source: lemon-0.x/lemon/goldberg_tarjan.h @ 2539:c25f62a6452d

/* -*- 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_GOLDBERG_TARJAN_H
#define LEMON_GOLDBERG_TARJAN_H

#include <vector>
#include <queue>

#include <lemon/error.h>
#include <lemon/bits/invalid.h>
#include <lemon/tolerance.h>
#include <lemon/maps.h>
#include <lemon/graph_utils.h>
#include <lemon/dynamic_tree.h>
#include <limits>

/// \file
/// \ingroup max_flow
/// \brief Implementation of the preflow algorithm.

namespace lemon {

  /// \brief Default traits class of GoldbergTarjan class.
  ///
  /// Default traits class of GoldbergTarjan class.
  /// \param _Graph Graph type.
  /// \param _CapacityMap Type of capacity map.
  template <typename _Graph, typename _CapacityMap>
  struct GoldbergTarjanDefaultTraits {

    /// \brief The graph type the algorithm runs on. 
    typedef _Graph Graph;

    /// \brief The type of the map that stores the edge capacities.
    ///
    /// The type of the map that stores the edge capacities.
    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.
    typedef _CapacityMap CapacityMap;

    /// \brief The type of the length of the edges.
    typedef typename CapacityMap::Value Value;

    /// \brief The map type that stores the flow values.
    ///
    /// The map type that stores the flow values. 
    /// It must meet the \ref concepts::ReadWriteMap "ReadWriteMap" concept.
    typedef typename Graph::template EdgeMap<Value> FlowMap;

    /// \brief Instantiates a FlowMap.
    ///
    /// This function instantiates a \ref FlowMap. 
    /// \param graph The graph, to which we would like to define the flow map.
    static FlowMap* createFlowMap(const Graph& graph) {
      return new FlowMap(graph);
    }

    /// \brief The eleavator type used by GoldbergTarjan algorithm.
    /// 
    /// The elevator type used by GoldbergTarjan algorithm.
    ///
    /// \sa Elevator
    /// \sa LinkedElevator
    typedef LinkedElevator<Graph, typename Graph::Node> Elevator;
    
    /// \brief Instantiates an Elevator.
    ///
    /// This function instantiates a \ref Elevator. 
    /// \param graph The graph, to which we would like to define the elevator.
    /// \param max_level The maximum level of the elevator.
    static Elevator* createElevator(const Graph& graph, int max_level) {
      return new Elevator(graph, max_level);
    }

    /// \brief The tolerance used by the algorithm
    ///
    /// The tolerance used by the algorithm to handle inexact computation.
    typedef Tolerance<Value> Tolerance;

  };

  /// \ingroup max_flow
  /// \brief Goldberg-Tarjan algorithms class.
  ///
  /// This class provides an implementation of the \e GoldbergTarjan
  /// \e algorithm producing a flow of maximum value in a directed
  /// graph. The GoldbergTarjan algorithm is a theoretical improvement
  /// of the Goldberg's \ref Preflow "preflow" algorithm by using the \ref
  /// DynamicTree "dynamic tree" data structure of Sleator and Tarjan.
  /// 
  /// The original preflow algorithm with \e highest \e label
  /// heuristic has \f$O(n^2\sqrt{e})\f$ or with \e FIFO heuristic has
  /// \f$O(n^3)\f$ time complexity. The current algorithm improved
  /// this complexity to \f$O(nm\log(\frac{n^2}{m}))\f$. The algorithm
  /// builds limited size dynamic trees on the residual graph, which
  /// can be used to make multilevel push operations and gives a
  /// better bound on the number of non-saturating pushes.
  ///
  /// \param Graph The directed graph type the algorithm runs on.
  /// \param CapacityMap The capacity map type.
  /// \param _Traits Traits class to set various data types used by
  /// the algorithm.  The default traits class is \ref
  /// GoldbergTarjanDefaultTraits.  See \ref
  /// GoldbergTarjanDefaultTraits for the documentation of a
  /// Goldberg-Tarjan traits class.
  ///
  /// \author Tamas Hamori and Balazs Dezso
#ifdef DOXYGEN
  template <typename _Graph, typename _CapacityMap, typename _Traits> 
#else
  template <typename _Graph,
            typename _CapacityMap = typename _Graph::template EdgeMap<int>,
            typename _Traits = 
            GoldbergTarjanDefaultTraits<_Graph, _CapacityMap> >
#endif
  class GoldbergTarjan {
  public:

