// -*- 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 <hugo/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 should 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. 

   ///After running an algorithm of the class, the actual flow 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 capacity map type.

   ///\param FlowMap The flow map type.                                                                                                           

   ///\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 ExpResGraphWrapper<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

     };

     enum StatusEnum {

       AFTER_NOTHING,

       AFTER_AUGMENTING,

       AFTER_FAST_AUGMENTING, 

       AFTER_PRE_FLOW_PHASE_1,      

       AFTER_PRE_FLOW_PHASE_2

     };

     /// Don not needle this flag only if necessary.

     StatusEnum status;

     int number_of_augmentations;

     template<typename IntMap>

     class TrickyReachedMap {

     protected:

       IntMap* map;

       int* number_of_augmentations;

     public:

       TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : 

 	map(&_map), number_of_augmentations(&_number_of_augmentations) { }

       void set(const Node& n, bool b) {

 	if (b)

 	  map->set(n, *number_of_augmentations);

 	else 

 	  map->set(n, *number_of_augmentations-1);

       }

       bool operator[](const Node& n) const { 

 	return (*map)[n]==*number_of_augmentations; 

       }

     };

     ///Constructor

     ///\todo Document, please.

     ///

     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), 

       status(AFTER_NOTHING), number_of_augmentations(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.

     ///

     ///\todo NO_FLOW should be the default 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();

     bool augmentOnShortestPath2();

     /// 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() const {

       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) const {

       NodeIt v;

       switch (status) {

       case AFTER_PRE_FLOW_PHASE_1:

 	for(g->first(v); g->valid(v); g->next(v)) {

 	  if (level[v] < n) {

 	    M.set(v, false);

 	  } else {

 	    M.set(v, true);

 	  }

 	}

 	break;

       case AFTER_PRE_FLOW_PHASE_2:

       case AFTER_NOTHING:

 	minMinCut(M);

 	break;

       case AFTER_AUGMENTING:

 	for(g->first(v); g->valid(v); g->next(v)) {

 	  if (level[v]) {

 	    M.set(v, true);

 	  } else {

 	    M.set(v, false);

 	  }

 	}

 	break;

       case AFTER_FAST_AUGMENTING:

 	for(g->first(v); g->valid(v); g->next(v)) {

 	  if (level[v]==number_of_augmentations) {

 	    M.set(v, true);

 	  } else {

 	    M.set(v, false);

 	  }

 	}

 	break;

       }

     }

     ///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) const {

       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) const {

       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) const { minMinCut(M); }

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

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

     /// 

     void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; }

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

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

     ///

     void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; }

     /// 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; status=AFTER_NOTHING; }

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

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

     /// 

     void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }

   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) const { 

 	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;

 	  }

 	}

       }

     }

     status=AFTER_PRE_FLOW_PHASE_1;

   }

   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)

     status=AFTER_PRE_FLOW_PHASE_2;

   }

   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);

       }

     }

     status=AFTER_AUGMENTING;

     return _augment;

   }

   template <typename Graph, typename Num, typename CapMap, typename FlowMap>

   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath2()

   {

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

     bool _augment=false;

     if (status!=AFTER_FAST_AUGMENTING) {

       FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0); 

       number_of_augmentations=1;

     } else {

       ++number_of_augmentations;

     }

     TrickyReachedMap<ReachedMap> 

       tricky_reached_map(level, number_of_augmentations);

     //ReachedMap level(res_graph);

 //    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);

     BfsIterator<ResGW, TrickyReachedMap<ReachedMap> > 

       bfs(res_graph, tricky_reached_map);

     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);

       }

     }

     status=AFTER_FAST_AUGMENTING;

     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);

 	}

       }

     }

     status=AFTER_AUGMENTING;

     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)

     status=AFTER_AUGMENTING;

     return _augment;

   }

 } //namespace hugo

 #endif //HUGO_MAX_FLOW_H