// -*- 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