jacint@620: // -*- C++ -*-
jacint@620: #ifndef HUGO_MAX_FLOW_H
jacint@620: #define HUGO_MAX_FLOW_H
jacint@620: 
jacint@620: ///\ingroup galgs
jacint@620: ///\file
jacint@620: ///\brief Maximum flow algorithm.
jacint@620: 
jacint@620: #define H0 20
jacint@620: #define H1 1
jacint@620: 
jacint@620: #include <vector>
jacint@620: #include <queue>
jacint@620: #include <stack>
jacint@620: 
jacint@620: #include <graph_wrapper.h>
jacint@620: #include <bfs_iterator.h>
jacint@620: #include <invalid.h>
jacint@620: #include <maps.h>
jacint@620: #include <for_each_macros.h>
jacint@620: 
jacint@620: /// \file
jacint@620: /// \brief Dimacs file format reader.
jacint@620: 
jacint@620: namespace hugo {
jacint@620: 
jacint@620:   /// \addtogroup galgs
jacint@620:   /// @{
jacint@620: 
jacint@620:   ///Maximum flow algorithms class.
jacint@620: 
jacint@620:   ///This class provides various algorithms for finding a flow of
jacint@620:   ///maximum value in a directed graph. The \e source node, the \e
jacint@620:   ///target node, the \e capacity of the edges and the \e starting \e
jacint@620:   ///flow value of the edges can be passed to the algorithm by the
jacint@620:   ///constructor. It is possible to change these quantities using the
jacint@620:   ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
jacint@620:   ///\ref resetFlow. Before any subsequent runs of any algorithm of
jacint@620:   ///the class \ref resetFlow should be called, otherwise it will
jacint@620:   ///start from a maximum flow.
jacint@620: 
jacint@620:   ///After running an algorithm of the class, the maximum value of a
jacint@620:   ///value can be obtained by calling \ref flowValue(). The minimum
jacint@620:   ///value cut can be written into a \c node map of \c bools by
jacint@620:   ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
jacint@620:   ///the inclusionwise minimum and maximum of the minimum value
jacint@620:   ///cuts, resp.)
jacint@620: 
jacint@620:   ///\param Graph The undirected graph type the algorithm runs on.
jacint@620:   ///\param Num The number type of the capacities and the flow values.
jacint@620:   ///\param The type of the capacity map.
jacint@620:   ///\param The type of the flow map.
jacint@620: 
jacint@620:   ///\author Marton Makai, Jacint Szabo
jacint@620:   template <typename Graph, typename Num, 
jacint@620: 	    typename CapMap=typename Graph::template EdgeMap<Num>, 
jacint@620:             typename FlowMap=typename Graph::template EdgeMap<Num> >
jacint@620:   class MaxFlow {
jacint@620:     
jacint@620:     typedef typename Graph::Node Node;
jacint@620:     typedef typename Graph::NodeIt NodeIt;
jacint@620:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@620:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@620: 
jacint@620:     typedef typename std::vector<std::stack<Node> > VecStack;
jacint@620:     typedef typename Graph::template NodeMap<Node> NNMap;
jacint@620:     typedef typename std::vector<Node> VecNode;
jacint@620:     
jacint@620:     typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
jacint@620:     typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
jacint@620:     typedef typename ResGW::Edge ResGWEdge;
jacint@620:     //typedef typename ResGW::template NodeMap<bool> ReachedMap;  //fixme
jacint@620:     typedef typename Graph::template NodeMap<int> ReachedMap;
jacint@620:     
jacint@620:     const Graph* g;
jacint@620:     Node s;
jacint@620:     Node t;
jacint@620:     const CapMap* capacity;  
jacint@620:     FlowMap* flow;
jacint@620:     int n;          //the number of nodes of G
jacint@620: 
jacint@620:     //level works as a bool map in augmenting path algorithms and is
jacint@620:     //used by bfs for storing reached information.  In preflow, it
jacint@620:     //shows the levels of nodes. 
jacint@620:     ReachedMap level;
jacint@620:     
jacint@620:     //excess is needed only in preflow
jacint@620:     typename Graph::template NodeMap<Num> excess; 
jacint@620: 
jacint@620: 
jacint@620:     //fixme
jacint@620:     //   protected:
jacint@620:     //     MaxFlow() { }
jacint@620:     //     void set(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, 
jacint@620:     // 	     FlowMap& _flow) 
jacint@620:     //       {
jacint@620:     // 	g=&_G; 
jacint@620:     // 	s=_s; 
jacint@620:     // 	t=_t; 
jacint@620:     // 	capacity=&_capacity;
jacint@620:     // 	flow=&_flow;
jacint@620:     // 	n=_G.nodeNum;
jacint@620:     // 	level.set (_G); //kellene vmi ilyesmi fv 
jacint@620:     // 	excess(_G,0); //itt is
jacint@620:     //       }
jacint@620: 
jacint@620:   public:
jacint@620:  
jacint@620:     ///Indicates the property of the starting flow. 
jacint@620: 
jacint@620:     ///Indicates the property of the starting flow. The meanings: 
jacint@620:     ///- \c ZERO_FLOW: constant zero flow
jacint@620:     ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
jacint@620:     ///the sum of the out-flows in every node except the source and
jacint@620:     ///the target.
jacint@620:     ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at
jacint@620:     ///least the sum of the out-flows in every node except the source.
jacint@620:     enum flowEnum{
jacint@620:       ZERO_FLOW=0,
jacint@620:       GEN_FLOW=1,
jacint@620:       PRE_FLOW=2
jacint@620:     };
jacint@620: 
jacint@620:     MaxFlow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, 
jacint@620: 	    FlowMap& _flow) :
jacint@620:       g(&_G), s(_s), t(_t), capacity(&_capacity), 
jacint@620:       flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0) {}
jacint@620: 
jacint@620:     ///Runs a maximum flow algorithm.
jacint@620: 
jacint@620:     ///Runs a preflow algorithm, which is the fastest maximum flow
jacint@620:     ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
jacint@620:     ///\pre The starting flow must be a 
jacint@620:     /// - constant zero flow if \c fe is \c ZERO_FLOW,
jacint@620:     /// - an arbitary flow if \c fe is \c GEN_FLOW, 
jacint@620:     /// - an arbitary preflow if \c fe is \c PRE_FLOW.
jacint@620:     void run( flowEnum fe=ZERO_FLOW ) {
jacint@620:       preflow(fe);
jacint@620:     }
jacint@620:     
jacint@620:     ///Runs a preflow algorithm.
