// -*- C++ -*-

 /*

 Heuristics: 

  2 phase

  gap

  list 'level_list' on the nodes on level i implemented by hand

  stack 'active' on the active nodes on level i implemented by hand

  runs heuristic 'highest label' for H1*n relabels

  runs heuristic 'bound decrease' for H0*n relabels, starts with 'highest label'

 Parameters H0 and H1 are initialized to 20 and 10.

 Constructors:

 Preflow(Graph, Node, Node, CapMap, FlowMap)

 Members:

 void run()

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

 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.

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

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

 */

 #ifndef HUGO_PREFLOW_H

 #define HUGO_PREFLOW_H

 #define H0 20

 #define H1 1

 #include <vector>

 #include <queue>

 namespace hugo {

   template <typename Graph, typename T, 

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

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

   class Preflow {

     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;

     FlowMap& flow;

     const CapMap& capacity;  

     T value;

   public:

     Preflow(const Graph& _G, Node _s, Node _t, const CapMap& _capacity, 

 	    FlowMap& _flow ) :

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

     void run() {

       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<Node> active(n,INVALID);

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

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

       //We use it in both phases.

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

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

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

       /*

 	List of the nodes in level i<n.

       */

       /*Reverse_bfs from t, 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;

 	InEdgeIt e;

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

 	  Node w=G.tail(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);

 	  }

 	}

       }

       level.set(s,n);

       /* Starting flow. It is everywhere 0 at the moment. */     

       OutEdgeIt e;

       for(G.first(e,s); G.valid(e); G.next(e)) 

 	{

 	  T c=capacity[e];

 	  if ( c == 0 ) continue;

 	  Node w=G.head(e);

 	  if ( level[w] < n ) {	  

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

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

 	      active[level[w]]=w;

 	    }

 	    flow.set(e, c); 

 	    excess.set(w, excess[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;

 	    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;

 	      InEdgeIt e;

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

 		if ( capacity[e] == flow[e] ) continue;

 		Node u=G.tail(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;

 		  }

 		}

 	      }

 	      OutEdgeIt f;

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

 		if ( 0 == flow[f] ) continue;

 		Node u=G.head(f);

 		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

 	  OutEdgeIt e;

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

 	    if ( flow[e] == capacity[e] ) continue; 

 	    Node v=G.head(e);            

 	    //e=wv	    

 	    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 cap=capacity[e];

 	      T flo=flow[e];

 	      T remcap=cap-flo;

 	      if ( remcap >= exc ) {       

 		/*A nonsaturating push.*/

 		flow.set(e, flo+exc);

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

 		exc=0;

 		break; 

 	      } else { 

 		/*A saturating push.*/

 		flow.set(e, cap);

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

 		exc-=remcap;

 	      }

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

 	      newlevel = level[v];

 	    }	    

 	  } //for out edges wv 

 	if ( exc > 0 ) {	

 	  InEdgeIt e;

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

 	    if( flow[e] == 0 ) continue; 

 	    Node v=G.tail(e);  

 	    //e=vw

 	    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 flo=flow[e];

 	      if ( flo >= exc ) { 

 		/*A nonsaturating push.*/

 		flow.set(e, flo-exc);

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

 		exc=0;

 		break; 

 	      } else {                                               

 		/*A saturating push.*/

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

 		exc-=flo;

 		flow.set(e,0);

 	      }  

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

 	      newlevel = level[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

 	    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

 	    //gapping starts

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

 	      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;

 		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.head(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.tail(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.tail(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.head(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);

     }

   };

 } //namespace hugo

 #endif //PREFLOW_H