// -*- C++ -*-
#ifndef HUGO_MAX_FLOW_H
#define HUGO_MAX_FLOW_H

#include <vector>
#include <queue>
#include <stack>

#include <hugo/graph_wrapper.h>
#include <bfs_dfs.h>
#include <hugo/invalid.h>
#include <hugo/maps.h>
#include <for_each_macros.h>

/// \file
/// \brief Maximum flow algorithms.
/// \ingroup galgs

namespace hugo {

  /// \addtogroup galgs
  /// @{                                                                                                                                        
  ///Maximum flow algorithms class.

  ///This class provides various algorithms for finding a flow of
  ///maximum value in a directed graph. The \e source node, the \e
  ///target node, the \e capacity of the edges and the \e starting \e
  ///flow value of the edges can be passed to the algorithm through the
  ///constructor. It is possible to change these quantities using the
  ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
  ///\ref resetFlow. Before any subsequent runs of any algorithm of
  ///the class \ref resetFlow should be called, otherwise it will
  ///start from a maximum flow.                                                                                                                 
  ///After running an algorithm of the class, the maximum value of a
  ///value can be obtained by calling \ref flowValue(). The minimum
  ///value cut can be written into a \c node map of \c bools by
  ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
  ///the inclusionwise minimum and maximum of the minimum value
  ///cuts, resp.)                                                                                                                               
  ///\param Graph The undirected graph type the algorithm runs on.
  ///\param Num The number type of the capacities and the flow values.
  ///\param CapMap The type of the capacity map.
  ///\param FlowMap The type of the flow map.                                                                                                           
  ///\author Marton Makai, Jacint Szabo 
  template <typename Graph, typename Num,
	    typename CapMap=typename Graph::template EdgeMap<Num>,
            typename FlowMap=typename Graph::template EdgeMap<Num> >
  class MaxFlow {
  protected:
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::EdgeIt EdgeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename std::vector<std::stack<Node> > VecStack;
    typedef typename Graph::template NodeMap<Node> NNMap;
    typedef typename std::vector<Node> VecNode;

    const Graph* g;
    Node s;
    Node t;
    const CapMap* capacity;
    FlowMap* flow;
    int n;      //the number of nodes of G
    typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
    typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
    typedef typename ResGW::Edge ResGWEdge;
    //typedef typename ResGW::template NodeMap<bool> ReachedMap;
    typedef typename Graph::template NodeMap<int> ReachedMap;


    //level works as a bool map in augmenting path algorithms and is
    //used by bfs for storing reached information.  In preflow, it
    //shows the levels of nodes.     
    ReachedMap level;

    //excess is needed only in preflow
    typename Graph::template NodeMap<Num> excess;

    //fixme    
//   protected:
    //     MaxFlow() { }
    //     void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
    // 	     FlowMap& _flow)
    //       {
    // 	g=&_G;
    // 	s=_s;
    // 	t=_t;
    // 	capacity=&_capacity;
    // 	flow=&_flow;
    // 	n=_G.nodeNum;
    // 	level.set (_G); //kellene vmi ilyesmi fv
    // 	excess(_G,0); //itt is
    //       }

    // constants used for heuristics
    static const int H0=20;
    static const int H1=1;

  public:

    ///Indicates the property of the starting flow.

    ///Indicates the property of the starting flow. The meanings are as follows:
    ///- \c ZERO_FLOW: constant zero flow
    ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
    ///the sum of the out-flows in every node except the \e source and
    ///the \e target.
    ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at 
    ///least the sum of the out-flows in every node except the \e source.
    ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be 
    ///set to the constant zero flow in the beginning of the algorithm in this case.
    enum flowEnum{
      ZERO_FLOW,
      GEN_FLOW,
      PRE_FLOW,
      NO_FLOW
    };

    MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity,
	    FlowMap& _flow) :
      g(&_G), s(_s), t(_t), capacity(&_capacity),
      flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {}

    ///Runs a maximum flow algorithm.