jacint@620: 
jacint@620:     ///Runs a preflow algorithm. The preflow algorithms provide the
jacint@620:     ///fastest way to compute a maximum flow in a directed graph.
jacint@620:     ///\pre The starting flow must be a 
jacint@620:     /// - constant zero flow if \c fe is \c ZERO_FLOW,
jacint@620:     /// - an arbitary flow if \c fe is \c GEN_FLOW, 
jacint@620:     /// - an arbitary preflow if \c fe is \c PRE_FLOW.
jacint@620:     void preflow(flowEnum fe) {
jacint@620:       preflowPhase1(fe);
jacint@620:       preflowPhase2();
jacint@620:     }
jacint@620:     // Heuristics: 
jacint@620:     //   2 phase
jacint@620:     //   gap
jacint@620:     //   list 'level_list' on the nodes on level i implemented by hand
jacint@620:     //   stack 'active' on the active nodes on level i
jacint@620:     //   runs heuristic 'highest label' for H1*n relabels
jacint@620:     //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
jacint@620:     //   Parameters H0 and H1 are initialized to 20 and 1.
jacint@620: 
jacint@620:     ///Runs the first phase of the preflow algorithm.
jacint@620:     
jacint@620:     ///The preflow algorithm consists of two phases, this method runs the
jacint@620:     ///first phase. After the first phase the maximum flow value and a
jacint@620:     ///minimum value cut can already be computed, though a maximum flow
jacint@620:     ///is net yet obtained. So after calling this method \ref flowValue
jacint@620:     ///and \ref actMinCut gives proper results. 
jacint@620:     ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
jacint@620:     ///give minimum value cuts unless calling \ref preflowPhase2.
jacint@620:     ///\pre The starting flow must be a 
jacint@620:     /// - constant zero flow if \c fe is \c ZERO_FLOW,
jacint@620:     /// - an arbitary flow if \c fe is \c GEN_FLOW, 
jacint@620:     /// - an arbitary preflow if \c fe is \c PRE_FLOW.
jacint@620:     void preflowPhase1( flowEnum fe );
jacint@620: 
jacint@620:     ///Runs the second phase of the preflow algorithm.
jacint@620:     
jacint@620:     ///The preflow algorithm consists of two phases, this method runs
jacint@620:     ///the second phase. After calling \ref preflowPhase1 and then
jacint@620:     ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
jacint@620:     ///\ref minMinCut and \ref maxMinCut give proper results.
jacint@620:     ///\pre \ref preflowPhase1 must be called before.
jacint@620:     void preflowPhase2();
jacint@620: 
jacint@620:     /// Starting from a flow, this method searches for an augmenting path 
jacint@620:     /// according to the Edmonds-Karp algorithm 
jacint@620:     /// and augments the flow on if any. 
jacint@620:     /// The return value shows if the augmentation was successful.
jacint@620:     bool augmentOnShortestPath();
jacint@620: 
jacint@620:     /// Starting from a flow, this method searches for an augmenting blockin 
jacint@620:     /// flow according to Dinits' algorithm and augments the flow on if any. 
jacint@620:     /// The blocking flow is computed in a physically constructed 
jacint@620:     /// residual graph of type \c Mutablegraph.
jacint@620:     /// The return value show sif the augmentation was succesful.
jacint@620:     template<typename MutableGraph> bool augmentOnBlockingFlow();
jacint@620: 
jacint@620:     /// The same as \c augmentOnBlockingFlow<MutableGraph> but the 
jacint@620:     /// residual graph is not constructed physically.
jacint@620:     /// The return value shows if the augmentation was succesful.
jacint@620:     bool augmentOnBlockingFlow2();
jacint@620: 
jacint@620:     /// Returns the actual flow value.
jacint@620:     /// More precisely, it returns the negative excess of s, thus 
jacint@620:     /// this works also for preflows.
jacint@620:     ///Can be called already after \ref preflowPhase1.
jacint@620: 
jacint@620:     Num flowValue() { 
jacint@620:       Num a=0;
jacint@620:       FOR_EACH_INC_LOC(OutEdgeIt, e, *g, s) a+=(*flow)[e];
jacint@620:       FOR_EACH_INC_LOC(InEdgeIt, e, *g, s) a-=(*flow)[e];
jacint@620:       return a;
jacint@620:       //marci figyu: excess[t] epp ezt adja preflow 0. fazisa utan
jacint@620:     }
jacint@620: 
jacint@620:     ///Returns a minimum value cut after calling \ref preflowPhase1.
jacint@620: 
jacint@620:     ///After the first phase of the preflow algorithm the maximum flow
jacint@620:     ///value and a minimum value cut can already be computed. This
jacint@620:     ///method can be called after running \ref preflowPhase1 for
jacint@620:     ///obtaining a minimum value cut.
jacint@620:     ///\warning: Gives proper result only right after calling \ref
jacint@620:     ///preflowPhase1.
jacint@620:     ///\todo We have to make some status variable which shows the actual state 
jacint@620:     /// of the class. This enables us to determine which methods are valid 
jacint@620:     /// for MinCut computation
jacint@620:     template<typename _CutMap>
jacint@620:     void actMinCut(_CutMap& M) {
jacint@620:       NodeIt v;
jacint@620:       for(g->first(v); g->valid(v); g->next(v)) {
jacint@620: 	if ( level[v] < n ) {
jacint@620: 	  M.set(v,false);
jacint@620: 	} else {
jacint@620: 	  M.set(v,true);
jacint@620: 	}
jacint@620:       }
jacint@620:     }
jacint@620:     
jacint@620:     ///Returns the inclusionwise minimum of the minimum value cuts.
jacint@620: 
jacint@620:     ///Sets \c M to the characteristic vector of the minimum value cut
jacint@620:     ///which is inclusionwise minimum. It is computed by processing
jacint@620:     ///a bfs from the source node \c s in the residual graph.
jacint@620:     ///\pre M should be a node map of bools initialized to false.
jacint@620:     ///\pre \c flow must be a maximum flow.
jacint@620:     template<typename _CutMap>
jacint@620:     void minMinCut(_CutMap& M) {
jacint@620:     
jacint@620:       std::queue<Node> queue;
jacint@620:       
jacint@620:       M.set(s,true);      
jacint@620:       queue.push(s);
jacint@620: 
jacint@620:       while (!queue.empty()) {
jacint@620:         Node w=queue.front();
jacint@620: 	queue.pop();
jacint@620: 
jacint@620: 	OutEdgeIt e;
jacint@620: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
jacint@620: 	  Node v=g->head(e);
jacint@620: 	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
jacint@620: 	    queue.push(v);
jacint@620: 	    M.set(v, true);
jacint@620: 	  }
jacint@620: 	} 
jacint@620: 
jacint@620: 	InEdgeIt f;
jacint@620: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
jacint@620: 	  Node v=g->tail(f);
jacint@620: 	  if (!M[v] && (*flow)[f] > 0 ) {
jacint@620: 	    queue.push(v);
jacint@620: 	    M.set(v, true);
jacint@620: 	  }
jacint@620: 	} 
jacint@620:       }
jacint@620:     }
jacint@620: 
jacint@620: 
jacint@620:     ///Returns the inclusionwise maximum of the minimum value cuts.