    typedef _Traits Traits;
    typedef typename Traits::Graph Graph;
    typedef typename Traits::CapacityMap CapacityMap;
    typedef typename Traits::Value Value; 

    typedef typename Traits::FlowMap FlowMap;
    typedef typename Traits::Elevator Elevator;
    typedef typename Traits::Tolerance Tolerance;
    
  protected:

    GRAPH_TYPEDEFS(typename Graph);

    typedef typename Graph::template NodeMap<Node> NodeNodeMap;
    typedef typename Graph::template NodeMap<int> IntNodeMap;

    typedef typename Graph::template NodeMap<Edge> EdgeNodeMap;
    typedef typename Graph::template EdgeMap<Edge> EdgeEdgeMap;

    typedef typename std::vector<Node> VecNode;
 
    typedef DynamicTree<Value,IntNodeMap,Tolerance> DynTree;

    const Graph& _graph;
    const CapacityMap* _capacity;
    int _node_num; //the number of nodes of G

    Node _source;
    Node _target;

    FlowMap* _flow;
    bool _local_flow;

    Elevator* _level;
    bool _local_level;

    typedef typename Graph::template NodeMap<Value> ExcessMap;
    ExcessMap* _excess;
    
    Tolerance _tolerance;

    bool _phase;

    // constant for treesize
    static const double _tree_bound = 2;
    int _max_tree_size;
    
    //tags for the dynamic tree
    DynTree *_dt; 
    //datastructure of dyanamic tree
    IntNodeMap *_dt_index;
    //datastrucure for solution of the communication between the two class
    EdgeNodeMap *_dt_edges; 
    //nodeMap for storing the outgoing edge from the node in the tree  

    //max of the type Value
    const Value _max_value;
            
  public:

    typedef GoldbergTarjan Create;

    ///\name Named template parameters

    ///@{

    template <typename _FlowMap>
    struct DefFlowMapTraits : public Traits {
      typedef _FlowMap FlowMap;
      static FlowMap *createFlowMap(const Graph&) {
        throw UninitializedParameter();
      }
    };

    /// \brief \ref named-templ-param "Named parameter" for setting
    /// FlowMap type
    ///
    /// \ref named-templ-param "Named parameter" for setting FlowMap
    /// type
    template <typename _FlowMap>
    struct DefFlowMap 
      : public GoldbergTarjan<Graph, CapacityMap, 
                              DefFlowMapTraits<_FlowMap> > {
      typedef GoldbergTarjan<Graph, CapacityMap, 
                             DefFlowMapTraits<_FlowMap> > Create;
    };

    template <typename _Elevator>
    struct DefElevatorTraits : public Traits {
      typedef _Elevator Elevator;
      static Elevator *createElevator(const Graph&, int) {
        throw UninitializedParameter();
      }
    };

    /// \brief \ref named-templ-param "Named parameter" for setting
    /// Elevator type
    ///
    /// \ref named-templ-param "Named parameter" for setting Elevator
    /// type
    template <typename _Elevator>
    struct DefElevator 
      : public GoldbergTarjan<Graph, CapacityMap, 
                              DefElevatorTraits<_Elevator> > {
      typedef GoldbergTarjan<Graph, CapacityMap, 
                             DefElevatorTraits<_Elevator> > Create;
    };

    template <typename _Elevator>
    struct DefStandardElevatorTraits : public Traits {
      typedef _Elevator Elevator;
      static Elevator *createElevator(const Graph& graph, int max_level) {
        return new Elevator(graph, max_level);
      }
    };

