// -*- C++ -*-

//The same as preflow.h, using ResGraphWrapper

#ifndef LEMON_PREFLOW_RES_H

#define LEMON_PREFLOW_RES_H

#define H0 20

#define H1 1

#include <vector>

#include <queue>

#include <graph_wrapper.h>

#include<iostream>

namespace lemon {

  template <typename Graph, typename T, 

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

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

  class PreflowRes {

    typedef typename Graph::Node Node;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

    const Graph& G;

    Node s;

    Node t;

    const CapMap& capacity;  

    FlowMap& flow;

    T value;

    bool constzero;

    typedef ResGraphWrapper<const Graph, T, CapMap, FlowMap> ResGW;

    typedef typename ResGW::OutEdgeIt ResOutEdgeIt;

    typedef typename ResGW::InEdgeIt ResInEdgeIt;

    typedef typename ResGW::Edge ResEdge;

  public:

    PreflowRes(Graph& _G, Node _s, Node _t, CapMap& _capacity, 

	    FlowMap& _flow, bool _constzero ) :

      G(_G), s(_s), t(_t), capacity(_capacity), flow(_flow), constzero(_constzero) {}

    void run() {

      ResGW res_graph(G, capacity, flow);

      value=0;                //for the subsequent runs

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

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

      std::vector<Node> active(n-1,INVALID);

      typename Graph::template NodeMap<Node> next(G,INVALID);

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

      //We use it in both phases.

      typename Graph::template NodeMap<Node> left(G,INVALID);

      typename Graph::template NodeMap<Node> right(G,INVALID);

      std::vector<Node> level_list(n,INVALID);

      /*

	List of the nodes in level i<n.

      */

      /*

	Reverse_bfs from t in the residual graph, 

	to find the starting level.

      */

      level.set(t,0);

      std::queue<Node> bfs_queue;

      bfs_queue.push(t);

      while (!bfs_queue.empty()) {

	Node v=bfs_queue.front();	

	bfs_queue.pop();

	int l=level[v]+1;

	ResInEdgeIt e;

	for(res_graph.first(e,v); res_graph.valid(e); 

	    res_graph.next(e)) {

	  Node w=res_graph.source(e);

	  if ( level[w] == n && w != s ) {

	    bfs_queue.push(w);

	    Node first=level_list[l];

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

	    right.set(w,first);

	    level_list[l]=w;

	    level.set(w, l);

	  }

	}

      }

      if ( !constzero ) {

	/*

	  Counting the excess

	*/

	NodeIt v;

	for(G.first(v); G.valid(v); G.next(v)) {

	  T exc=0;

	  InEdgeIt e;

	  for(G.first(e,v); G.valid(e); G.next(e)) exc+=flow[e];

	  OutEdgeIt f;

	  for(G.first(f,v); G.valid(f); G.next(f)) exc-=flow[f];

	  excess.set(v,exc);	  

	  //putting the active nodes into the stack

	  int lev=level[v];

	  if ( exc > 0 && lev < n ) {

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

	    active[lev]=v;

	  }

	}

      }

      //the starting flow

      ResOutEdgeIt e;

      for(res_graph.first(e,s); res_graph.valid(e); 

	  res_graph.next(e)) {

	  Node w=res_graph.target(e);

	  if ( level[w] < n ) {	  

	    if ( excess[w] == 0 && w!=t ) {

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

	      active[level[w]]=w;

	    }

	    T rem=res_graph.resCap(e);

	    excess.set(w, excess[w]+rem);

	    res_graph.augment(e, rem ); 

	  }

      }

      /* 

	 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;

	    level.set(s,0);

	    std::queue<Node> bfs_queue;

	    bfs_queue.push(s);

	    while (!bfs_queue.empty()) {

	      Node v=bfs_queue.front();	

	      bfs_queue.pop();

	      int l=level[v]+1;

	      ResInEdgeIt e;

	      for(res_graph.first(e,v); 

		  res_graph.valid(e); res_graph.next(e)) {

		Node u=res_graph.source(e);

		if ( level[u] >= n ) { 

		  bfs_queue.push(u);

		  level.set(u, l);

		  if ( excess[u] > 0 ) {

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

		    active[l]=u;

		  }

		}

	      }

	    }

	    b=n-2;

	  }

	}

	if ( !G.valid(active[b]) ) --b; 

	else {

	  end=false;  

