/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2007

 * 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 <ext/hash_set>

#include <limits>

#include <lemon/maps.h>

#include <lemon/graph_utils.h>

#include <lemon/graph_adaptor.h>

#include <lemon/iterable_maps.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) {

	    _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 (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) {

	    _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;

	  }

	}

      }

    }

  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);

      _last.resize(_node_num);

      _dormant.resize(_node_num);

      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