jacint@620: 
jacint@620:     ///Sets \c M to the characteristic vector of the minimum value cut
jacint@620:     ///which is inclusionwise maximum. It is computed by processing a
jacint@620:     ///backward bfs from the target node \c t in the residual graph.
jacint@620:     ///\pre M should be a node map of bools initialized to false.
jacint@620:     ///\pre \c flow must be a maximum flow.
jacint@620:     template<typename _CutMap>
jacint@620:     void maxMinCut(_CutMap& M) {
jacint@620: 
jacint@620:       NodeIt v;
jacint@620:       for(g->first(v) ; g->valid(v); g->next(v)) {
jacint@620: 	M.set(v, true);
jacint@620:       }
jacint@620: 
jacint@620:       std::queue<Node> queue;
jacint@620:       
jacint@620:       M.set(t,false);        
jacint@620:       queue.push(t);
jacint@620: 
jacint@620:       while (!queue.empty()) {
jacint@620:         Node w=queue.front();
jacint@620: 	queue.pop();
jacint@620: 
jacint@620: 
jacint@620: 	InEdgeIt e;
jacint@620: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
jacint@620: 	  Node v=g->tail(e);
jacint@620: 	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
jacint@620: 	    queue.push(v);
jacint@620: 	    M.set(v, false);
jacint@620: 	  }
jacint@620: 	}
jacint@620: 	
jacint@620: 	OutEdgeIt f;
jacint@620: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
jacint@620: 	  Node v=g->head(f);
jacint@620: 	  if (M[v] && (*flow)[f] > 0 ) {
jacint@620: 	    queue.push(v);
jacint@620: 	    M.set(v, false);
jacint@620: 	  }
jacint@620: 	}
jacint@620:       }
jacint@620:     }
jacint@620: 
jacint@620: 
jacint@620:     ///Returns a minimum value cut.
jacint@620: 
jacint@620:     ///Sets \c M to the characteristic vector of a minimum value cut.
jacint@620:     ///\pre M should be a node map of bools initialized to false.
jacint@620:     ///\pre \c flow must be a maximum flow.
jacint@620:     template<typename CutMap>
jacint@620:     void minCut(CutMap& M) { minMinCut(M); }
jacint@620: 
jacint@620:     ///Resets the source node to \c _s.
jacint@620: 
jacint@620:     ///Resets the source node to \c _s.
jacint@620:     ///
jacint@620:     void resetSource(Node _s) { s=_s; }
jacint@620: 
jacint@620: 
jacint@620:     ///Resets the target node to \c _t.
jacint@620: 
jacint@620:     ///Resets the target node to \c _t.
jacint@620:     ///
jacint@620:     void resetTarget(Node _t) { t=_t; }
jacint@620:    
jacint@620:     /// Resets the edge map of the capacities to _cap.
jacint@620: 
jacint@620:     /// Resets the edge map of the capacities to _cap.
jacint@620:     ///
jacint@620:     void resetCap(const CapMap& _cap) { capacity=&_cap; }
jacint@620:     
jacint@620:     /// Resets the edge map of the flows to _flow.
jacint@620: 
jacint@620:     /// Resets the edge map of the flows to _flow.
jacint@620:     ///
jacint@620:     void resetFlow(FlowMap& _flow) { flow=&_flow; }
jacint@620: 
jacint@620: 
jacint@620:   private:
jacint@620: 
jacint@620:     int push(Node w, VecStack& active) {
jacint@620:       
jacint@620:       int lev=level[w];
jacint@620:       Num exc=excess[w];
jacint@620:       int newlevel=n;       //bound on the next level of w
jacint@620: 	  
jacint@620:       OutEdgeIt e;
jacint@620:       for(g->first(e,w); g->valid(e); g->next(e)) {
jacint@620: 	    
jacint@620: 	if ( (*flow)[e] >= (*capacity)[e] ) continue; 
jacint@620: 	Node v=g->head(e);            
jacint@620: 	    
jacint@620: 	if( lev > level[v] ) { //Push is allowed now
jacint@620: 	  
jacint@620: 	  if ( excess[v]<=0 && v!=t && v!=s ) {
jacint@620: 	    int lev_v=level[v];
jacint@620: 	    active[lev_v].push(v);
jacint@620: 	  }
jacint@620: 	  
jacint@620: 	  Num cap=(*capacity)[e];
jacint@620: 	  Num flo=(*flow)[e];
jacint@620: 	  Num remcap=cap-flo;
jacint@620: 	  
jacint@620: 	  if ( remcap >= exc ) { //A nonsaturating push.
jacint@620: 	    
jacint@620: 	    flow->set(e, flo+exc);
jacint@620: 	    excess.set(v, excess[v]+exc);
jacint@620: 	    exc=0;
jacint@620: 	    break; 
jacint@620: 	    
jacint@620: 	  } else { //A saturating push.
jacint@620: 	    flow->set(e, cap);
jacint@620: 	    excess.set(v, excess[v]+remcap);
jacint@620: 	    exc-=remcap;
jacint@620: 	  }
jacint@620: 	} else if ( newlevel > level[v] ) newlevel = level[v];
jacint@620:       } //for out edges wv 
jacint@620:       
jacint@620:       if ( exc > 0 ) {	
jacint@620: 	InEdgeIt e;
jacint@620: 	for(g->first(e,w); g->valid(e); g->next(e)) {
jacint@620: 	  
jacint@620: 	  if( (*flow)[e] <= 0 ) continue; 
jacint@620: 	  Node v=g->tail(e); 
jacint@620: 	  
jacint@620: 	  if( lev > level[v] ) { //Push is allowed now
jacint@620: 	    
jacint@620: 	    if ( excess[v]<=0 && v!=t && v!=s ) {
jacint@620: 	      int lev_v=level[v];
jacint@620: 	      active[lev_v].push(v);
jacint@620: 	    }
jacint@620: 	    
jacint@620: 	    Num flo=(*flow)[e];
jacint@620: 	    
jacint@620: 	    if ( flo >= exc ) { //A nonsaturating push.
