alpar@726: // -*- C++ -*-
jacint@749: #ifndef HUGO_MAX_FLOW_H
jacint@749: #define HUGO_MAX_FLOW_H
alpar@726: 
alpar@726: #include <vector>
alpar@726: #include <queue>
alpar@726: 
alpar@726: #include <hugo/graph_wrapper.h>
alpar@726: #include <hugo/invalid.h>
alpar@726: #include <hugo/maps.h>
alpar@726: 
alpar@726: /// \file
alpar@726: /// \ingroup galgs
alpar@726: 
alpar@726: namespace hugo {
alpar@726: 
alpar@726:   /// \addtogroup galgs
alpar@726:   /// @{                                                                                                                                        
alpar@726:   ///Maximum flow algorithms class.
alpar@726: 
alpar@726:   ///This class provides various algorithms for finding a flow of
alpar@726:   ///maximum value in a directed graph. The \e source node, the \e
alpar@726:   ///target node, the \e capacity of the edges and the \e starting \e
alpar@726:   ///flow value of the edges should be passed to the algorithm through the
alpar@726:   ///constructor. It is possible to change these quantities using the
alpar@726:   ///functions \ref resetSource, \ref resetTarget, \ref resetCap and
alpar@726:   ///\ref resetFlow. Before any subsequent runs of any algorithm of
alpar@726:   ///the class \ref resetFlow should be called. 
alpar@726: 
alpar@726:   ///After running an algorithm of the class, the actual flow value 
alpar@726:   ///can be obtained by calling \ref flowValue(). The minimum
alpar@726:   ///value cut can be written into a \c node map of \c bools by
alpar@726:   ///calling \ref minCut. (\ref minMinCut and \ref maxMinCut writes
alpar@726:   ///the inclusionwise minimum and maximum of the minimum value
alpar@726:   ///cuts, resp.)                                                                                                                               
alpar@726:   ///\param Graph The directed graph type the algorithm runs on.
alpar@726:   ///\param Num The number type of the capacities and the flow values.
alpar@726:   ///\param CapMap The capacity map type.
alpar@726:   ///\param FlowMap The flow map type.                                                                                                           
alpar@726:   ///\author Marton Makai, Jacint Szabo 
alpar@726:   template <typename Graph, typename Num,
alpar@726: 	    typename CapMap=typename Graph::template EdgeMap<Num>,
alpar@726:             typename FlowMap=typename Graph::template EdgeMap<Num> >
alpar@726:   class MaxFlow {
alpar@726:   protected:
alpar@726:     typedef typename Graph::Node Node;
alpar@726:     typedef typename Graph::NodeIt NodeIt;
alpar@726:     typedef typename Graph::EdgeIt EdgeIt;
alpar@726:     typedef typename Graph::OutEdgeIt OutEdgeIt;
alpar@726:     typedef typename Graph::InEdgeIt InEdgeIt;
alpar@726: 
alpar@726:     typedef typename std::vector<Node> VecFirst;
alpar@726:     typedef typename Graph::template NodeMap<Node> NNMap;
alpar@726:     typedef typename std::vector<Node> VecNode;
alpar@726: 
alpar@726:     const Graph* g;
alpar@726:     Node s;
alpar@726:     Node t;
alpar@726:     const CapMap* capacity;
alpar@726:     FlowMap* flow;
alpar@726:     int n;      //the number of nodes of G
alpar@726:     typedef ResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;   
alpar@726:     //typedef ExpResGraphWrapper<const Graph, Num, CapMap, FlowMap> ResGW;
alpar@726:     typedef typename ResGW::OutEdgeIt ResGWOutEdgeIt;
alpar@726:     typedef typename ResGW::Edge ResGWEdge;
alpar@726:     typedef typename Graph::template NodeMap<int> ReachedMap;
alpar@726: 
alpar@726: 
alpar@726:     //level works as a bool map in augmenting path algorithms and is
alpar@726:     //used by bfs for storing reached information.  In preflow, it
alpar@726:     //shows the levels of nodes.     
alpar@726:     ReachedMap level;
alpar@726: 
alpar@726:     //excess is needed only in preflow
alpar@726:     typename Graph::template NodeMap<Num> excess;
alpar@726: 
alpar@726:     // constants used for heuristics
alpar@726:     static const int H0=20;
alpar@726:     static const int H1=1;
alpar@726: 
alpar@726:   public:
alpar@726: 
alpar@726:     ///Indicates the property of the starting flow.
alpar@726: 
alpar@726:     ///Indicates the property of the starting flow. The meanings are as follows:
alpar@726:     ///- \c ZERO_FLOW: constant zero flow
alpar@726:     ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
alpar@726:     ///the sum of the out-flows in every node except the \e source and
alpar@726:     ///the \e target.
alpar@726:     ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at 
alpar@726:     ///least the sum of the out-flows in every node except the \e source.
alpar@726:     ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be 
alpar@726:     ///set to the constant zero flow in the beginning of the algorithm in this case.
alpar@726:     enum FlowEnum{
alpar@726:       ZERO_FLOW,
alpar@726:       GEN_FLOW,
alpar@726:       PRE_FLOW,
alpar@726:       NO_FLOW
alpar@726:     };
alpar@726: 
alpar@726:     enum StatusEnum {
alpar@726:       AFTER_NOTHING,
alpar@726:       AFTER_AUGMENTING,
alpar@726:       AFTER_FAST_AUGMENTING, 
alpar@726:       AFTER_PRE_FLOW_PHASE_1,      
alpar@726:       AFTER_PRE_FLOW_PHASE_2
alpar@726:     };
alpar@726: 
jacint@749:     /// Do not needle this flag only if necessary.
