// -*- C++ -*-
/*
preflow_push_hl.h
by jacint. 
Runs the highest label variant of the preflow push algorithm with 
running time O(n^2\sqrt(m)). 

Member functions:

void run() : runs the algorithm

 The following functions should be used after run() was already run.

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

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

Graph::EdgeMap<T> allflow() : returns the fixed maximum flow x

Graph::NodeMap<bool> mincut() : returns a 
     characteristic vector of a minimum cut. (An empty level 
     in the algorithm gives a minimum cut.)
*/

#ifndef PREFLOW_PUSH_HL_H
#define PREFLOW_PUSH_HL_H

#define A 1

#include <vector>
#include <stack>

#include <reverse_bfs.h>

namespace marci {

  template <typename Graph, typename T>
  class preflow_push_hl {
    
    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;
    typename Graph::EdgeMap<T> flow;
    typename Graph::EdgeMap<T> capacity; 
    T value;
    typename Graph::NodeMap<bool> mincutvector;

  public:

    preflow_push_hl(Graph& _G, NodeIt _s, NodeIt _t, 
		    typename Graph::EdgeMap<T>& _capacity) :
      G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity), 
      mincutvector(_G, true) { }


    /*
      The run() function runs the highest label preflow-push, 
      running time: O(n^2\sqrt(m))
    */
    void run() {
 
      std::cout<<"A is "<<A<<" ";

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

      int n=G.nodeNum(); 
      int b=n-2; 
      /*
	b is a bound on the highest level of an active node. 
	In the beginning it is at most n-2.
      */

      std::vector<int> numb(n);     //The number of nodes on level i < n.
      std::vector<std::stack<NodeIt> > stack(2*n-1);    
      //Stack of the active nodes in level i.


      /*Reverse_bfs from t, to find the starting level.*/
      reverse_bfs<Graph> bfs(G, t);
      bfs.run();
      for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) 
	{
	  int dist=bfs.dist(v);
	  level.set(v, dist);
	  ++numb[dist];
	}

      level.set(s,n);


      /* Starting flow. It is everywhere 0 at the moment. */     
      for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
	{
	  if ( capacity.get(e) > 0 ) {
	    NodeIt w=G.head(e);
	    if ( w!=s ) {	  
	      if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); 
	      flow.set(e, capacity.get(e)); 
	      excess.set(w, excess.get(w)+capacity.get(e));
	    }
	  }
	}

      /* 
	 End of preprocessing 
      */



      /*
	Push/relabel on the highest level active nodes.
      */
	
      /*While there exists an active node.*/
      while (b) { 

	/*We decrease the bound if there is no active node of level b.*/
	if (stack[b].empty()) {
	  --b;
	} else {

	  NodeIt w=stack[b].top();        //w is a highest label active node.
	  stack[b].pop();           
	
	  int newlevel=2*n-2;             //In newlevel we bound the next level of w.
	
	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
	    
	    if ( flow.get(e) < capacity.get(e) ) {              
	      /*e is an edge of the residual graph */

	      NodeIt v=G.head(e);               /*e is the edge wv.*/

	      if( level.get(w) == level.get(v)+1 ) {      
		/*Push is allowed now*/

		if ( excess.get(v)==0 && v != s && v !=t ) stack[level.get(v)].push(v); 
		/*v becomes active.*/

		if ( capacity.get(e)-flow.get(e) > excess.get(w) ) {       
		  /*A nonsaturating push.*/
		  
		  flow.set(e, flow.get(e)+excess.get(w));
		  excess.set(v, excess.get(v)+excess.get(w));
		  excess.set(w,0);
		  break; 

		} else { 
		  /*A saturating push.*/

		  excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e));
		  excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e));
		  flow.set(e, capacity.get(e));
		  if ( excess.get(w)==0 ) break;
		  /*If w is not active any more, then we go on to the next node.*/
		  
		}
	      } else {
		newlevel = newlevel < level.get(v) ? newlevel : level.get(v);
	      }
	    
	    } //if the out edge wv is in the res graph 
	 
	  } //for out edges wv 
	  

	  if ( excess.get(w) > 0 ) {	
	    
	    for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
	      NodeIt v=G.tail(e);  /*e is the edge vw.*/

	      if( flow.get(e) > 0 ) {             
		/*e is an edge of the residual graph */

		if( level.get(w)==level.get(v)+1 ) {  
		  /*Push is allowed now*/
		
		  if ( excess.get(v)==0 && v != s && v !=t) stack[level.get(v)].push(v); 
		  /*v becomes active.*/

		  if ( flow.get(e) > excess.get(w) ) { 
		    /*A nonsaturating push.*/
		  
		    flow.set(e, flow.get(e)-excess.get(w));
		    excess.set(v, excess.get(v)+excess.get(w));
		    excess.set(w,0);
		    break; 
		  } else {                                               
		    /*A saturating push.*/
		    
		    excess.set(v, excess.get(v)+flow.get(e));
		    excess.set(w, excess.get(w)-flow.get(e));
		    flow.set(e,0);
		    if ( excess.get(w)==0 ) break;
		  }  
		} else {
		  newlevel = newlevel < level.get(v) ? newlevel : level.get(v);
		}
		
	      } //if in edge vw is in the res graph 

	    } //for in edges vw

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


	  /*
	    Relabel
	  */
	  
	  if ( excess.get(w) > 0 ) {
	    
	    int oldlevel=level.get(w);	    
	    level.set(w,++newlevel);

	    if ( oldlevel < n ) {
	      --numb[oldlevel];

	      if ( !numb[oldlevel] && oldlevel < A*n ) {  //If the level of w gets empty. 
		
		for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
		  if (level.get(v) > oldlevel && level.get(v) < n ) level.set(v,n);  
		}
		for (int i=oldlevel+1 ; i!=n ; ++i) numb[i]=0; 
		if ( newlevel < n ) newlevel=n; 
	      } else { 
		if ( newlevel < n ) ++numb[newlevel]; 
	      }
	    } else { 
	    if ( newlevel < n ) ++numb[newlevel];
	    }
	    
	    stack[newlevel].push(w);
	    b=newlevel;

	  }

	} // if stack[b] is nonempty

      } // while(b)


      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);
    }



    /*
      Returns the maximum flow x found by the algorithm.
    */

    typename Graph::EdgeMap<T> allflow() {
      return flow;
    }



    /*
      Returns a minimum cut by using a reverse bfs from t in the residual graph.
    */
    
    typename Graph::NodeMap<bool> mincut() {
    
      std::queue<NodeIt> queue;
      
      mincutvector.set(t,false);      
      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 (mincutvector.get(v) && flow.get(e) < capacity.get(e) ) {
	    queue.push(v);
	    mincutvector.set(v, false);
	  }
	} // for

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

      }

      return mincutvector;
    
    }
  };
}//namespace marci
#endif