    ///Runs a preflow algorithm, which is the fastest maximum flow
    ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void run(flowEnum fe=ZERO_FLOW) {
      preflow(fe);
    }

                                                                                             
    ///Runs a preflow algorithm.  

    ///Runs a preflow algorithm. The preflow algorithms provide the
    ///fastest way to compute a maximum flow in a directed graph.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void preflow(flowEnum fe) {
      preflowPhase1(fe);
      preflowPhase2();
    }
    // Heuristics:
    //   2 phase
    //   gap
    //   list 'level_list' on the nodes on level i implemented by hand
    //   stack 'active' on the active nodes on level i                                                                                    
    //   runs heuristic 'highest label' for H1*n relabels
    //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
    //   Parameters H0 and H1 are initialized to 20 and 1.

    ///Runs 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, though a maximum flow
    ///is net yet obtained. So after calling this method \ref flowValue
    ///and \ref actMinCut gives proper results.
    ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
    ///give minimum value cuts unless calling \ref preflowPhase2.
    ///\pre The starting flow must be
    /// - a constant zero flow if \c fe is \c ZERO_FLOW,
    /// - an arbitary flow if \c fe is \c GEN_FLOW,
    /// - an arbitary preflow if \c fe is \c PRE_FLOW,
    /// - any map if \c fe is NO_FLOW.
    void preflowPhase1( flowEnum fe );

    ///Runs the second phase of the preflow algorithm.

    ///The preflow algorithm consists of two phases, this method runs
    ///the second phase. After calling \ref preflowPhase1 and then
    ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
    ///\ref minMinCut and \ref maxMinCut give proper results.
    ///\pre \ref preflowPhase1 must be called before.
    void preflowPhase2();

    /// Starting from a flow, this method searches for an augmenting path
    /// according to the Edmonds-Karp algorithm
    /// and augments the flow on if any.
    /// The return value shows if the augmentation was succesful.
    bool augmentOnShortestPath();

    /// Starting from a flow, this method searches for an augmenting blocking
    /// flow according to Dinits' algorithm and augments the flow on if any.
    /// The blocking flow is computed in a physically constructed
    /// residual graph of type \c Mutablegraph.
    /// The return value show sif the augmentation was succesful.
    template<typename MutableGraph> bool augmentOnBlockingFlow();

    /// The same as \c augmentOnBlockingFlow<MutableGraph> but the
    /// residual graph is not constructed physically.
    /// The return value shows if the augmentation was succesful.
    bool augmentOnBlockingFlow2();

    /// Returns the maximum value of a flow.

    /// Returns the maximum value of a flow, by counting the 
    /// over-flow of the target node \ref t.
    /// It can be called already after running \ref preflowPhase1.
    Num flowValue() {
      Num a=0;
      FOR_EACH_INC_LOC(InEdgeIt, e, *g, t) a+=(*flow)[e];
      FOR_EACH_INC_LOC(OutEdgeIt, e, *g, t) a-=(*flow)[e];
      return a;
      //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan   
    }

    ///Returns a minimum value cut after calling \ref preflowPhase1.

    ///After the first phase of the preflow algorithm the maximum flow
    ///value and a minimum value cut can already be computed. This
    ///method can be called after running \ref preflowPhase1 for
    ///obtaining a minimum value cut.
    /// \warning Gives proper result only right after calling \ref
    /// preflowPhase1.
    /// \todo We have to make some status variable which shows the
    /// actual state
    /// of the class. This enables us to determine which methods are valid
    /// for MinCut computation
    template<typename _CutMap>
    void actMinCut(_CutMap& M) {
      NodeIt v;
      for(g->first(v); g->valid(v); g->next(v)) {
	if ( level[v] < n ) {
	  M.set(v,false);
	} else {
	  M.set(v,true);
	}
      }
    }

    ///Returns the inclusionwise minimum of the minimum value cuts.

