// -*- C++ -*-
/*
preflow.h
by jacint. 
Heuristics: 
 2 phase
 gap
 list 'level_list' on the nodes on level i implemented by hand
 stack 'active' on the active nodes on level i implemented by hand
 runs heuristic 'highest label' for H1*n relabels
 runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'
 
Parameters H0 and H1 are initialized to 20 and 10.

The best preflow I could ever write.

The constructor runs the algorithm.

Members:

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

T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 

FlowMap Flow() : returns the fixed maximum flow x

void minMinCut(CutMap& M) : sets M to the characteristic vector of the 
     minimum min cut. M should be a map of bools initialized to false.

void maxMinCut(CutMap& M) : sets M to the characteristic vector of the 
     maximum min cut. M should be a map of bools initialized to false.

void minCut(CutMap& M) : sets M to the characteristic vector of 
     a min cut. M should be a map of bools initialized to false.

*/

#ifndef PREFLOW_H
#define PREFLOW_H

#define H0 20
#define H1 1

#include <vector>
#include <queue>

#include <time_measure.h>

namespace hugo {

  template <typename Graph, typename T, 
    typename FlowMap=typename Graph::EdgeMap<T>,
    typename CapMap=typename Graph::EdgeMap<T> >
  class preflow {
    
    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;  
    T value;

  public:
    double time;
    preflow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity ) :
      G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity)
    {

      bool phase=0;        //phase 0 is the 1st phase, phase 1 is the 2nd
      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 ( phase ) break;
	  
	  if ( !what_heur && !end && k > 0 ) {
	    b=k;
	    end=true;
	  } else {
	    phase=1;
	    time=currTime();
	    level.set(s,0);
	    std::queue<NodeIt> bfs_queue;
	    bfs_queue.push(s);
	    
	    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) {
		if ( capacity.get(e) == flow.get(e) ) continue;
		NodeIt u=G.tail(e);
		if ( level.get(u) >= n ) { 
		  bfs_queue.push(u);
		  level.set(u, l);
		  if ( excess.get(u) > 0 ) {
		    next.set(u,active[l]);
		    active[l]=u;
		  }
		}
	      }
	    
	      for(OutEdgeIt e=G.template first<OutEdgeIt>(v); e.valid(); ++e) {
		if ( 0 == flow.get(e) ) continue;
		NodeIt u=G.head(e);
		if ( level.get(u) >= n ) { 
		  bfs_queue.push(u);
		  level.set(u, l);
		  if ( excess.get(u) > 0 ) {
		    next.set(u,active[l]);
		    active[l]=u;
		  }
		}
	      }
	    }
	    b=n-2;
	    }
	    
	}
	  
	  
	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
	
	  if ( phase ) {
	    level.set(w,++newlevel);
	    next.set(w,active[newlevel]);
	    active[newlevel]=w;
	    b=newlevel;
	  } else {
	    //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; 
	      }
	    }
	  } //phase 0
	  
	  
	} // if ( exc > 0 )
	  
	
	}  // if stack[b] is nonempty
	
      } // while(true)


      value = excess.get(t);
      /*Max flow value.*/
     
    } //void run()





    /*
      Returns the maximum value of a flow.
     */

    T maxFlow() {
      return value;
    }



    /*
      For the maximum flow x found by the algorithm, 
      it returns the flow value on edge e, i.e. x(e). 
    */
   
    T flowOnEdge(EdgeIt e) {
      return flow.get(e);
    }



    FlowMap Flow() {
      return flow;
      }


    
    void Flow(FlowMap& _flow ) {
      for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v)
	_flow.set(v,flow.get(v));
	}



    /*
      Returns the minimum min cut, by a bfs from s in the residual graph.
    */
   
    template<typename _CutMap>
    void minMinCut(_CutMap& M) {
    
      std::queue<NodeIt> queue;
      
      M.set(s,true);      
      queue.push(s);

      while (!queue.empty()) {
        NodeIt w=queue.front();
	queue.pop();

	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
	  NodeIt v=G.head(e);
	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	} 

	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
	  NodeIt v=G.tail(e);
	  if (!M.get(v) && flow.get(e) > 0 ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	} 
      }
    }


  
    /*
      Returns the maximum min cut, by a reverse bfs 
      from t in the residual graph.
    */
    
    template<typename _CutMap>
    void maxMinCut(_CutMap& M) {
    
      std::queue<NodeIt> queue;
      
      M.set(t,true);        
      queue.push(t);

      while (!queue.empty()) {
        NodeIt w=queue.front();
	queue.pop();

	for(InEdgeIt e=G.template first<InEdgeIt>(w) ; e.valid(); ++e) {
	  NodeIt v=G.tail(e);
	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}

	for(OutEdgeIt e=G.template first<OutEdgeIt>(w) ; e.valid(); ++e) {
	  NodeIt v=G.head(e);
	  if (!M.get(v) && flow.get(e) > 0 ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}
      }

      for(EachNodeIt v=G.template first<EachNodeIt>() ; v.valid(); ++v) {
	M.set(v, !M.get(v));
      }

    }



    template<typename CutMap>
    void minCut(CutMap& M) {
      minMinCut(M);
    }


  };
}//namespace marci
#endif