// -*- C++ -*-

/*

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

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

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

*/

#ifndef PREFLOW_PUSH_MAX_FLOW_H

#define PREFLOW_PUSH_MAX_FLOW_H

#define A 1

#include <algorithm>

#include <vector>

#include <stack>

#include <reverse_bfs.h>

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_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;

    IntMap level;

    CapMap& capacity;  

    int empty_level;    //an empty level in the end of run()

    T value; 

  public:

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

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

    /*

      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() {

      int n=G.nodeNum(); 

      int b=n-2; 

      /*

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

      */

      IntMap level(G,n);      

      TMap excess(G); 

      FlowMap flow(G,0);

      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(n);    

      //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) 

	{

	  if ( capacity.get(e) == 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, capacity.get(e)); 

	    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) { 

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

	  --b;

	  continue;

	} 

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

	//  if ( level.get(w) < n ) { //Nem tudom ez mukodik-e

	  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.*/

	      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 != s && v !=t) 

		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

	  level.set(w,++newlevel);

	  --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.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.*/

      /* 

	 We count empty_level. The nodes above this level is a mincut.

      */

      while(true) {

	if(numb[empty_level]) ++empty_level;

	else break;

      } 

    } // void run()

    /*

      Returns the maximum value of a flow.

     */

    T maxflow() {

      return value;

    }

    /*

      Returns a minimum cut.

    */    

    template<typename CutMap>

    void mincut(CutMap& M) {

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

	if ( level.get(v) > empty_level ) M.set(v, true);

      }

    }

  };

}//namespace marci

#endif