jacint@620: 	      
jacint@620: 	      flow->set(e, flo-exc);
jacint@620: 	      excess.set(v, excess[v]+exc);
jacint@620: 	      exc=0;
jacint@620: 	      break; 
jacint@620: 	    } else {  //A saturating push.
jacint@620: 	      
jacint@620: 	      excess.set(v, excess[v]+flo);
jacint@620: 	      exc-=flo;
jacint@620: 	      flow->set(e,0);
jacint@620: 	    }  
jacint@620: 	  } else if ( newlevel > level[v] ) newlevel = level[v];
jacint@620: 	} //for in edges vw
jacint@620: 	
jacint@620:       } // if w still has excess after the out edge for cycle
jacint@620:       
jacint@620:       excess.set(w, exc);
jacint@620:       
jacint@620:       return newlevel;
jacint@620:     }
jacint@620: 
jacint@620: 
jacint@620:     void preflowPreproc ( flowEnum fe, VecStack& active, 
jacint@620: 			  VecNode& level_list, NNMap& left, NNMap& right ) {
jacint@620: 
jacint@620: 			    std::queue<Node> bfs_queue;
jacint@620:       
jacint@620: 			    switch ( fe ) {
jacint@620: 			    case ZERO_FLOW: 
jacint@620: 			      {
jacint@620: 				//Reverse_bfs from t, to find the starting level.
jacint@620: 				level.set(t,0);
jacint@620: 				bfs_queue.push(t);
jacint@620: 	
jacint@620: 				while (!bfs_queue.empty()) {
jacint@620: 	    
jacint@620: 				  Node v=bfs_queue.front();	
jacint@620: 				  bfs_queue.pop();
jacint@620: 				  int l=level[v]+1;
jacint@620: 	    
jacint@620: 				  InEdgeIt e;
jacint@620: 				  for(g->first(e,v); g->valid(e); g->next(e)) {
jacint@620: 				    Node w=g->tail(e);
jacint@620: 				    if ( level[w] == n && w != s ) {
jacint@620: 				      bfs_queue.push(w);
jacint@620: 				      Node first=level_list[l];
jacint@620: 				      if ( g->valid(first) ) left.set(first,w);
jacint@620: 				      right.set(w,first);
jacint@620: 				      level_list[l]=w;
jacint@620: 				      level.set(w, l);
jacint@620: 				    }
jacint@620: 				  }
jacint@620: 				}
jacint@620: 	  
jacint@620: 				//the starting flow
jacint@620: 				OutEdgeIt e;
jacint@620: 				for(g->first(e,s); g->valid(e); g->next(e)) 
jacint@620: 				  {
jacint@620: 				    Num c=(*capacity)[e];
jacint@620: 				    if ( c <= 0 ) continue;
jacint@620: 				    Node w=g->head(e);
jacint@620: 				    if ( level[w] < n ) {	  
jacint@620: 				      if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
jacint@620: 				      flow->set(e, c); 
jacint@620: 				      excess.set(w, excess[w]+c);
jacint@620: 				    }
jacint@620: 				  }
jacint@620: 				break;
jacint@620: 			      }
jacint@620: 	
jacint@620: 			    case GEN_FLOW:
jacint@620: 			    case PRE_FLOW:
jacint@620: 			      {
jacint@620: 				//Reverse_bfs from t in the residual graph, 
jacint@620: 				//to find the starting level.
jacint@620: 				level.set(t,0);
jacint@620: 				bfs_queue.push(t);
jacint@620: 	  
jacint@620: 				while (!bfs_queue.empty()) {
jacint@620: 	    
jacint@620: 				  Node v=bfs_queue.front();	
jacint@620: 				  bfs_queue.pop();
jacint@620: 				  int l=level[v]+1;
jacint@620: 	    
jacint@620: 				  InEdgeIt e;
jacint@620: 				  for(g->first(e,v); g->valid(e); g->next(e)) {
jacint@620: 				    if ( (*capacity)[e] <= (*flow)[e] ) continue;
jacint@620: 				    Node w=g->tail(e);
jacint@620: 				    if ( level[w] == n && w != s ) {
jacint@620: 				      bfs_queue.push(w);
jacint@620: 				      Node first=level_list[l];
jacint@620: 				      if ( g->valid(first) ) left.set(first,w);
jacint@620: 				      right.set(w,first);
jacint@620: 				      level_list[l]=w;
jacint@620: 				      level.set(w, l);
jacint@620: 				    }
jacint@620: 				  }
jacint@620: 	    
jacint@620: 				  OutEdgeIt f;
jacint@620: 				  for(g->first(f,v); g->valid(f); g->next(f)) {
jacint@620: 				    if ( 0 >= (*flow)[f] ) continue;
jacint@620: 				    Node w=g->head(f);
jacint@620: 				    if ( level[w] == n && w != s ) {
jacint@620: 				      bfs_queue.push(w);
jacint@620: 				      Node first=level_list[l];
jacint@620: 				      if ( g->valid(first) ) left.set(first,w);
jacint@620: 				      right.set(w,first);
jacint@620: 				      level_list[l]=w;
jacint@620: 				      level.set(w, l);
jacint@620: 				    }
jacint@620: 				  }
jacint@620: 				}
jacint@620: 	  
jacint@620: 	  
jacint@620: 				//the starting flow
jacint@620: 				OutEdgeIt e;
jacint@620: 				for(g->first(e,s); g->valid(e); g->next(e)) 
jacint@620: 				  {
jacint@620: 				    Num rem=(*capacity)[e]-(*flow)[e];
jacint@620: 				    if ( rem <= 0 ) continue;
jacint@620: 				    Node w=g->head(e);
jacint@620: 				    if ( level[w] < n ) {	  
jacint@620: 				      if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
jacint@620: 				      flow->set(e, (*capacity)[e]); 
jacint@620: 				      excess.set(w, excess[w]+rem);
jacint@620: 				    }
jacint@620: 				  }
jacint@620: 	  
jacint@620: 				InEdgeIt f;
jacint@620: 				for(g->first(f,s); g->valid(f); g->next(f)) 
jacint@620: 				  {
jacint@620: 				    if ( (*flow)[f] <= 0 ) continue;
jacint@620: 				    Node w=g->tail(f);
jacint@620: 				    if ( level[w] < n ) {	  