    /// \brief \ref named-templ-param "Named parameter" for setting
    /// Elevator type
    ///
    /// \ref named-templ-param "Named parameter" for setting Elevator
    /// type. The Elevator should be standard constructor interface, ie.
    /// the graph and the maximum level should be passed to it.
    template <typename _Elevator>
    struct DefStandardElevator 
      : public GoldbergTarjan<Graph, CapacityMap, 
                              DefStandardElevatorTraits<_Elevator> > {
      typedef GoldbergTarjan<Graph, CapacityMap, 
                             DefStandardElevatorTraits<_Elevator> > Create;
    };    


    ///\ref Exception for the case when s=t.

    ///\ref Exception for the case when the source equals the target.
    class InvalidArgument : public lemon::LogicError {
    public:
      virtual const char* what() const throw() {
        return "lemon::GoldbergTarjan::InvalidArgument";
      }
    };

  protected:
    
    GoldbergTarjan() {}

  public:

    /// \brief The constructor of the class.
    ///
    /// The constructor of the class. 
    /// \param graph The directed graph the algorithm runs on. 
    /// \param capacity The capacity of the edges. 
    /// \param source The source node.
    /// \param target The target node.
    /// Except the graph, all of these parameters can be reset by
    /// calling \ref source, \ref target, \ref capacityMap and \ref
    /// flowMap, resp.
    GoldbergTarjan(const Graph& graph, const CapacityMap& capacity,
                   Node source, Node target) 
      : _graph(graph), _capacity(&capacity), 
        _node_num(), _source(source), _target(target),
        _flow(0), _local_flow(false),
        _level(0), _local_level(false),
        _excess(0), _tolerance(), 
        _phase(), _max_tree_size(),
        _dt(0), _dt_index(0), _dt_edges(0), 
        _max_value(std::numeric_limits<Value>::max()) { 
      if (_source == _target) throw InvalidArgument();
    }

    /// \brief Destrcutor.
    ///
    /// Destructor.
    ~GoldbergTarjan() {
      destroyStructures();
    }
    
    /// \brief Sets the capacity map.
    ///
    /// Sets the capacity map.
    /// \return \c (*this)
    GoldbergTarjan& capacityMap(const CapacityMap& map) {
      _capacity = &map;
      return *this;
    }

    /// \brief Sets the flow map.
    ///
    /// Sets the flow map.
    /// \return \c (*this)
    GoldbergTarjan& flowMap(FlowMap& map) {
      if (_local_flow) {
        delete _flow;
        _local_flow = false;
      }
      _flow = &map;
      return *this;
    }

    /// \brief Returns the flow map.
    ///
    /// \return The flow map.
    const FlowMap& flowMap() {
      return *_flow;
    }

    /// \brief Sets the elevator.
    ///
    /// Sets the elevator.
    /// \return \c (*this)
    GoldbergTarjan& elevator(Elevator& elevator) {
      if (_local_level) {
        delete _level;
        _local_level = false;
      }
      _level = &elevator;
      return *this;
    }

    /// \brief Returns the elevator.
    ///
    /// \return The elevator.
    const Elevator& elevator() {
      return *_level;
    }

    /// \brief Sets the source node.
    ///
    /// Sets the source node.
    /// \return \c (*this)
    GoldbergTarjan& source(const Node& node) {
      _source = node;
      return *this;
    }

    /// \brief Sets the target node.
    ///
    /// Sets the target node.
    /// \return \c (*this)
    GoldbergTarjan& target(const Node& node) {
      _target = node;
      return *this;
    }
 
    /// \brief Sets the tolerance used by algorithm.
    ///
    /// Sets the tolerance used by algorithm.
    GoldbergTarjan& tolerance(const Tolerance& tolerance) const {
      _tolerance = tolerance;
      if (_dt) {
        _dt->tolerance(_tolerance);
      }
      return *this;
    } 

