// -*- 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 CapMap=typename Graph::EdgeMap<T>, 

	    typename FlowMap=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;

    const CapMap& capacity;  

    FlowMap& flow;

    T value;

  public:

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

	    FlowMap& _flow ) :

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

    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