    ///Sets \c M to the characteristic vector of the minimum value cut
    ///which is inclusionwise minimum. It is computed by processing
    ///a bfs from the source node \c s in the residual graph.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow.
    template<typename _CutMap>
    void minMinCut(_CutMap& M) {

      std::queue<Node> queue;

      M.set(s,true);
      queue.push(s);

      while (!queue.empty()) {
        Node w=queue.front();
	queue.pop();

	OutEdgeIt e;
	for(g->first(e,w) ; g->valid(e); g->next(e)) {
	  Node v=g->head(e);
	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}

	InEdgeIt f;
	for(g->first(f,w) ; g->valid(f); g->next(f)) {
	  Node v=g->tail(f);
	  if (!M[v] && (*flow)[f] > 0 ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}
      }
    }

    ///Returns the inclusionwise maximum of the minimum value cuts.

    ///Sets \c M to the characteristic vector of the minimum value cut
    ///which is inclusionwise maximum. It is computed by processing a
    ///backward bfs from the target node \c t in the residual graph.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow. 
    template<typename _CutMap>
    void maxMinCut(_CutMap& M) {

      NodeIt v;
      for(g->first(v) ; g->valid(v); g->next(v)) {
	M.set(v, true);
      }

      std::queue<Node> queue;

      M.set(t,false);
      queue.push(t);

      while (!queue.empty()) {
        Node w=queue.front();
	queue.pop();

	InEdgeIt e;
	for(g->first(e,w) ; g->valid(e); g->next(e)) {
	  Node v=g->tail(e);
	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
	    queue.push(v);
	    M.set(v, false);
	  }
	}

	OutEdgeIt f;
	for(g->first(f,w) ; g->valid(f); g->next(f)) {
	  Node v=g->head(f);
	  if (M[v] && (*flow)[f] > 0 ) {
	    queue.push(v);
	    M.set(v, false);
	  }
	}
      }
    }

    ///Returns a minimum value cut.

    ///Sets \c M to the characteristic vector of a minimum value cut.
    ///\pre M should be a node map of bools initialized to false.
    ///\pre \c flow must be a maximum flow.    
    template<typename CutMap>
    void minCut(CutMap& M) { minMinCut(M); }

    ///Resets the source node to \c _s.

    ///Resets the source node to \c _s.
    /// 
    void resetSource(Node _s) { s=_s; }

    ///Resets the target node to \c _t.

    ///Resets the target node to \c _t.
    ///
    void resetTarget(Node _t) { t=_t; }

    /// Resets the edge map of the capacities to _cap.

    /// Resets the edge map of the capacities to _cap.
    /// 
    void resetCap(const CapMap& _cap) { capacity=&_cap; }

    /// Resets the edge map of the flows to _flow.

    /// Resets the edge map of the flows to _flow.
    /// 
    void resetFlow(FlowMap& _flow) { flow=&_flow; }


  private:

    int push(Node w, VecStack& active) {

      int lev=level[w];
      Num exc=excess[w];
      int newlevel=n;       //bound on the next level of w

      OutEdgeIt e;
      for(g->first(e,w); g->valid(e); g->next(e)) {

	if ( (*flow)[e] >= (*capacity)[e] ) continue;
	Node v=g->head(e);

	if( lev > level[v] ) { //Push is allowed now

	  if ( excess[v]<=0 && v!=t && v!=s ) {
	    int lev_v=level[v];
	    active[lev_v].push(v);
	  }

	  Num cap=(*capacity)[e];
	  Num flo=(*flow)[e];
	  Num remcap=cap-flo;

	  if ( remcap >= exc ) { //A nonsaturating push.

	    flow->set(e, flo+exc);
	    excess.set(v, excess[v]+exc);
	    exc=0;
	    break;