    /// \brief Returns the tolerance used by algorithm.
    ///
    /// Returns the tolerance used by algorithm.
    const Tolerance& tolerance() const {
      return tolerance;
    } 

         
  private:
    
    void createStructures() {
      _node_num = countNodes(_graph);

      _max_tree_size = int((double(_node_num) * double(_node_num)) / 
                           double(countEdges(_graph)));

      if (!_flow) {
        _flow = Traits::createFlowMap(_graph);
        _local_flow = true;
      }
      if (!_level) {
        _level = Traits::createElevator(_graph, _node_num);
        _local_level = true;
      }
      if (!_excess) {
        _excess = new ExcessMap(_graph);
      }
      if (!_dt_index && !_dt) {
        _dt_index = new IntNodeMap(_graph);
        _dt = new DynTree(*_dt_index, _tolerance);
      }
      if (!_dt_edges) {
        _dt_edges = new EdgeNodeMap(_graph);
      }
    }

    void destroyStructures() {
      if (_local_flow) {
        delete _flow;
      }
      if (_local_level) {
        delete _level;
      }
      if (_excess) {
        delete _excess;
      }
      if (_dt) {
        delete _dt;
      }
      if (_dt_index) {
        delete _dt_index;
      }
      if (_dt_edges) {
        delete _dt_edges;
      }
    }

    bool sendOut(Node n, Value& excess) {

      Node w = _dt->findRoot(n);
      
      while (w != n) {
      
        Value rem;      
        Node u = _dt->findCost(n, rem);

        if (_tolerance.positive(rem) && !_level->active(w) && w != _target) {
          _level->activate(w);
        }

        if (!_tolerance.less(rem, excess)) {
          _dt->addCost(n, - excess);
          _excess->set(w, (*_excess)[w] + excess);
          excess = 0;
          return true;
        }
        
        
        _dt->addCost(n, - rem);

        excess -= rem;
        _excess->set(w, (*_excess)[w] + rem);
        
        _dt->cut(u);
        _dt->addCost(u, _max_value);
          
        Edge e = (*_dt_edges)[u];
        _dt_edges->set(u, INVALID);
        
        if (u == _graph.source(e)) {
          _flow->set(e, (*_capacity)[e]);
        } else {
          _flow->set(e, 0);
        }           

        w = _dt->findRoot(n);
      }      
      return false;
    }

    bool sendIn(Node n, Value& excess) {

      Node w = _dt->findRoot(n);
      
      while (w != n) {
      
        Value rem;      
        Node u = _dt->findCost(n, rem);

        if (_tolerance.positive(rem) && !_level->active(w) && w != _source) {
          _level->activate(w);
        }

        if (!_tolerance.less(rem, excess)) {
          _dt->addCost(n, - excess);
          _excess->set(w, (*_excess)[w] + excess);
          excess = 0;
          return true;
        }
        
        
        _dt->addCost(n, - rem);

        excess -= rem;
        _excess->set(w, (*_excess)[w] + rem);
        
        _dt->cut(u);
        _dt->addCost(u, _max_value);
          
        Edge e = (*_dt_edges)[u];
        _dt_edges->set(u, INVALID);
        
        if (u == _graph.source(e)) {
          _flow->set(e, (*_capacity)[e]);
        } else {
          _flow->set(e, 0);
        }           

        w = _dt->findRoot(n);
      }      
      return false;
    }

    void cutChildren(Node n) {
    
      for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
        
        Node v = _graph.target(e);
        
        if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) {
          _dt->cut(v);
          _dt_edges->set(v, INVALID);
          Value rem;
          _dt->findCost(v, rem);
          _dt->addCost(v, - rem);
          _dt->addCost(v, _max_value);
          _flow->set(e, rem);

