/// Implementation of the HaoOrlin algorithms class for testing network 

 /// Implementation of the Hao-Orlin algorithm class for testing network 

   /// Hao-Orlin calculates a minimum cut in a directed graph 

   /// 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

   /// \f$D=(V,A)\f$. It takes a fixed node \f$ source \in V \f$ and

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

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

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

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

   /// with \f$ source \in X \f$ and minimal out-degree) and in the

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

   /// second phase it determines a minimum cut with \f$ source \f$ on the

   /// out-degree) and in the second phase it determines a minimum cut

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

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

   /// and minimal out-degree). Obviously, the smaller of these two

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

   /// cuts will be a minimum cut of \f$ D \f$. The algorithm is a

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

   /// modified push-relabel preflow algorithm and our implementation

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

   /// calculates the minimum cut in \f$ O(n^3) \f$ time (we use the

   /// push-relabel preflow algorithm and our implementation calculates

   /// highest-label rule). The purpose of such an algorithm is testing

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

   /// network reliability. For an undirected graph with \f$ n \f$

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

   /// nodes and \f$ e \f$ edges you can use the algorithm of Nagamochi

   /// purpose of such algorithm is testing network reliability. For an

   /// and Ibaraki which solves the undirected problem in 

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

   /// \f$ O(ne + n^2 \log(n)) \f$ time: it is implemented in the MinCut 

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

   /// algorithm

   /// which solves the undirected problem in 

   /// class.

   /// \f$ O(nm + n^2 \log(n)) \f$ time: it is implemented in the

   /// NagamochiIbaraki algorithm class.

   protected:

   private:

     typedef typename Graph::Node Node;

     const Graph& _graph;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     const Graph* _graph;

     FlowMap* _flow;

     FlowMap* _preflow;

     Node _source;

     Node _source, _target;

     typedef ResGraphAdaptor<const Graph, Value, CapacityMap, 

     // Bucketing structure

                             FlowMap, Tolerance> OutResGraph;

     std::vector<Node> _first, _last;

     typedef typename OutResGraph::Edge OutResEdge;

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

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

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

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

     OutResGraph* _out_res_graph;

     std::vector<bool> _dormant;

     typedef RevGraphAdaptor<const Graph> RevGraph;

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

     RevGraph* _rev_graph;

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

     typedef ResGraphAdaptor<const RevGraph, Value, CapacityMap, 

                             FlowMap, Tolerance> InResGraph;

     typedef typename InResGraph::Edge InResEdge;

     InResGraph* _in_res_graph;

     typedef IterableBoolMap<Graph, Node> WakeMap;

     WakeMap* _wake;

     typedef typename Graph::template NodeMap<int> DistMap;

     DistMap* _dist;  

       _graph(&graph), _capacity(&capacity), 

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

       _preflow(0), _source(), _target(), 

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

       _out_res_graph(0), _rev_graph(0), _in_res_graph(0),

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

       _wake(0),_dist(0), _excess(0), _source_set(0), 

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

       _highest_active(), _active_nodes(), _dormant_max(), _dormant(), 

       _tolerance(tolerance) {}

       _min_cut(), _min_cut_map(0), _tolerance(tolerance) {}

       if (_dist) {

       if (_next) {

         delete _dist;

 	delete _next;

       }

       }

       if (_wake) {

       if (_prev) {

         delete _wake;

 	delete _prev;

       }

       }

       if (_preflow) {

       if (_active) {

         delete _preflow;

 	delete _active;

       }

       if (_bucket) {

 	delete _bucket;

       }

       if (_flow) {

         delete _flow;

     template <typename ResGraph>

     void findMinCutOut() {

     void findMinCut(const Node& target, bool out, ResGraph& res_graph) {

       typedef typename ResGraph::Edge ResEdge;

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

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

 	_excess->set(n, 0);

       }

       for (typename Graph::EdgeIt it(*_graph); it != INVALID; ++it) {

         (*_preflow)[it] = 0;      

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

       }

 	_flow->set(e, 0);

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

       }

         (*_wake)[it] = true;

         (*_dist)[it] = 1;

       int bucket_num = 1;

         (*_excess)[it] = 0;

         (*_source_set)[it] = false;