jacint@620: 				      if ( excess[w] <= 0 && w!=t ) active[level[w]].push(w);
jacint@620: 				      excess.set(w, excess[w]+(*flow)[f]);
jacint@620: 				      flow->set(f, 0); 
jacint@620: 				    }
jacint@620: 				  }  
jacint@620: 				break;
jacint@620: 			      } //case PRE_FLOW
jacint@620: 			    }
jacint@620: 			  } //preflowPreproc
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:     void relabel(Node w, int newlevel, VecStack& active,  
jacint@620: 		 VecNode& level_list, NNMap& left, 
jacint@620: 		 NNMap& right, int& b, int& k, bool what_heur ) 
jacint@620:     {
jacint@620: 
jacint@620:       Num lev=level[w];	
jacint@620:       
jacint@620:       Node right_n=right[w];
jacint@620:       Node left_n=left[w];
jacint@620:       
jacint@620:       //unlacing starts
jacint@620:       if ( g->valid(right_n) ) {
jacint@620: 	if ( g->valid(left_n) ) {
jacint@620: 	  right.set(left_n, right_n);
jacint@620: 	  left.set(right_n, left_n);
jacint@620: 	} else {
jacint@620: 	  level_list[lev]=right_n;   
jacint@620: 	  left.set(right_n, INVALID);
jacint@620: 	} 
jacint@620:       } else {
jacint@620: 	if ( g->valid(left_n) ) {
jacint@620: 	  right.set(left_n, INVALID);
jacint@620: 	} else { 
jacint@620: 	  level_list[lev]=INVALID;   
jacint@620: 	} 
jacint@620:       } 
jacint@620:       //unlacing ends
jacint@620: 		
jacint@620:       if ( !g->valid(level_list[lev]) ) {
jacint@620: 	      
jacint@620: 	//gapping starts
jacint@620: 	for (int i=lev; i!=k ; ) {
jacint@620: 	  Node v=level_list[++i];
jacint@620: 	  while ( g->valid(v) ) {
jacint@620: 	    level.set(v,n);
jacint@620: 	    v=right[v];
jacint@620: 	  }
jacint@620: 	  level_list[i]=INVALID;
jacint@620: 	  if ( !what_heur ) {
jacint@620: 	    while ( !active[i].empty() ) {
jacint@620: 	      active[i].pop();    //FIXME: ezt szebben kene
jacint@620: 	    }
jacint@620: 	  }	     
jacint@620: 	}
jacint@620: 	
jacint@620: 	level.set(w,n);
jacint@620: 	b=lev-1;
jacint@620: 	k=b;
jacint@620: 	//gapping ends
jacint@620: 	
jacint@620:       } else {
jacint@620: 	
jacint@620: 	if ( newlevel == n ) level.set(w,n); 
jacint@620: 	else {
jacint@620: 	  level.set(w,++newlevel);
jacint@620: 	  active[newlevel].push(w);
jacint@620: 	  if ( what_heur ) b=newlevel;
jacint@620: 	  if ( k < newlevel ) ++k;      //now k=newlevel
jacint@620: 	  Node first=level_list[newlevel];
jacint@620: 	  if ( g->valid(first) ) left.set(first,w);
jacint@620: 	  right.set(w,first);
jacint@620: 	  left.set(w,INVALID);
jacint@620: 	  level_list[newlevel]=w;
jacint@620: 	}
jacint@620:       }
jacint@620:       
jacint@620:     } //relabel
jacint@620: 
jacint@620: 
jacint@620:     template<typename MapGraphWrapper> 
jacint@620:     class DistanceMap {
jacint@620:     protected:
jacint@620:       const MapGraphWrapper* g;
jacint@620:       typename MapGraphWrapper::template NodeMap<int> dist; 
jacint@620:     public:
jacint@620:       DistanceMap(MapGraphWrapper& _g) : g(&_g), dist(*g, g->nodeNum()) { }
jacint@620:       void set(const typename MapGraphWrapper::Node& n, int a) { 
jacint@620: 	dist.set(n, a); 
jacint@620:       }
jacint@620:       int operator[](const typename MapGraphWrapper::Node& n) 
jacint@620:       { return dist[n]; }
jacint@620:       //       int get(const typename MapGraphWrapper::Node& n) const { 
jacint@620:       // 	return dist[n]; }
jacint@620:       //       bool get(const typename MapGraphWrapper::Edge& e) const { 
jacint@620:       // 	return (dist.get(g->tail(e))<dist.get(g->head(e))); }
jacint@620:       bool operator[](const typename MapGraphWrapper::Edge& e) const { 
jacint@620: 	return (dist[g->tail(e)]<dist[g->head(e)]); 
jacint@620:       }
jacint@620:     };
jacint@620:     
jacint@620:   };
jacint@620: 
jacint@620: 
jacint@620:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
jacint@620:   void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase1( flowEnum fe ) 
jacint@620:   {
jacint@620:       
jacint@620:     int heur0=(int)(H0*n);  //time while running 'bound decrease' 
jacint@620:     int heur1=(int)(H1*n);  //time while running 'highest label'
jacint@620:     int heur=heur1;         //starting time interval (#of relabels)
jacint@620:     int numrelabel=0;
jacint@620:      
jacint@620:     bool what_heur=1;       
jacint@620:     //It is 0 in case 'bound decrease' and 1 in case 'highest label'
jacint@620: 
jacint@620:     bool end=false;     
jacint@620:     //Needed for 'bound decrease', true means no active nodes are above bound b.
jacint@620: 
jacint@620:     int k=n-2;  //bound on the highest level under n containing a node
jacint@620:     int b=k;    //bound on the highest level under n of an active node
jacint@620:       
jacint@620:     VecStack active(n);
jacint@620:       
jacint@620:     NNMap left(*g, INVALID);
jacint@620:     NNMap right(*g, INVALID);
jacint@620:     VecNode level_list(n,INVALID);
jacint@620:     //List of the nodes in level i<n, set to n.