	  } else { //A saturating push.
	    flow->set(e, cap);
	    excess.set(v, excess[v]+remcap);
	    exc-=remcap;
	  }
	} else if ( newlevel > level[v] ) newlevel = level[v];
      } //for out edges wv

      if ( exc > 0 ) {
	InEdgeIt e;
	for(g->first(e,w); g->valid(e); g->next(e)) {

	  if( (*flow)[e] <= 0 ) continue;
	  Node v=g->tail(e);

	  if( lev > level[v] ) { //Push is allowed now

	    if ( excess[v]<=0 && v!=t && v!=s ) {
	      int lev_v=level[v];
	      active[lev_v].push(v);
	    }

	    Num flo=(*flow)[e];

	    if ( flo >= exc ) { //A nonsaturating push.

	      flow->set(e, flo-exc);
	      excess.set(v, excess[v]+exc);
	      exc=0;
	      break;
	    } else {  //A saturating push.

	      excess.set(v, excess[v]+flo);
	      exc-=flo;
	      flow->set(e,0);
	    }
	  } else if ( newlevel > level[v] ) newlevel = level[v];
	} //for in edges vw

      } // if w still has excess after the out edge for cycle

      excess.set(w, exc);

      return newlevel;
    }


    void preflowPreproc(flowEnum fe, VecStack& active,
			VecNode& level_list, NNMap& left, NNMap& right)
    {
      std::queue<Node> bfs_queue;

      switch (fe) {
      case NO_FLOW:   //flow is already set to const zero in this case
      case ZERO_FLOW:
	{
	  //Reverse_bfs from t, to find the starting level.
	  level.set(t,0);
	  bfs_queue.push(t);

	  while (!bfs_queue.empty()) {

	    Node v=bfs_queue.front();
	    bfs_queue.pop();
	    int l=level[v]+1;

	    InEdgeIt e;
	    for(g->first(e,v); g->valid(e); g->next(e)) {
	      Node w=g->tail(e);
	      if ( level[w] == n && w != s ) {
		bfs_queue.push(w);
		Node first=level_list[l];
		if ( g->valid(first) ) left.set(first,w);
		right.set(w,first);
		level_list[l]=w;
		level.set(w, l);
	      }
	    }
	  }

	  //the starting flow
	  OutEdgeIt e;
	  for(g->first(e,s); g->valid(e); g->next(e))
	    {
	      Num c=(*capacity)[e];
	      if ( c <= 0 ) continue;
	      Node w=g->head(e);
	      if ( level[w] < n ) {
		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
		flow->set(e, c);
		excess.set(w, excess[w]+c);
	      }
	    }
	  break;
	}

      case GEN_FLOW:
      case PRE_FLOW:
	{
	  //Reverse_bfs from t in the residual graph,
	  //to find the starting level.
	  level.set(t,0);
	  bfs_queue.push(t);

	  while (!bfs_queue.empty()) {

	    Node v=bfs_queue.front();
	    bfs_queue.pop();
	    int l=level[v]+1;

	    InEdgeIt e;
	    for(g->first(e,v); g->valid(e); g->next(e)) {
	      if ( (*capacity)[e] <= (*flow)[e] ) continue;
	      Node w=g->tail(e);
	      if ( level[w] == n && w != s ) {
		bfs_queue.push(w);
		Node first=level_list[l];
		if ( g->valid(first) ) left.set(first,w);
		right.set(w,first);
		level_list[l]=w;
		level.set(w, l);
	      }
	    }

	    OutEdgeIt f;
	    for(g->first(f,v); g->valid(f); g->next(f)) {
	      if ( 0 >= (*flow)[f] ) continue;
	      Node w=g->head(f);
	      if ( level[w] == n && w != s ) {
		bfs_queue.push(w);
		Node first=level_list[l];
		if ( g->valid(first) ) left.set(first,w);
		right.set(w,first);
		level_list[l]=w;
		level.set(w, l);
	      }
	    }
	  }