	  Node w=active[b];

	  active[b]=next[w];

	  int lev=level[w];

	  T exc=excess[w];

	  int newlevel=n;       //bound on the next level of w

	  ResOutEdgeIt e;

	  for(res_graph.first(e,w); res_graph.valid(e); res_graph.next(e)) {

	    Node v=res_graph.target(e);            

	    if( lev > level[v] ) {      

	      /*Push is allowed now*/

	      if ( excess[v]==0 && v!=t && v!=s ) {

		int lev_v=level[v];

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

		active[lev_v]=v;

	      }

	      T remcap=res_graph.resCap(e);

	      if ( remcap >= exc ) {       

		/*A nonsaturating push.*/

		res_graph.augment(e, exc);

		excess.set(v, excess[v]+exc);

		exc=0;

		break; 

	      } else { 

		/*A saturating push.*/

		res_graph.augment(e, remcap);

		excess.set(v, excess[v]+remcap);

		exc-=remcap;

	      }

	    } else if ( newlevel > level[v] ){

	      newlevel = level[v];

	    }	    

	  }

	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

	    Node right_n=right[w];

	    Node left_n=left[w];

	    if ( G.valid(right_n) ) {

	      if ( G.valid(left_n) ) {

		right.set(left_n, right_n);

		left.set(right_n, left_n);

	      } else {

		level_list[lev]=right_n;   

		left.set(right_n, INVALID);

	      } 

	    } else {

	      if ( G.valid(left_n) ) {

		right.set(left_n, INVALID);

	      } else { 

		level_list[lev]=INVALID;   

	      } 

	    } 

	    //unlacing ends

	    if ( !G.valid(level_list[lev]) ) {

	       //gapping starts

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

		Node v=level_list[++i];

		while ( G.valid(v) ) {

		  level.set(v,n);

		  v=right[v];

		}

		level_list[i]=INVALID;

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

	      }	     

	      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;      //now k=newlevel

		Node first=level_list[newlevel];

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

		right.set(w,first);

		left.set(w,INVALID);

		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[t];

      /*Max flow value.*/

    } //void run()

    /*

      Returns the maximum value of a flow.

     */

    T flowValue() {

      return value;

    }

    FlowMap Flow() {

      return flow;

      }

    void Flow(FlowMap& _flow ) {

      NodeIt v;

      for(G.first(v) ; G.valid(v); G.next(v))

	_flow.set(v,flow[v]);

    }

    /*

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

    */

    template<typename _CutMap>

    void minMinCut(_CutMap& M) {

      std::queue<Node> queue;

      M.set(s,true);      

      queue.push(s);

      while (!queue.empty()) {

        Node w=queue.front();

	queue.pop();

	OutEdgeIt e;

	for(G.first(e,w) ; G.valid(e); G.next(e)) {

	  Node v=G.target(e);

	  if (!M[v] && flow[e] < capacity[e] ) {

	    queue.push(v);

	    M.set(v, true);

	  }

	} 

	InEdgeIt f;

	for(G.first(f,w) ; G.valid(f); G.next(f)) {

	  Node v=G.source(f);

	  if (!M[v] && flow[f] > 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<Node> queue;

      M.set(t,true);        

      queue.push(t);

      while (!queue.empty()) {

        Node w=queue.front();

	queue.pop();

	InEdgeIt e;

	for(G.first(e,w) ; G.valid(e); G.next(e)) {

	  Node v=G.source(e);

	  if (!M[v] && flow[e] < capacity[e] ) {

	    queue.push(v);

	    M.set(v, true);

	  }

	}

	OutEdgeIt f;

	for(G.first(f,w) ; G.valid(f); G.next(f)) {

	  Node v=G.target(f);

	  if (!M[v] && flow[f] > 0 ) {

	    queue.push(v);

	    M.set(v, true);

	  }

	}

      }

      NodeIt v;

      for(G.first(v) ; G.valid(v); G.next(v)) {

	M.set(v, !M[v]);

      }

    }

    template<typename CutMap>

    void minCut(CutMap& M) {

      minMinCut(M);

    }

    void resetTarget (Node _t) {t=_t;}

    void resetSource (Node _s) {s=_s;}

    void resetCap (CapMap _cap) {capacity=_cap;}

    void resetFlow (FlowMap _flow, bool _constzero) {

      flow=_flow;

      constzero=_constzero;

    }

  };

} //namespace lemon

#endif //LEMON_PREFLOW_RES_H