        }      
      }

      for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
        
        Node v = _graph.source(e);
        
        if ((*_dt_edges)[v] != INVALID && (*_dt_edges)[v] == e) {
          _dt->cut(v);
          _dt_edges->set(v, INVALID);
          Value rem;
          _dt->findCost(v, rem);
          _dt->addCost(v, - rem);
          _dt->addCost(v, _max_value);
          _flow->set(e, (*_capacity)[e] - rem);

        }      
      }
    }

    void extractTrees() {
      for (NodeIt n(_graph); n != INVALID; ++n) {
        
        Node w = _dt->findRoot(n);
      
        while (w != n) {
      
          Value rem;      
          Node u = _dt->findCost(n, rem);

          _dt->cut(u);
          _dt->addCost(u, - rem);
          _dt->addCost(u, _max_value);
          
          Edge e = (*_dt_edges)[u];
          _dt_edges->set(u, INVALID);
          
          if (u == _graph.source(e)) {
            _flow->set(e, (*_capacity)[e] - rem);
          } else {
            _flow->set(e, rem);
          }
          
          w = _dt->findRoot(n);
        }      
      }
    }

  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 initial solution or
    /// execution then you have to call one \ref init() function and then
    /// the startFirstPhase() and if you need the startSecondPhase().  
    
    ///@{

    /// \brief Initializes the internal data structures.
    ///
    /// Initializes the internal data structures.
    ///
    void init() {
      createStructures();

      for (NodeIt n(_graph); n != INVALID; ++n) {
        _excess->set(n, 0);
      }

      for (EdgeIt e(_graph); e != INVALID; ++e) {
        _flow->set(e, 0);
      }

      _dt->clear();
      for (NodeIt v(_graph); v != INVALID; ++v) {
        (*_dt_edges)[v] = INVALID;
        _dt->makeTree(v);
        _dt->addCost(v, _max_value);
      }

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

      _level->initStart();
      _level->initAddItem(_target);

      std::vector<Node> queue;
      reached.set(_source, true);

      queue.push_back(_target);
      reached.set(_target, true);
      while (!queue.empty()) {
        _level->initNewLevel();
        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);
              _level->initAddItem(u);
              nqueue.push_back(u);
            }
          }
        }
        queue.swap(nqueue);
      }
      _level->initFinish();

      for (OutEdgeIt e(_graph, _source); e != INVALID; ++e) {
        if (_tolerance.positive((*_capacity)[e])) {
          Node u = _graph.target(e);
          if ((*_level)[u] == _level->maxLevel()) continue;
          _flow->set(e, (*_capacity)[e]);
          _excess->set(u, (*_excess)[u] + (*_capacity)[e]);
          if (u != _target && !_level->active(u)) {
            _level->activate(u);
          }
        }
      }
    }

    /// \brief Starts the first phase of the preflow algorithm.
    ///
    /// The preflow algorithm consists of two phases, this method runs
    /// the first phase. After the first phase the maximum flow value
    /// and a minimum value cut can already be computed, although a
    /// maximum flow is not yet obtained. So after calling this method
    /// \ref flowValue() returns the value of a maximum flow and \ref
    /// minCut() returns a minimum cut.     
    /// \pre One of the \ref init() functions should be called. 
    void startFirstPhase() {
      _phase = true;
      Node n;

      while ((n = _level->highestActive()) != INVALID) {
        Value excess = (*_excess)[n];
        int level = _level->highestActiveLevel();
        int new_level = _level->maxLevel();

        if (_dt->findRoot(n) != n) {
          if (sendOut(n, excess)) goto no_more_push;
        }
        
        for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
          Value rem = (*_capacity)[e] - (*_flow)[e];
          Node v = _graph.target(e);
          
          if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue;

          if ((*_level)[v] < level) {
            
            if (_dt->findSize(n) + _dt->findSize(v) < 
                _tree_bound * _max_tree_size) {
              _dt->addCost(n, -_max_value);
              _dt->addCost(n, rem);
              _dt->link(n, v);
              _dt_edges->set(n, e);
              if (sendOut(n, excess)) goto no_more_push;
            } else {
              if (!_level->active(v) && v != _target) {
                _level->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 (new_level > (*_level)[v]) {
            new_level = (*_level)[v];
          }
        }

