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/* -*- mode: C++; indent-tabs-mode: nil; -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library.
 *
 * Copyright (C) 2003-2009
 * 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