jacint@97: // -*- C++ -*-
jacint@78: /*
jacint@78: preflow_push_max_flow_h
jacint@78: by jacint. 
jacint@78: Runs a preflow push algorithm with the modification, 
jacint@83: that we do not push on nodes with level at least n. 
jacint@83: Moreover, if a level gets empty, we set all nodes above that
jacint@78: level to level n. Hence, in the end, we arrive at a maximum preflow 
jacint@78: with value of a max flow value. An empty level gives a minimum cut.
jacint@78: 
jacint@78: Member functions:
jacint@78: 
jacint@78: void run() : runs the algorithm
jacint@78: 
jacint@78:   The following functions should be used after run() was already run.
jacint@78: 
jacint@78: T maxflow() : returns the value of a maximum flow
jacint@78: 
jacint@97: void mincut(CutMap& M) : sets M to the characteristic vector of a 
jacint@97:      minimum cut. M should be a map of bools initialized to false.
jacint@97: 
jacint@78: */
jacint@78: 
jacint@78: #ifndef PREFLOW_PUSH_MAX_FLOW_H
jacint@78: #define PREFLOW_PUSH_MAX_FLOW_H
jacint@78: 
jacint@97: #define A 1
jacint@97: 
jacint@78: #include <algorithm>
jacint@78: #include <vector>
jacint@78: #include <stack>
jacint@78: 
jacint@78: #include <reverse_bfs.h>
jacint@78: 
jacint@78: 
alpar@105: namespace hugo {
jacint@78: 
jacint@97:   template <typename Graph, typename T,  
jacint@97:     typename FlowMap=typename Graph::EdgeMap<T>, typename CapMap=typename Graph::EdgeMap<T>, 
jacint@97:     typename IntMap=typename Graph::NodeMap<int>, typename TMap=typename Graph::NodeMap<T> >
jacint@78:   class preflow_push_max_flow {
jacint@78:     
jacint@78:     typedef typename Graph::NodeIt NodeIt;
jacint@78:     typedef typename Graph::EachNodeIt EachNodeIt;
jacint@78:     typedef typename Graph::OutEdgeIt OutEdgeIt;
jacint@78:     typedef typename Graph::InEdgeIt InEdgeIt;
jacint@78:     
jacint@78:     Graph& G;
jacint@78:     NodeIt s;
jacint@78:     NodeIt t;
jacint@97:     IntMap level;
jacint@97:     CapMap& capacity;  
jacint@97:     int empty_level;    //an empty level in the end of run()
jacint@97:     T value; 
jacint@97:     
jacint@78:   public:
jacint@97:       
jacint@97:     preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, CapMap& _capacity) :
jacint@97:       G(_G), s(_s), t(_t), level(_G), capacity(_capacity) { }
jacint@78: 
jacint@78: 
jacint@78:     /*
jacint@83:       The run() function runs a modified version of the 
jacint@83:       highest label preflow-push, which only 
jacint@78:       finds a maximum preflow, hence giving the value of a maximum flow.
jacint@78:     */
jacint@78:     void run() {
jacint@78:  
jacint@97:       int n=G.nodeNum(); 
jacint@78:       int b=n-2; 
jacint@83:       /*
jacint@97: 	b is a bound on the highest level of an active node. 
jacint@83:       */
jacint@97: 
jacint@97:       IntMap level(G,n);      
jacint@97:       TMap excess(G); 
jacint@97:       FlowMap flow(G,0);
jacint@97: 
jacint@97:       std::vector<int> numb(n);    
jacint@97:       /*
jacint@97: 	The number of nodes on level i < n. It is
jacint@97: 	initialized to n+1, because of the reverse_bfs-part.
jacint@97:       */
jacint@97: 
jacint@97:       std::vector<std::stack<NodeIt> > stack(n);    
jacint@97:       //Stack of the active nodes in level i.