alpar@726:     StatusEnum status;
alpar@726: 
alpar@726: //     int number_of_augmentations;
alpar@726: 
alpar@726: 
alpar@726: //     template<typename IntMap>
alpar@726: //     class TrickyReachedMap {
alpar@726: //     protected:
alpar@726: //       IntMap* map;
alpar@726: //       int* number_of_augmentations;
alpar@726: //     public:
alpar@726: //       TrickyReachedMap(IntMap& _map, int& _number_of_augmentations) : 
alpar@726: // 	map(&_map), number_of_augmentations(&_number_of_augmentations) { }
alpar@726: //       void set(const Node& n, bool b) {
alpar@726: // 	if (b)
alpar@726: // 	  map->set(n, *number_of_augmentations);
alpar@726: // 	else 
alpar@726: // 	  map->set(n, *number_of_augmentations-1);
alpar@726: //       }
alpar@726: //       bool operator[](const Node& n) const { 
alpar@726: // 	return (*map)[n]==*number_of_augmentations; 
alpar@726: //       }
alpar@726: //     };
alpar@726:     
alpar@726:     ///Constructor
alpar@726: 
alpar@726:     ///\todo Document, please.
alpar@726:     ///
alpar@726:     MaxFlow(const Graph& _G, Node _s, Node _t,
marci@745: 	    const CapMap& _capacity, FlowMap& _flow) :
alpar@726:       g(&_G), s(_s), t(_t), capacity(&_capacity),
alpar@726:       flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), 
alpar@726:       status(AFTER_NOTHING) { }
alpar@726: 
alpar@726:     ///Runs a maximum flow algorithm.
alpar@726: 
alpar@726:     ///Runs a preflow algorithm, which is the fastest maximum flow
alpar@726:     ///algorithm up-to-date. The default for \c fe is ZERO_FLOW.
alpar@726:     ///\pre The starting flow must be
alpar@726:     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
alpar@726:     /// - an arbitary flow if \c fe is \c GEN_FLOW,
alpar@726:     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
alpar@726:     /// - any map if \c fe is NO_FLOW.
alpar@726:     void run(FlowEnum fe=ZERO_FLOW) {
alpar@726:       preflow(fe);
alpar@726:     }
alpar@726: 
alpar@726:                                                                               
alpar@726:     ///Runs a preflow algorithm.  
alpar@726: 
alpar@726:     ///Runs a preflow algorithm. The preflow algorithms provide the
alpar@726:     ///fastest way to compute a maximum flow in a directed graph.
alpar@726:     ///\pre The starting flow must be
alpar@726:     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
alpar@726:     /// - an arbitary flow if \c fe is \c GEN_FLOW,
alpar@726:     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
alpar@726:     /// - any map if \c fe is NO_FLOW.
alpar@726:     ///
alpar@726:     ///\todo NO_FLOW should be the default flow.
alpar@726:     void preflow(FlowEnum fe) {
alpar@726:       preflowPhase1(fe);
alpar@726:       preflowPhase2();
alpar@726:     }
alpar@726:     // Heuristics:
alpar@726:     //   2 phase
alpar@726:     //   gap
alpar@726:     //   list 'level_list' on the nodes on level i implemented by hand
alpar@726:     //   stack 'active' on the active nodes on level i                                                                                    
alpar@726:     //   runs heuristic 'highest label' for H1*n relabels
alpar@726:     //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
alpar@726:     //   Parameters H0 and H1 are initialized to 20 and 1.
alpar@726: 
alpar@726:     ///Runs the first phase of the preflow algorithm.
alpar@726: 
alpar@726:     ///The preflow algorithm consists of two phases, this method runs the
alpar@726:     ///first phase. After the first phase the maximum flow value and a
alpar@726:     ///minimum value cut can already be computed, though a maximum flow
jacint@749:     ///is not yet obtained. So after calling this method \ref flowValue
alpar@726:     ///and \ref actMinCut gives proper results.
alpar@726:     ///\warning: \ref minCut, \ref minMinCut and \ref maxMinCut do not
alpar@726:     ///give minimum value cuts unless calling \ref preflowPhase2.
alpar@726:     ///\pre The starting flow must be
alpar@726:     /// - a constant zero flow if \c fe is \c ZERO_FLOW,
alpar@726:     /// - an arbitary flow if \c fe is \c GEN_FLOW,
alpar@726:     /// - an arbitary preflow if \c fe is \c PRE_FLOW,
alpar@726:     /// - any map if \c fe is NO_FLOW.
alpar@726:     void preflowPhase1(FlowEnum fe)
alpar@726:     {
alpar@726: 
alpar@726:       int heur0=(int)(H0*n);  //time while running 'bound decrease'
alpar@726:       int heur1=(int)(H1*n);  //time while running 'highest label'
alpar@726:       int heur=heur1;         //starting time interval (#of relabels)
alpar@726:       int numrelabel=0;
alpar@726: 
alpar@726:       bool what_heur=1;
alpar@726:       //It is 0 in case 'bound decrease' and 1 in case 'highest label'
alpar@726: 
alpar@726:       bool end=false;
alpar@726:       //Needed for 'bound decrease', true means no active nodes are above bound
alpar@726:       //b.
alpar@726: 
alpar@726:       int k=n-2;  //bound on the highest level under n containing a node
alpar@726:       int b=k;    //bound on the highest level under n of an active node
alpar@726: 
alpar@726:       VecFirst first(n, INVALID);
alpar@726:       NNMap next(*g, INVALID); //maybe INVALID is not needed
alpar@726: 
alpar@726:       NNMap left(*g, INVALID);
alpar@726:       NNMap right(*g, INVALID);
alpar@726:       VecNode level_list(n,INVALID);
alpar@726:       //List of the nodes in level i<n, set to n.
