// -*- 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