        for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
          Value rem = (*_flow)[e];
          Node v = _graph.source(e);
          if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue;

          if ((*_level)[v] < level) {
            
            if (_dt->findSize(n) + _dt->findSize(v) < 
                _tree_bound * _max_tree_size) {
              _dt->addCost(n, - _max_value);
              _dt->addCost(n, rem);
              _dt->link(n, v);
              _dt_edges->set(n, e);
              if (sendOut(n, excess)) goto no_more_push;
            } else {
              if (!_level->active(v) && v != _target) {
                _level->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 (new_level > (*_level)[v]) {
            new_level = (*_level)[v];
          }
        }
                
      no_more_push:

        _excess->set(n, excess);
        
        if (excess != 0) {
          cutChildren(n);
          if (new_level + 1 < _level->maxLevel()) {
            _level->liftHighestActive(new_level + 1);
          } else {
            _level->liftHighestActiveToTop();
          }
          if (_level->emptyLevel(level)) {
            _level->liftToTop(level);
          }
        } else {
          _level->deactivate(n);
        }       
      }
      extractTrees();
    }

    /// \brief Starts the second phase of the preflow algorithm.
    ///
    /// The preflow algorithm consists of two phases, this method runs
    /// the second phase. After calling \ref init() and \ref
    /// startFirstPhase() and then \ref startSecondPhase(), \ref
    /// flowMap() return a maximum flow, \ref flowValue() returns the
    /// value of a maximum flow, \ref minCut() returns a minimum cut
    /// \pre The \ref init() and startFirstPhase() functions should be
    /// called before.
    void startSecondPhase() {
      _phase = false;
      
      typename Graph::template NodeMap<bool> reached(_graph, false);
      for (NodeIt n(_graph); n != INVALID; ++n) {
        reached.set(n, (*_level)[n] < _level->maxLevel());
      }

      _level->initStart();
      _level->initAddItem(_source);
 
      std::vector<Node> queue;
      queue.push_back(_source);
      reached.set(_source, true);

      while (!queue.empty()) {
        _level->initNewLevel();
        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 v = _graph.target(e);
            if (!reached[v] && _tolerance.positive((*_flow)[e])) {
              reached.set(v, true);
              _level->initAddItem(v);
              nqueue.push_back(v);
            }
          }
          for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
            Node u = _graph.source(e);
            if (!reached[u] && 
                _tolerance.positive((*_capacity)[e] - (*_flow)[e])) {
              reached.set(u, true);
              _level->initAddItem(u);
              nqueue.push_back(u);
            }
          }
        }
        queue.swap(nqueue);
      }
      _level->initFinish();

      for (NodeIt n(_graph); n != INVALID; ++n) {
        if (!reached[n]) {
          _level->markToBottom(n);
        } else if ((*_excess)[n] > 0 && _target != n) {
          _level->activate(n);
        }
      }

      Node n;

      while ((n = _level->highestActive()) != INVALID) {
        Value excess = (*_excess)[n];
        int level = _level->highestActiveLevel();
        int new_level = _level->maxLevel();

        if (_dt->findRoot(n) != n) {
          if (sendIn(n, excess)) goto no_more_push;
        }
        
        for (OutEdgeIt e(_graph, n); e != INVALID; ++e) {
          Value rem = (*_capacity)[e] - (*_flow)[e];
          Node v = _graph.target(e);
          
          if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue;

          if ((*_level)[v] < level) {
            
            if (_dt->findSize(n) + _dt->findSize(v) < 
                _tree_bound * _max_tree_size) {
              _dt->addCost(n, -_max_value);
              _dt->addCost(n, rem);
              _dt->link(n, v);
              _dt_edges->set(n, e);
              if (sendIn(n, excess)) goto no_more_push;
            } else {
              if (!_level->active(v) && v != _source) {
                _level->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 (new_level > (*_level)[v]) {
            new_level = (*_level)[v];
          }
        }

        for (InEdgeIt e(_graph, n); e != INVALID; ++e) {
          Value rem = (*_flow)[e];
          Node v = _graph.source(e);
          if (!_tolerance.positive(rem) && (*_dt_edges)[v] != e) continue;

          if ((*_level)[v] < level) {
            
            if (_dt->findSize(n) + _dt->findSize(v) < 
                _tree_bound * _max_tree_size) {
              _dt->addCost(n, - _max_value);
              _dt->addCost(n, rem);
              _dt->link(n, v);
              _dt_edges->set(n, e);
              if (sendIn(n, excess)) goto no_more_push;
            } else {
              if (!_level->active(v) && v != _source) {
                _level->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 (new_level > (*_level)[v]) {
            new_level = (*_level)[v];
          }
        }
                
      no_more_push:

        _excess->set(n, excess);
        
        if (excess != 0) {
          cutChildren(n);
          if (new_level + 1 < _level->maxLevel()) {
            _level->liftHighestActive(new_level + 1);
          } else {
            _level->liftHighestActiveToTop();
          }
          if (_level->emptyLevel(level)) {
            _level->liftToTop(level);
          }
        } else {
          _level->deactivate(n);
        }       
      }
      extractTrees();
    }

    /// \brief Runs the Goldberg-Tarjan algorithm.  
    ///
    /// Runs the Goldberg-Tarjan algorithm.
    /// \note pf.run() is just a shortcut of the following code.
    /// \code
    ///   pf.init();
    ///   pf.startFirstPhase();
    ///   pf.startSecondPhase();
    /// \endcode
    void run() {
      init();
      startFirstPhase();
      startSecondPhase();
    }

    /// \brief Runs the Goldberg-Tarjan algorithm to compute the minimum cut.  
    ///
    /// Runs the Goldberg-Tarjan algorithm to compute the minimum cut.
    /// \note pf.runMinCut() is just a shortcut of the following code.
    /// \code
    ///   pf.init();
    ///   pf.startFirstPhase();
    /// \endcode
    void runMinCut() {
      init();
      startFirstPhase();
    }

    /// @}

    /// \name Query Functions 
    /// The result of the Goldberg-Tarjan algorithm can be obtained
    /// using these functions.
    /// \n
    /// Before the use of these functions, either run() or start() must
    /// be called.
    
    ///@{

    /// \brief Returns the value of the maximum flow.
    ///
    /// Returns the value of the maximum flow by returning the excess
    /// of the target node \c t. This value equals to the value of
    /// the maximum flow already after the first phase.
    Value flowValue() const {
      return (*_excess)[_target];
    }

    /// \brief Returns true when the node is on the source side of minimum cut.
    ///
    /// Returns true when the node is on the source side of minimum
    /// cut. This method can be called both after running \ref
    /// startFirstPhase() and \ref startSecondPhase().
    bool minCut(const Node& node) const {
      return ((*_level)[node] == _level->maxLevel()) == _phase;
    }
 
    /// \brief Returns a minimum value cut.
    ///
    /// Sets the \c cutMap to the characteristic vector of a minimum value
    /// cut. This method can be called both after running \ref
    /// startFirstPhase() and \ref startSecondPhase(). The result after second
    /// phase could be changed slightly if inexact computation is used.
    /// \pre The \c cutMap should be a bool-valued node-map.
    template <typename CutMap>
    void minCutMap(CutMap& cutMap) const {
      for (NodeIt n(_graph); n != INVALID; ++n) {
        cutMap.set(n, minCut(n));
      }
    }

    /// \brief Returns the flow on the edge.
    ///
    /// Sets the \c flowMap to the flow on the edges. This method can
    /// be called after the second phase of algorithm.
    Value flow(const Edge& edge) const {
      return (*_flow)[edge];
    }

    /// @}

  }; 
  
} //namespace lemon

#endif