src/work/jacint/preflow_max_flow.h
author jacint
Sat, 21 Feb 2004 21:40:59 +0000
changeset 110 3c53698842dd
permissions -rw-r--r--
leiras
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// -*- C++ -*-
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/*
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preflow_max_flow.h
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by jacint. 
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Runs the first phase of preflow.h
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The constructor runs the algorithm.
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Members:
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T maxFlow() : returns the value of a maximum flow
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CutMap minCut() : returns the characteristic vector of a min cut. 
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*/
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#ifndef PREFLOW_MAX_FLOW_H
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#define PREFLOW_MAX_FLOW_H
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#define H0 20
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#define H1 1
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#include <vector>
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#include <queue>
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namespace hugo {
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  template <typename Graph, typename T, 
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    typename FlowMap=typename Graph::EdgeMap<T>,
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    typename CapMap=typename Graph::EdgeMap<T>, 
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    typename CutMap=typename Graph::NodeMap<bool> >
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  class preflow_max_flow {
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    typedef typename Graph::NodeIt NodeIt;
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    typedef typename Graph::EdgeIt EdgeIt;
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    typedef typename Graph::EachNodeIt EachNodeIt;
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    typedef typename Graph::OutEdgeIt OutEdgeIt;
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    typedef typename Graph::InEdgeIt InEdgeIt;
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    Graph& G;
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    NodeIt s;
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    NodeIt t;
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    FlowMap flow;
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    CapMap& capacity;  
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    CutMap cut;
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    T value;
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  public:
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    preflow_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :
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      G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), cut(_G, false)
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    {
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      int n=G.nodeNum(); 
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      int heur0=(int)(H0*n);  //time while running 'bound decrease' 
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      int heur1=(int)(H1*n);  //time while running 'highest label'
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      int heur=heur1;         //starting time interval (#of relabels)
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      bool what_heur=1;       
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      /*
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	what_heur is 0 in case 'bound decrease' 
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	and 1 in case 'highest label'
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      */
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      bool end=false;     
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      /*
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	Needed for 'bound decrease', 'true'
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	means no active nodes are above bound b.
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      */
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      int relabel=0;
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      int k=n-2;  //bound on the highest level under n containing a node
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      int b=k;    //bound on the highest level under n of an active node
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      typename Graph::NodeMap<int> level(G,n);      
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      typename Graph::NodeMap<T> excess(G); 
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      std::vector<NodeIt> active(n);
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      typename Graph::NodeMap<NodeIt> next(G);
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      //Stack of the active nodes in level i < n.
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      //We use it in both phases.
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      typename Graph::NodeMap<NodeIt> left(G);
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      typename Graph::NodeMap<NodeIt> right(G);
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      std::vector<NodeIt> level_list(n);
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      /*
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	List of the nodes in level i<n.
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      */
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      /*Reverse_bfs from t, to find the starting level.*/
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      level.set(t,0);
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      std::queue<NodeIt> bfs_queue;
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      bfs_queue.push(t);
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      while (!bfs_queue.empty()) {
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	NodeIt v=bfs_queue.front();	
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	bfs_queue.pop();
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	int l=level.get(v)+1;
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	for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
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	  NodeIt w=G.tail(e);
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	  if ( level.get(w) == n && w != s ) {
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	    bfs_queue.push(w);
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	    NodeIt first=level_list[l];
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	    if ( first != 0 ) left.set(first,w);
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	    right.set(w,first);
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	    level_list[l]=w;
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	    level.set(w, l);
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	  }
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	}
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      }
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      level.set(s,n);
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      /* Starting flow. It is everywhere 0 at the moment. */     
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      for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
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	{
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	  T c=capacity.get(e);
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	  if ( c == 0 ) continue;
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	  NodeIt w=G.head(e);
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	  if ( level.get(w) < n ) {	  
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	    if ( excess.get(w) == 0 && w!=t ) {
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	      next.set(w,active[level.get(w)]);
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	      active[level.get(w)]=w;
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	    }
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	    flow.set(e, c); 
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	    excess.set(w, excess.get(w)+c);
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	  }
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	}
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      /* 
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	 End of preprocessing 
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      */
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      /*
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	Push/relabel on the highest level active nodes.
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      */	
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      while ( true ) {
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	if ( b == 0 ) {
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	  if ( !what_heur && !end && k > 0 ) {
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	    b=k;
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	    end=true;
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	  } else break;
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	}
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	if ( active[b] == 0 ) --b; 
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	else {
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	  end=false;  
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	  NodeIt w=active[b];
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	  active[b]=next.get(w);
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	  int lev=level.get(w);
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	  T exc=excess.get(w);
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	  int newlevel=n;       //bound on the next level of w
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	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
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	    if ( flow.get(e) == capacity.get(e) ) continue; 
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	    NodeIt v=G.head(e);            
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	    //e=wv	    
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	    if( lev > level.get(v) ) {      
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	      /*Push is allowed now*/
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	      if ( excess.get(v)==0 && v!=t && v!=s ) {
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		int lev_v=level.get(v);
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		next.set(v,active[lev_v]);
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		active[lev_v]=v;
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	      }
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	      T cap=capacity.get(e);
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	      T flo=flow.get(e);
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	      T remcap=cap-flo;
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	      if ( remcap >= exc ) {       
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		/*A nonsaturating push.*/
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		flow.set(e, flo+exc);
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		excess.set(v, excess.get(v)+exc);
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		exc=0;
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		break; 
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	      } else { 
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		/*A saturating push.*/
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		flow.set(e, cap);
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		excess.set(v, excess.get(v)+remcap);
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		exc-=remcap;
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	      }
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	    } else if ( newlevel > level.get(v) ){
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	      newlevel = level.get(v);
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	    }	    
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	  } //for out edges wv 
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	if ( exc > 0 ) {	
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	  for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
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	    if( flow.get(e) == 0 ) continue; 
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	    NodeIt v=G.tail(e);  
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	    //e=vw
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	    if( lev > level.get(v) ) {  
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	      /*Push is allowed now*/
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	      if ( excess.get(v)==0 && v!=t && v!=s ) {
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		int lev_v=level.get(v);
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		next.set(v,active[lev_v]);
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		active[lev_v]=v;
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	      }
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	      T flo=flow.get(e);
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	      if ( flo >= exc ) { 
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		/*A nonsaturating push.*/
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		flow.set(e, flo-exc);
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		excess.set(v, excess.get(v)+exc);
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		exc=0;
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		break; 
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	      } else {                                               
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		/*A saturating push.*/
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		excess.set(v, excess.get(v)+flo);
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		exc-=flo;
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		flow.set(e,0);
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	      }  
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	    } else if ( newlevel > level.get(v) ) {
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	      newlevel = level.get(v);
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	    }	    
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	  } //for in edges vw
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	} // if w still has excess after the out edge for cycle
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	excess.set(w, exc);
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	/*
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	  Relabel
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	*/
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	if ( exc > 0 ) {
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	  //now 'lev' is the old level of w
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	  //unlacing starts
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	  NodeIt right_n=right.get(w);
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	  NodeIt left_n=left.get(w);
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	  if ( right_n != 0 ) {
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	    if ( left_n != 0 ) {
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	      right.set(left_n, right_n);
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	      left.set(right_n, left_n);
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	    } else {
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	      level_list[lev]=right_n;   
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	      left.set(right_n, 0);
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	    } 
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	  } else {
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	    if ( left_n != 0 ) {
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	      right.set(left_n, 0);
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	    } else { 
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	      level_list[lev]=0;   
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	    } 
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	  } 
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	  //unlacing ends
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	  //gapping starts
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	  if ( level_list[lev]==0 ) {
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	    for (int i=lev; i!=k ; ) {
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	      NodeIt v=level_list[++i];
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	      while ( v != 0 ) {
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		level.set(v,n);
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		v=right.get(v);
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	      }
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	      level_list[i]=0;
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	      if ( !what_heur ) active[i]=0;
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	    }	     
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	    level.set(w,n);
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	    b=lev-1;
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	    k=b;
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	    //gapping ends
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	  } else {
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	    if ( newlevel == n ) level.set(w,n); 
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	    else {
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	      level.set(w,++newlevel);
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	      next.set(w,active[newlevel]);
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	      active[newlevel]=w;
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	      if ( what_heur ) b=newlevel;
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	      if ( k < newlevel ) ++k;
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	      NodeIt first=level_list[newlevel];
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	      if ( first != 0 ) left.set(first,w);
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	      right.set(w,first);
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	      left.set(w,0);
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	      level_list[newlevel]=w;
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	    }
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	  }
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	  ++relabel; 
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	  if ( relabel >= heur ) {
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	    relabel=0;
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	    if ( what_heur ) {
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	      what_heur=0;
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	      heur=heur0;
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	      end=false;
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	    } else {
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	      what_heur=1;
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	      heur=heur1;
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	      b=k; 
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	    }
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	  }
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	} // if ( exc > 0 )
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	}  // if stack[b] is nonempty
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      } // while(true)
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      for( EachNodeIt v=G.template first<EachNodeIt>(); 
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	   v.valid(); ++v) 
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	if (level.get(v) >= n ) cut.set(v,true);
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      value = excess.get(t);
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      /*Max flow value.*/
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    } //void run()
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    T maxFlow() {
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      return value;
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    }
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    CutMap minCut() {
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      return cut;
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    }
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  };
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}//namespace 
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#endif 
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