	  //the starting flow
	  OutEdgeIt e;
	  for(g->first(e,s); g->valid(e); g->next(e))
	    {
	      Num rem=(*capacity)[e]-(*flow)[e];
	      if ( rem <= 0 ) continue;
	      Node w=g->head(e);
	      if ( level[w] < n ) {
		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
		flow->set(e, (*capacity)[e]);
		excess.set(w, excess[w]+rem);
	      }
	    }

	  InEdgeIt f;
	  for(g->first(f,s); g->valid(f); g->next(f))
	    {
	      if ( (*flow)[f] <= 0 ) continue;
	      Node w=g->tail(f);
	      if ( level[w] < n ) {
		if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
		excess.set(w, excess[w]+(*flow)[f]);
		flow->set(f, 0);
	      }
	    }
	  break;
	} //case PRE_FLOW
      }
    } //preflowPreproc



    void relabel(Node w, int newlevel, VecStack& active,
		 VecNode& level_list, NNMap& left,
		 NNMap& right, int& b, int& k, bool what_heur )
    {

      Num lev=level[w];

      Node right_n=right[w];
      Node left_n=left[w];

      //unlacing starts
      if ( g->valid(right_n) ) {
	if ( g->valid(left_n) ) {
	  right.set(left_n, right_n);
	  left.set(right_n, left_n);
	} else {
	  level_list[lev]=right_n;
	  left.set(right_n, INVALID);
	}
      } else {
	if ( g->valid(left_n) ) {
	  right.set(left_n, INVALID);
	} else {
	  level_list[lev]=INVALID;
	}
      }
      //unlacing ends

      if ( !g->valid(level_list[lev]) ) {

	//gapping starts
	for (int i=lev; i!=k ; ) {
	  Node v=level_list[++i];
	  while ( g->valid(v) ) {
	    level.set(v,n);
	    v=right[v];
	  }
	  level_list[i]=INVALID;
	  if ( !what_heur ) {
	    while ( !active[i].empty() ) {
	      active[i].pop();    //FIXME: ezt szebben kene
	    }
	  }
	}

	level.set(w,n);
	b=lev-1;
	k=b;
	//gapping ends

      } else {

	if ( newlevel == n ) level.set(w,n);
	else {
	  level.set(w,++newlevel);
	  active[newlevel].push(w);
	  if ( what_heur ) b=newlevel;
	  if ( k < newlevel ) ++k;      //now k=newlevel
	  Node first=level_list[newlevel];
	  if ( g->valid(first) ) left.set(first,w);
	  right.set(w,first);
	  left.set(w,INVALID);
	  level_list[newlevel]=w;
	}
      }

    } //relabel


    template<typename MapGraphWrapper>
    class DistanceMap {
    protected:
      const MapGraphWrapper* g;
      typename MapGraphWrapper::template NodeMap<int> dist;
    public:
      DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
      void set(const typename MapGraphWrapper::Node& n, int a) {
	dist.set(n, a);
      }
      int operator[](const typename MapGraphWrapper::Node& n)
      { return dist[n]; }
      //       int get(const typename MapGraphWrapper::Node& n) const {
      // 	return dist[n]; }
      //       bool get(const typename MapGraphWrapper::Edge& e) const {
      // 	return (dist.get(g->tail(e))<dist.get(g->head(e))); }
      bool operator[](const typename MapGraphWrapper::Edge& e) const {
	return (dist[g->tail(e)]<dist[g->head(e)]);
      }
    };

  };


  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe )
  {

    int heur0=(int)(H0*n);  //time while running 'bound decrease'
    int heur1=(int)(H1*n);  //time while running 'highest label'
    int heur=heur1;         //starting time interval (#of relabels)
    int numrelabel=0;

    bool what_heur=1;
    //It is 0 in case 'bound decrease' and 1 in case 'highest label'

    bool end=false;
    //Needed for 'bound decrease', true means no active nodes are above bound
    //b.

    int k=n-2;  //bound on the highest level under n containing a node
    int b=k;    //bound on the highest level under n of an active node

    VecStack active(n);

    NNMap left(*g, INVALID);
    NNMap right(*g, INVALID);
    VecNode level_list(n,INVALID);
    //List of the nodes in level i<n, set to n.

    NodeIt v;
    for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
    //setting each node to level n

    if ( fe == NO_FLOW ) {
      EdgeIt e;
      for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
    }

    switch (fe) { //computing the excess
    case PRE_FLOW:
      {
	NodeIt v;
	for(g->first(v); g->valid(v); g->next(v)) {
	  Num exc=0;

	  InEdgeIt e;
	  for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
	  OutEdgeIt f;
	  for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];

	  excess.set(v,exc);

	  //putting the active nodes into the stack
	  int lev=level[v];
	  if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
	}
	break;
      }
    case GEN_FLOW:
      {
	NodeIt v;
	for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);

	Num exc=0;
	InEdgeIt e;
	for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
	OutEdgeIt f;
	for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
	excess.set(t,exc);
	break;
      }
    case ZERO_FLOW:
    case NO_FLOW:
      {
	NodeIt v;
        for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
	break;
      }
    }

    preflowPreproc(fe, active, level_list, left, right);
    //End of preprocessing


    //Push/relabel on the highest level active nodes.
    while ( true ) {
      if ( b == 0 ) {
	if ( !what_heur && !end && k > 0 ) {
	  b=k;
	  end=true;
	} else break;
      }

      if ( active[b].empty() ) --b;
      else {
	end=false;
	Node w=active[b].top();
	active[b].pop();
	int newlevel=push(w,active);
	if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list,
				     left, right, b, k, what_heur);

	++numrelabel;
	if ( numrelabel >= heur ) {
	  numrelabel=0;
	  if ( what_heur ) {
	    what_heur=0;
	    heur=heur0;
	    end=false;
	  } else {
	    what_heur=1;
	    heur=heur1;
	    b=k;
	  }
	}
      }
    }
  }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2()
  {

    int k=n-2;  //bound on the highest level under n containing a node
    int b=k;    //bound on the highest level under n of an active node

    VecStack active(n);
    level.set(s,0);
    std::queue<Node> bfs_queue;
    bfs_queue.push(s);

    while (!bfs_queue.empty()) {

      Node v=bfs_queue.front();
      bfs_queue.pop();
      int l=level[v]+1;

      InEdgeIt e;
      for(g->first(e,v); g->valid(e); g->next(e)) {
	if ( (*capacity)[e] <= (*flow)[e] ) continue;
	Node u=g->tail(e);
	if ( level[u] >= n ) {
	  bfs_queue.push(u);
	  level.set(u, l);
	  if ( excess[u] > 0 ) active[l].push(u);
	}
      }

      OutEdgeIt f;
      for(g->first(f,v); g->valid(f); g->next(f)) {
	if ( 0 >= (*flow)[f] ) continue;
	Node u=g->head(f);
	if ( level[u] >= n ) {
	  bfs_queue.push(u);
	  level.set(u, l);
	  if ( excess[u] > 0 ) active[l].push(u);
	}
      }
    }
    b=n-2;

    while ( true ) {

      if ( b == 0 ) break;

      if ( active[b].empty() ) --b;
      else {
	Node w=active[b].top();
	active[b].pop();
	int newlevel=push(w,active);

	//relabel
	if ( excess[w] > 0 ) {
	  level.set(w,++newlevel);
	  active[newlevel].push(w);
	  b=newlevel;
	}
      }  // if stack[b] is nonempty
    } // while(true)
  }



  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath()
  {
    ResGW res_graph(*g, *capacity, *flow);
    bool _augment=false;

    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
    bfs.pushAndSetReached(s);

    typename ResGW::template NodeMap<ResGWEdge> pred(res_graph);
    pred.set(s, INVALID);

    typename ResGW::template NodeMap<Num> free(res_graph);