jacint@97: 
jacint@78: 
jacint@78:       /*Reverse_bfs from t, to find the starting level.*/
jacint@97:       level.set(t,0);
jacint@97:       std::queue<NodeIt> bfs_queue;
jacint@97:       bfs_queue.push(t);
jacint@97: 
jacint@97:       while (!bfs_queue.empty()) {
jacint@97: 
jacint@97: 	NodeIt v=bfs_queue.front();	
jacint@97: 	bfs_queue.pop();
jacint@97: 	int l=level.get(v)+1;
jacint@97: 
jacint@97: 	for(InEdgeIt e=G.template first<InEdgeIt>(v); e.valid(); ++e) {
jacint@97: 	  NodeIt w=G.tail(e);
jacint@97: 	  if ( level.get(w) == n ) {
jacint@97: 	    bfs_queue.push(w);
jacint@97: 	    ++numb[l];
jacint@97: 	    level.set(w, l);
jacint@97: 	  }
jacint@78: 	}
jacint@97:       }
jacint@97: 	
jacint@78:       level.set(s,n);
jacint@78: 
jacint@97: 
jacint@97: 
jacint@97:       /* Starting flow. It is everywhere 0 at the moment. */     
jacint@83:       for(OutEdgeIt e=G.template first<OutEdgeIt>(s); e.valid(); ++e) 
jacint@78: 	{
jacint@97: 	  if ( capacity.get(e) == 0 ) continue;
jacint@97: 	  NodeIt w=G.head(e);
jacint@97: 	  if ( level.get(w) < n ) {	  
jacint@97: 	    if ( excess.get(w) == 0 && w!=t ) stack[level.get(w)].push(w); 
jacint@83: 	    flow.set(e, capacity.get(e)); 
jacint@83: 	    excess.set(w, excess.get(w)+capacity.get(e));
jacint@83: 	  }
jacint@78: 	}
jacint@97:       
jacint@78:       /* 
jacint@78: 	 End of preprocessing 
jacint@78:       */
jacint@78: 
jacint@78: 
jacint@97:       /*
jacint@97: 	Push/relabel on the highest level active nodes.
jacint@97:       */
jacint@97:       /*While there exists an active node.*/
jacint@97:       while (b) { 
jacint@97: 	if ( stack[b].empty() ) { 
jacint@97: 	  --b;
jacint@97: 	  continue;
jacint@97: 	} 
jacint@97: 	
jacint@97: 	NodeIt w=stack[b].top();        //w is a highest label active node.
jacint@97: 	stack[b].pop();           
jacint@97: 	int lev=level.get(w);
jacint@97: 	int exc=excess.get(w);
jacint@97: 	int newlevel=2*n-2;      //In newlevel we bound the next level of w.
jacint@97: 	
jacint@97: 	//  if ( level.get(w) < n ) { //Nem tudom ez mukodik-e
jacint@97: 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@97: 	    
jacint@97: 	    if ( flow.get(e) == capacity.get(e) ) continue; 
jacint@97: 	    NodeIt v=G.head(e);            
jacint@97: 	    //e=wv	    
jacint@97: 	    
jacint@97: 	    if( lev > level.get(v) ) {      
jacint@97: 	      /*Push is allowed now*/
jacint@97: 	      
jacint@97: 	      if ( excess.get(v)==0 && v != s && v !=t ) 
jacint@97: 		stack[level.get(v)].push(v); 
jacint@97: 	      /*v becomes active.*/
jacint@97: 	      
jacint@97: 	      int cap=capacity.get(e);
jacint@97: 	      int flo=flow.get(e);
jacint@97: 	      int remcap=cap-flo;
jacint@97: 	      
jacint@97: 	      if ( remcap >= exc ) {       
jacint@97: 		/*A nonsaturating push.*/
jacint@97: 		
jacint@97: 		flow.set(e, flo+exc);
jacint@97: 		excess.set(v, excess.get(v)+exc);
jacint@97: 		exc=0;
jacint@97: 		break; 
jacint@97: 		
jacint@97: 	      } else { 
jacint@97: 		/*A saturating push.*/
jacint@97: 		
jacint@97: 		flow.set(e, cap );
jacint@97: 		excess.set(v, excess.get(v)+remcap);
jacint@97: 		exc-=remcap;
jacint@97: 	      }
jacint@97: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@97: 	    
jacint@97: 	  } //for out edges wv 
jacint@97: 	
jacint@97: 	
jacint@97: 	if ( exc > 0 ) {	
jacint@97: 	  for( InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@97: 	    
jacint@97: 	    if( flow.get(e) == 0 ) continue; 
jacint@97: 	    NodeIt v=G.tail(e);  
jacint@97: 	    //e=vw
jacint@97: 	    
jacint@97: 	    if( lev > level.get(v) ) {  
jacint@97: 	      /*Push is allowed now*/
jacint@97: 	      
jacint@97: 	      if ( excess.get(v)==0 && v != s && v !=t) 
jacint@97: 		stack[level.get(v)].push(v); 
jacint@97: 	      /*v becomes active.*/
jacint@97: 	      
jacint@97: 	      int flo=flow.get(e);
jacint@97: 	      
jacint@97: 	      if ( flo >= exc ) { 
jacint@97: 		/*A nonsaturating push.*/
jacint@97: 		
jacint@97: 		flow.set(e, flo-exc);
jacint@97: 		excess.set(v, excess.get(v)+exc);
jacint@97: 		exc=0;
jacint@97: 		break; 
jacint@97: 	      } else {                                               
jacint@97: 		/*A saturating push.*/
jacint@97: 		
jacint@97: 		excess.set(v, excess.get(v)+flo);
jacint@97: 		exc-=flo;
jacint@97: 		flow.set(e,0);
jacint@97: 	      }  
jacint@97: 	    } else if ( newlevel > level.get(v) ) newlevel = level.get(v);
jacint@97: 	    
jacint@97: 	  } //for in edges vw
jacint@97: 	  
jacint@97: 	} // if w still has excess after the out edge for cycle
jacint@97: 	
jacint@97: 	excess.set(w, exc);
jacint@97: 	
jacint@97: 	
jacint@97: 	/*
jacint@97: 	  Relabel
jacint@97: 	*/
jacint@97: 	  
jacint@97: 	if ( exc > 0 ) {
jacint@97: 	  //now 'lev' is the old level of w
jacint@97: 	  level.set(w,++newlevel);
jacint@97: 	  --numb[lev];
jacint@97: 	    
jacint@97: 	  if ( !numb[lev] && lev < A*n ) {  //If the level of w gets empty. 
jacint@97: 	      
jacint@97: 	    for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
jacint@97: 	      if (level.get(v) > lev ) level.set(v,n);  
jacint@97: 	    }
jacint@97: 	    for (int i=lev+1 ; i!=n ; ++i) numb[i]=0; 
jacint@97: 	    if ( newlevel < n ) newlevel=n; 
jacint@97: 	  } else if ( newlevel < n ) {
jacint@97: 	    ++numb[newlevel]; 
jacint@97: 	    stack[newlevel].push(w);
jacint@97: 	    b=newlevel;
jacint@97: 	  }
jacint@97: 	}
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78:       } //while(b)
jacint@78: 
jacint@78:       value=excess.get(t);
jacint@78:       /*Max flow value.*/
jacint@78:       
jacint@78: 
jacint@97:       /* 
jacint@97: 	 We count empty_level. The nodes above this level is a mincut.
jacint@78:       */
jacint@97:       while(true) {
jacint@97: 	if(numb[empty_level]) ++empty_level;
jacint@78: 	else break;
jacint@78:       } 
jacint@78:       
jacint@78:     } // void run()
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78:     /*
jacint@78:       Returns the maximum value of a flow.
jacint@78:      */
jacint@78: 
jacint@78:     T maxflow() {
jacint@78:       return value;
jacint@78:     }
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78:     /*
jacint@78:       Returns a minimum cut.
jacint@97:     */    
jacint@97:     template<typename CutMap>
jacint@97:     void mincut(CutMap& M) {
jacint@97: 
jacint@97:       for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) {
jacint@97: 	if ( level.get(v) > empty_level ) M.set(v, true);
jacint@97:       }
jacint@78:     }
jacint@97: 
jacint@78: 
jacint@78:   };
alpar@105: }//namespace hugo
jacint@78: #endif 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: