// -*- C++ -*-

//hogy kell azt megcsinalni hogy a konstruktorban a FlowMap-nek legyen default erteke (a 0 map)

/*

preflow_aug.h

by jacint. 

The same as preflow.h, the only difference is that here 

we start from a given flow. 

The constructor runs the algorithm: 

template <typename Graph, typename T, 

    typename Graph_EdgeMap_T_1=typename Graph::EdgeMap<T>,

    typename Graph_EdgeMap_T_2=typename Graph::EdgeMap<T> > 

PreflowAug(Graph G, G_NodeIt s, G_NodeIt t, G_EdgeMap_T_1 capacity, 

   G_EdgeMap_T_2 flow, bool flow_type)

'capacity' must be non-negative, if flow_type=0 then 

'flow' must be a flow, otherwise it must be a preflow.

Members:

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

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

G_EdgeMap_T_2 flow() : returns the fixed maximum flow x

void minMinCut(G_NodeMap_bool& M) :

     sets M to the characteristic vector of the 

     minimum min cut. M must be initialized to false.

void maxMinCut(G_NodeMap_bool& M) : 

     sets M to the characteristic vector of the 

     maximum min cut. M must be initialized to false.

void minCut(G_NodeMap_bool& M) :

     sets M to the characteristic vector of a  

     min cut. M must be initialized to false.

*/

#ifndef PREFLOW_H

#define PREFLOW_H

#define H0 20

#define H1 1

#include <vector>

#include <queue>

#include <iostream> //for error handling

#include <time_measure.h>

namespace hugo {

  template <typename Graph, typename T, 

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

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

  class PreflowAug {

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::EachNodeIt EachNodeIt;

    typedef typename Graph::EachEdgeIt EachEdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

    Graph& G;

    NodeIt s;

    NodeIt t;

    CapMap& capacity;  

    FlowMap& _flow;

    bool flow_type;

    T value;

  public:

    double time;

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

	       CapMap& _capacity, FlowMap& __flow, bool _flow_type ) :

      G(_G), s(_s), t(_t), capacity(_capacity), _flow(__flow), 

      flow_type(_flow_type)

    {

      bool phase=0;        //phase 0 is the 1st phase, phase 1 is the 2nd

      int n=G.nodeNum(); 

      int heur0=(int)(H0*n);  //time while running 'bound decrease' 

      int heur1=(int)(H1*n);  //time while running 'highest label'

      int heur=heur1;         //starting time interval (#of relabels)

      bool what_heur=1;       

      /*

	what_heur is 0 in case 'bound decrease' 

	and 1 in case 'highest label'

      */

      bool end=false;     

      /*

	Needed for 'bound decrease', 'true'

	means no active nodes are above bound b.

      */

      int relabel=0;

      int k=n-2;  //bound on the highest level under n containing a node

      int b=k;    //bound on the highest level under n of an active node

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

      typename Graph::NodeMap<T> excess(G); 

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

      typename Graph::NodeMap<NodeIt> next(G);

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

      //We use it in both phases.

      typename Graph::NodeMap<NodeIt> left(G);

      typename Graph::NodeMap<NodeIt> right(G);

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

      /*

	List of the nodes in level i<n.

      */

      /*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) {

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

	  NodeIt w=G.tail(e);

	  if ( level.get(w) == n && w != s ) {

	    bfs_queue.push(w);

	    NodeIt first=level_list[l];

	    if ( first.valid() ) left.set(first,w);

	    right.set(w,first);

	    level_list[l]=w;

	    level.set(w, l);

	  }

	}

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

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

	  NodeIt w=G.head(e);

	  if ( level.get(w) == n && w != s ) {

	    bfs_queue.push(w);

	    NodeIt first=level_list[l];

	    if ( first != 0 ) left.set(first,w);

	    right.set(w,first);

	    level_list[l]=w;

	    level.set(w, l);

	  }

	}

      }

      level.set(s,n);

      /*The starting excess.*/

      if ( flow_type ) {

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

	  if ( _flow.get(e) > 0 ) {

	    T flo=_flow.get(e);

	    NodeIt u=G.tail(e);

	    NodeIt v=G.head(e);

	    excess.set(u, excess.get(u)-flo);

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

	  }

	}

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

	  if ( excess.get(v) < 0 ) {

	    std::cerr<<"It is not a pre_flow."<<std::endl;

	    exit(1);

	  } else {

	    next.set(v,active[level.get(v)]);

	    active[level.get(v)]=v;}

	}

      }

      /* 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)-_flow.get(e);

	  if ( c == 0 ) continue;

	  NodeIt w=G.head(e);

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

	    if ( excess.get(w) == 0 && w!=t ) {

	      next.set(w,active[level.get(w)]);

	      active[level.get(w)]=w;

	    }

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

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

	  }

	}

      /* 

	 End of preprocessing 

      */

      /*

	Push/relabel on the highest level active nodes.

      */	

      while ( true ) {

	if ( b == 0 ) {

	  if ( phase ) break;

	  if ( !what_heur && !end && k > 0 ) {

	    b=k;

	    end=true;

	  } else {

	    phase=1;

	    time=currTime();

	    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 ) {

		    next.set(u,active[l]);

		    active[l]=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 ) {

		    next.set(u,active[l]);

		    active[l]=u;

		  }

		}

	      }

	    }

	    b=n-2;

	    }

	}

	if ( active[b] == 0 ) --b; 

	else {

	  end=false;  

	  NodeIt w=active[b];

	  active[b]=next.get(w);

	  int lev=level.get(w);

	  T exc=excess.get(w);

	  int newlevel=n;       //bound on 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 ) {

		int lev_v=level.get(v);

		next.set(v,active[lev_v]);

		active[lev_v]=v;

	      }

	      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!=t && v!=s ) {

		int lev_v=level.get(v);

		next.set(v,active[lev_v]);

		active[lev_v]=v;

	      }

	      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

	  if ( phase ) {

	    level.set(w,++newlevel);

	    next.set(w,active[newlevel]);

	    active[newlevel]=w;

	    b=newlevel;

	  } else {

	    //unlacing starts

	    NodeIt right_n=right.get(w);

	    NodeIt left_n=left.get(w);

	    if ( right_n != 0 ) {

	      if ( left_n != 0 ) {

		right.set(left_n, right_n);

		left.set(right_n, left_n);

	      } else {

		level_list[lev]=right_n;   

		left.set(right_n, 0);

	      } 

	    } else {

	      if ( left_n != 0 ) {

		right.set(left_n, 0);

	      } else { 

		level_list[lev]=0;   

	      } 

	    } 

	    //unlacing ends

	    //gapping starts

	    if ( level_list[lev]==0 ) {

	      for (int i=lev; i!=k ; ) {

		NodeIt v=level_list[++i];

		while ( v != 0 ) {

		  level.set(v,n);

		  v=right.get(v);

		}

		level_list[i]=0;

		if ( !what_heur ) active[i]=0;

	      }	     

	      level.set(w,n);

	      b=lev-1;

	      k=b;

	      //gapping ends

	    } else {

	      if ( newlevel == n ) level.set(w,n); 

	      else {

		level.set(w,++newlevel);

		next.set(w,active[newlevel]);

		active[newlevel]=w;

		if ( what_heur ) b=newlevel;

		if ( k < newlevel ) ++k;

		NodeIt first=level_list[newlevel];

		if ( first != 0 ) left.set(first,w);

		right.set(w,first);

		left.set(w,0);

		level_list[newlevel]=w;

	      }

	    }

	    ++relabel; 

	    if ( relabel >= heur ) {

	      relabel=0;

	      if ( what_heur ) {

		what_heur=0;

		heur=heur0;

		end=false;

	      } else {

		what_heur=1;

		heur=heur1;

		b=k; 

	      }

	    }

	  } //phase 0

	} // if ( exc > 0 )

	}  // 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 flow(EdgeIt e) {

      return _flow.get(e);

    }

    FlowMap flow() {

      return _flow;

      }

    void flow(FlowMap& __flow ) {

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

	__flow.set(v,_flow.get(v));

	}

    /*

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

    */

    template<typename _CutMap>

    void minMinCut(_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 minCut(CutMap& M) {

      minMinCut(M);

    }

  };

}//namespace marci

#endif