// -*- 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 directed 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)