// -*- 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