alpar@726: 
marci@745:       preflowPreproc(fe, next, first, level_list, left, right);
alpar@726:       //End of preprocessing
alpar@726: 
alpar@726:       //Push/relabel on the highest level active nodes.
alpar@726:       while ( true ) {
alpar@726: 	if ( b == 0 ) {
alpar@726: 	  if ( !what_heur && !end && k > 0 ) {
alpar@726: 	    b=k;
alpar@726: 	    end=true;
alpar@726: 	  } else break;
alpar@726: 	}
alpar@726: 
marci@745: 	if ( !g->valid(first[b]) ) --b;
alpar@726: 	else {
alpar@726: 	  end=false;
alpar@726: 	  Node w=first[b];
alpar@726: 	  first[b]=next[w];
marci@745: 	  int newlevel=push(w, next, first);
marci@745: 	  if ( excess[w] > 0 ) relabel(w, newlevel, next, first, level_list,
alpar@726: 				       left, right, b, k, what_heur);
alpar@726: 
alpar@726: 	  ++numrelabel;
alpar@726: 	  if ( numrelabel >= heur ) {
alpar@726: 	    numrelabel=0;
alpar@726: 	    if ( what_heur ) {
alpar@726: 	      what_heur=0;
alpar@726: 	      heur=heur0;
alpar@726: 	      end=false;
alpar@726: 	    } else {
alpar@726: 	      what_heur=1;
alpar@726: 	      heur=heur1;
alpar@726: 	      b=k;
alpar@726: 	    }
alpar@726: 	  }
alpar@726: 	}
alpar@726:       }
alpar@726: 
alpar@726:       status=AFTER_PRE_FLOW_PHASE_1;
alpar@726:     }
alpar@726: 
alpar@726: 
alpar@726:     ///Runs the second phase of the preflow algorithm.
alpar@726: 
alpar@726:     ///The preflow algorithm consists of two phases, this method runs
alpar@726:     ///the second phase. After calling \ref preflowPhase1 and then
alpar@726:     ///\ref preflowPhase2 the methods \ref flowValue, \ref minCut,
alpar@726:     ///\ref minMinCut and \ref maxMinCut give proper results.
alpar@726:     ///\pre \ref preflowPhase1 must be called before.
alpar@726:     void preflowPhase2()
alpar@726:     {
alpar@726: 
alpar@726:       int k=n-2;  //bound on the highest level under n containing a node
alpar@726:       int b=k;    //bound on the highest level under n of an active node
alpar@726: 
alpar@726:     
alpar@726:       VecFirst first(n, INVALID);
alpar@726:       NNMap next(*g, INVALID); //maybe INVALID is not needed
alpar@726:       level.set(s,0);
alpar@726:       std::queue<Node> bfs_queue;
alpar@726:       bfs_queue.push(s);
alpar@726: 
alpar@726:       while (!bfs_queue.empty()) {
alpar@726: 
alpar@726: 	Node v=bfs_queue.front();
alpar@726: 	bfs_queue.pop();
alpar@726: 	int l=level[v]+1;
alpar@726: 
alpar@726: 	InEdgeIt e;
alpar@726: 	for(g->first(e,v); g->valid(e); g->next(e)) {
alpar@726: 	  if ( (*capacity)[e] <= (*flow)[e] ) continue;
alpar@726: 	  Node u=g->tail(e);
alpar@726: 	  if ( level[u] >= n ) {
alpar@726: 	    bfs_queue.push(u);
alpar@726: 	    level.set(u, l);
alpar@726: 	    if ( excess[u] > 0 ) {
alpar@726: 	      next.set(u,first[l]);
alpar@726: 	      first[l]=u;
alpar@726: 	    }
alpar@726: 	  }
alpar@726: 	}
alpar@726: 
alpar@726: 	OutEdgeIt f;
alpar@726: 	for(g->first(f,v); g->valid(f); g->next(f)) {
alpar@726: 	  if ( 0 >= (*flow)[f] ) continue;
alpar@726: 	  Node u=g->head(f);
alpar@726: 	  if ( level[u] >= n ) {
alpar@726: 	    bfs_queue.push(u);
alpar@726: 	    level.set(u, l);
alpar@726: 	    if ( excess[u] > 0 ) {
alpar@726: 	      next.set(u,first[l]);
alpar@726: 	      first[l]=u;
alpar@726: 	    }
alpar@726: 	  }
alpar@726: 	}
alpar@726:       }
alpar@726:       b=n-2;
alpar@726: 
alpar@726:       while ( true ) {
alpar@726: 
alpar@726: 	if ( b == 0 ) break;
alpar@726: 
marci@745: 	if ( !g->valid(first[b]) ) --b;
alpar@726: 	else {
alpar@726: 
alpar@726: 	  Node w=first[b];
alpar@726: 	  first[b]=next[w];
alpar@726: 	  int newlevel=push(w,next, first/*active*/);
alpar@726: 
alpar@726: 	  //relabel
alpar@726: 	  if ( excess[w] > 0 ) {
alpar@726: 	    level.set(w,++newlevel);
alpar@726: 	    next.set(w,first[newlevel]);
alpar@726: 	    first[newlevel]=w;
alpar@726: 	    b=newlevel;
alpar@726: 	  }
jacint@749: 	} 
alpar@726:       } // while(true)
alpar@726: 
alpar@726:       status=AFTER_PRE_FLOW_PHASE_2;
alpar@726:     }
alpar@726: 
alpar@726: 
alpar@726:     /// Returns the maximum value of a flow.
alpar@726: 
alpar@726:     /// Returns the maximum value of a flow, by counting the 
alpar@726:     /// over-flow of the target node \ref t.
alpar@726:     /// It can be called already after running \ref preflowPhase1.
alpar@726:     Num flowValue() const {
alpar@726:       Num a=0;
alpar@735:       for(InEdgeIt e(*g,t);g->valid(e);g->next(e)) a+=(*flow)[e];
alpar@735:       for(OutEdgeIt e(*g,t);g->valid(e);g->next(e)) a-=(*flow)[e];
marci@745:       return a;
alpar@726:       //marci figyu: excess[t] epp ezt adja preflow 1. fazisa utan   
alpar@726:     }
jacint@749: 
alpar@726: 
alpar@726:     ///Returns a minimum value cut after calling \ref preflowPhase1.
alpar@726: 
alpar@726:     ///After the first phase of the preflow algorithm the maximum flow
alpar@726:     ///value and a minimum value cut can already be computed. This
alpar@726:     ///method can be called after running \ref preflowPhase1 for
alpar@726:     ///obtaining a minimum value cut.
alpar@726:     /// \warning Gives proper result only right after calling \ref
alpar@726:     /// preflowPhase1.
alpar@726:     /// \todo We have to make some status variable which shows the
alpar@726:     /// actual state
alpar@726:     /// of the class. This enables us to determine which methods are valid
alpar@726:     /// for MinCut computation
alpar@726:     template<typename _CutMap>
alpar@726:     void actMinCut(_CutMap& M) const {
alpar@726:       NodeIt v;
alpar@726:       switch (status) {
alpar@726:       case AFTER_PRE_FLOW_PHASE_1:
alpar@726: 	for(g->first(v); g->valid(v); g->next(v)) {
alpar@726: 	  if (level[v] < n) {
alpar@726: 	    M.set(v, false);
alpar@726: 	  } else {
alpar@726: 	    M.set(v, true);
alpar@726: 	  }
alpar@726: 	}
alpar@726: 	break;
alpar@726:       case AFTER_PRE_FLOW_PHASE_2:
alpar@726:       case AFTER_NOTHING:
marci@745:       case AFTER_AUGMENTING:
marci@745:       case AFTER_FAST_AUGMENTING:
alpar@726: 	minMinCut(M);
alpar@726: 	break;
alpar@726:       }
alpar@726:     }
alpar@726: 
alpar@726:     ///Returns the inclusionwise minimum of the minimum value cuts.
alpar@726: 
alpar@726:     ///Sets \c M to the characteristic vector of the minimum value cut
alpar@726:     ///which is inclusionwise minimum. It is computed by processing
alpar@726:     ///a bfs from the source node \c s in the residual graph.
alpar@726:     ///\pre M should be a node map of bools initialized to false.
alpar@726:     ///\pre \c flow must be a maximum flow.
alpar@726:     template<typename _CutMap>
alpar@726:     void minMinCut(_CutMap& M) const {
alpar@726:       std::queue<Node> queue;
alpar@726: 
alpar@726:       M.set(s,true);
alpar@726:       queue.push(s);
alpar@726: 
alpar@726:       while (!queue.empty()) {
alpar@726:         Node w=queue.front();
alpar@726: 	queue.pop();
alpar@726: 
alpar@726: 	OutEdgeIt e;
alpar@726: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
alpar@726: 	  Node v=g->head(e);
alpar@726: 	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
alpar@726: 	    queue.push(v);
alpar@726: 	    M.set(v, true);
alpar@726: 	  }
alpar@726: 	}
alpar@726: 
alpar@726: 	InEdgeIt f;
alpar@726: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
alpar@726: 	  Node v=g->tail(f);
alpar@726: 	  if (!M[v] && (*flow)[f] > 0 ) {
alpar@726: 	    queue.push(v);
alpar@726: 	    M.set(v, true);
alpar@726: 	  }
alpar@726: 	}
alpar@726:       }
alpar@726:     }
alpar@726: 
alpar@726:     ///Returns the inclusionwise maximum of the minimum value cuts.
alpar@726: 
alpar@726:     ///Sets \c M to the characteristic vector of the minimum value cut
alpar@726:     ///which is inclusionwise maximum. It is computed by processing a
alpar@726:     ///backward bfs from the target node \c t in the residual graph.
alpar@726:     ///\pre M should be a node map of bools initialized to false.
alpar@726:     ///\pre \c flow must be a maximum flow. 
alpar@726:     template<typename _CutMap>
alpar@726:     void maxMinCut(_CutMap& M) const {
alpar@726: 
alpar@726:       NodeIt v;
alpar@726:       for(g->first(v) ; g->valid(v); g->next(v)) {
alpar@726: 	M.set(v, true);
alpar@726:       }
alpar@726: 
alpar@726:       std::queue<Node> queue;
alpar@726: 
alpar@726:       M.set(t,false);
alpar@726:       queue.push(t);
alpar@726: 
alpar@726:       while (!queue.empty()) {
alpar@726:         Node w=queue.front();
alpar@726: 	queue.pop();
alpar@726: 
alpar@726: 	InEdgeIt e;
alpar@726: 	for(g->first(e,w) ; g->valid(e); g->next(e)) {
alpar@726: 	  Node v=g->tail(e);
alpar@726: 	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
alpar@726: 	    queue.push(v);
alpar@726: 	    M.set(v, false);
alpar@726: 	  }
alpar@726: 	}
alpar@726: 
alpar@726: 	OutEdgeIt f;
alpar@726: 	for(g->first(f,w) ; g->valid(f); g->next(f)) {
alpar@726: 	  Node v=g->head(f);
alpar@726: 	  if (M[v] && (*flow)[f] > 0 ) {
alpar@726: 	    queue.push(v);
alpar@726: 	    M.set(v, false);
alpar@726: 	  }
alpar@726: 	}
alpar@726:       }
alpar@726:     }
alpar@726: 
alpar@726:     ///Returns a minimum value cut.
alpar@726: 
alpar@726:     ///Sets \c M to the characteristic vector of a minimum value cut.
alpar@726:     ///\pre M should be a node map of bools initialized to false.
alpar@726:     ///\pre \c flow must be a maximum flow.    
alpar@726:     template<typename CutMap>
alpar@726:     void minCut(CutMap& M) const { minMinCut(M); }
alpar@726: 
alpar@726:     ///Resets the source node to \c _s.
alpar@726: 
alpar@726:     ///Resets the source node to \c _s.
alpar@726:     /// 
alpar@726:     void resetSource(Node _s) { s=_s; status=AFTER_NOTHING; }
alpar@726: 
alpar@726:     ///Resets the target node to \c _t.
alpar@726: 
alpar@726:     ///Resets the target node to \c _t.
alpar@726:     ///
alpar@726:     void resetTarget(Node _t) { t=_t; status=AFTER_NOTHING; }
alpar@726: 
alpar@726:     /// Resets the edge map of the capacities to _cap.
alpar@726: 
alpar@726:     /// Resets the edge map of the capacities to _cap.
alpar@726:     /// 
alpar@726:     void resetCap(const CapMap& _cap)
alpar@726:     { capacity=&_cap; status=AFTER_NOTHING; }
alpar@726: 
alpar@726:     /// Resets the edge map of the flows to _flow.
alpar@726: 
alpar@726:     /// Resets the edge map of the flows to _flow.
alpar@726:     /// 
alpar@726:     void resetFlow(FlowMap& _flow) { flow=&_flow; status=AFTER_NOTHING; }
alpar@726: 
alpar@726: 
alpar@726:   private:
alpar@726: 
alpar@726:     int push(Node w, NNMap& next, VecFirst& first) {
alpar@726: 
alpar@726:       int lev=level[w];
alpar@726:       Num exc=excess[w];
alpar@726:       int newlevel=n;       //bound on the next level of w
alpar@726: 
alpar@726:       OutEdgeIt e;
alpar@726:       for(g->first(e,w); g->valid(e); g->next(e)) {
alpar@726: 
alpar@726: 	if ( (*flow)[e] >= (*capacity)[e] ) continue;
alpar@726: 	Node v=g->head(e);
alpar@726: 
alpar@726: 	if( lev > level[v] ) { //Push is allowed now
alpar@726: 
alpar@726: 	  if ( excess[v]<=0 && v!=t && v!=s ) {
alpar@726: 	    next.set(v,first[level[v]]);
alpar@726: 	    first[level[v]]=v;
alpar@726: 	  }
alpar@726: 
alpar@726: 	  Num cap=(*capacity)[e];
alpar@726: 	  Num flo=(*flow)[e];
alpar@726: 	  Num remcap=cap-flo;
alpar@726: 
alpar@726: 	  if ( remcap >= exc ) { //A nonsaturating push.
alpar@726: 
alpar@726: 	    flow->set(e, flo+exc);
alpar@726: 	    excess.set(v, excess[v]+exc);
alpar@726: 	    exc=0;
alpar@726: 	    break;
alpar@726: 
alpar@726: 	  } else { //A saturating push.
alpar@726: 	    flow->set(e, cap);
alpar@726: 	    excess.set(v, excess[v]+remcap);
alpar@726: 	    exc-=remcap;
alpar@726: 	  }
alpar@726: 	} else if ( newlevel > level[v] ) newlevel = level[v];
alpar@726:       } //for out edges wv
alpar@726: 
alpar@726:       if ( exc > 0 ) {
alpar@726: 	InEdgeIt e;
alpar@726: 	for(g->first(e,w); g->valid(e); g->next(e)) {
alpar@726: 
alpar@726: 	  if( (*flow)[e] <= 0 ) continue;
alpar@726: 	  Node v=g->tail(e);
alpar@726: 
alpar@726: 	  if( lev > level[v] ) { //Push is allowed now
alpar@726: 
alpar@726: 	    if ( excess[v]<=0 && v!=t && v!=s ) {
alpar@726: 	      next.set(v,first[level[v]]);
alpar@726: 	      first[level[v]]=v;
alpar@726: 	    }
alpar@726: 
alpar@726: 	    Num flo=(*flow)[e];
alpar@726: 
alpar@726: 	    if ( flo >= exc ) { //A nonsaturating push.
alpar@726: 
alpar@726: 	      flow->set(e, flo-exc);
alpar@726: 	      excess.set(v, excess[v]+exc);
alpar@726: 	      exc=0;
alpar@726: 	      break;
alpar@726: 	    } else {  //A saturating push.
alpar@726: 
alpar@726: 	      excess.set(v, excess[v]+flo);
alpar@726: 	      exc-=flo;
alpar@726: 	      flow->set(e,0);
alpar@726: 	    }
alpar@726: 	  } else if ( newlevel > level[v] ) newlevel = level[v];
alpar@726: 	} //for in edges vw
alpar@726: 
alpar@726:       } // if w still has excess after the out edge for cycle
alpar@726: 
alpar@726:       excess.set(w, exc);
alpar@726: 
alpar@726:       return newlevel;
alpar@726:     }
alpar@726: 
alpar@726: 
jacint@749: 
alpar@726:     void preflowPreproc(FlowEnum fe, NNMap& next, VecFirst& first,
alpar@726: 			VecNode& level_list, NNMap& left, NNMap& right)
alpar@726:     {
jacint@749:       switch (fe) { //setting excess
jacint@749: 	case NO_FLOW: 
jacint@749: 	{
jacint@749: 	  EdgeIt e;
jacint@749: 	  for(g->first(e); g->valid(e); g->next(e)) flow->set(e,0);
jacint@749: 	  
jacint@749: 	  NodeIt v;
jacint@749: 	  for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
jacint@749: 	  break;
jacint@749: 	}
jacint@749: 	case ZERO_FLOW: 
jacint@749: 	{
jacint@749: 	  NodeIt v;
jacint@749: 	  for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
jacint@749: 	  break;
jacint@749: 	}
jacint@749: 	case GEN_FLOW:
jacint@749: 	{
jacint@749: 	  NodeIt v;
jacint@749: 	  for(g->first(v); g->valid(v); g->next(v)) excess.set(v,0);
jacint@749: 
jacint@749: 	  Num exc=0;
jacint@749: 	  InEdgeIt e;
jacint@749: 	  for(g->first(e,t); g->valid(e); g->next(e)) exc+=(*flow)[e];
jacint@749: 	  OutEdgeIt f;
jacint@749: 	  for(g->first(f,t); g->valid(f); g->next(f)) exc-=(*flow)[f];
jacint@749: 	  excess.set(t,exc);
jacint@749: 	  break;
jacint@749: 	}
jacint@749: 	default: break;
jacint@749:       }
jacint@749: 
jacint@749:       NodeIt v;
jacint@749:       for(g->first(v); g->valid(v); g->next(v)) level.set(v,n);
jacint@749:       //setting each node to level n
jacint@749:       
alpar@726:       std::queue<Node> bfs_queue;
alpar@726: 
jacint@749: 
alpar@726:       switch (fe) {
jacint@749:       case NO_FLOW:   //flow is already set to const zero
alpar@726:       case ZERO_FLOW:
alpar@726: 	{
alpar@726: 	  //Reverse_bfs from t, to find the starting level.
alpar@726: 	  level.set(t,0);
alpar@726: 	  bfs_queue.push(t);
alpar@726: 
alpar@726: 	  while (!bfs_queue.empty()) {
alpar@726: 
alpar@726: 	    Node v=bfs_queue.front();
alpar@726: 	    bfs_queue.pop();
alpar@726: 	    int l=level[v]+1;
alpar@726: 
alpar@726: 	    InEdgeIt e;
alpar@726: 	    for(g->first(e,v); g->valid(e); g->next(e)) {
alpar@726: 	      Node w=g->tail(e);
alpar@726: 	      if ( level[w] == n && w != s ) {
alpar@726: 		bfs_queue.push(w);
alpar@726: 		Node z=level_list[l];
alpar@726: 		if ( g->valid(z) ) left.set(z,w);
alpar@726: 		right.set(w,z);
alpar@726: 		level_list[l]=w;
alpar@726: 		level.set(w, l);
alpar@726: 	      }
alpar@726: 	    }
alpar@726: 	  }
alpar@726: 
alpar@726: 	  //the starting flow
alpar@726: 	  OutEdgeIt e;
alpar@726: 	  for(g->first(e,s); g->valid(e); g->next(e))
alpar@726: 	    {
alpar@726: 	      Num c=(*capacity)[e];
alpar@726: 	      if ( c <= 0 ) continue;
alpar@726: 	      Node w=g->head(e);
alpar@726: 	      if ( level[w] < n ) {
jacint@749: 		if ( excess[w] <= 0 && w!=t ) //putting into the stack
jacint@749: 		  { 
alpar@726: 		    next.set(w,first[level[w]]);
alpar@726: 		    first[level[w]]=w;
alpar@726: 		  }
alpar@726: 		flow->set(e, c);
alpar@726: 		excess.set(w, excess[w]+c);
alpar@726: 	      }
alpar@726: 	    }
alpar@726: 	  break;
alpar@726: 	}
alpar@726: 
alpar@726:       case GEN_FLOW:
jacint@749: 	{
jacint@749: 	  //Reverse_bfs from t in the residual graph,
jacint@749: 	  //to find the starting level.
jacint@749: 	  level.set(t,0);
jacint@749: 	  bfs_queue.push(t);
jacint@749: 
jacint@749: 	  while (!bfs_queue.empty()) {
jacint@749: 
jacint@749: 	    Node v=bfs_queue.front();
jacint@749: 	    bfs_queue.pop();
jacint@749: 	    int l=level[v]+1;
jacint@749: 
jacint@749: 	    InEdgeIt e;
jacint@749: 	    for(g->first(e,v); g->valid(e); g->next(e)) {
jacint@749: 	      if ( (*capacity)[e] <= (*flow)[e] ) continue;
jacint@749: 	      Node w=g->tail(e);
jacint@749: 	      if ( level[w] == n && w != s ) {
jacint@749: 		bfs_queue.push(w);
jacint@749: 		Node z=level_list[l];
jacint@749: 		if ( g->valid(z) ) left.set(z,w);
jacint@749: 		right.set(w,z);
jacint@749: 		level_list[l]=w;
jacint@749: 		level.set(w, l);
jacint@749: 	      }
jacint@749: 	    }
jacint@749: 
jacint@749: 	    OutEdgeIt f;
jacint@749: 	    for(g->first(f,v); g->valid(f); g->next(f)) {
jacint@749: 	      if ( 0 >= (*flow)[f] ) continue;
jacint@749: 	      Node w=g->head(f);
jacint@749: 	      if ( level[w] == n && w != s ) {
jacint@749: 		bfs_queue.push(w);
jacint@749: 		Node z=level_list[l];
jacint@749: 		if ( g->valid(z) ) left.set(z,w);
jacint@749: 		right.set(w,z);
jacint@749: 		level_list[l]=w;
jacint@749: 		level.set(w, l);
jacint@749: 	      }
jacint@749: 	    }
jacint@749: 	  }
jacint@749: 
jacint@749: 	  //the starting flow
jacint@749: 	  OutEdgeIt e;
jacint@749: 	  for(g->first(e,s); g->valid(e); g->next(e))
jacint@749: 	    {
jacint@749: 	      Num rem=(*capacity)[e]-(*flow)[e];
jacint@749: 	      if ( rem <= 0 ) continue;
jacint@749: 	      Node w=g->head(e);
jacint@749: 	      if ( level[w] < n ) {
jacint@749: 		if ( excess[w] <= 0 && w!=t ) //putting into the stack
jacint@749: 		  {
jacint@749: 		    next.set(w,first[level[w]]);
jacint@749: 		    first[level[w]]=w;
jacint@749: 		  }   
jacint@749: 		flow->set(e, (*capacity)[e]);
jacint@749: 		excess.set(w, excess[w]+rem);
jacint@749: 	      }
jacint@749: 	    }
jacint@749: 
jacint@749: 	  InEdgeIt f;
jacint@749: 	  for(g->first(f,s); g->valid(f); g->next(f))
jacint@749: 	    {
jacint@749: 	      if ( (*flow)[f] <= 0 ) continue;
jacint@749: 	      Node w=g->tail(f);
jacint@749: 	      if ( level[w] < n ) {
jacint@749: 		if ( excess[w] <= 0 && w!=t )
jacint@749: 		  {
jacint@749: 		    next.set(w,first[level[w]]);
jacint@749: 		    first[level[w]]=w;
jacint@749: 		  }  
jacint@749: 		excess.set(w, excess[w]+(*flow)[f]);
jacint@749: 		flow->set(f, 0);
jacint@749: 	      }
jacint@749: 	    }
jacint@749: 	  break;
jacint@749: 	} //case GEN_FLOW
jacint@749:     
alpar@726:       case PRE_FLOW:
alpar@726: 	{
alpar@726: 	  //Reverse_bfs from t in the residual graph,
alpar@726: 	  //to find the starting level.
alpar@726: 	  level.set(t,0);
alpar@726: 	  bfs_queue.push(t);
alpar@726: 
alpar@726: 	  while (!bfs_queue.empty()) {
alpar@726: 
alpar@726: 	    Node v=bfs_queue.front();
alpar@726: 	    bfs_queue.pop();
alpar@726: 	    int l=level[v]+1;
alpar@726: 
alpar@726: 	    InEdgeIt e;
alpar@726: 	    for(g->first(e,v); g->valid(e); g->next(e)) {
alpar@726: 	      if ( (*capacity)[e] <= (*flow)[e] ) continue;
alpar@726: 	      Node w=g->tail(e);
alpar@726: 	      if ( level[w] == n && w != s ) {
alpar@726: 		bfs_queue.push(w);
alpar@726: 		Node z=level_list[l];
alpar@726: 		if ( g->valid(z) ) left.set(z,w);
alpar@726: 		right.set(w,z);
alpar@726: 		level_list[l]=w;
alpar@726: 		level.set(w, l);
alpar@726: 	      }
alpar@726: 	    }
alpar@726: 
alpar@726: 	    OutEdgeIt f;
alpar@726: 	    for(g->first(f,v); g->valid(f); g->next(f)) {
alpar@726: 	      if ( 0 >= (*flow)[f] ) continue;
alpar@726: 	      Node w=g->head(f);
alpar@726: 	      if ( level[w] == n && w != s ) {
alpar@726: 		bfs_queue.push(w);
alpar@726: 		Node z=level_list[l];
alpar@726: 		if ( g->valid(z) ) left.set(z,w);
alpar@726: 		right.set(w,z);
alpar@726: 		level_list[l]=w;
alpar@726: 		level.set(w, l);
alpar@726: 	      }
alpar@726: 	    }
alpar@726: 	  }
alpar@726: 
alpar@726: 
alpar@726: 	  //the starting flow
alpar@726: 	  OutEdgeIt e;
alpar@726: 	  for(g->first(e,s); g->valid(e); g->next(e))
alpar@726: 	    {
alpar@726: 	      Num rem=(*capacity)[e]-(*flow)[e];
alpar@726: 	      if ( rem <= 0 ) continue;
alpar@726: 	      Node w=g->head(e);
alpar@726: 	      if ( level[w] < n ) {
alpar@726: 		flow->set(e, (*capacity)[e]);
alpar@726: 		excess.set(w, excess[w]+rem);
alpar@726: 	      }
alpar@726: 	    }
alpar@726: 
alpar@726: 	  InEdgeIt f;
alpar@726: 	  for(g->first(f,s); g->valid(f); g->next(f))
alpar@726: 	    {
alpar@726: 	      if ( (*flow)[f] <= 0 ) continue;
alpar@726: 	      Node w=g->tail(f);
alpar@726: 	      if ( level[w] < n ) {
alpar@726: 		excess.set(w, excess[w]+(*flow)[f]);
alpar@726: 		flow->set(f, 0);
alpar@726: 	      }
alpar@726: 	    }
jacint@749: 	  
jacint@749: 	  NodeIt w; //computing the excess
jacint@749: 	  for(g->first(w); g->valid(w); g->next(w)) {
jacint@749: 	    Num exc=0;
jacint@749: 
jacint@749: 	    InEdgeIt e;
jacint@749: 	    for(g->first(e,w); g->valid(e); g->next(e)) exc+=(*flow)[e];
jacint@749: 	    OutEdgeIt f;
jacint@749: 	    for(g->first(f,w); g->valid(f); g->next(f)) exc-=(*flow)[f];
jacint@749: 
jacint@749: 	    excess.set(w,exc);
jacint@749: 
jacint@749: 	    //putting the active nodes into the stack
jacint@749: 	    int lev=level[w];
jacint@749: 	    if ( exc > 0 && lev < n && w != t ) 
jacint@749: 	      {
jacint@749: 		next.set(w,first[lev]);
jacint@749: 		first[lev]=w;
jacint@749: 	      }
jacint@749: 	  }
alpar@726: 	  break;
alpar@726: 	} //case PRE_FLOW
alpar@726:       }
alpar@726:     } //preflowPreproc
alpar@726: 
alpar@726: 
alpar@726:     void relabel(Node w, int newlevel, NNMap& next, VecFirst& first,
alpar@726: 		 VecNode& level_list, NNMap& left,
alpar@726: 		 NNMap& right, int& b, int& k, bool what_heur )
alpar@726:     {
alpar@726: 
alpar@726:       Num lev=level[w];
alpar@726: 
alpar@726:       Node right_n=right[w];
alpar@726:       Node left_n=left[w];
alpar@726: 
alpar@726:       //unlacing starts
alpar@726:       if ( g->valid(right_n) ) {
alpar@726: 	if ( g->valid(left_n) ) {
alpar@726: 	  right.set(left_n, right_n);
alpar@726: 	  left.set(right_n, left_n);
alpar@726: 	} else {
alpar@726: 	  level_list[lev]=right_n;
alpar@726: 	  left.set(right_n, INVALID);
alpar@726: 	}
alpar@726:       } else {
alpar@726: 	if ( g->valid(left_n) ) {
alpar@726: 	  right.set(left_n, INVALID);
alpar@726: 	} else {
alpar@726: 	  level_list[lev]=INVALID;
alpar@726: 	}
alpar@726:       }
alpar@726:       //unlacing ends
alpar@726: 
alpar@726:       if ( !g->valid(level_list[lev]) ) {
alpar@726: 
alpar@726: 	//gapping starts
alpar@726: 	for (int i=lev; i!=k ; ) {
alpar@726: 	  Node v=level_list[++i];
alpar@726: 	  while ( g->valid(v) ) {
alpar@726: 	    level.set(v,n);
alpar@726: 	    v=right[v];
alpar@726: 	  }
alpar@726: 	  level_list[i]=INVALID;
alpar@726: 	  if ( !what_heur ) first[i]=INVALID;
alpar@726: 	}
alpar@726: 
alpar@726: 	level.set(w,n);
alpar@726: 	b=lev-1;
alpar@726: 	k=b;
alpar@726: 	//gapping ends
alpar@726: 
alpar@726:       } else {
alpar@726: 
alpar@726: 	if ( newlevel == n ) level.set(w,n);
alpar@726: 	else {
alpar@726: 	  level.set(w,++newlevel);
alpar@726: 	  next.set(w,first[newlevel]);
alpar@726: 	  first[newlevel]=w;
alpar@726: 	  if ( what_heur ) b=newlevel;
alpar@726: 	  if ( k < newlevel ) ++k;      //now k=newlevel
alpar@726: 	  Node z=level_list[newlevel];
alpar@726: 	  if ( g->valid(z) ) left.set(z,w);
alpar@726: 	  right.set(w,z);
alpar@726: 	  left.set(w,INVALID);
alpar@726: 	  level_list[newlevel]=w;
alpar@726: 	}
alpar@726:       }
alpar@726:     } //relabel
jacint@749: 
jacint@749:     void printexcess() {////
jacint@749:       std::cout << "Excesses:" <<std::endl;
jacint@749: 
jacint@749:       NodeIt v;
jacint@749:       for(g->first(v); g->valid(v); g->next(v)) {
jacint@749: 	std::cout << 1+(g->id(v)) << ":" << excess[v]<<std::endl; 
jacint@749:       }
jacint@749:     }
jacint@749: 
jacint@749:  void printlevel() {////
jacint@749:       std::cout << "Levels:" <<std::endl;
jacint@749: 
jacint@749:       NodeIt v;
jacint@749:       for(g->first(v); g->valid(v); g->next(v)) {
jacint@749: 	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
jacint@749:       }
jacint@749:     }
jacint@749: 
jacint@749: void printactive() {////
jacint@749:       std::cout << "Levels:" <<std::endl;
jacint@749: 
jacint@749:       NodeIt v;
jacint@749:       for(g->first(v); g->valid(v); g->next(v)) {
jacint@749: 	std::cout << 1+(g->id(v)) << ":" << level[v]<<std::endl; 
jacint@749:       }
jacint@749:     }
jacint@749: 
jacint@749: 
alpar@726:   };  //class MaxFlow
alpar@726: } //namespace hugo
alpar@726: 
alpar@726: #endif //HUGO_MAX_FLOW_H
alpar@726: 
alpar@726: 
alpar@726: 
alpar@726: