// -*- C++ -*-

 /*

 preflow_hl3.h

 by jacint. 

 Runs the highest label variant of the preflow push algorithm with 

 running time O(n^2\sqrt(m)), with the felszippantos 'empty level' 

 and with the two-phase heuristic: if there is no active node of

 level at most n, then we go into phase 1, do a bfs

 from s, and flow the excess back to s.

 In phase 1 we shift everything downwards by n.

 'A' is a parameter for the empty_level heuristic

 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) 

 FlowMap allflow() : returns the fixed maximum flow x

 void mincut(CutMap& M) : sets M to the characteristic vector of a 

      minimum cut. M should be a map of bools initialized to false.

 void min_mincut(CutMap& M) : sets M to the characteristic vector of the 

      minimum min cut. M should be a map of bools initialized to false.

 void max_mincut(CutMap& M) : sets M to the characteristic vector of the 

      maximum min cut. M should be a map of bools initialized to false.

 */

 #ifndef PREFLOW_HL3_H

 #define PREFLOW_HL3_H

 #define A 1

 #include <vector>

 #include <stack>

 #include <queue>

 namespace marci {

   template <typename Graph, typename T, 

     typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, 

     typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> >

   class preflow_hl3 {

     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;

     FlowMap flow;

     CapMap& capacity;  

     T value;

   public:

     preflow_hl3(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) :

       G(_G), s(_s), t(_t), flow(_G, 0), capacity(_capacity) { }

     void run() {

       bool phase=0;

       int n=G.nodeNum(); 

       int b=n-2; 

       /*

 	b is a bound on the highest level of the stack. 

 	In the beginning it is at most n-2.

       */

       IntMap level(G,n);      

       TMap excess(G); 

       std::vector<int> numb(n);    

       /*

 	The number of nodes on level i < n. It is

 	initialized to n+1, because of the reverse_bfs-part.

 	Needed only in phase 0.

       */

       std::vector<std::stack<NodeIt> > stack(n);    

       //Stack of the active nodes in level i < n.

       //We use it in both phases.

       /*Reverse_bfs from t, to find the starting level.*/

       level.set(t,0);

       std::queue<NodeIt> bfs_queue;

       bfs_queue.push(t);

       while (!bfs_queue.empty()) {

 	NodeIt v=bfs_queue.front();	

 	bfs_queue.pop();

 	int l=level.get(v)+1;

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

 	  NodeIt w=G.tail(e);

 	  if ( level.get(w) == n ) {

 	    bfs_queue.push(w);

 	    ++numb[l];

 	    level.set(w, l);

 	  }

 	}

       }

       level.set(s,n);

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

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

 	{

 	  T c=capacity.get(e);

 	  if ( c == 0 ) continue;

 	  NodeIt w=G.head(e);

 	  if ( level.get(w) < n ) {	  

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

 	    flow.set(e, c); 

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

 	  }

 	}

       /* 

 	 End of preprocessing 

       */

       /*

 	Push/relabel on the highest level active nodes.

       */	

       /*While there exists an active node.*/

       while ( true ) {

 	if ( b == 0 ) {

 	  if ( phase ) break; 

 	  phase=1;

 	  level.set(s,0);

 	  std::queue<NodeIt> bfs_queue;

 	  bfs_queue.push(s);

 	  while (!bfs_queue.empty()) {

 	    NodeIt v=bfs_queue.front();	

 	    bfs_queue.pop();

 	    int l=level.get(v)+1;

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

 	      if ( capacity.get(e) == flow.get(e) ) continue;

 	      NodeIt u=G.tail(e);

 	      if ( level.get(u) == n ) { 

 		bfs_queue.push(u);

 		level.set(u, l);

 		if ( excess.get(u) > 0 ) stack[l].push(u);

 	      }

 	    }

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

 	      if ( 0 == flow.get(e) ) continue;

 	      NodeIt u=G.head(e);

 	      if ( level.get(u) == n ) { 

 		bfs_queue.push(u);

 		level.set(u, l);

 		if ( excess.get(u) > 0 ) stack[l].push(u);

 	      }

 	    }

 	  }

 	  b=n-2;

 	}

 	if ( stack[b].empty() ) --b;

 	else {

 	  NodeIt w=stack[b].top();        //w is a highest label active node.

 	  stack[b].pop();           

 	  int lev=level.get(w);

 	  int exc=excess.get(w);

 	  int newlevel=n;                 //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) ) continue; 

 	    NodeIt v=G.head(e);            

 	    //e=wv	    

 	    if( lev > level.get(v) ) {      

 	      /*Push is allowed now*/

 	      if ( excess.get(v)==0 && v !=t && v!=s ) 

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

 	      /*v becomes active.*/

 	      int cap=capacity.get(e);

 	      int flo=flow.get(e);

 	      int remcap=cap-flo;

 	      if ( remcap >= exc ) {       

 		/*A nonsaturating push.*/

 		flow.set(e, flo+exc);

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

 		exc=0;

 		break; 

 	      } else { 

 		/*A saturating push.*/

 		flow.set(e, cap );

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

 		exc-=remcap;

 	      }

 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);

 	  } //for out edges wv 

 	if ( exc > 0 ) {	

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

 	    if( flow.get(e) == 0 ) continue; 

 	    NodeIt v=G.tail(e);  

 	    //e=vw

 	    if( lev > level.get(v) ) {  

 	      /*Push is allowed now*/

 	      if ( excess.get(v)==0 && v !=t && v!=s ) 

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

 	      /*v becomes active.*/

 	      int flo=flow.get(e);

 	      if ( flo >= exc ) { 

 		/*A nonsaturating push.*/

 		flow.set(e, flo-exc);

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

 		exc=0;

 		break; 

 	      } else {                                               

 		/*A saturating push.*/

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

 		exc-=flo;

 		flow.set(e,0);

 	      }  

 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);

 	  } //for in edges vw

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

 	excess.set(w, exc);

 	/*

 	  Relabel

 	*/

 	if ( exc > 0 ) {

 	  //now 'lev' is the old level of w

 	  if ( phase ) {

 	    level.set(w,++newlevel);

 	    stack[newlevel].push(w);

 	    b=newlevel;

 	  } else {

 	    if ( newlevel >= n-2 || --numb[lev] == 0 ) {

 	      level.set(w,n);

 	      if ( newlevel < n ) {

 		std::queue<NodeIt> bfs_queue;

 		bfs_queue.push(w);

 		while (!bfs_queue.empty()) {

 		  NodeIt v=bfs_queue.front();	

 		  bfs_queue.pop();

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

 		    if ( capacity.get(e) == flow.get(e) ) continue;

 		    NodeIt u=G.head(e);

 		    if ( level.get(u) < n ) { 

 		      bfs_queue.push(u);

 		      --numb[level.get(u)];

 		      level.set(u, n);

 		    }

 		  }

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

 		    if ( 0 == flow.get(e) ) continue;

 		    NodeIt u=G.tail(e);

 		    if ( level.get(u) < n ) { 

 		      bfs_queue.push(u);

 		      --numb[level.get(u)];

 		      level.set(u, n);

 		    }

 		  }

 		}

 	      }

 	      b=n-1;

 	    } else {

 	      level.set(w,++newlevel);

 	      stack[newlevel].push(w);

 	      ++numb[newlevel];

 	      b=newlevel;

 	    }

 	  }

 	}

 	} // if stack[b] is nonempty

       } // while(true)

       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.

     */

     FlowMap allflow() {

       return flow;

     }

     /*

       Returns the minimum min cut, by a bfs from s in the residual graph.

     */

     template<typename CutMap>

     void mincut(CutMap& M) {

       std::queue<NodeIt> queue;

       M.set(s,true);      

       queue.push(s);

       while (!queue.empty()) {

         NodeIt w=queue.front();

 	queue.pop();

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

 	  NodeIt v=G.head(e);

 	  if (!M.get(v) && flow.get(e) < capacity.get(e) ) {

 	    queue.push(v);

 	    M.set(v, true);

 	  }

 	} 

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

 	  NodeIt v=G.tail(e);

 	  if (!M.get(v) && flow.get(e) > 0 ) {

 	    queue.push(v);

 	    M.set(v, true);

 	  }

 	} 

       }

     }

     /*

       Returns the maximum min cut, by a reverse bfs 

       from t in the residual graph.

     */

     template<typename CutMap>

     void max_mincut(CutMap& M) {

       std::queue<NodeIt> queue;

       M.set(t,true);        

       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 (!M.get(v) && flow.get(e) < capacity.get(e) ) {

 	    queue.push(v);

 	    M.set(v, true);

 	  }

 	}

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

 	  NodeIt v=G.head(e);

 	  if (!M.get(v) && flow.get(e) > 0 ) {

 	    queue.push(v);

 	    M.set(v, true);

 	  }

 	}

       }

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

 	M.set(v, !M.get(v));

       }

     }

     template<typename CutMap>

     void min_mincut(CutMap& M) {

       mincut(M);

     }

   };

 }//namespace marci

 #endif