# HG changeset patch
# User jacint
# Date 1084359113 0
# Node ID 6e917be931afc5b5d80e41671bb9e397e3bbe4ce
# Parent  e09818232531e81f0d6f6a502a598957f9f4b8d9


diff -r e09818232531 -r 6e917be931af src/work/jacint/max_save.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/work/jacint/max_save.h	Wed May 12 10:51:53 2004 +0000
@@ -0,0 +1,1136 @@
+// -*- C++ -*-
+#ifndef HUGO_MAX_FLOW_H
+#define HUGO_MAX_FLOW_H
+
+///\ingroup galgs
+///\file
+///\brief Maximum flow algorithm.
+
+#define H0 20
+#define H1 1
+
+#include <vector>
+#include <queue>
+#include <stack>
+
+#include <graph_wrapper.h>
+#include <bfs_iterator.h>
+#include <invalid.h>
+#include <maps.h>
+#include <for_each_macros.h>
+
+/// \file
+/// \brief Dimacs file format reader.
+
+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 by the
+  ///constructor. It is possible to change these quantities using the
+  ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
+  ///\ref resetFlow. Before any subsequent runs of any algorithm of
+  ///the class \ref resetFlow should be called, otherwise it will
+  ///start from a maximum flow.
+
+  ///After running an algorithm of the class, the maximum value of a
+  ///value can be obtained by calling \ref flowValue(). The minimum
+  ///value cut can be written into a \c node map of \c bools by
+  ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
+  ///the inclusionwise minimum and maximum of the minimum value
+  ///cuts, resp.)
+
+  ///\param Graph The undirected graph type the algorithm runs on.
+  ///\param Num The number type of the capacities and the flow values.
+  ///\param The type of the capacity map.
+  ///\param 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 {
+    
+    typedef typename Graph::Node Node;
+    typedef typename Graph::NodeIt NodeIt;
+    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;
+    
+    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;  //fixme
+    typedef typename Graph::template NodeMap<int> ReachedMap;
+    
+    const Graph* g;
+    Node s;
+    Node t;
+    const CapMap* capacity;  
+    FlowMap* flow;
+    int n;          //the number of nodes of G
+
+    //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
+    //       }
+
+  public:
+ 
+    ///Indicates the property of the starting flow. 
+
+    ///Indicates the property of the starting flow. The meanings: 
+    ///- \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 source and
+    ///the 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 source.
+    enum flowEnum{
+      ZERO_FLOW=0,
+      GEN_FLOW=1,
+      PRE_FLOW=2
+    };
+
+    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.
+    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.
+    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.
+    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 successful.
+    bool augmentOnShortestPath();
+
+    /// Starting from a flow, this method searches for an augmenting blockin 
+    /// 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 actual flow value.
+    /// More precisely, it returns the negative excess of s, thus 
+    /// this works also for preflows.
+    ///Can be called already after \ref preflowPhase1.
+
+    Num flowValue() { 
+      Num a=0;
+      FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e];
+      FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e];
+      return a;
+      //marci figyu: excess[t] epp ezt adja preflow 0. 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 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
+      
+    switch ( fe ) {
+    case PRE_FLOW:
+      {
+	//counting the excess
+	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:
+      {
+	//Counting the excess of t
+	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;
+      }
+    default:
+      break;
+    }
+      
+    preflowPreproc( fe, active, level_list, left, right );
+    //End of preprocessing 
+      
+      
+    //Push/relabel on the highest level active nodes.
+    while ( true ) {
+      if ( b == 0 ) {
+	if ( !what_heur && !end && k > 0 ) {
+	  b=k;
+	  end=true;
+	} else break;
+      }
+	
+      if ( active[b].empty() ) --b; 
+      else {
+	end=false;  
+	Node w=active[b].top();
+	active[b].pop();
+	int newlevel=push(w,active);
+	if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, 
+				     left, right, b, k, what_heur);
+	  
+	++numrelabel; 
+	if ( numrelabel >= heur ) {
+	  numrelabel=0;
+	  if ( what_heur ) {
+	    what_heur=0;
+	    heur=heur0;
+	    end=false;
+	  } else {
+	    what_heur=1;
+	    heur=heur1;
+	    b=k; 
+	  }
+	}
+      } 
+    } 
+  }
+
+
+
+  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
+  void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() 
+  {
+      
+    int k=n-2;  //bound on the highest level under n containing a node
+    int b=k;    //bound on the highest level under n of an active node
+      
+    VecStack active(n);
+    level.set(s,0);
+    std::queue<Node> bfs_queue;
+    bfs_queue.push(s);
+	    
+    while (!bfs_queue.empty()) {
+	
+      Node v=bfs_queue.front();	
+      bfs_queue.pop();
+      int l=level[v]+1;
+	      
+      InEdgeIt e;
+      for(g->first(e,v); g->valid(e); g->next(e)) {
+	if ( (*capacity)[e] <= (*flow)[e] ) continue;
+	Node u=g->tail(e);
+	if ( level[u] >= n ) { 
+	  bfs_queue.push(u);
+	  level.set(u, l);
+	  if ( excess[u] > 0 ) active[l].push(u);
+	}
+      }
+	
+      OutEdgeIt f;
+      for(g->first(f,v); g->valid(f); g->next(f)) {
+	if ( 0 >= (*flow)[f] ) continue;
+	Node u=g->head(f);
+	if ( level[u] >= n ) { 
+	  bfs_queue.push(u);
+	  level.set(u, l);
+	  if ( excess[u] > 0 ) active[l].push(u);
+	}
+      }
+    }
+    b=n-2;
+
+    while ( true ) {
+	
+      if ( b == 0 ) break;
+
+      if ( active[b].empty() ) --b; 
+      else {
+	Node w=active[b].top();
+	active[b].pop();
+	int newlevel=push(w,active);	  
+
+	//relabel
+	if ( excess[w] > 0 ) {
+	  level.set(w,++newlevel);
+	  active[newlevel].push(w);
+	  b=newlevel;
+	}
+      }  // if stack[b] is nonempty
+    } // while(true)
+  }
+
+
+
+  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
+  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() 
+  {
+    ResGW res_graph(*g, *capacity, *flow);
+    bool _augment=false;
+      
+    //ReachedMap level(res_graph);
+    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
+    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
+    bfs.pushAndSetReached(s);
+	
+    typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); 
+    pred.set(s, INVALID);
+      
+    typename ResGW::template NodeMap<Num> free(res_graph);
+	
+    //searching for augmenting path
+    while ( !bfs.finished() ) { 
+      ResGWOutEdgeIt e=bfs;
+      if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
+	Node v=res_graph.tail(e);
+	Node w=res_graph.head(e);
+	pred.set(w, e);
+	if (res_graph.valid(pred[v])) {
+	  free.set(w, std::min(free[v], res_graph.resCap(e)));
+	} else {
+	  free.set(w, res_graph.resCap(e)); 
+	}
+	if (res_graph.head(e)==t) { _augment=true; break; }
+      }
+	
+      ++bfs;
+    } //end of searching augmenting path
+
+    if (_augment) {
+      Node n=t;
+      Num augment_value=free[t];
+      while (res_graph.valid(pred[n])) { 
+	ResGWEdge e=pred[n];
+	res_graph.augment(e, augment_value); 
+	n=res_graph.tail(e);
+      }
+    }
+
+    return _augment;
+  }
+
+
+
+
+
+
+
+
+
+  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
+  template<typename MutableGraph> 
+  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() 
+  {      
+    typedef MutableGraph MG;
+    bool _augment=false;
+
+    ResGW res_graph(*g, *capacity, *flow);
+
+    //bfs for distances on the residual graph
+    //ReachedMap level(res_graph);
+    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
+    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
+    bfs.pushAndSetReached(s);
+    typename ResGW::template NodeMap<int> 
+      dist(res_graph); //filled up with 0's
+
+    //F will contain the physical copy of the residual graph
+    //with the set of edges which are on shortest paths
+    MG F;
+    typename ResGW::template NodeMap<typename MG::Node> 
+      res_graph_to_F(res_graph);
+    {
+      typename ResGW::NodeIt n;
+      for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
+	res_graph_to_F.set(n, F.addNode());
+      }
+    }
+
+    typename MG::Node sF=res_graph_to_F[s];
+    typename MG::Node tF=res_graph_to_F[t];
+    typename MG::template EdgeMap<ResGWEdge> original_edge(F);
+    typename MG::template EdgeMap<Num> residual_capacity(F);
+
+    while ( !bfs.finished() ) { 
+      ResGWOutEdgeIt e=bfs;
+      if (res_graph.valid(e)) {
+	if (bfs.isBNodeNewlyReached()) {
+	  dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
+	  typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
+	  original_edge.update();
+	  original_edge.set(f, e);
+	  residual_capacity.update();
+	  residual_capacity.set(f, res_graph.resCap(e));
+	} else {
+	  if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
+	    typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
+	    original_edge.update();
+	    original_edge.set(f, e);
+	    residual_capacity.update();
+	    residual_capacity.set(f, res_graph.resCap(e));
+	  }
+	}
+      }
+      ++bfs;
+    } //computing distances from s in the residual graph
+
+    bool __augment=true;
+
+    while (__augment) {
+      __augment=false;
+      //computing blocking flow with dfs
+      DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
+      typename MG::template NodeMap<typename MG::Edge> pred(F);
+      pred.set(sF, INVALID);
+      //invalid iterators for sources
+
+      typename MG::template NodeMap<Num> free(F);
+
+      dfs.pushAndSetReached(sF);      
+      while (!dfs.finished()) {
+	++dfs;
+	if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {
+	  if (dfs.isBNodeNewlyReached()) {
+	    typename MG::Node v=F.aNode(dfs);
+	    typename MG::Node w=F.bNode(dfs);
+	    pred.set(w, dfs);
+	    if (F.valid(pred[v])) {
+	      free.set(w, std::min(free[v], residual_capacity[dfs]));
+	    } else {
+	      free.set(w, residual_capacity[dfs]); 
+	    }
+	    if (w==tF) { 
+	      __augment=true; 
+	      _augment=true;
+	      break; 
+	    }
+	      
+	  } else {
+	    F.erase(/*typename MG::OutEdgeIt*/(dfs));
+	  }
+	} 
+      }
+
+      if (__augment) {
+	typename MG::Node n=tF;
+	Num augment_value=free[tF];
+	while (F.valid(pred[n])) { 
+	  typename MG::Edge e=pred[n];
+	  res_graph.augment(original_edge[e], augment_value); 
+	  n=F.tail(e);
+	  if (residual_capacity[e]==augment_value) 
+	    F.erase(e); 
+	  else 
+	    residual_capacity.set(e, residual_capacity[e]-augment_value);
+	}
+      }
+	
+    }
+            
+    return _augment;
+  }
+
+
+
+
+
+
+  template <typename Graph, typename Num, typename CapMap, typename FlowMap>
+  bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() 
+  {
+    bool _augment=false;
+
+    ResGW res_graph(*g, *capacity, *flow);
+      
+    //ReachedMap level(res_graph);
+    FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
+    BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
+
+    bfs.pushAndSetReached(s);
+    DistanceMap<ResGW> dist(res_graph);
+    while ( !bfs.finished() ) { 
+      ResGWOutEdgeIt e=bfs;
+      if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
+	dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
+      }
+      ++bfs;
+    } //computing distances from s in the residual graph
+
+      //Subgraph containing the edges on some shortest paths
+    ConstMap<typename ResGW::Node, bool> true_map(true);
+    typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 
+      DistanceMap<ResGW> > FilterResGW;
+    FilterResGW filter_res_graph(res_graph, true_map, dist);
+
+    //Subgraph, which is able to delete edges which are already 
+    //met by the dfs
+    typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> 
+      first_out_edges(filter_res_graph);
+    typename FilterResGW::NodeIt v;
+    for(filter_res_graph.first(v); filter_res_graph.valid(v); 
+	filter_res_graph.next(v)) 
+      {
+ 	typename FilterResGW::OutEdgeIt e;
+ 	filter_res_graph.first(e, v);
+ 	first_out_edges.set(v, e);
+      }
+    typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
+      template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
+    ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);
+
+    bool __augment=true;
+
+    while (__augment) {
+
+      __augment=false;
+      //computing blocking flow with dfs
+      DfsIterator< ErasingResGW, 
+	typename ErasingResGW::template NodeMap<bool> > 
+	dfs(erasing_res_graph);
+      typename ErasingResGW::
+	template NodeMap<typename ErasingResGW::OutEdgeIt> 
+	pred(erasing_res_graph); 
+      pred.set(s, INVALID);
+      //invalid iterators for sources
+
+      typename ErasingResGW::template NodeMap<Num> 
+	free1(erasing_res_graph);
+
+      dfs.pushAndSetReached(
+			    typename ErasingResGW::Node(
+							typename FilterResGW::Node(
+										   typename ResGW::Node(s)
+										   )
+							)
+			    );
+      while (!dfs.finished()) {
+	++dfs;
+	if (erasing_res_graph.valid(
+				    typename ErasingResGW::OutEdgeIt(dfs))) 
+ 	  { 
+  	    if (dfs.isBNodeNewlyReached()) {
+	  
+ 	      typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
+ 	      typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);
+
+ 	      pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
+ 	      if (erasing_res_graph.valid(pred[v])) {
+ 		free1.set(w, std::min(free1[v], res_graph.resCap(
+								 typename ErasingResGW::OutEdgeIt(dfs))));
+ 	      } else {
+ 		free1.set(w, res_graph.resCap(
+					      typename ErasingResGW::OutEdgeIt(dfs))); 
+ 	      }
+	      
+ 	      if (w==t) { 
+ 		__augment=true; 
+ 		_augment=true;
+ 		break; 
+ 	      }
+ 	    } else {
+ 	      erasing_res_graph.erase(dfs);
+	    }
+	  }
+      }	
+
+      if (__augment) {
+	typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t));
+	// 	  typename ResGW::NodeMap<Num> a(res_graph);
+	// 	  typename ResGW::Node b;
+	// 	  Num j=a[b];
+	// 	  typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
+	// 	  typename FilterResGW::Node b1;
+	// 	  Num j1=a1[b1];
+	// 	  typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
+	// 	  typename ErasingResGW::Node b2;
+	// 	  Num j2=a2[b2];
+	Num augment_value=free1[n];
+	while (erasing_res_graph.valid(pred[n])) { 
+	  typename ErasingResGW::OutEdgeIt e=pred[n];
+	  res_graph.augment(e, augment_value);
+	  n=erasing_res_graph.tail(e);
+	  if (res_graph.resCap(e)==0)
+	    erasing_res_graph.erase(e);
+	}
+      }
+      
+    } //while (__augment) 
+            
+    return _augment;
+  }
+
+
+
+  /// @}
+  
+} //END OF NAMESPACE HUGO
+
+#endif //HUGO_MAX_FLOW_H
+
+
+
+