jacint@620: 
jacint@620:     NodeIt v;
jacint@620:     for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
jacint@620:     //setting each node to level n
jacint@620:       
jacint@620:     switch ( fe ) {
jacint@620:     case PRE_FLOW:
jacint@620:       {
jacint@620: 	//counting the excess
jacint@620: 	NodeIt v;
jacint@620: 	for(g->first(v); g->valid(v); g->next(v)) {
jacint@620: 	  Num exc=0;
jacint@620: 	  
jacint@620: 	  InEdgeIt e;
jacint@620: 	  for(g->first(e,v); g->valid(e); g->next(e)) exc+=(*flow)[e];
jacint@620: 	  OutEdgeIt f;
jacint@620: 	  for(g->first(f,v); g->valid(f); g->next(f)) exc-=(*flow)[f];
jacint@620: 	    
jacint@620: 	  excess.set(v,exc);	  
jacint@620: 	    
jacint@620: 	  //putting the active nodes into the stack
jacint@620: 	  int lev=level[v];
jacint@620: 	  if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
jacint@620: 	}
jacint@620: 	break;
jacint@620:       }
jacint@620:     case GEN_FLOW:
jacint@620:       {
jacint@620: 	//Counting the excess of t
jacint@620: 	Num exc=0;
jacint@620: 	  
jacint@620: 	InEdgeIt e;
jacint@620: 	for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
jacint@620: 	OutEdgeIt f;
jacint@620: 	for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
jacint@620: 	  
jacint@620: 	excess.set(t,exc);	
jacint@620: 	  
jacint@620: 	break;
jacint@620:       }
jacint@620:     default:
jacint@620:       break;
jacint@620:     }
jacint@620:       
jacint@620:     preflowPreproc( fe, active, level_list, left, right );
jacint@620:     //End of preprocessing 
jacint@620:       
jacint@620:       
jacint@620:     //Push/relabel on the highest level active nodes.
jacint@620:     while ( true ) {
jacint@620:       if ( b == 0 ) {
jacint@620: 	if ( !what_heur && !end && k > 0 ) {
jacint@620: 	  b=k;
jacint@620: 	  end=true;
jacint@620: 	} else break;
jacint@620:       }
jacint@620: 	
jacint@620:       if ( active[b].empty() ) --b; 
jacint@620:       else {
jacint@620: 	end=false;  
jacint@620: 	Node w=active[b].top();
jacint@620: 	active[b].pop();
jacint@620: 	int newlevel=push(w,active);
jacint@620: 	if ( excess[w] > 0 ) relabel(w, newlevel, active, level_list, 
jacint@620: 				     left, right, b, k, what_heur);
jacint@620: 	  
jacint@620: 	++numrelabel; 
jacint@620: 	if ( numrelabel >= heur ) {
jacint@620: 	  numrelabel=0;
jacint@620: 	  if ( what_heur ) {
jacint@620: 	    what_heur=0;
jacint@620: 	    heur=heur0;
jacint@620: 	    end=false;
jacint@620: 	  } else {
jacint@620: 	    what_heur=1;
jacint@620: 	    heur=heur1;
jacint@620: 	    b=k; 
jacint@620: 	  }
jacint@620: 	}
jacint@620:       } 
jacint@620:     } 
jacint@620:   }
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
jacint@620:   void MaxFlow<Graph, Num, CapMap, FlowMap>::preflowPhase2() 
jacint@620:   {
jacint@620:       
jacint@620:     int k=n-2;  //bound on the highest level under n containing a node
jacint@620:     int b=k;    //bound on the highest level under n of an active node
jacint@620:       
jacint@620:     VecStack active(n);
jacint@620:     level.set(s,0);
jacint@620:     std::queue<Node> bfs_queue;
jacint@620:     bfs_queue.push(s);
jacint@620: 	    
jacint@620:     while (!bfs_queue.empty()) {
jacint@620: 	
jacint@620:       Node v=bfs_queue.front();	
jacint@620:       bfs_queue.pop();
jacint@620:       int l=level[v]+1;
jacint@620: 	      
jacint@620:       InEdgeIt e;
jacint@620:       for(g->first(e,v); g->valid(e); g->next(e)) {
jacint@620: 	if ( (*capacity)[e] <= (*flow)[e] ) continue;
jacint@620: 	Node u=g->tail(e);
jacint@620: 	if ( level[u] >= n ) { 
jacint@620: 	  bfs_queue.push(u);
jacint@620: 	  level.set(u, l);
jacint@620: 	  if ( excess[u] > 0 ) active[l].push(u);
jacint@620: 	}
jacint@620:       }
jacint@620: 	
jacint@620:       OutEdgeIt f;
jacint@620:       for(g->first(f,v); g->valid(f); g->next(f)) {
jacint@620: 	if ( 0 >= (*flow)[f] ) continue;
jacint@620: 	Node u=g->head(f);
jacint@620: 	if ( level[u] >= n ) { 
jacint@620: 	  bfs_queue.push(u);
jacint@620: 	  level.set(u, l);
jacint@620: 	  if ( excess[u] > 0 ) active[l].push(u);
jacint@620: 	}
jacint@620:       }
jacint@620:     }
jacint@620:     b=n-2;
jacint@620: 
jacint@620:     while ( true ) {
jacint@620: 	
jacint@620:       if ( b == 0 ) break;
jacint@620: 
jacint@620:       if ( active[b].empty() ) --b; 
jacint@620:       else {
jacint@620: 	Node w=active[b].top();
jacint@620: 	active[b].pop();
jacint@620: 	int newlevel=push(w,active);	  
jacint@620: 
jacint@620: 	//relabel
jacint@620: 	if ( excess[w] > 0 ) {
jacint@620: 	  level.set(w,++newlevel);
jacint@620: 	  active[newlevel].push(w);
jacint@620: 	  b=newlevel;
jacint@620: 	}
jacint@620:       }  // if stack[b] is nonempty
jacint@620:     } // while(true)
jacint@620:   }
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
jacint@620:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnShortestPath() 
jacint@620:   {
jacint@620:     ResGW res_graph(*g, *capacity, *flow);
jacint@620:     bool _augment=false;
jacint@620:       
jacint@620:     //ReachedMap level(res_graph);
jacint@620:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
jacint@620:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
jacint@620:     bfs.pushAndSetReached(s);
jacint@620: 	
jacint@620:     typename ResGW::template NodeMap<ResGWEdge> pred(res_graph); 
jacint@620:     pred.set(s, INVALID);
jacint@620:       
jacint@620:     typename ResGW::template NodeMap<Num> free(res_graph);
jacint@620: 	
jacint@620:     //searching for augmenting path
jacint@620:     while ( !bfs.finished() ) { 
jacint@620:       ResGWOutEdgeIt e=bfs;
jacint@620:       if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
jacint@620: 	Node v=res_graph.tail(e);
jacint@620: 	Node w=res_graph.head(e);
jacint@620: 	pred.set(w, e);
jacint@620: 	if (res_graph.valid(pred[v])) {
jacint@620: 	  free.set(w, std::min(free[v], res_graph.resCap(e)));
jacint@620: 	} else {
jacint@620: 	  free.set(w, res_graph.resCap(e)); 
jacint@620: 	}
jacint@620: 	if (res_graph.head(e)==t) { _augment=true; break; }
jacint@620:       }
jacint@620: 	
jacint@620:       ++bfs;
jacint@620:     } //end of searching augmenting path
jacint@620: 
jacint@620:     if (_augment) {
jacint@620:       Node n=t;
jacint@620:       Num augment_value=free[t];
jacint@620:       while (res_graph.valid(pred[n])) { 
jacint@620: 	ResGWEdge e=pred[n];
jacint@620: 	res_graph.augment(e, augment_value); 
jacint@620: 	n=res_graph.tail(e);
jacint@620:       }
jacint@620:     }
jacint@620: 
jacint@620:     return _augment;
jacint@620:   }
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
jacint@620:   template<typename MutableGraph> 
jacint@620:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow() 
jacint@620:   {      
jacint@620:     typedef MutableGraph MG;
jacint@620:     bool _augment=false;
jacint@620: 
jacint@620:     ResGW res_graph(*g, *capacity, *flow);
jacint@620: 
jacint@620:     //bfs for distances on the residual graph
jacint@620:     //ReachedMap level(res_graph);
jacint@620:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
jacint@620:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
jacint@620:     bfs.pushAndSetReached(s);
jacint@620:     typename ResGW::template NodeMap<int> 
jacint@620:       dist(res_graph); //filled up with 0's
jacint@620: 
jacint@620:     //F will contain the physical copy of the residual graph
jacint@620:     //with the set of edges which are on shortest paths
jacint@620:     MG F;
jacint@620:     typename ResGW::template NodeMap<typename MG::Node> 
jacint@620:       res_graph_to_F(res_graph);
jacint@620:     {
jacint@620:       typename ResGW::NodeIt n;
jacint@620:       for(res_graph.first(n); res_graph.valid(n); res_graph.next(n)) {
jacint@620: 	res_graph_to_F.set(n, F.addNode());
jacint@620:       }
jacint@620:     }
jacint@620: 
jacint@620:     typename MG::Node sF=res_graph_to_F[s];
jacint@620:     typename MG::Node tF=res_graph_to_F[t];
jacint@620:     typename MG::template EdgeMap<ResGWEdge> original_edge(F);
jacint@620:     typename MG::template EdgeMap<Num> residual_capacity(F);
jacint@620: 
jacint@620:     while ( !bfs.finished() ) { 
jacint@620:       ResGWOutEdgeIt e=bfs;
jacint@620:       if (res_graph.valid(e)) {
jacint@620: 	if (bfs.isBNodeNewlyReached()) {
jacint@620: 	  dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
jacint@620: 	  typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
jacint@620: 	  original_edge.update();
jacint@620: 	  original_edge.set(f, e);
jacint@620: 	  residual_capacity.update();
jacint@620: 	  residual_capacity.set(f, res_graph.resCap(e));
jacint@620: 	} else {
jacint@620: 	  if (dist[res_graph.head(e)]==(dist[res_graph.tail(e)]+1)) {
jacint@620: 	    typename MG::Edge f=F.addEdge(res_graph_to_F[res_graph.tail(e)], res_graph_to_F[res_graph.head(e)]);
jacint@620: 	    original_edge.update();
jacint@620: 	    original_edge.set(f, e);
jacint@620: 	    residual_capacity.update();
jacint@620: 	    residual_capacity.set(f, res_graph.resCap(e));
jacint@620: 	  }
jacint@620: 	}
jacint@620:       }
jacint@620:       ++bfs;
jacint@620:     } //computing distances from s in the residual graph
jacint@620: 
jacint@620:     bool __augment=true;
jacint@620: 
jacint@620:     while (__augment) {
jacint@620:       __augment=false;
jacint@620:       //computing blocking flow with dfs
jacint@620:       DfsIterator< MG, typename MG::template NodeMap<bool> > dfs(F);
jacint@620:       typename MG::template NodeMap<typename MG::Edge> pred(F);
jacint@620:       pred.set(sF, INVALID);
jacint@620:       //invalid iterators for sources
jacint@620: 
jacint@620:       typename MG::template NodeMap<Num> free(F);
jacint@620: 
jacint@620:       dfs.pushAndSetReached(sF);      
jacint@620:       while (!dfs.finished()) {
jacint@620: 	++dfs;
jacint@620: 	if (F.valid(/*typename MG::OutEdgeIt*/(dfs))) {
jacint@620: 	  if (dfs.isBNodeNewlyReached()) {
jacint@620: 	    typename MG::Node v=F.aNode(dfs);
jacint@620: 	    typename MG::Node w=F.bNode(dfs);
jacint@620: 	    pred.set(w, dfs);
jacint@620: 	    if (F.valid(pred[v])) {
jacint@620: 	      free.set(w, std::min(free[v], residual_capacity[dfs]));
jacint@620: 	    } else {
jacint@620: 	      free.set(w, residual_capacity[dfs]); 
jacint@620: 	    }
jacint@620: 	    if (w==tF) { 
jacint@620: 	      __augment=true; 
jacint@620: 	      _augment=true;
jacint@620: 	      break; 
jacint@620: 	    }
jacint@620: 	      
jacint@620: 	  } else {
jacint@620: 	    F.erase(/*typename MG::OutEdgeIt*/(dfs));
jacint@620: 	  }
jacint@620: 	} 
jacint@620:       }
jacint@620: 
jacint@620:       if (__augment) {
jacint@620: 	typename MG::Node n=tF;
jacint@620: 	Num augment_value=free[tF];
jacint@620: 	while (F.valid(pred[n])) { 
jacint@620: 	  typename MG::Edge e=pred[n];
jacint@620: 	  res_graph.augment(original_edge[e], augment_value); 
jacint@620: 	  n=F.tail(e);
jacint@620: 	  if (residual_capacity[e]==augment_value) 
jacint@620: 	    F.erase(e); 
jacint@620: 	  else 
jacint@620: 	    residual_capacity.set(e, residual_capacity[e]-augment_value);
jacint@620: 	}
jacint@620:       }
jacint@620: 	
jacint@620:     }
jacint@620:             
jacint@620:     return _augment;
jacint@620:   }
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:   template <typename Graph, typename Num, typename CapMap, typename FlowMap>
jacint@620:   bool MaxFlow<Graph, Num, CapMap, FlowMap>::augmentOnBlockingFlow2() 
jacint@620:   {
jacint@620:     bool _augment=false;
jacint@620: 
jacint@620:     ResGW res_graph(*g, *capacity, *flow);
jacint@620:       
jacint@620:     //ReachedMap level(res_graph);
jacint@620:     FOR_EACH_LOC(typename Graph::NodeIt, e, *g) level.set(e, 0);
jacint@620:     BfsIterator<ResGW, ReachedMap> bfs(res_graph, level);
jacint@620: 
jacint@620:     bfs.pushAndSetReached(s);
jacint@620:     DistanceMap<ResGW> dist(res_graph);
jacint@620:     while ( !bfs.finished() ) { 
jacint@620:       ResGWOutEdgeIt e=bfs;
jacint@620:       if (res_graph.valid(e) && bfs.isBNodeNewlyReached()) {
jacint@620: 	dist.set(res_graph.head(e), dist[res_graph.tail(e)]+1);
jacint@620:       }
jacint@620:       ++bfs;
jacint@620:     } //computing distances from s in the residual graph
jacint@620: 
jacint@620:       //Subgraph containing the edges on some shortest paths
jacint@620:     ConstMap<typename ResGW::Node, bool> true_map(true);
jacint@620:     typedef SubGraphWrapper<ResGW, ConstMap<typename ResGW::Node, bool>, 
jacint@620:       DistanceMap<ResGW> > FilterResGW;
jacint@620:     FilterResGW filter_res_graph(res_graph, true_map, dist);
jacint@620: 
jacint@620:     //Subgraph, which is able to delete edges which are already 
jacint@620:     //met by the dfs
jacint@620:     typename FilterResGW::template NodeMap<typename FilterResGW::OutEdgeIt> 
jacint@620:       first_out_edges(filter_res_graph);
jacint@620:     typename FilterResGW::NodeIt v;
jacint@620:     for(filter_res_graph.first(v); filter_res_graph.valid(v); 
jacint@620: 	filter_res_graph.next(v)) 
jacint@620:       {
jacint@620:  	typename FilterResGW::OutEdgeIt e;
jacint@620:  	filter_res_graph.first(e, v);
jacint@620:  	first_out_edges.set(v, e);
jacint@620:       }
jacint@620:     typedef ErasingFirstGraphWrapper<FilterResGW, typename FilterResGW::
jacint@620:       template NodeMap<typename FilterResGW::OutEdgeIt> > ErasingResGW;
jacint@620:     ErasingResGW erasing_res_graph(filter_res_graph, first_out_edges);
jacint@620: 
jacint@620:     bool __augment=true;
jacint@620: 
jacint@620:     while (__augment) {
jacint@620: 
jacint@620:       __augment=false;
jacint@620:       //computing blocking flow with dfs
jacint@620:       DfsIterator< ErasingResGW, 
jacint@620: 	typename ErasingResGW::template NodeMap<bool> > 
jacint@620: 	dfs(erasing_res_graph);
jacint@620:       typename ErasingResGW::
jacint@620: 	template NodeMap<typename ErasingResGW::OutEdgeIt> 
jacint@620: 	pred(erasing_res_graph); 
jacint@620:       pred.set(s, INVALID);
jacint@620:       //invalid iterators for sources
jacint@620: 
jacint@620:       typename ErasingResGW::template NodeMap<Num> 
jacint@620: 	free1(erasing_res_graph);
jacint@620: 
jacint@620:       dfs.pushAndSetReached(
jacint@620: 			    typename ErasingResGW::Node(
jacint@620: 							typename FilterResGW::Node(
jacint@620: 										   typename ResGW::Node(s)
jacint@620: 										   )
jacint@620: 							)
jacint@620: 			    );
jacint@620:       while (!dfs.finished()) {
jacint@620: 	++dfs;
jacint@620: 	if (erasing_res_graph.valid(
jacint@620: 				    typename ErasingResGW::OutEdgeIt(dfs))) 
jacint@620:  	  { 
jacint@620:   	    if (dfs.isBNodeNewlyReached()) {
jacint@620: 	  
jacint@620:  	      typename ErasingResGW::Node v=erasing_res_graph.aNode(dfs);
jacint@620:  	      typename ErasingResGW::Node w=erasing_res_graph.bNode(dfs);
jacint@620: 
jacint@620:  	      pred.set(w, /*typename ErasingResGW::OutEdgeIt*/(dfs));
jacint@620:  	      if (erasing_res_graph.valid(pred[v])) {
jacint@620:  		free1.set(w, std::min(free1[v], res_graph.resCap(
jacint@620: 								 typename ErasingResGW::OutEdgeIt(dfs))));
jacint@620:  	      } else {
jacint@620:  		free1.set(w, res_graph.resCap(
jacint@620: 					      typename ErasingResGW::OutEdgeIt(dfs))); 
jacint@620:  	      }
jacint@620: 	      
jacint@620:  	      if (w==t) { 
jacint@620:  		__augment=true; 
jacint@620:  		_augment=true;
jacint@620:  		break; 
jacint@620:  	      }
jacint@620:  	    } else {
jacint@620:  	      erasing_res_graph.erase(dfs);
jacint@620: 	    }
jacint@620: 	  }
jacint@620:       }	
jacint@620: 
jacint@620:       if (__augment) {
jacint@620: 	typename ErasingResGW::Node n=typename FilterResGW::Node(typename ResGW::Node(t));
jacint@620: 	// 	  typename ResGW::NodeMap<Num> a(res_graph);
jacint@620: 	// 	  typename ResGW::Node b;
jacint@620: 	// 	  Num j=a[b];
jacint@620: 	// 	  typename FilterResGW::NodeMap<Num> a1(filter_res_graph);
jacint@620: 	// 	  typename FilterResGW::Node b1;
jacint@620: 	// 	  Num j1=a1[b1];
jacint@620: 	// 	  typename ErasingResGW::NodeMap<Num> a2(erasing_res_graph);
jacint@620: 	// 	  typename ErasingResGW::Node b2;
jacint@620: 	// 	  Num j2=a2[b2];
jacint@620: 	Num augment_value=free1[n];
jacint@620: 	while (erasing_res_graph.valid(pred[n])) { 
jacint@620: 	  typename ErasingResGW::OutEdgeIt e=pred[n];
jacint@620: 	  res_graph.augment(e, augment_value);
jacint@620: 	  n=erasing_res_graph.tail(e);
jacint@620: 	  if (res_graph.resCap(e)==0)
jacint@620: 	    erasing_res_graph.erase(e);
jacint@620: 	}
jacint@620:       }
jacint@620:       
jacint@620:     } //while (__augment) 
jacint@620:             
jacint@620:     return _augment;
jacint@620:   }
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620:   /// @}
jacint@620:   
jacint@620: } //END OF NAMESPACE HUGO
jacint@620: 
jacint@620: #endif //HUGO_MAX_FLOW_H
jacint@620: 
jacint@620: 
jacint@620: 
jacint@620: