jacint@836: // -*- C++ -*-
jacint@836: #ifndef HUGO_PREFLOW_H
jacint@836: #define HUGO_PREFLOW_H
jacint@836: 
jacint@836: #include <vector>
jacint@836: #include <queue>
jacint@836: 
jacint@836: #include <hugo/invalid.h>
jacint@836: #include <hugo/maps.h>
jacint@836: 
jacint@836: /// \file
jacint@836: /// \ingroup flowalgs
jacint@836: 
jacint@836: namespace hugo {
jacint@836: 
jacint@836:   /// \addtogroup flowalgs
jacint@836:   /// @{                                                   
jacint@836: 
alpar@851:   ///%Preflow algorithms class.
jacint@836: 
jacint@836:   ///This class provides an implementation of the \e preflow \e
jacint@836:   ///algorithm producing a flow of maximum value in a directed
jacint@836:   ///graph. The preflow algorithms are the fastest max flow algorithms
alpar@851:   ///up to now. The \e source node, the \e target node, the \e
jacint@836:   ///capacity of the edges and the \e starting \e flow value of the
jacint@836:   ///edges should be passed to the algorithm through the
jacint@836:   ///constructor. It is possible to change these quantities using the
jacint@836:   ///functions \ref setSource, \ref setTarget, \ref setCap and \ref
jacint@836:   ///setFlow.
jacint@836:   ///
alpar@851:   ///After running \ref phase1() or \ref preflow(), the actual flow
jacint@836:   ///value can be obtained by calling \ref flowValue(). The minimum
alpar@851:   ///value cut can be written into a <tt>bool</tt> node map by
alpar@851:   ///calling \ref minCut(). (\ref minMinCut() and \ref maxMinCut() writes
jacint@836:   ///the inclusionwise minimum and maximum of the minimum value cuts,
jacint@836:   ///resp.)
jacint@836:   ///
jacint@836:   ///\param Graph The directed graph type the algorithm runs on.
jacint@836:   ///\param Num The number type of the capacities and the flow values.
jacint@836:   ///\param CapMap The capacity map type.
jacint@836:   ///\param FlowMap The flow map type.
jacint@836:   ///
jacint@836:   ///\author Jacint Szabo 
jacint@836:   template <typename Graph, typename Num,
jacint@836: 	    typename CapMap=typename Graph::template EdgeMap<Num>,
jacint@836:             typename FlowMap=typename Graph::template EdgeMap<Num> >
jacint@836:   class Preflow {
jacint@836:   protected:
jacint@836:     typedef typename Graph::Node Node;
jacint@836:     typedef typename Graph::NodeIt NodeIt;
jacint@836:     typedef typename Graph::EdgeIt EdgeIt;
jacint@836:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@836:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@836: 
jacint@836:     typedef typename Graph::template NodeMap<Node> NNMap;
jacint@836:     typedef typename std::vector<Node> VecNode;
jacint@836: 
jacint@836:     const Graph* g;
jacint@836:     Node s;
jacint@836:     Node t;
jacint@836:     const CapMap* capacity;
jacint@836:     FlowMap* flow;
jacint@836:     int n;      //the number of nodes of G
jacint@836:     
jacint@836:     typename Graph::template NodeMap<int> level;  
jacint@836:     typename Graph::template NodeMap<Num> excess;
jacint@836: 
jacint@836:     // constants used for heuristics
jacint@836:     static const int H0=20;
jacint@836:     static const int H1=1;
jacint@836: 
jacint@836:     public:
jacint@836: 
jacint@836:     ///Indicates the property of the starting flow map.
jacint@836: 
jacint@836:     ///Indicates the property of the starting flow map. The meanings are as follows:
jacint@836:     ///- \c ZERO_FLOW: constant zero flow
jacint@836:     ///- \c GEN_FLOW: any flow, i.e. the sum of the in-flows equals to
jacint@836:     ///the sum of the out-flows in every node except the \e source and
jacint@836:     ///the \e target.
jacint@836:     ///- \c PRE_FLOW: any preflow, i.e. the sum of the in-flows is at 
jacint@836:     ///least the sum of the out-flows in every node except the \e source.
jacint@836:     ///- \c NO_FLOW: indicates an unspecified edge map. \ref flow will be 
jacint@836:     ///set to the constant zero flow in the beginning of the algorithm in this case.
jacint@836:     ///
jacint@836:     enum FlowEnum{
jacint@836:       NO_FLOW,
jacint@836:       ZERO_FLOW,
jacint@836:       GEN_FLOW,
jacint@836:       PRE_FLOW
jacint@836:     };
jacint@836: 
jacint@836:     ///Indicates the state of the preflow algorithm.
jacint@836: 
jacint@836:     ///Indicates the state of the preflow algorithm. The meanings are as follows:
jacint@836:     ///- \c AFTER_NOTHING: before running the algorithm or at an unspecified state.
jacint@836:     ///- \c AFTER_PREFLOW_PHASE_1: right after running \c phase1
jacint@836:     ///- \c AFTER_PREFLOW_PHASE_2: after running \ref phase2()
jacint@836:     ///
jacint@836:     enum StatusEnum {
jacint@836:       AFTER_NOTHING,
jacint@836:       AFTER_PREFLOW_PHASE_1,      
jacint@836:       AFTER_PREFLOW_PHASE_2
jacint@836:     };
jacint@836:     
jacint@836:     protected: 
jacint@836:       FlowEnum flow_prop;
jacint@836:     StatusEnum status; // Do not needle this flag only if necessary.
jacint@836:     
jacint@836:   public: 
jacint@836:     ///The constructor of the class.
jacint@836: 
jacint@836:     ///The constructor of the class. 
jacint@836:     ///\param _G The directed graph the algorithm runs on. 
jacint@836:     ///\param _s The source node.
jacint@836:     ///\param _t The target node.
jacint@836:     ///\param _capacity The capacity of the edges. 
jacint@836:     ///\param _flow The flow of the edges. 
jacint@836:     ///Except the graph, all of these parameters can be reset by
jacint@836:     ///calling \ref setSource, \ref setTarget, \ref setCap and \ref
jacint@836:     ///setFlow, resp.
jacint@836:       Preflow(const Graph& _G, Node _s, Node _t, 
jacint@836: 	      const CapMap& _capacity, FlowMap& _flow) :
jacint@836: 	g(&_G), s(_s), t(_t), capacity(&_capacity),
jacint@836: 	flow(&_flow), n(_G.nodeNum()), level(_G), excess(_G,0), 
jacint@836: 	flow_prop(NO_FLOW), status(AFTER_NOTHING) { }
jacint@836: 
jacint@836: 
jacint@836:                                                                               
jacint@836:     ///Runs the preflow algorithm.  
jacint@836: 
alpar@851:     ///Runs the preflow algorithm.
alpar@851:     ///
jacint@836:     void run() {
jacint@836:       phase1(flow_prop);
jacint@836:       phase2();
jacint@836:     }
jacint@836:     
jacint@836:     ///Runs the preflow algorithm.  
jacint@836:     
jacint@836:     ///Runs the preflow algorithm. 
jacint@836:     ///\pre The starting flow map must be
jacint@836:     /// - a constant zero flow if \c fp is \c ZERO_FLOW,
jacint@836:     /// - an arbitrary flow if \c fp is \c GEN_FLOW,
jacint@836:     /// - an arbitrary preflow if \c fp is \c PRE_FLOW,
jacint@836:     /// - any map if \c fp is NO_FLOW.
jacint@836:     ///If the starting flow map is a flow or a preflow then 
jacint@836:     ///the algorithm terminates faster.
jacint@836:     void run(FlowEnum fp) {
jacint@836:       flow_prop=fp;
jacint@836:       run();
jacint@836:     }
jacint@836:       
jacint@836:     ///Runs the first phase of the preflow algorithm.
jacint@836: 
jacint@836:     ///The preflow algorithm consists of two phases, this method runs the
jacint@836:     ///first phase. After the first phase the maximum flow value and a
jacint@836:     ///minimum value cut can already be computed, though a maximum flow
jacint@836:     ///is not yet obtained. So after calling this method \ref flowValue
jacint@836:     ///and \ref minCut gives proper results.
alpar@851:     ///\warning \ref minMinCut and \ref maxMinCut do not
jacint@836:     ///give minimum value cuts unless calling \ref phase2.
jacint@836:     ///\pre The starting flow must be
jacint@836:     /// - a constant zero flow if \c fp is \c ZERO_FLOW,
jacint@836:     /// - an arbitary flow if \c fp is \c GEN_FLOW,
jacint@836:     /// - an arbitary preflow if \c fp is \c PRE_FLOW,
jacint@836:     /// - any map if \c fp is NO_FLOW.
jacint@836:     void phase1(FlowEnum fp)
jacint@836:     {
jacint@836:       flow_prop=fp;
jacint@836:       phase1();
jacint@836:     }
jacint@836: 
jacint@836:     
jacint@836:     ///Runs the first phase of the preflow algorithm.
jacint@836: 
jacint@836:     ///The preflow algorithm consists of two phases, this method runs the
jacint@836:     ///first phase. After the first phase the maximum flow value and a
jacint@836:     ///minimum value cut can already be computed, though a maximum flow
jacint@836:     ///is not yet obtained. So after calling this method \ref flowValue
jacint@836:     ///and \ref actMinCut gives proper results.
alpar@851:     ///\warning \ref minCut, \ref minMinCut and \ref maxMinCut do not
jacint@836:     ///give minimum value cuts unless calling \ref phase2.
jacint@836:     void phase1()
jacint@836:     {
jacint@836:       int heur0=(int)(H0*n);  //time while running 'bound decrease'
jacint@836:       int heur1=(int)(H1*n);  //time while running 'highest label'
jacint@836:       int heur=heur1;         //starting time interval (#of relabels)
jacint@836:       int numrelabel=0;
jacint@836: 
jacint@836:       bool what_heur=1;
jacint@836:       //It is 0 in case 'bound decrease' and 1 in case 'highest label'
jacint@836: 
jacint@836:       bool end=false;
jacint@836:       //Needed for 'bound decrease', true means no active 
jacint@836:       //nodes are above bound b.
jacint@836: 
jacint@836:       int k=n-2;  //bound on the highest level under n containing a node
jacint@836:       int b=k;    //bound on the highest level under n of an active node
jacint@836: 
jacint@836:       VecNode first(n, INVALID);
jacint@836:       NNMap next(*g, INVALID);
jacint@836: 
jacint@836:       NNMap left(*g, INVALID);
jacint@836:       NNMap right(*g, INVALID);
jacint@836:       VecNode level_list(n,INVALID);
jacint@836:       //List of the nodes in level i<n, set to n.
jacint@836: 
jacint@836:       preflowPreproc(first, next, level_list, left, right);
jacint@836: 
jacint@836:       //Push/relabel on the highest level active nodes.
jacint@836:       while ( true ) {
jacint@836: 	if ( b == 0 ) {
jacint@836: 	  if ( !what_heur && !end && k > 0 ) {
jacint@836: 	    b=k;
jacint@836: 	    end=true;
jacint@836: 	  } else break;
jacint@836: 	}
jacint@836: 
jacint@836: 	if ( first[b]==INVALID ) --b;
jacint@836: 	else {
jacint@836: 	  end=false;
jacint@836: 	  Node w=first[b];
jacint@836: 	  first[b]=next[w];
jacint@836: 	  int newlevel=push(w, next, first);
jacint@836: 	  if ( excess[w] > 0 ) relabel(w, newlevel, first, next, level_list, 
jacint@836: 				       left, right, b, k, what_heur);
jacint@836: 
jacint@836: 	  ++numrelabel;
jacint@836: 	  if ( numrelabel >= heur ) {
jacint@836: 	    numrelabel=0;
jacint@836: 	    if ( what_heur ) {
jacint@836: 	      what_heur=0;
jacint@836: 	      heur=heur0;
jacint@836: 	      end=false;
jacint@836: 	    } else {
jacint@836: 	      what_heur=1;
jacint@836: 	      heur=heur1;
jacint@836: 	      b=k;
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	}
jacint@836:       }
jacint@836:       flow_prop=PRE_FLOW;
jacint@836:       status=AFTER_PREFLOW_PHASE_1;
jacint@836:     }
jacint@836:     // Heuristics:
jacint@836:     //   2 phase
jacint@836:     //   gap
jacint@836:     //   list 'level_list' on the nodes on level i implemented by hand
jacint@836:     //   stack 'active' on the active nodes on level i      
jacint@836:     //   runs heuristic 'highest label' for H1*n relabels
jacint@836:     //   runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
jacint@836:     //   Parameters H0 and H1 are initialized to 20 and 1.
jacint@836: 
jacint@836: 
jacint@836:     ///Runs the second phase of the preflow algorithm.
jacint@836: 
jacint@836:     ///The preflow algorithm consists of two phases, this method runs
jacint@836:     ///the second phase. After calling \ref phase1 and then
jacint@836:     ///\ref phase2 the methods \ref flowValue, \ref minCut,
jacint@836:     ///\ref minMinCut and \ref maxMinCut give proper results.
jacint@836:     ///\pre \ref phase1 must be called before.
jacint@836:     void phase2()
jacint@836:     {
jacint@836: 
jacint@836:       int k=n-2;  //bound on the highest level under n containing a node
jacint@836:       int b=k;    //bound on the highest level under n of an active node
jacint@836: 
jacint@836:     
jacint@836:       VecNode first(n, INVALID);
jacint@836:       NNMap next(*g, INVALID); 
jacint@836:       level.set(s,0);
jacint@836:       std::queue<Node> bfs_queue;
jacint@836:       bfs_queue.push(s);
jacint@836: 
jacint@836:       while ( !bfs_queue.empty() ) {
jacint@836: 
jacint@836: 	Node v=bfs_queue.front();
jacint@836: 	bfs_queue.pop();
jacint@836: 	int l=level[v]+1;
jacint@836: 
jacint@836: 	for(InEdgeIt e(*g,v); e!=INVALID; ++e) {
jacint@836: 	  if ( (*capacity)[e] <= (*flow)[e] ) continue;
jacint@836: 	  Node u=g->tail(e);
jacint@836: 	  if ( level[u] >= n ) {
jacint@836: 	    bfs_queue.push(u);
jacint@836: 	    level.set(u, l);
jacint@836: 	    if ( excess[u] > 0 ) {
jacint@836: 	      next.set(u,first[l]);
jacint@836: 	      first[l]=u;
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	}
jacint@836: 
jacint@836: 	for(OutEdgeIt e(*g,v); e!=INVALID; ++e) {
jacint@836: 	  if ( 0 >= (*flow)[e] ) continue;
jacint@836: 	  Node u=g->head(e);
jacint@836: 	  if ( level[u] >= n ) {
jacint@836: 	    bfs_queue.push(u);
jacint@836: 	    level.set(u, l);
jacint@836: 	    if ( excess[u] > 0 ) {
jacint@836: 	      next.set(u,first[l]);
jacint@836: 	      first[l]=u;
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	}
jacint@836:       }
jacint@836:       b=n-2;
jacint@836: 
jacint@836:       while ( true ) {
jacint@836: 
jacint@836: 	if ( b == 0 ) break;
jacint@836: 	if ( first[b]==INVALID ) --b;
jacint@836: 	else {
jacint@836: 	  Node w=first[b];
jacint@836: 	  first[b]=next[w];
jacint@836: 	  int newlevel=push(w,next, first);
jacint@836: 	  
jacint@836: 	  //relabel
jacint@836: 	  if ( excess[w] > 0 ) {
jacint@836: 	    level.set(w,++newlevel);
jacint@836: 	    next.set(w,first[newlevel]);
jacint@836: 	    first[newlevel]=w;
jacint@836: 	    b=newlevel;
jacint@836: 	  }
jacint@836: 	} 
jacint@836:       } // while(true)
jacint@836:       flow_prop=GEN_FLOW;
jacint@836:       status=AFTER_PREFLOW_PHASE_2;
jacint@836:     }
jacint@836: 
jacint@836:     /// Returns the value of the maximum flow.
jacint@836: 
jacint@836:     /// Returns the value of the maximum flow by returning the excess
jacint@836:     /// of the target node \ref t. This value equals to the value of
jacint@836:     /// the maximum flow already after running \ref phase1.
jacint@836:     Num flowValue() const {
jacint@836:       return excess[t];
jacint@836:     }
jacint@836: 
jacint@836: 
jacint@836:     ///Returns a minimum value cut.
jacint@836: 
jacint@836:     ///Sets \c M to the characteristic vector of a minimum value
jacint@836:     ///cut. This method can be called both after running \ref
jacint@836:     ///phase1 and \ref phase2. It is much faster after
marci@849:     ///\ref phase1.  \pre M should be a bool-valued node-map. \pre
jacint@836:     ///If \ref mincut is called after \ref phase2 then M should
jacint@836:     ///be initialized to false.
jacint@836:     template<typename _CutMap>
jacint@836:     void minCut(_CutMap& M) const {
jacint@836:       switch ( status ) {
jacint@836: 	case AFTER_PREFLOW_PHASE_1:
jacint@836: 	for(NodeIt v(*g); v!=INVALID; ++v) {
jacint@836: 	  if (level[v] < n) {
jacint@836: 	    M.set(v, false);
jacint@836: 	  } else {
jacint@836: 	    M.set(v, true);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	break;
jacint@836: 	case AFTER_PREFLOW_PHASE_2:
jacint@836: 	minMinCut(M);
jacint@836: 	break;
jacint@836: 	case AFTER_NOTHING:
jacint@836: 	break;
jacint@836:       }
jacint@836:     }
jacint@836: 
jacint@836:     ///Returns the inclusionwise minimum of the minimum value cuts.
jacint@836: 
jacint@836:     ///Sets \c M to the characteristic vector of the minimum value cut
jacint@836:     ///which is inclusionwise minimum. It is computed by processing a
jacint@836:     ///bfs from the source node \c s in the residual graph.  \pre M
jacint@836:     ///should be a node map of bools initialized to false.  \pre \ref
jacint@836:     ///phase2 should already be run.
jacint@836:     template<typename _CutMap>
jacint@836:     void minMinCut(_CutMap& M) const {
jacint@836: 
jacint@836:       std::queue<Node> queue;
jacint@836:       M.set(s,true);
jacint@836:       queue.push(s);
jacint@836:       
jacint@836:       while (!queue.empty()) {
jacint@836: 	Node w=queue.front();
jacint@836: 	queue.pop();
jacint@836: 	
jacint@836: 	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	  Node v=g->head(e);
jacint@836: 	  if (!M[v] && (*flow)[e] < (*capacity)[e] ) {
jacint@836: 	    queue.push(v);
jacint@836: 	    M.set(v, true);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	
jacint@836: 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	  Node v=g->tail(e);
jacint@836: 	  if (!M[v] && (*flow)[e] > 0 ) {
jacint@836: 	    queue.push(v);
jacint@836: 	    M.set(v, true);
jacint@836: 	  }
jacint@836: 	}
jacint@836:       }
jacint@836:     }
jacint@836:     
jacint@836:     ///Returns the inclusionwise maximum of the minimum value cuts.
jacint@836: 
jacint@836:     ///Sets \c M to the characteristic vector of the minimum value cut
jacint@836:     ///which is inclusionwise maximum. It is computed by processing a
jacint@836:     ///backward bfs from the target node \c t in the residual graph.
jacint@836:     ///\pre \ref phase2() or preflow() should already be run.
jacint@836:     template<typename _CutMap>
jacint@836:     void maxMinCut(_CutMap& M) const {
jacint@836: 
jacint@836:       for(NodeIt v(*g) ; v!=INVALID; ++v) M.set(v, true);
jacint@836: 
jacint@836:       std::queue<Node> queue;
jacint@836: 
jacint@836:       M.set(t,false);
jacint@836:       queue.push(t);
jacint@836: 
jacint@836:       while (!queue.empty()) {
jacint@836:         Node w=queue.front();
jacint@836: 	queue.pop();
jacint@836: 
jacint@836: 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	  Node v=g->tail(e);
jacint@836: 	  if (M[v] && (*flow)[e] < (*capacity)[e] ) {
jacint@836: 	    queue.push(v);
jacint@836: 	    M.set(v, false);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 
jacint@836: 	for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	  Node v=g->head(e);
jacint@836: 	  if (M[v] && (*flow)[e] > 0 ) {
jacint@836: 	    queue.push(v);
jacint@836: 	    M.set(v, false);
jacint@836: 	  }
jacint@836: 	}
jacint@836:       }
jacint@836:     }
jacint@836: 
jacint@836:     ///Sets the source node to \c _s.
jacint@836: 
jacint@836:     ///Sets the source node to \c _s.
jacint@836:     /// 
jacint@836:     void setSource(Node _s) { 
jacint@836:       s=_s; 
jacint@836:       if ( flow_prop != ZERO_FLOW ) flow_prop=NO_FLOW;
jacint@836:       status=AFTER_NOTHING; 
jacint@836:     }
jacint@836: 
jacint@836:     ///Sets the target node to \c _t.
jacint@836: 
jacint@836:     ///Sets the target node to \c _t.
jacint@836:     ///
jacint@836:     void setTarget(Node _t) { 
jacint@836:       t=_t; 
jacint@836:       if ( flow_prop == GEN_FLOW ) flow_prop=PRE_FLOW;
jacint@836:       status=AFTER_NOTHING; 
jacint@836:     }
jacint@836: 
jacint@836:     /// Sets the edge map of the capacities to _cap.
jacint@836: 
jacint@836:     /// Sets the edge map of the capacities to _cap.
jacint@836:     /// 
jacint@836:     void setCap(const CapMap& _cap) { 
jacint@836:       capacity=&_cap; 
jacint@836:       status=AFTER_NOTHING; 
jacint@836:     }
jacint@836: 
jacint@836:     /// Sets the edge map of the flows to _flow.
jacint@836: 
jacint@836:     /// Sets the edge map of the flows to _flow.
jacint@836:     /// 
jacint@836:     void setFlow(FlowMap& _flow) { 
jacint@836:       flow=&_flow; 
jacint@836:       flow_prop=NO_FLOW;
jacint@836:       status=AFTER_NOTHING; 
jacint@836:     }
jacint@836: 
jacint@836: 
jacint@836:   private:
jacint@836: 
jacint@836:     int push(Node w, NNMap& next, VecNode& first) {
jacint@836: 
jacint@836:       int lev=level[w];
jacint@836:       Num exc=excess[w];
jacint@836:       int newlevel=n;       //bound on the next level of w
jacint@836: 
jacint@836:       for(OutEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	if ( (*flow)[e] >= (*capacity)[e] ) continue;
jacint@836: 	Node v=g->head(e);
jacint@836: 
jacint@836: 	if( lev > level[v] ) { //Push is allowed now
jacint@836: 	  
jacint@836: 	  if ( excess[v]<=0 && v!=t && v!=s ) {
jacint@836: 	    next.set(v,first[level[v]]);
jacint@836: 	    first[level[v]]=v;
jacint@836: 	  }
jacint@836: 
jacint@836: 	  Num cap=(*capacity)[e];
jacint@836: 	  Num flo=(*flow)[e];
jacint@836: 	  Num remcap=cap-flo;
jacint@836: 	  
jacint@836: 	  if ( remcap >= exc ) { //A nonsaturating push.
jacint@836: 	    
jacint@836: 	    flow->set(e, flo+exc);
jacint@836: 	    excess.set(v, excess[v]+exc);
jacint@836: 	    exc=0;
jacint@836: 	    break;
jacint@836: 
jacint@836: 	  } else { //A saturating push.
jacint@836: 	    flow->set(e, cap);
jacint@836: 	    excess.set(v, excess[v]+remcap);
jacint@836: 	    exc-=remcap;
jacint@836: 	  }
jacint@836: 	} else if ( newlevel > level[v] ) newlevel = level[v];
jacint@836:       } //for out edges wv
jacint@836: 
jacint@836:       if ( exc > 0 ) {
jacint@836: 	for(InEdgeIt e(*g,w) ; e!=INVALID; ++e) {
jacint@836: 	  
jacint@836: 	  if( (*flow)[e] <= 0 ) continue;
jacint@836: 	  Node v=g->tail(e);
jacint@836: 
jacint@836: 	  if( lev > level[v] ) { //Push is allowed now
jacint@836: 
jacint@836: 	    if ( excess[v]<=0 && v!=t && v!=s ) {
jacint@836: 	      next.set(v,first[level[v]]);
jacint@836: 	      first[level[v]]=v;
jacint@836: 	    }
jacint@836: 
jacint@836: 	    Num flo=(*flow)[e];
jacint@836: 
jacint@836: 	    if ( flo >= exc ) { //A nonsaturating push.
jacint@836: 
jacint@836: 	      flow->set(e, flo-exc);
jacint@836: 	      excess.set(v, excess[v]+exc);
jacint@836: 	      exc=0;
jacint@836: 	      break;
jacint@836: 	    } else {  //A saturating push.
jacint@836: 
jacint@836: 	      excess.set(v, excess[v]+flo);
jacint@836: 	      exc-=flo;
jacint@836: 	      flow->set(e,0);
jacint@836: 	    }
jacint@836: 	  } else if ( newlevel > level[v] ) newlevel = level[v];
jacint@836: 	} //for in edges vw
jacint@836: 
jacint@836:       } // if w still has excess after the out edge for cycle
jacint@836: 
jacint@836:       excess.set(w, exc);
jacint@836:       
jacint@836:       return newlevel;
jacint@836:     }
jacint@836:     
jacint@836:     
jacint@836:     
jacint@836:     void preflowPreproc(VecNode& first, NNMap& next, 
jacint@836: 			VecNode& level_list, NNMap& left, NNMap& right)
jacint@836:     {
jacint@836:       for(NodeIt v(*g); v!=INVALID; ++v) level.set(v,n);
jacint@836:       std::queue<Node> bfs_queue;
jacint@836:       
jacint@836:       if ( flow_prop == GEN_FLOW || flow_prop == PRE_FLOW ) {
jacint@836: 	//Reverse_bfs from t in the residual graph,
jacint@836: 	//to find the starting level.
jacint@836: 	level.set(t,0);
jacint@836: 	bfs_queue.push(t);
jacint@836: 	
jacint@836: 	while ( !bfs_queue.empty() ) {
jacint@836: 	  
jacint@836: 	  Node v=bfs_queue.front();
jacint@836: 	  bfs_queue.pop();
jacint@836: 	  int l=level[v]+1;
jacint@836: 	  
jacint@836: 	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
jacint@836: 	    if ( (*capacity)[e] <= (*flow)[e] ) continue;
jacint@836: 	    Node w=g->tail(e);
jacint@836: 	    if ( level[w] == n && w != s ) {
jacint@836: 	      bfs_queue.push(w);
jacint@836: 	      Node z=level_list[l];
jacint@836: 	      if ( z!=INVALID ) left.set(z,w);
jacint@836: 	      right.set(w,z);
jacint@836: 	      level_list[l]=w;
jacint@836: 	      level.set(w, l);
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	  
jacint@836: 	  for(OutEdgeIt e(*g,v) ; e!=INVALID; ++e) {
jacint@836: 	    if ( 0 >= (*flow)[e] ) continue;
jacint@836: 	    Node w=g->head(e);
jacint@836: 	    if ( level[w] == n && w != s ) {
jacint@836: 	      bfs_queue.push(w);
jacint@836: 	      Node z=level_list[l];
jacint@836: 	      if ( z!=INVALID ) left.set(z,w);
jacint@836: 	      right.set(w,z);
jacint@836: 	      level_list[l]=w;
jacint@836: 	      level.set(w, l);
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	} //while
jacint@836:       } //if
jacint@836: 
jacint@836: 
jacint@836:       switch (flow_prop) {
jacint@836: 	case NO_FLOW:  
jacint@836: 	for(EdgeIt e(*g); e!=INVALID; ++e) flow->set(e,0);
jacint@836: 	case ZERO_FLOW:
jacint@836: 	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
jacint@836: 	
jacint@836: 	//Reverse_bfs from t, to find the starting level.
jacint@836: 	level.set(t,0);
jacint@836: 	bfs_queue.push(t);
jacint@836: 	
jacint@836: 	while ( !bfs_queue.empty() ) {
jacint@836: 	  
jacint@836: 	  Node v=bfs_queue.front();
jacint@836: 	  bfs_queue.pop();
jacint@836: 	  int l=level[v]+1;
jacint@836: 	  
jacint@836: 	  for(InEdgeIt e(*g,v) ; e!=INVALID; ++e) {
jacint@836: 	    Node w=g->tail(e);
jacint@836: 	    if ( level[w] == n && w != s ) {
jacint@836: 	      bfs_queue.push(w);
jacint@836: 	      Node z=level_list[l];
jacint@836: 	      if ( z!=INVALID ) left.set(z,w);
jacint@836: 	      right.set(w,z);
jacint@836: 	      level_list[l]=w;
jacint@836: 	      level.set(w, l);
jacint@836: 	    }
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	
jacint@836: 	//the starting flow
jacint@836: 	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) {
jacint@836: 	  Num c=(*capacity)[e];
jacint@836: 	  if ( c <= 0 ) continue;
jacint@836: 	  Node w=g->head(e);
jacint@836: 	  if ( level[w] < n ) {
jacint@836: 	    if ( excess[w] <= 0 && w!=t ) { //putting into the stack
jacint@836: 	      next.set(w,first[level[w]]);
jacint@836: 	      first[level[w]]=w;
jacint@836: 	    }
jacint@836: 	    flow->set(e, c);
jacint@836: 	    excess.set(w, excess[w]+c);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	break;
jacint@836: 
jacint@836: 	case GEN_FLOW:
jacint@836: 	for(NodeIt v(*g); v!=INVALID; ++v) excess.set(v,0);
jacint@836: 	{
jacint@836: 	  Num exc=0;
jacint@836: 	  for(InEdgeIt e(*g,t) ; e!=INVALID; ++e) exc+=(*flow)[e];
jacint@836: 	  for(OutEdgeIt e(*g,t) ; e!=INVALID; ++e) exc-=(*flow)[e];
jacint@836: 	  excess.set(t,exc);
jacint@836: 	}
jacint@836: 
jacint@836: 	//the starting flow
jacint@836: 	for(OutEdgeIt e(*g,s); e!=INVALID; ++e)	{
jacint@836: 	  Num rem=(*capacity)[e]-(*flow)[e];
jacint@836: 	  if ( rem <= 0 ) continue;
jacint@836: 	  Node w=g->head(e);
jacint@836: 	  if ( level[w] < n ) {
jacint@836: 	    if ( excess[w] <= 0 && w!=t ) { //putting into the stack
jacint@836: 	      next.set(w,first[level[w]]);
jacint@836: 	      first[level[w]]=w;
jacint@836: 	    }   
jacint@836: 	    flow->set(e, (*capacity)[e]);
jacint@836: 	    excess.set(w, excess[w]+rem);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	
jacint@836: 	for(InEdgeIt e(*g,s); e!=INVALID; ++e) {
jacint@836: 	  if ( (*flow)[e] <= 0 ) continue;
jacint@836: 	  Node w=g->tail(e);
jacint@836: 	  if ( level[w] < n ) {
jacint@836: 	    if ( excess[w] <= 0 && w!=t ) {
jacint@836: 	      next.set(w,first[level[w]]);
jacint@836: 	      first[level[w]]=w;
jacint@836: 	    }  
jacint@836: 	    excess.set(w, excess[w]+(*flow)[e]);
jacint@836: 	    flow->set(e, 0);
jacint@836: 	  }
jacint@836: 	}
jacint@836: 	break;
jacint@836: 
jacint@836: 	case PRE_FLOW:	
jacint@836: 	//the starting flow
jacint@836: 	for(OutEdgeIt e(*g,s) ; e!=INVALID; ++e) {
jacint@836: 	  Num rem=(*capacity)[e]-(*flow)[e];
jacint@836: 	  if ( rem <= 0 ) continue;
jacint@836: 	  Node w=g->head(e);
jacint@836: 	  if ( level[w] < n ) flow->set(e, (*capacity)[e]);
jacint@836: 	}
jacint@836: 	
jacint@836: 	for(InEdgeIt e(*g,s) ; e!=INVALID; ++e) {
jacint@836: 	  if ( (*flow)[e] <= 0 ) continue;
jacint@836: 	  Node w=g->tail(e);
jacint@836: 	  if ( level[w] < n ) flow->set(e, 0);
jacint@836: 	}
jacint@836: 	
jacint@836: 	//computing the excess
jacint@836: 	for(NodeIt w(*g); w!=INVALID; ++w) {
jacint@836: 	  Num exc=0;
jacint@836: 	  for(InEdgeIt e(*g,w); e!=INVALID; ++e) exc+=(*flow)[e];
jacint@836: 	  for(OutEdgeIt e(*g,w); e!=INVALID; ++e) exc-=(*flow)[e];
jacint@836: 	  excess.set(w,exc);
jacint@836: 	  
jacint@836: 	  //putting the active nodes into the stack
jacint@836: 	  int lev=level[w];
jacint@836: 	    if ( exc > 0 && lev < n && Node(w) != t ) {
jacint@836: 	      next.set(w,first[lev]);
jacint@836: 	      first[lev]=w;
jacint@836: 	    }
jacint@836: 	}
jacint@836: 	break;
jacint@836:       } //switch
jacint@836:     } //preflowPreproc
jacint@836: 
jacint@836: 
jacint@836:     void relabel(Node w, int newlevel, VecNode& first, NNMap& next, 
jacint@836: 		 VecNode& level_list, NNMap& left,
jacint@836: 		 NNMap& right, int& b, int& k, bool what_heur )
jacint@836:     {
jacint@836: 
jacint@836:       int lev=level[w];
jacint@836: 
jacint@836:       Node right_n=right[w];
jacint@836:       Node left_n=left[w];
jacint@836: 
jacint@836:       //unlacing starts
jacint@836:       if ( right_n!=INVALID ) {
jacint@836: 	if ( left_n!=INVALID ) {
jacint@836: 	  right.set(left_n, right_n);
jacint@836: 	  left.set(right_n, left_n);
jacint@836: 	} else {
jacint@836: 	  level_list[lev]=right_n;
jacint@836: 	  left.set(right_n, INVALID);
jacint@836: 	}
jacint@836:       } else {
jacint@836: 	if ( left_n!=INVALID ) {
jacint@836: 	  right.set(left_n, INVALID);
jacint@836: 	} else {
jacint@836: 	  level_list[lev]=INVALID;
jacint@836: 	}
jacint@836:       }
jacint@836:       //unlacing ends
jacint@836: 
jacint@836:       if ( level_list[lev]==INVALID ) {
jacint@836: 
jacint@836: 	//gapping starts
jacint@836: 	for (int i=lev; i!=k ; ) {
jacint@836: 	  Node v=level_list[++i];
jacint@836: 	  while ( v!=INVALID ) {
jacint@836: 	    level.set(v,n);
jacint@836: 	    v=right[v];
jacint@836: 	  }
jacint@836: 	  level_list[i]=INVALID;
jacint@836: 	  if ( !what_heur ) first[i]=INVALID;
jacint@836: 	}
jacint@836: 
jacint@836: 	level.set(w,n);
jacint@836: 	b=lev-1;
jacint@836: 	k=b;
jacint@836: 	//gapping ends
jacint@836: 
jacint@836:       } else {
jacint@836: 
jacint@836: 	if ( newlevel == n ) level.set(w,n);
jacint@836: 	else {
jacint@836: 	  level.set(w,++newlevel);
jacint@836: 	  next.set(w,first[newlevel]);
jacint@836: 	  first[newlevel]=w;
jacint@836: 	  if ( what_heur ) b=newlevel;
jacint@836: 	  if ( k < newlevel ) ++k;      //now k=newlevel
jacint@836: 	  Node z=level_list[newlevel];
jacint@836: 	  if ( z!=INVALID ) left.set(z,w);
jacint@836: 	  right.set(w,z);
jacint@836: 	  left.set(w,INVALID);
jacint@836: 	  level_list[newlevel]=w;
jacint@836: 	}
jacint@836:       }
jacint@836:     } //relabel
jacint@836: 
jacint@836:   }; 
jacint@836: } //namespace hugo
jacint@836: 
jacint@836: #endif //HUGO_PREFLOW_H
jacint@836: 
jacint@836: 
jacint@836: 
jacint@836: