// -*- C++ -*-

//run gyorsan tudna adni a minmincutot a 2 fazis elejen , ne vegyuk be konstruktorba egy cutmapet?
//constzero jo igy?

//majd marci megmondja betegyem-e bfs-t meg resgraphot

//constzero helyett az kell hogy flow-e vagy csak preflow, ha flow akor csak
//excess[t]-t kell szmaolni

/*
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.

Constructors:

Preflow(Graph, Node, Node, CapMap, FlowMap, bool) : bool must be false if 
     FlowMap is not constant zero, and should be true if it is

Members:

void run()

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

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.

FIXME reset

*/

#ifndef HUGO_PREFLOW_H
#define HUGO_PREFLOW_H

#define H0 20
#define H1 1

#include <vector>
#include <queue>
#include <stack>

namespace hugo {

  template <typename Graph, typename T, 
	    typename CapMap=typename Graph::template EdgeMap<T>, 
            typename FlowMap=typename Graph::template EdgeMap<T> >
  class Preflow {
    
    typedef typename Graph::Node Node;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::InEdgeIt InEdgeIt;
    
    const Graph& G;
    Node s;
    Node t;
    const CapMap& capacity;  
    FlowMap& flow;
    T value;
    bool constzero;
    bool isflow;

  public:
    Preflow(Graph& _G, Node _s, Node _t, CapMap& _capacity, 
	    FlowMap& _flow, bool _constzero, bool _isflow ) :
      G(_G), s(_s), t(_t), capacity(_capacity), flow(_flow), constzero(_constzero), isflow(_isflow) {}
    
    
    void run() {
      
      value=0;                //for the subsequent runs

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

      std::vector<std::stack<Node> > active(n);
      /*      std::vector<Node> active(n-1,INVALID);
      typename Graph::template NodeMap<Node> next(G,INVALID);
      //Stack of the active nodes in level i < n.
      //We use it in both phases.*/

      typename Graph::template NodeMap<Node> left(G,INVALID);
      typename Graph::template NodeMap<Node> right(G,INVALID);
      std::vector<Node> level_list(n,INVALID);
      /*
	List of the nodes in level i<n.
      */


      if ( constzero ) {
     
	/*Reverse_bfs from t, to find the starting level.*/
	level.set(t,0);
	std::queue<Node> bfs_queue;
	bfs_queue.push(t);
	
	while (!bfs_queue.empty()) {
	  
	  Node v=bfs_queue.front();	
	  bfs_queue.pop();
	  int l=level[v]+1;
	  
	  InEdgeIt e;
	  for(G.first(e,v); G.valid(e); G.next(e)) {
	    Node w=G.tail(e);
	    if ( level[w] == n && w != s ) {
	      bfs_queue.push(w);
	      Node first=level_list[l];
	      if ( G.valid(first) ) left.set(first,w);
	      right.set(w,first);
	      level_list[l]=w;
	      level.set(w, l);
	    }
	  }
	}

	//the starting flow
	OutEdgeIt e;
	for(G.first(e,s); G.valid(e); G.next(e)) 
	{
	  T c=capacity[e];
	  if ( c == 0 ) continue;
	  Node w=G.head(e);
	  if ( level[w] < n ) {	  
	    if ( excess[w] == 0 && w!=t ) active[level[w]].push(w);
	    flow.set(e, c); 
	    excess.set(w, excess[w]+c);
	  }
	}
      }
      else 
      {
	
	/*
	  Reverse_bfs from t in the residual graph, 
	  to find the starting level.
	*/
	level.set(t,0);
	std::queue<Node> bfs_queue;
	bfs_queue.push(t);
	
	while (!bfs_queue.empty()) {
	  
	  Node v=bfs_queue.front();	
	  bfs_queue.pop();
	  int l=level[v]+1;
	  
	  InEdgeIt e;
	  for(G.first(e,v); G.valid(e); G.next(e)) {
	    if ( capacity[e] == flow[e] ) continue;
	    Node w=G.tail(e);
	    if ( level[w] == n && w != s ) {
	      bfs_queue.push(w);
	      Node first=level_list[l];
	      if ( G.valid(first) ) left.set(first,w);
	      right.set(w,first);
	      level_list[l]=w;
	      level.set(w, l);
	    }
	  }
	    
	  OutEdgeIt f;
	  for(G.first(f,v); G.valid(f); G.next(f)) {
	    if ( 0 == flow[f] ) continue;
	    Node w=G.head(f);
	    if ( level[w] == n && w != s ) {
	      bfs_queue.push(w);
	      Node first=level_list[l];
	      if ( G.valid(first) ) left.set(first,w);
	      right.set(w,first);
	      level_list[l]=w;
	      level.set(w, l);
	    }
	  }
	}
      
	
	/*
	  Counting the excess
	*/

	if ( !isflow ) {
	  NodeIt v;
	  for(G.first(v); G.valid(v); G.next(v)) {
	    T exc=0;
	    
	    InEdgeIt e;
	    for(G.first(e,v); G.valid(e); G.next(e)) exc+=flow[e];
	    OutEdgeIt f;
	    for(G.first(f,v); G.valid(f); G.next(f)) exc-=flow[f];
	    
	    excess.set(v,exc);	  
	    
	    //putting the active nodes into the stack
	    int lev=level[v];
	    if ( exc > 0 && lev < n && v != t ) active[lev].push(v);
	  }
	} else {
	  T exc=0;
	    
	  InEdgeIt e;
	  for(G.first(e,t); G.valid(e); G.next(e)) exc+=flow[e];
	  OutEdgeIt f;
	  for(G.first(f,t); G.valid(f); G.next(f)) exc-=flow[f];

	  excess.set(t,exc);	  
	}


	//the starting flow
	OutEdgeIt e;
	for(G.first(e,s); G.valid(e); G.next(e)) 
	{
	  T rem=capacity[e]-flow[e];
	  if ( rem == 0 ) continue;
	  Node w=G.head(e);
	  if ( level[w] < n ) {	  
	    if ( excess[w] == 0 && w!=t ) active[level[w]].push(w);
	    flow.set(e, capacity[e]); 
	    excess.set(w, excess[w]+rem);
	  }
	}
	
	InEdgeIt f;
	for(G.first(f,s); G.valid(f); G.next(f)) 
	{
	  if ( flow[f] == 0 ) continue;
	  Node w=G.tail(f);
	  if ( level[w] < n ) {	  
	    if ( excess[w] == 0 && w!=t ) active[level[w]].push(w);
	    excess.set(w, excess[w]+flow[f]);
	    flow.set(f, 0); 
	  }
	}
      }




      /* 
	 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;
	    level.set(s,0);
	    std::queue<Node> bfs_queue;
	    bfs_queue.push(s);
	    
	    while (!bfs_queue.empty()) {
	      
	      Node v=bfs_queue.front();	
	      bfs_queue.pop();
	      int l=level[v]+1;
	      
	      InEdgeIt e;
	      for(G.first(e,v); G.valid(e); G.next(e)) {
		if ( capacity[e] == flow[e] ) continue;
		Node u=G.tail(e);
		if ( level[u] >= n ) { 
		  bfs_queue.push(u);
		  level.set(u, l);
		  if ( excess[u] > 0 ) active[l].push(u);
		}
	      }
	    
	      OutEdgeIt f;
	      for(G.first(f,v); G.valid(f); G.next(f)) {
		if ( 0 == flow[f] ) continue;
		Node u=G.head(f);
		if ( level[u] >= n ) { 
		  bfs_queue.push(u);
		  level.set(u, l);
		  if ( excess[u] > 0 ) active[l].push(u);
		}
	      }
	    }
	    b=n-2;
	    }
	    
	}
	  

	///	  
	if ( active[b].empty() ) --b; 
	else {
	  end=false;  

	  Node w=active[b].top();
	  active[b].pop();
	  int lev=level[w];
	  T exc=excess[w];
	  int newlevel=n;       //bound on the next level of w
	  
	  OutEdgeIt e;
	  for(G.first(e,w); G.valid(e); G.next(e)) {
	    
	    if ( flow[e] == capacity[e] ) continue; 
	    Node v=G.head(e);            
	    //e=wv	    
	    
	    if( lev > level[v] ) {      
	      /*Push is allowed now*/
	      
	      if ( excess[v]==0 && v!=t && v!=s ) {
		int lev_v=level[v];
		active[lev_v].push(v);
	      }
	      
	      T cap=capacity[e];
	      T flo=flow[e];
	      T remcap=cap-flo;
	      
	      if ( remcap >= exc ) {       
		/*A nonsaturating push.*/
		
		flow.set(e, flo+exc);
		excess.set(v, excess[v]+exc);
		exc=0;
		break; 
		
	      } else { 
		/*A saturating push.*/
		
		flow.set(e, cap);
		excess.set(v, excess[v]+remcap);
		exc-=remcap;
	      }
	    } else if ( newlevel > level[v] ){
	      newlevel = level[v];
	    }	    
	    
	  } //for out edges wv 
	
	
	if ( exc > 0 ) {	
	  InEdgeIt e;
	  for(G.first(e,w); G.valid(e); G.next(e)) {
	    
	    if( flow[e] == 0 ) continue; 
	    Node v=G.tail(e);  
	    //e=vw
	    
	    if( lev > level[v] ) {  
	      /*Push is allowed now*/
	      
	      if ( excess[v]==0 && v!=t && v!=s ) {
		int lev_v=level[v];
		active[lev_v].push(v);
	      }
	      
	      T flo=flow[e];
	      
	      if ( flo >= exc ) { 
		/*A nonsaturating push.*/
		
		flow.set(e, flo-exc);
		excess.set(v, excess[v]+exc);
		exc=0;
		break; 
	      } else {                                               
		/*A saturating push.*/
		
		excess.set(v, excess[v]+flo);
		exc-=flo;
		flow.set(e,0);
	      }  
	    } else if ( newlevel > level[v] ) {
	      newlevel = level[v];
	    }	    
	  } //for in edges vw
	  
	} // if w still has excess after the out edge for cycle
	
	excess.set(w, exc);
	///	push

 
	/*
	  Relabel
	*/
	

	if ( exc > 0 ) {
	  //now 'lev' is the old level of w
	
	  if ( phase ) {
	    level.set(w,++newlevel);
	    active[newlevel].push(w);
	    b=newlevel;
	  } else {
	    //unlacing starts
	    Node right_n=right[w];
	    Node left_n=left[w];

	    if ( G.valid(right_n) ) {
	      if ( G.valid(left_n) ) {
		right.set(left_n, right_n);
		left.set(right_n, left_n);
	      } else {
		level_list[lev]=right_n;   
		left.set(right_n, INVALID);
	      } 
	    } else {
	      if ( G.valid(left_n) ) {
		right.set(left_n, INVALID);
	      } else { 
		level_list[lev]=INVALID;   
	      } 
	    } 
	    //unlacing ends
		
	    if ( !G.valid(level_list[lev]) ) {
	      
	       //gapping starts
	      for (int i=lev; i!=k ; ) {
		Node v=level_list[++i];
		while ( G.valid(v) ) {
		  level.set(v,n);
		  v=right[v];
		}
		level_list[i]=INVALID;
		if ( !what_heur ) {
		  while ( !active[i].empty() ) {
		    active[i].pop();    //FIXME: ezt szebben kene
		  }
		}	     
	      }

	      level.set(w,n);
	      b=lev-1;
	      k=b;
	      //gapping ends
	    
	    } else {
	      
	      if ( newlevel == n ) level.set(w,n); 
	      else {
		level.set(w,++newlevel);
		active[newlevel].push(w);
		if ( what_heur ) b=newlevel;
		if ( k < newlevel ) ++k;      //now k=newlevel
		Node first=level_list[newlevel];
		if ( G.valid(first) ) left.set(first,w);
		right.set(w,first);
		left.set(w,INVALID);
		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[t];
      /*Max flow value.*/
     
    } //void run()





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

    T flowValue() {
      return value;
    }


    FlowMap Flow() {
      return flow;
      }


    void Flow(FlowMap& _flow ) {
      NodeIt v;
      for(G.first(v) ; G.valid(v); G.next(v))
	_flow.set(v,flow[v]);
    }



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

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

	OutEdgeIt e;
	for(G.first(e,w) ; G.valid(e); G.next(e)) {
	  Node v=G.head(e);
	  if (!M[v] && flow[e] < capacity[e] ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	} 

	InEdgeIt f;
	for(G.first(f,w) ; G.valid(f); G.next(f)) {
	  Node v=G.tail(f);
	  if (!M[v] && flow[f] > 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<Node> queue;
      
      M.set(t,true);        
      queue.push(t);

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


	InEdgeIt e;
	for(G.first(e,w) ; G.valid(e); G.next(e)) {
	  Node v=G.tail(e);
	  if (!M[v] && flow[e] < capacity[e] ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}
	
	OutEdgeIt f;
	for(G.first(f,w) ; G.valid(f); G.next(f)) {
	  Node v=G.head(f);
	  if (!M[v] && flow[f] > 0 ) {
	    queue.push(v);
	    M.set(v, true);
	  }
	}
      }

      NodeIt v;
      for(G.first(v) ; G.valid(v); G.next(v)) {
	M.set(v, !M[v]);
      }

    }



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

    
    void resetTarget (Node _t) {t=_t;}
    void resetSource (Node _s) {s=_s;}
   
    void resetCap (CapMap _cap) {capacity=_cap;}

    void resetFlow (FlowMap _flow, bool _constzero) {
      flow=_flow;
      constzero=_constzero;
    }



  };

} //namespace hugo

#endif //PREFLOW_H