)[a]);

            _excess->set(u, (*_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->set(a, (*_flow)[a] + excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(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->set(a, (*_flow)[a] - excess);

                _excess->set(v, (*_excess)[v] + excess);

                excess = 0;

                goto no_more_push;

              } else {

                excess -= rem;

                _excess->set(v, (*_excess)[v] + rem);

                _flow->set(a, 0);

              }

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

              next_bucket = (*_bucket)[v];

            }

          }

        no_more_push:

          _excess->set(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->set((*_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->set(n, bucket_num);

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

              _next->set(n, INVALID);

              _prev->set(n, INVALID);

              _dormant[bucket_num] = true;

              ++bucket_num;

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

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

                ++_highest;

              }

            } else {

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

              _prev->set((*_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->set(n, *_highest);

              _next->set(n, _first[*_highest]);

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

                _prev->set(_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->set(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->set(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->set((*_next)[target], (*_prev)[target]);

              new_target = (*_next)[target];

            }

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

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

            } else {

              _next->set((*_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->set(target, 0);

          _source_set->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->set(v, (*_excess)[v] + rem);

            _flow->set(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->set(v, (*_excess)[v] + rem);

            _flow->set(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 \c run(...).

    /// \n

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

    /// first you must call \ref init(), then the \ref calculateIn() or

    /// \ref calculateIn() functions.

    /// @{

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures. It creates

    /// the maps, residual graph adaptors and some bucket structures

    /// for the algorithm.

    void init() {

      init(NodeIt(_graph));

    }

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures. It creates

    /// the maps, residual graph adaptor and some bucket structures

    /// for the algorithm. Node \c source  is used as the push-relabel

    /// algorithm's source.

    void init(const Node& source) {

      _source = source;

      _node_num = countNodes(_graph);

      _first.resize(_node_num + 1);

      _last.resize(_node_num + 1);

      _dormant.resize(_node_num + 1);

      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 Calculates a minimum cut with \f$ source \f$ on the

    /// source-side.

    ///

    /// 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 out-degree).

    void calculateOut() {

      findMinCutOut();

    }

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

    /// target-side.

    ///

    /// Calculates a minimum cut with \f$ source \f$ on the

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

    /// \in X \f$ and minimal out-degree).

    void calculateIn() {

      findMinCutIn();

    }

    /// \brief Runs the algorithm.

    ///

    /// 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 Runs the algorithm.

    ///

    /// Runs the algorithm. It uses the given \c source node, finds a

    /// proper \c target 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

    /// Before using these functions, either \ref run(), \ref

    /// calculateOut() or \ref calculateIn() must be called.

    /// @{

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

    ///

    /// Returns the value of the minimum value cut.

    Value minCutValue() const {

      return _min_cut;

    }

    /// \brief Returns a minimum cut.

    ///

    /// Sets \c nodeMap to the characteristic vector of a minimum

    /// value cut: it will give a nonempty set \f$ X\subsetneq V \f$

    /// with minimal out-degree (i.e. \c nodeMap will be true exactly

    /// for the nodes of \f$ X \f$).  \pre nodeMap should be a

    /// bool-valued node-map.

    template <typename NodeMap>

    Value minCutMap(NodeMap& nodeMap) const {

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

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

      }

      return _min_cut;

    }

    /// @}

  }; //class HaoOrlin

} //namespace lemon

#endif //LEMON_HAO_ORLIN_H