       {

       }

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

       _dormant[0].push_front(_source);

 	reached.set(_source, true);

       (*_source_set)[_source] = true;

       _dormant_max = 0;

 	bool first_set = true;

       (*_wake)[_source] = false;

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

       _level_size[0] = 1;

 	  if (reached[t]) continue;

       _level_size[1] = _node_num - 1;

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

 	  _sets.front().push_front(bucket_num);

       _target = target;

 	  _dormant[bucket_num] = !first_set;

       (*_dist)[target] = 0;

 	  _bucket->set(t, bucket_num);

       for (ResOutEdgeIt it(res_graph, _source); it != INVALID; ++it) {

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

         Value delta = res_graph.rescap(it);

 	  _next->set(t, INVALID);

         (*_excess)[_source] -= delta;

 	  _prev->set(t, INVALID);

         res_graph.augment(it, delta);

         Node a = res_graph.target(it);

 	  ++bucket_num;

         if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) {

           _active_nodes[(*_dist)[a]].push_front(a);

 	  std::vector<Node> queue;

           if (_highest_active < (*_dist)[a]) {

 	  queue.push_back(t);

             _highest_active = (*_dist)[a];

 	  reached.set(t, true);

           }

         }

 	  while (!queue.empty()) {

         (*_excess)[a] += delta;

 	    _sets.front().push_front(bucket_num);

       }

 	    _dormant[bucket_num] = !first_set;

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

       do {

 	    std::vector<Node> nqueue;

 	Node n;

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

 	while ((n = findActiveNode()) != INVALID) {

 	      Node n = queue[i];

 	  for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) {

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

             Node a = res_graph.target(e);

 		Node u = _graph.source(e);

             if ((*_dist)[a] >= (*_dist)[n] || !(*_wake)[a]) continue;

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

 	    Value delta = res_graph.rescap(e);

 		  reached.set(u, true);

 	    if (_tolerance.positive((*_excess)[n] - delta)) {

 		  addItem(u, bucket_num);

               (*_excess)[n] -= delta;

 		  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;

 	      }

 	      delta = (*_excess)[n];

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

               (*_excess)[n] = 0;

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

 	    }

 	    res_graph.augment(e, delta);

 	      while (next_bucket != *_highest) {

 	    if ((*_excess)[a] == 0 && a != _target) {

 		--_highest;

 	      _active_nodes[(*_dist)[a]].push_front(a);

 	      }

 	    }

 	    (*_excess)[a] += delta;

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

             if ((*_excess)[n] == 0) break;

 		_sets.back().push_front(bucket_num);

 	  }

 		_dormant[bucket_num] = false;

 	  if ((*_excess)[n] != 0) {

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

 	    relabel(n, res_graph);

 		++bucket_num;

           }

 	      }

 	}

 	      --_highest;

 	Value current_value = cutValue(out);

 	      _bucket->set(n, *_highest);

  	if (_min_cut > current_value){

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

           if (out) {

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

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

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

               _min_cut_map->set(it, !(*_wake)[it]);

 	      } else {

             } 

 		_last[*_highest] = n;

           } else {

 	      }

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

 	      _first[*_highest] = n;	      

               _min_cut_map->set(it, (*_wake)[it]);

 	    }

             } 

 	  } else {

           }

 	    deactivate(n);

 	  _min_cut = current_value;

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

  	}

 	      ++_highest;

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

       } while (selectNewSink(res_graph));

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

     }

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

 	      }

     template <typename ResGraph>

 	    }

     void relabel(const Node& n, ResGraph& res_graph) {

 	  }

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

 	}

       int k = (*_dist)[n];

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

       if (_level_size[k] == 1) {

 	  _min_cut = (*_excess)[target];

 	++_dormant_max;

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

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

 	    _min_cut_map->set(i, true);

 	  if ((*_wake)[it] && (*_dist)[it] >= k) {

 	  }

 	    (*_wake)[it] = false;

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

 	    _dormant[_dormant_max].push_front(it);

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

 	    --_level_size[(*_dist)[it]];

 	    Node n = _first[*it];

 	  }

 	    while (n != INVALID) {

 	}

 	      _min_cut_map->set(n, false);

         --_highest_active;

 	      n = (*_next)[n];

       } else {	

 	    }

         int new_dist = _node_num;

 	  }

         for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e) {

 	}

           Node t = res_graph.target(e);

           if ((*_wake)[t] && new_dist > (*_dist)[t]) {

 	{

             new_dist = (*_dist)[t];

 	  Node new_target;

           }

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

         }

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

         if (new_dist == _node_num) {

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

 	  ++_dormant_max;

 	    new_target = (*_prev)[target];

 	  (*_wake)[n] = false;

 	  } else {

 	  _dormant[_dormant_max].push_front(n);

 	    _sets.back().pop_back();

 	  --_level_size[(*_dist)[n]];

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

 	} else {	    

 	      _sets.pop_back();

 	  --_level_size[(*_dist)[n]];

 	      if (_sets.empty())

 	  (*_dist)[n] = new_dist + 1;

 		break;

 	  _highest_active = (*_dist)[n];

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

 	  _active_nodes[_highest_active].push_front(n);

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

 	  ++_level_size[(*_dist)[n]];

 		_dormant[*it] = false;

 	}

 	      }

       }

 	    }

     }

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

 	  }

     template <typename ResGraph>

     bool selectNewSink(ResGraph& res_graph) {

 	  _bucket->set(target, 0);

       typedef typename ResGraph::OutEdgeIt ResOutEdgeIt;

 	  _source_set->set(target, true);	  

       Node old_target = _target;

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

       (*_wake)[_target] = false;

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

       --_level_size[(*_dist)[_target]];

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

       _dormant[0].push_front(_target);

 	    Node v = _graph.target(e);

       (*_source_set)[_target] = true;

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

       if (int(_dormant[0].size()) == _node_num){

 	      activate(v);

         _dormant[0].clear();

 	    }

 	return false;

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

       }

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

 	  }

       bool wake_was_empty = false;

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

       if(_wake->trueNum() == 0) {

 	    Value rem = (*_flow)[e];

 	while (!_dormant[_dormant_max].empty()){

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

 	  (*_wake)[_dormant[_dormant_max].front()] = true;

 	    Node v = _graph.source(e);

 	  ++_level_size[(*_dist)[_dormant[_dormant_max].front()]];

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

 	  _dormant[_dormant_max].pop_front();

 	      activate(v);

 	}

 	    }

 	--_dormant_max;

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

 	wake_was_empty = true;

 	    _flow->set(e, 0);

       }

 	  }

       int min_dist = std::numeric_limits<int>::max();

 	  target = new_target;

       for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

 	  if ((*_active)[target]) {

 	if (min_dist > (*_dist)[it]){

 	    deactivate(target);

 	  _target = it;

 	  }

 	  min_dist = (*_dist)[it];

 	}

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

       }

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

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

       if (wake_was_empty){

 	    ++_highest;

 	for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

 	  }

           if ((*_excess)[it] != 0 && it != _target) {

 	}

             _active_nodes[(*_dist)[it]].push_front(it);

       }

             if (_highest_active < (*_dist)[it]) {

     }    

               _highest_active = (*_dist)[it];		    

             }

     void findMinCutIn() {

 	  }

 	}

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

       }

 	_excess->set(n, 0);

       }

       Node n = old_target;

       for (ResOutEdgeIt e(res_graph, n); e != INVALID; ++e){

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

         Node a = res_graph.target(e);

 	_flow->set(e, 0);

 	if (!(*_wake)[a]) continue;

       }

         Value delta = res_graph.rescap(e);

         res_graph.augment(e, delta);

       int bucket_num = 1;

         (*_excess)[n] -= delta;

         if ((*_excess)[a] == 0 && (*_wake)[a] && a != _target) {

           _active_nodes[(*_dist)[a]].push_front(a);

           if (_highest_active < (*_dist)[a]) {

             _highest_active = (*_dist)[a];

           }

         }

         (*_excess)[a] += delta;

       }

       return true;

       {

     }

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

     Node findActiveNode() {

 	reached.set(_source, true);

       while (_highest_active > 0 && _active_nodes[_highest_active].empty()){ 

 	--_highest_active;

 	bool first_set = true;

       }

       if( _highest_active > 0) {

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

        	Node n = _active_nodes[_highest_active].front();

 	  if (reached[t]) continue;

 	_active_nodes[_highest_active].pop_front();

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

 	return n;

 	  _sets.front().push_front(bucket_num);

       } else {

 	  _dormant[bucket_num] = !first_set;

 	return INVALID;

       }

 	  _bucket->set(t, bucket_num);

     }

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

 	  _next->set(t, INVALID);

     Value cutValue(bool out) {

 	  _prev->set(t, INVALID);

       Value value = 0;

       if (out) {

 	  ++bucket_num;

         for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

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

 	  std::vector<Node> queue;

             if (!(*_wake)[_graph->source(e)]){

 	  queue.push_back(t);

               value += (*_capacity)[e];

 	  reached.set(t, true);

             }	

           }

 	  while (!queue.empty()) {

         }

 	    _sets.front().push_front(bucket_num);

       } else {

 	    _dormant[bucket_num] = !first_set;

         for (typename WakeMap::TrueIt it(*_wake); it != INVALID; ++it) {

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

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

             if (!(*_wake)[_graph->target(e)]){

 	    std::vector<Node> nqueue;

               value += (*_capacity)[e];

 	    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])) {

       return value;

 		  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) {

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

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

 	    new_target = (*_prev)[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;

 	  }

 	}

       }

     }

       init(NodeIt(*_graph));

       init(NodeIt(_graph));

       _node_num = countNodes(*_graph);

       _node_num = countNodes(_graph);

       _first.resize(_node_num);

       _last.resize(_node_num);

       _level_size.resize(_node_num, 0);

       _active_nodes.resize(_node_num);

       if (!_flow) {

 	_flow = new FlowMap(_graph);

       if (!_preflow) {

       }

         _preflow = new FlowMap(*_graph);

       if (!_next) {

       }

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

       if (!_wake) {

       }

         _wake = new WakeMap(*_graph);

       if (!_prev) {

       }

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

       if (!_dist) {

       }

         _dist = new DistMap(*_graph);

       if (!_active) {

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

       }

       if (!_bucket) {

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

         _excess = new ExcessMap(*_graph);

 	_excess = new ExcessMap(_graph);

         _source_set = new SourceSetMap(*_graph);

 	_source_set = new SourceSetMap(_graph);

       }

       if (!_out_res_graph) {

         _out_res_graph = new OutResGraph(*_graph, *_capacity, *_preflow);

       }

       if (!_rev_graph) {

         _rev_graph = new RevGraph(*_graph);

       }

       if (!_in_res_graph) {

         _in_res_graph = new InResGraph(*_rev_graph, *_capacity, *_preflow);

         _min_cut_map = new MinCutMap(*_graph);

 	_min_cut_map = new MinCutMap(_graph);

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

     /// target-side.

     ///  and minimal out-degree).

     void calculateOut() {

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

         if (it != _source) {

           calculateOut(it);

           return;

         }

       }

     }

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

     /// source-side.

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

     /// 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$

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

     ///  and minimal out-degree). The \c target is the initial target

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

     /// for the push-relabel algorithm.

     void calculateOut(const Node& target) {

       findMinCut(target, true, *_out_res_graph);

     }

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

     /// sink-side.

     ///

     /// \brief 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 out-degree).

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

       findMinCutIn();

         if (it != _source) {

     }

           calculateIn(it);

           return;

         }

       }

     }

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

     /// sink-side.

     ///

     /// \brief 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 out-degree).  

     /// The \c target is the initial

     /// target for the push-relabel algorithm.

     void calculateIn(const Node& target) {

       findMinCut(target, false, *_in_res_graph);

     }

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

       calculateOut();

         if (it != _source) {

       calculateIn();

           calculateOut(it);

           calculateIn(it);

           return;

         }

       }

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

       calculateOut();

         if (it != _source) {

       calculateIn();

           calculateOut(it);

           calculateIn(it);

           return;

         }

       }

     }

     /// \brief Runs the algorithm.

     ///

     /// Runs the algorithm. It just calls the \ref init() and then

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

     void run(const Node& s, const Node& t) {

       init(s); 

       calculateOut(t);

       calculateIn(t);

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

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