// -*- C++ -*-

 /*

 preflow_hl2.h

 by jacint. 

 Runs the highest label variant of the preflow push algorithm with 

 running time O(n^2\sqrt(m)). 

 Heuristics:

   gap: we iterate through the nodes for finding the nodes above 

        the gap and under level n. So it is quite slow.

   numb: we maintain the number of nodes in level i.

   highest label

 'A' is a parameter for the gap, we only upgrade the nodes to level n,

   if the gap is under A*n.

 The constructor runs the algorithm.

 Members:

 T maxFlow() : returns the value of a maximum flow

 T flowOnEdge(EdgeIt e) : for a fixed maximum flow x it returns x(e) 

 FlowMap Flow() : 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 minMinCut(CutMap& M) : sets M to the characteristic vector of the 

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

 void maxMinCut(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_HL2_H

 #define PREFLOW_HL2_H

 #define A .9

 #include <vector>

 #include <stack>

 #include <queue>

 namespace hugo {

   template <typename Graph, typename T, 

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

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

   class preflow_hl2 {

     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_hl2(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) :

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

       int n=G.nodeNum(); 

       int b=n-2; 

       /*

 	b is a bound on the highest level of an active node. 

       */

       typename Graph::NodeMap<int> level(G,n);      

       typename Graph::NodeMap<T> 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.

       */

       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.*/

       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 ( w!=s ) {	  

 	    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 (b) { 

 	if ( stack[b].empty() ) { 

 	  --b;

 	  continue;

 	} 

 	NodeIt w=stack[b].top();   

 	stack[b].pop();           

 	int lev=level.get(w);

 	T exc=excess.get(w);

 	int newlevel=2*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 != s && v !=t ) 

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

 	      /*v becomes active.*/

 	      T cap=capacity.get(e);

 	      T flo=flow.get(e);

 	      T 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 != s && v !=t) 

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

 	      /*v becomes active.*/

 	      T 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

 	  level.set(w,++newlevel);

 	  if ( lev < n ) {

 	    --numb[lev];

 	    if ( !numb[lev] && lev < A*n ) {  //If the level of w gets empty. 

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

 		if (level.get(v) > lev && level.get(v) < n ) level.set(v,n);  

 	      }

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

 	      if ( newlevel < n ) newlevel=n; 

 	    } else { 

 	      if ( newlevel < n ) ++numb[newlevel]; 

 	    }

 	  } 

 	  stack[newlevel].push(w);

 	  b=newlevel;

 	}

       } // 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(const EdgeIt e) {

       return flow.get(e);

     }

     /*

       Returns the maximum flow x found by the algorithm.

     */

     FlowMap Flow() {

       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 maxMinCut(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 minMinCut(CutMap& M) {

       minCut(M);

     }

   };

 }//namespace marci

 #endif