    //searching for augmenting path
    while ( !bfs.finished() ) {
      ResGWOutEdgeIt e=bfs;
      if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
	Node v=res_graph.tail(e);
	Node w=res_graph.head(e);
	pred.set(w, e);
	if (res_graph.valid(pred[v])) {
	  free.set(w, std::min(free[v], res_graph.resCap(e)));
	} else {
	  free.set(w, res_graph.resCap(e));
	}
	if (res_graph.head(e)==t) { _augment=true; break; }
      }

      ++bfs;
    } //end of searching augmenting path

    if (_augment) {
      Node n=t;
      Num augment_value=free[t];
      while (res_graph.valid(pred[n])) {
	ResGWEdge e=pred[n];
	res_graph.augment(e, augment_value);
	n=res_graph.tail(e);
      }
    }

    return _augment;
  }







  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  template<typename MutableGraph>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow()
  {
    typedef MutableGraph MG;
    bool _augment=false;

    ResGW res_graph(*g, *capacity, *flow);

    //bfs for distances on the residual graph
    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
    bfs.pushAndSetReached(s);
    typename ResGW::template NodeMap<int>
      dist(res_graph); //filled up with 0's

    //F will contain the physical copy of the residual graph
    //with the set of edges which are on shortest paths
    MG F;
    typename ResGW::template NodeMap<typename MG::Node>
      res_graph_to_F(res_graph);
    {
      typename ResGW::NodeIt n;
      for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
	res_graph_to_F.set(n, F.addNode());
      }
    }

    typename MG::Node sF=res_graph_to_F[s];
    typename MG::Node tF=res_graph_to_F[t];
    typename MG::template EdgeMap<ResGWEdge> original_edge(F);
    typename MG::template EdgeMap<Num> residual_capacity(F);

    while ( !bfs.finished() ) {
      ResGWOutEdgeIt e=bfs;
      if (res_graph.valid(e)) {
	if (bfs.isBNodeNewlyReached()) {
	  dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
	  typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
					res_graph_to_F[res_graph.head(e)]);
	  original_edge.update();
	  original_edge.set(f, e);
	  residual_capacity.update();
	  residual_capacity.set(f, res_graph.resCap(e));
	} else {
	  if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
	    typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)],
					  res_graph_to_F[res_graph.head(e)]);
	    original_edge.update();
	    original_edge.set(f, e);
	    residual_capacity.update();
	    residual_capacity.set(f, res_graph.resCap(e));
	  }
	}
      }
      ++bfs;
    } //computing distances from s in the residual graph

    bool __augment=true;

    while (__augment) {
      __augment=false;
      //computing blocking flow with dfs
      DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
      typename MG::template NodeMap<typename MG::Edge> pred(F);
      pred.set(sF, INVALID);
      //invalid iterators for sources

      typename MG::template NodeMap<Num> free(F);

      dfs.pushAndSetReached(sF);
      while (!dfs.finished()) {
	++dfs;
	if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {
	  if (dfs.isBNodeNewlyReached()) {
	    typename MG::Node v=F.aNode(dfs);
	    typename MG::Node w=F.bNode(dfs);
	    pred.set(w, dfs);
	    if (F.valid(pred[v])) {
	      free.set(w, std::min(free[v], residual_capacity[dfs]));
	    } else {
	      free.set(w, residual_capacity[dfs]);
	    }
	    if (w==tF) {
	      __augment=true;
	      _augment=true;
	      break;
	    }

	  } else {
	    F.erase(/*typename MG::OutEdgeIt*/(dfs));
	  }
	}
      }

      if (__augment) {
	typename MG::Node n=tF;
	Num augment_value=free[tF];
	while (F.valid(pred[n])) {
	  typename MG::Edge e=pred[n];
	  res_graph.augment(original_edge[e], augment_value);
	  n=F.tail(e);
	  if (residual_capacity[e]==augment_value)
	    F.erase(e);
	  else
	    residual_capacity.set(e, residual_capacity[e]-augment_value);
	}
      }

    }

    return _augment;
  }




  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2()
  {
    bool _augment=false;

    ResGW res_graph(*g, *capacity, *flow);

    //ReachedMap level(res_graph);
    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);

    bfs.pushAndSetReached(s);
    DistanceMap<ResGW> dist(res_graph);
    while ( !bfs.finished() ) {
      ResGWOutEdgeIt e=bfs;
      if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
	dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
      }
      ++bfs;
    } //computing distances from s in the residual graph

      //Subgraph containing the edges on some shortest paths
    ConstMap<typename ResGW::Node, bool> true_map(true);
    typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>,
      DistanceMap<ResGW> > FilterResGW;
    FilterResGW filter_res_graph(res_graph, true_map, dist);

    //Subgraph, which is able to delete edges which are already
    //met by the dfs
    typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt>
      first_out_edges(filter_res_graph);
    typename FilterResGW::NodeIt v;
    for(filter_res_graph.first(v); filter_res_graph.valid(v);
	filter_res_graph.next(v))
      {
 	typename FilterResGW::OutEdgeIt e;
 	filter_res_graph.first(e, v);
 	first_out_edges.set(v, e);
      }
    typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
      template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
    ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);

    bool __augment=true;

    while (__augment) {

      __augment=false;
      //computing blocking flow with dfs
      DfsIterator< ErasingResGW,
	typename ErasingResGW::template NodeMap<bool> >
	dfs(erasing_res_graph);
      typename ErasingResGW::
	template NodeMap<typename ErasingResGW::OutEdgeIt>
	pred(erasing_res_graph);
      pred.set(s, INVALID);
      //invalid iterators for sources

      typename ErasingResGW::template NodeMap<Num>
	free1(erasing_res_graph);

      dfs.pushAndSetReached
	///\bug hugo 0.2
	(typename ErasingResGW::Node
	 (typename FilterResGW::Node
	  (typename ResGW::Node(s)
	   )
	  )
	 );
      while (!dfs.finished()) {
	++dfs;
	if (erasing_res_graph.valid(typename ErasingResGW::OutEdgeIt(dfs)))
 	  {
  	    if (dfs.isBNodeNewlyReached()) {

 	      typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
 	      typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);

 	      pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
 	      if (erasing_res_graph.valid(pred[v])) {
 		free1.set
		  (w, std::min(free1[v], res_graph.resCap
			       (typename ErasingResGW::OutEdgeIt(dfs))));
 	      } else {
 		free1.set
		  (w, res_graph.resCap
		   (typename ErasingResGW::OutEdgeIt(dfs)));
 	      }

 	      if (w==t) {
 		__augment=true;
 		_augment=true;
 		break;
 	      }
 	    } else {
 	      erasing_res_graph.erase(dfs);
	    }
	  }
      }

      if (__augment) {
	typename ErasingResGW::Node
	  n=typename FilterResGW::Node(typename ResGW::Node(t));
	// 	  typename ResGW::NodeMap<Num> a(res_graph);
	// 	  typename ResGW::Node b;
	// 	  Num j=a[b];
	// 	  typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
	// 	  typename FilterResGW::Node b1;
	// 	  Num j1=a1[b1];
	// 	  typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
	// 	  typename ErasingResGW::Node b2;
	// 	  Num j2=a2[b2];
	Num augment_value=free1[n];
	while (erasing_res_graph.valid(pred[n])) {
	  typename ErasingResGW::OutEdgeIt e=pred[n];
	  res_graph.augment(e, augment_value);
	  n=erasing_res_graph.tail(e);
	  if (res_graph.resCap(e)==0)
	    erasing_res_graph.erase(e);
	}
      }

    } //while (__augment)

    return _augment;
  }


} //namespace hugo

#endif //HUGO_MAX_FLOW_H