// -*- C++ -*-

#ifndef HUGO_AUGMENTING_FLOW_H

#define HUGO_AUGMENTING_FLOW_H

#include <vector>

#include <queue>

#include <stack>

#include <iostream>

#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 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; 

// //       }

// //     };

//     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) { }

//     ///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();

//     /// 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:

//       case AFTER_AUGMENTING:

//       case AFTER_FAST_AUGMENTING:

// 	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 )

//     {

//       //FIXME jacint: ez mitol num

// //      Num lev=level[w];

//       int 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 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 Graph::template EdgeMap<Num>,

            typename FlowMap=typename Graph::template EdgeMap<Num> >

  class AugmentingFlow {

  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; 

      }

    };

    AugmentingFlow(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) { }

    /// 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();