/* -*- C++ -*-

  *

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

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_HAO_ORLIN_H

 #define LEMON_HAO_ORLIN_H

 #include <vector>

 #include <list>

 #include <limits>

 #include <lemon/maps.h>

 #include <lemon/graph_utils.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 _Graph 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 _Graph::EdgeMap<int>.

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

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

   ///

   /// \author Attila Bernath and Balazs Dezso

 #ifdef DOXYGEN

   template <typename _Graph, typename _CapacityMap, typename _Tolerance>

 #else

   template <typename _Graph,

 	    typename _CapacityMap = typename _Graph::template EdgeMap<int>,

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

 #endif

   class HaoOrlin {

   private:

     typedef _Graph Graph;

     typedef _CapacityMap CapacityMap;

     typedef _Tolerance Tolerance;

     typedef typename CapacityMap::Value Value;

     GRAPH_TYPEDEFS(typename Graph);

     const Graph& _graph;

     const CapacityMap* _capacity;

     typedef typename Graph::template EdgeMap<Value> FlowMap;

     FlowMap* _flow;

     Node _source;

     int _node_num;

     // Bucketing structure

     std::vector<Node> _first, _last;

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

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

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

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

     std::vector<bool> _dormant;

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

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

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

     ExcessMap* _excess;

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

     SourceSetMap* _source_set;

     Value _min_cut;

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

     MinCutMap* _min_cut_map;

     Tolerance _tolerance;

   public: 

     /// \brief Constructor

     ///

     /// Constructor of the algorithm class. 

     HaoOrlin(const Graph& 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 (EdgeIt e(_graph); e != INVALID; ++e) {

 	_flow->set(e, 0);

       }

       int bucket_num = 1;

       {

 	typename Graph::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 (InEdgeIt e(_graph, n); e != INVALID; ++e) {

 		Node u = _graph.source(e);

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

 		  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 (OutEdgeIt e(_graph, _source); e != INVALID; ++e) {

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

 	    Node u = _graph.target(e);

 	    _flow->set(e, (*_capacity)[e]);

 	    _excess->set(u, (*_excess)[u] + (*_capacity)[e]);

 	    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 (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

 	    Node v = _graph.target(e);

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

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

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

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

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

 		activate(v);

 	      }

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

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

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

 		excess = 0;

 		goto no_more_push;

 	      } else {

 		excess -= rem;

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

 		_flow->set(e, (*_capacity)[e]);

 	      }

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

 	      next_bucket = (*_bucket)[v];

 	    }

 	  }

 	  for (InEdgeIt e(_graph, n); e != INVALID; ++e) {

 	    Node v = _graph.source(e);

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

 	    Value rem = (*_flow)[e];

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

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

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

 		activate(v);

 	      }

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

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

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

 		excess = 0;

 		goto no_more_push;

 	      } else {

 		excess -= rem;

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

 		_flow->set(e, 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 (OutEdgeIt e(_graph, target); e != INVALID; ++e) {

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

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

 	    Node v = _graph.target(e);

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

 	      activate(v);

 	    }

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

 	    _flow->set(e, (*_capacity)[e]);

 	  }

 	  for (InEdgeIt e(_graph, target); e != INVALID; ++e) {

 	    Value rem = (*_flow)[e];

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

 	    Node v = _graph.source(e);

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

 	      activate(v);

 	    }

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

 	    _flow->set(e, 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 (EdgeIt e(_graph); e != INVALID; ++e) {

 	_flow->set(e, 0);

       }

       int bucket_num = 1;

       {

 	typename Graph::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 (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

 		Node u = _graph.target(e);

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

 		  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 (InEdgeIt e(_graph, _source); e != INVALID; ++e) {

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

 	    Node u = _graph.source(e);

 	    _flow->set(e, (*_capacity)[e]);

 	    _excess->set(u, (*_excess)[u] + (*_capacity)[e]);

 	    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 (InEdgeIt e(_graph, n); e != INVALID; ++e) {

 	    Node v = _graph.source(e);

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

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

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

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

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

 		activate(v);

 	      }

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

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

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

 		excess = 0;

 		goto no_more_push;

 	      } else {

 		excess -= rem;

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

 		_flow->set(e, (*_capacity)[e]);

 	      }

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

 	      next_bucket = (*_bucket)[v];

 	    }

 	  }

 	  for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {

 	    Node v = _graph.target(e);

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

 	    Value rem = (*_flow)[e];

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

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

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

 		activate(v);

 	      }

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

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

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

 		excess = 0;

 		goto no_more_push;

 	      } else {

 		excess -= rem;

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

 		_flow->set(e, 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 (InEdgeIt e(_graph, target); e != INVALID; ++e) {

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

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

 	    Node v = _graph.source(e);

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

 	      activate(v);

 	    }

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

 	    _flow->set(e, (*_capacity)[e]);

 	  }

 	  for (OutEdgeIt e(_graph, target); e != INVALID; ++e) {

 	    Value rem = (*_flow)[e];

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

 	    Node v = _graph.target(e);

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

 	      activate(v);

 	    }

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

 	    _flow->set(e, 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 Graph::template NodeMap<Node>(_graph);

       }

       if (!_prev) {

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

       }

       if (!_active) {

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

       }

       if (!_bucket) {

 	_bucket = new typename Graph::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 minCut() 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 minCut(NodeMap& nodeMap) const {

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

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

       }

       return minCut();

     }

     /// @}

   }; //class HaoOrlin 

 } //namespace lemon

 #endif //LEMON_HAO_ORLIN_H