// -*- 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

 //#include <algorithm>

 #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() {

       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] ) {  //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