// -*- C++ -*-

 /*

 preflow_push_hl.hh

 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(Edge_iterator e) : for a fixed maximum flow x it returns x(e) 

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

 NodeMap<graph_type, 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.hh>

 namespace marci {

   template <typename Graph, typename T, typename FlowMap, typename CapacityMap>

   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;

     typedef typename Graph::EachEdgeIt EachEdgeIt;

     Graph& G;

     NodeIt s;

     NodeIt t;

     Graph::EdgeMap<T> flow;

     Graph::EdgeMap<T> capacity; 

     T value;

     Graph::NodeMap<bool> mincutvector;

   public:

     preflow_push_hl(Graph& _G, NodeIt _s, NodeIt _t, 

 		    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() {

       Graph::NodeMap<int> level(G);         //level of Node

       Graph::NodeMap<T> excess(G);          //excess of Node

       int n=G.nodeNum();                        //number of Nodes 

       int b=n; 

       /*b is a bound on the highest level of an active Node. In the beginning it is at most n-2.*/

       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<list_graph> bfs(G, t);

       bfs.run();

       for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) {

 	level.set(v, bfs.dist(v)); 

 	//std::cout << "the level of " << v << " is " << bfs.dist(v);

       }

       /*The level of s is fixed to n*/ 

       level.set(s,n);

       /* Starting flow. It is everywhere 0 at the moment. */

       for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i) 

 	{

 	  NodeIt w=G.head(i);

 	  flow.set(i, capacity.get(i)); 

 	  stack[bfs.dist(w)].push(w); 

 	  excess.set(w, capacity.get(i));

 	}

       /* 

 	 End of preprocessing 

       */

       /*

 	Push/relabel on the highest level active Nodes.

       */

       /*While there exists 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 the highest label active Node.

 	  stack[b].pop();                    //We delete w from the stack.

 	  int newlevel=2*n-2;                   //In newlevel we maintain the next level of w.

 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {

 	    NodeIt v=G.head(e);

 	    /*e is the Edge wv.*/

 	    if (flow.get(e)<capacity.get(e)) {              

 	      /*e is an Edge of the residual graph */

 	      if(level.get(w)==level.get(v)+1) {      

 		/*Push is allowed now*/

 		if (capacity.get(e)-flow.get(e) > excess.get(w)) {       

 		  /*A nonsaturating push.*/

 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 

 		  /*v becomes active.*/

 		  flow.set(e, flow.get(e)+excess.get(w));

 		  excess.set(v, excess.get(v)+excess.get(w));

 		  excess.set(w,0);

 		  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;

 		  break; 

 		} else { 

 		  /*A saturating push.*/

 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 

 		  /*v becomes active.*/

 		  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));

 		  //std::cout << w<<" " <<v<<" elore elen sat pump "   << std::endl;

 		  if (excess.get(w)==0) break;

 		  /*If w is not active any more, then we go on to the next Node.*/

 		} // if (capacity.get(e)-flow.get(e) > excess.get(w))

 	      } // if(level.get(w)==level.get(v)+1)

 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}

 	    } //if (flow.get(e)<capacity.get(e))

 	  } //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e) 

 	  for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {

 	    NodeIt v=G.tail(e);

 	    /*e is the Edge vw.*/

 	    if (excess.get(w)==0) break;

 	    /*It may happen, that w became inactive in the first for cycle.*/		

 	    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 (flow.get(e) > excess.get(w)) { 

 		  /*A nonsaturating push.*/

 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 

 		  /*v becomes active.*/

 		  flow.set(e, flow.get(e)-excess.get(w));

 		  excess.set(v, excess.get(v)+excess.get(w));

 		  excess.set(w,0);

 		  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;

 		  break; 

 		} else {                                               

 		  /*A saturating push.*/

 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 

 		  /*v becomes active.*/

 		  excess.set(v, excess.get(v)+flow.get(e));

 		  excess.set(w, excess.get(w)-flow.get(e));

 		  flow.set(e,0);

 		  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;

 		  if (excess.get(w)==0) { break;}

 		} //if (flow.get(e) > excess.get(v)) 

 	      } //if(level.get(w)==level.get(v)+1)

 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}

 	    } //if (flow.get(e)>0)

 	  } //for

 	  if (excess.get(w)>0) {

 	    level.set(w,++newlevel);

 	    stack[newlevel].push(w);

 	    b=newlevel;

 	    //std::cout << "The new level of " << w << " is "<< newlevel <<std::endl; 

 	  }

 	} //else

       } //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.

     */

     EdgeMap<graph_type, T> allflow() {

       return flow;

     }

     /*

       Returns a minimum cut by using a reverse bfs from t in the residual graph.

     */

     NodeMap<graph_type, 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