/*

 preflow_push_max_flow_h

 by jacint. 

 Runs a preflow push algorithm with the modification, 

 that we do not push on nodes with level at least n. 

 Moreover, if a level gets empty, we set all nodes above that

 level to level n. Hence, in the end, we arrive at a maximum preflow 

 with value of a max flow value. An empty level gives a minimum cut.

 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

 NodeMap<bool> mincut(): returns a 

      characteristic vector of a minimum cut.

 */

 #ifndef PREFLOW_PUSH_MAX_FLOW_H

 #define PREFLOW_PUSH_MAX_FLOW_H

 #include <algorithm>

 #include <vector>

 #include <stack>

 #include <reverse_bfs.h>

 namespace marci {

   template <typename Graph, typename T>

   class preflow_push_max_flow {

     typedef typename Graph::NodeIt NodeIt;

     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>& capacity; 

     T value;

     typename Graph::NodeMap<bool> mincutvector;    

   public:

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

 			    typename Graph::EdgeMap<T>& _capacity) : 

       G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { }

     /*

       The run() function runs a modified version of the 

       highest label preflow-push, which only 

       finds a maximum preflow, hence giving the value of a maximum flow.

     */

     void run() {

       typename Graph::EdgeMap<T> flow(G, 0); 

       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);

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

 	    stack[level.get(w)].push(w); 

 	    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 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.*/

 		  flow.set(e,0);

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

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

 		  //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);}

 	      //std::cout << "Leveldecrease of Node " << w << " to " << newlevel << std::endl; 

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

 	  } //for in-Edge

 	  /*

 	    Relabel

 	  */

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

 	    /*Now newlevel <= n*/

 	    int l=level.get(w);	        //l is the old level of w.

 	    --numb[l];

 	    if (newlevel == n) {

 	      level.set(w,n);

 	    } else {

 	      if (numb[l]) {

 		/*If the level of w remains nonempty.*/

 		level.set(w,++newlevel);

 		++numb[newlevel];

 		stack[newlevel].push(w);

 		b=newlevel;

 	      } else { 

 		/*If the level of w gets empty.*/

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

 		  if (level.get(v) >= l ) { 

 		    level.set(v,n);  

 		  }

 		}

 		for (int i=l+1 ; i!=n ; ++i) numb[i]=0; 

 	      } //if (numb[l])

 	    } // if (newlevel = n)

 	  } // if (excess.get(w)>0)

 	} //else

       } //while(b)

       value=excess.get(t);

       /*Max flow value.*/

       /*

 	We find an empty level, e. The Nodes above this level give 

 	a minimum cut.

       */

       int e=1;

       while(e) {

 	if(numb[e]) ++e;

 	else break;

       } 

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

 	if (level.get(v) > e) mincutvector.set(v, true);

       }

     } // void run()

     /*

       Returns the maximum value of a flow.

      */

     T maxflow() {

       return value;

     }

     /*

       Returns a minimum cut.

     */

     typename Graph::NodeMap<bool> mincut() {

       return mincutvector;

     }

   };

 }//namespace marci

 #endif