// -*- C++ -*-

 /*

 preflow_max_flow.h

 by jacint. 

 Runs the first phase of preflow.h

 The constructor runs the algorithm.

 Members:

 T maxFlow() : returns the value of a maximum flow

 CutMap minCut() : returns the characteristic vector of a min cut. 

 */

 #ifndef PREFLOW_MAX_FLOW_H

 #define PREFLOW_MAX_FLOW_H

 #define H0 20

 #define H1 1

 #include <vector>

 #include <queue>

 namespace hugo {

   template <typename Graph, typename T, 

     typename FlowMap=typename Graph::EdgeMap<T>,

     typename CapMap=typename Graph::EdgeMap<T>, 

     typename CutMap=typename Graph::NodeMap<bool> >

   class preflow_max_flow {

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::EdgeIt EdgeIt;

     typedef typename Graph::EachNodeIt EachNodeIt;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::InEdgeIt InEdgeIt;

     Graph& G;

     NodeIt s;

     NodeIt t;

     FlowMap flow;

     CapMap& capacity;  

     CutMap cut;

     T value;

   public:

     preflow_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :

       G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), cut(_G, false)

     {

       int n=G.nodeNum(); 

       int heur0=(int)(H0*n);  //time while running 'bound decrease' 

       int heur1=(int)(H1*n);  //time while running 'highest label'

       int heur=heur1;         //starting time interval (#of relabels)

       bool what_heur=1;       

       /*

 	what_heur is 0 in case 'bound decrease' 

 	and 1 in case 'highest label'

       */

       bool end=false;     

       /*

 	Needed for 'bound decrease', 'true'

 	means no active nodes are above bound b.

       */

       int relabel=0;

       int k=n-2;  //bound on the highest level under n containing a node

       int b=k;    //bound on the highest level under n of an active node

       typename Graph::NodeMap<int> level(G,n);      

       typename Graph::NodeMap<T> excess(G); 

       std::vector<NodeIt> active(n);

       typename Graph::NodeMap<NodeIt> next(G);

       //Stack of the active nodes in level i < n.

       //We use it in both phases.

       typename Graph::NodeMap<NodeIt> left(G);

       typename Graph::NodeMap<NodeIt> right(G);

       std::vector<NodeIt> level_list(n);

       /*

 	List of the nodes in level i<n.

       */

       /*Reverse_bfs from t, to find the starting level.*/

       level.set(t,0);

       std::queue<NodeIt> bfs_queue;

       bfs_queue.push(t);

       while (!bfs_queue.empty()) {

 	NodeIt v=bfs_queue.front();	

 	bfs_queue.pop();

 	int l=level.get(v)+1;

 	for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {

 	  NodeIt w=G.tail(e);

 	  if ( level.get(w) == n && w != s ) {

 	    bfs_queue.push(w);

 	    NodeIt first=level_list[l];

 	    if ( first != 0 ) left.set(first,w);

 	    right.set(w,first);

 	    level_list[l]=w;

 	    level.set(w, l);

 	  }

 	}

       }

       level.set(s,n);

       /* Starting flow. It is everywhere 0 at the moment. */     

       for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 

 	{

 	  T c=capacity.get(e);

 	  if ( c == 0 ) continue;

 	  NodeIt w=G.head(e);

 	  if ( level.get(w) < n ) {	  

 	    if ( excess.get(w) == 0 && w!=t ) {

 	      next.set(w,active[level.get(w)]);

 	      active[level.get(w)]=w;

 	    }

 	    flow.set(e, c); 

 	    excess.set(w, excess.get(w)+c);

 	  }

 	}

       /* 

 	 End of preprocessing 

       */

       /*

 	Push/relabel on the highest level active nodes.

       */	

       while ( true ) {

 	if ( b == 0 ) {

 	  if ( !what_heur && !end && k > 0 ) {

 	    b=k;

 	    end=true;

 	  } else break;

 	}

 	if ( active[b] == 0 ) --b; 

 	else {

 	  end=false;  

 	  NodeIt w=active[b];

 	  active[b]=next.get(w);

 	  int lev=level.get(w);

 	  T exc=excess.get(w);

 	  int newlevel=n;       //bound on the next level of w

 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {

 	    if ( flow.get(e) == capacity.get(e) ) continue; 

 	    NodeIt v=G.head(e);            

 	    //e=wv	    

 	    if( lev > level.get(v) ) {      

 	      /*Push is allowed now*/

 	      if ( excess.get(v)==0 && v!=t && v!=s ) {

 		int lev_v=level.get(v);

 		next.set(v,active[lev_v]);

 		active[lev_v]=v;

 	      }

 	      T cap=capacity.get(e);

 	      T flo=flow.get(e);

 	      T remcap=cap-flo;

 	      if ( remcap >= exc ) {       

 		/*A nonsaturating push.*/

 		flow.set(e, flo+exc);

 		excess.set(v, excess.get(v)+exc);

 		exc=0;

 		break; 

 	      } else { 

 		/*A saturating push.*/

 		flow.set(e, cap);

 		excess.set(v, excess.get(v)+remcap);

 		exc-=remcap;

 	      }

 	    } else if ( newlevel > level.get(v) ){

 	      newlevel = level.get(v);

 	    }	    

 	  } //for out edges wv 

 	if ( exc > 0 ) {	

 	  for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {

 	    if( flow.get(e) == 0 ) continue; 

 	    NodeIt v=G.tail(e);  

 	    //e=vw

 	    if( lev > level.get(v) ) {  

 	      /*Push is allowed now*/

 	      if ( excess.get(v)==0 && v!=t && v!=s ) {

 		int lev_v=level.get(v);

 		next.set(v,active[lev_v]);

 		active[lev_v]=v;

 	      }

 	      T flo=flow.get(e);

 	      if ( flo >= exc ) { 

 		/*A nonsaturating push.*/

 		flow.set(e, flo-exc);

 		excess.set(v, excess.get(v)+exc);

 		exc=0;

 		break; 

 	      } else {                                               

 		/*A saturating push.*/

 		excess.set(v, excess.get(v)+flo);

 		exc-=flo;

 		flow.set(e,0);

 	      }  

 	    } else if ( newlevel > level.get(v) ) {

 	      newlevel = level.get(v);

 	    }	    

 	  } //for in edges vw

 	} // if w still has excess after the out edge for cycle

 	excess.set(w, exc);

 	/*

 	  Relabel

 	*/

 	if ( exc > 0 ) {

 	  //now 'lev' is the old level of w

 	  //unlacing starts

 	  NodeIt right_n=right.get(w);

 	  NodeIt left_n=left.get(w);

 	  if ( right_n != 0 ) {

 	    if ( left_n != 0 ) {

 	      right.set(left_n, right_n);

 	      left.set(right_n, left_n);

 	    } else {

 	      level_list[lev]=right_n;   

 	      left.set(right_n, 0);

 	    } 

 	  } else {

 	    if ( left_n != 0 ) {

 	      right.set(left_n, 0);

 	    } else { 

 	      level_list[lev]=0;   

 	    } 

 	  } 

 	  //unlacing ends

 	  //gapping starts

 	  if ( level_list[lev]==0 ) {

 	    for (int i=lev; i!=k ; ) {

 	      NodeIt v=level_list[++i];

 	      while ( v != 0 ) {

 		level.set(v,n);

 		v=right.get(v);

 	      }

 	      level_list[i]=0;

 	      if ( !what_heur ) active[i]=0;

 	    }	     

 	    level.set(w,n);

 	    b=lev-1;

 	    k=b;

 	    //gapping ends

 	  } else {

 	    if ( newlevel == n ) level.set(w,n); 

 	    else {

 	      level.set(w,++newlevel);

 	      next.set(w,active[newlevel]);

 	      active[newlevel]=w;

 	      if ( what_heur ) b=newlevel;

 	      if ( k < newlevel ) ++k;

 	      NodeIt first=level_list[newlevel];

 	      if ( first != 0 ) left.set(first,w);

 	      right.set(w,first);

 	      left.set(w,0);

 	      level_list[newlevel]=w;

 	    }

 	  }

 	  ++relabel; 

 	  if ( relabel >= heur ) {

 	    relabel=0;

 	    if ( what_heur ) {

 	      what_heur=0;

 	      heur=heur0;

 	      end=false;

 	    } else {

 	      what_heur=1;

 	      heur=heur1;

 	      b=k; 

 	    }

 	  }

 	} // if ( exc > 0 )

 	}  // if stack[b] is nonempty

       } // while(true)

       for( EachNodeIt v=G.template first<EachNodeIt>(); 

 	   v.valid(); ++v) 

 	if (level.get(v) >= n ) cut.set(v,true);

       value = excess.get(t);

       /*Max flow value.*/

     } //void run()

     T maxFlow() {

       return value;

     }

     CutMap minCut() {

       return cut;

     }

   };

 }//namespace 

 #endif