jacint@78: /*
jacint@78: preflow_push_max_flow_h
jacint@78: by jacint. 
jacint@78: Runs a preflow push algorithm with the modification, 
jacint@78: that we do not push on Nodes with level at least n. 
jacint@78: 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@78: NodeMap<Graph, bool> mincut(): returns a 
jacint@78:      characteristic vector of a minimum cut.
jacint@78: */
jacint@78: 
jacint@78: #ifndef PREFLOW_PUSH_MAX_FLOW_H
jacint@78: #define PREFLOW_PUSH_MAX_FLOW_H
jacint@78: 
jacint@78: #include <algorithm>
jacint@78: #include <vector>
jacint@78: #include <stack>
jacint@78: 
jacint@78: #include <list_graph.hh>
jacint@78: #include <reverse_bfs.h>
jacint@78: 
jacint@78: 
jacint@78: namespace marci {
jacint@78: 
jacint@78:   template <typename Graph, typename 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@78:     typename Graph::EdgeMap<T>& capacity; 
jacint@78:     T value;
jacint@78:     typename Graph::NodeMap<bool> mincutvector;    
jacint@78: 
jacint@78: 
jacint@78:      
jacint@78:   public:
jacint@78:         
jacint@78:     preflow_push_max_flow(Graph& _G, NodeIt _s, NodeIt _t, typename Graph::EdgeMap<T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { }
jacint@78: 
jacint@78: 
jacint@78:     /*
jacint@78:       The run() function runs a modified version of the 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@78:       typename Graph::EdgeMap<T> flow(G, 0);         //the flow value, 0 everywhere  
jacint@78:       typename Graph::NodeMap<int> level(G);         //level of Node
jacint@78:       typename Graph::NodeMap<T> excess(G);          //excess of Node
jacint@78:             
jacint@78:       int n=G.nodeNum();                        //number of Nodes 
jacint@78:       int b=n-2; 
jacint@78:       /*b is a bound on the highest level of an active Node. In the beginning it is at most n-2.*/
jacint@78:       
jacint@78:       std::vector<int> numb(n);                                //The number of Nodes on level i < n.
jacint@78: 
jacint@78:       std::vector<std::stack<NodeIt> > stack(2*n-1);    //Stack of the active Nodes in level i.
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78:       /*Reverse_bfs from t, to find the starting level.*/
jacint@78: 
jacint@78:       reverse_bfs<Graph> bfs(G, t);
jacint@78:       bfs.run();
jacint@78:       for(EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) 
jacint@78: 	{
jacint@78: 	  int dist=bfs.dist(v);
jacint@78: 	  level.set(v, dist); 
jacint@78: 	  ++numb[dist];
jacint@78: 	}
jacint@78: 
jacint@78:       /*The level of s is fixed to n*/ 
jacint@78:       level.set(s,n);
jacint@78: 
jacint@78: 
jacint@78:       /* Starting flow. It is everywhere 0 at the moment. */
jacint@78:      
jacint@78:       for(OutEdgeIt i=G.template first<OutEdgeIt>(s); i.valid(); ++i) 
jacint@78: 	{
jacint@78: 	  NodeIt w=G.head(i);
jacint@78: 	  flow.set(i, capacity.get(i)); 
jacint@78: 	  stack[bfs.dist(w)].push(w); 
jacint@78: 	  excess.set(w, capacity.get(i));
jacint@78: 	}
jacint@78: 
jacint@78: 
jacint@78:       /* 
jacint@78: 	 End of preprocessing 
jacint@78:       */
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78:       /*
jacint@78: 	Push/relabel on the highest level active Nodes.
jacint@78:       */
jacint@78: 	
jacint@78:       /*While there exists an active Node.*/
jacint@78:       while (b) { 
jacint@78: 
jacint@78: 	/*We decrease the bound if there is no active Node of level b.*/
jacint@78: 	if (stack[b].empty()) {
jacint@78: 	  --b;
jacint@78: 	} else {
jacint@78: 
jacint@78: 	  NodeIt w=stack[b].top();    //w is the highest label active Node.
jacint@78: 	  stack[b].pop();                    //We delete w from the stack.
jacint@78: 	
jacint@78: 	  int newlevel=2*n-2;                //In newlevel we maintain the next level of w.
jacint@78: 	
jacint@78: 	  for(OutEdgeIt e=G.template first<OutEdgeIt>(w); e.valid(); ++e) {
jacint@78: 	    NodeIt v=G.head(e);
jacint@78: 	    /*e is the Edge wv.*/
jacint@78: 
jacint@78: 	    if (flow.get(e)<capacity.get(e)) {              
jacint@78: 	      /*e is an Edge of the residual graph */
jacint@78: 
jacint@78: 	      if(level.get(w)==level.get(v)+1) {      
jacint@78: 		/*Push is allowed now*/
jacint@78: 
jacint@78: 		if (capacity.get(e)-flow.get(e) > excess.get(w)) {       
jacint@78: 		  /*A nonsaturating push.*/
jacint@78: 		  
jacint@78: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@78: 		  /*v becomes active.*/
jacint@78: 		  
jacint@78: 		  flow.set(e, flow.get(e)+excess.get(w));
jacint@78: 		  excess.set(v, excess.get(v)+excess.get(w));
jacint@78: 		  excess.set(w,0);
jacint@78: 		  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;
jacint@78: 		  break; 
jacint@78: 		} else { 
jacint@78: 		  /*A saturating push.*/
jacint@78: 
jacint@78: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@78: 		  /*v becomes active.*/
jacint@78: 
jacint@78: 		  excess.set(v, excess.get(v)+capacity.get(e)-flow.get(e));
jacint@78: 		  excess.set(w, excess.get(w)-capacity.get(e)+flow.get(e));
jacint@78: 		  flow.set(e, capacity.get(e));
jacint@78: 		  //std::cout << w <<" " << v <<" elore elen sat pump "   << std::endl;
jacint@78: 		  if (excess.get(w)==0) break; 
jacint@78: 		  /*If w is not active any more, then we go on to the next Node.*/
jacint@78: 		  
jacint@78: 		} // if (capacity.get(e)-flow.get(e) > excess.get(w))
jacint@78: 	      } // if (level.get(w)==level.get(v)+1)
jacint@78: 	    
jacint@78: 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@78: 	    
jacint@78: 	    } //if (flow.get(e)<capacity.get(e))
jacint@78: 	 
jacint@78: 	  } //for(OutEdgeIt e=G.first_OutEdge(w); e.valid(); ++e) 
jacint@78: 	  
jacint@78: 
jacint@78: 
jacint@78: 	  for(InEdgeIt e=G.template first<InEdgeIt>(w); e.valid(); ++e) {
jacint@78: 	    NodeIt v=G.tail(e);
jacint@78: 	    /*e is the Edge vw.*/
jacint@78: 
jacint@78: 	    if (excess.get(w)==0) break;
jacint@78: 	    /*It may happen, that w became inactive in the first 'for' cycle.*/		
jacint@78:   
jacint@78: 	    if(flow.get(e)>0) {             
jacint@78: 	      /*e is an Edge of the residual graph */
jacint@78: 
jacint@78: 	      if(level.get(w)==level.get(v)+1) {  
jacint@78: 		/*Push is allowed now*/
jacint@78: 		
jacint@78: 		if (flow.get(e) > excess.get(w)) { 
jacint@78: 		  /*A nonsaturating push.*/
jacint@78: 		  
jacint@78: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@78: 		  /*v becomes active.*/
jacint@78: 
jacint@78: 		  flow.set(e, flow.get(e)-excess.get(w));
jacint@78: 		  excess.set(v, excess.get(v)+excess.get(w));
jacint@78: 		  excess.set(w,0);
jacint@78: 		  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;
jacint@78: 		  break; 
jacint@78: 		} else {                                               
jacint@78: 		  /*A saturating push.*/
jacint@78: 		  
jacint@78: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@78: 		  /*v becomes active.*/
jacint@78: 		  
jacint@78: 		  flow.set(e,0);
jacint@78: 		  excess.set(v, excess.get(v)+flow.get(e));
jacint@78: 		  excess.set(w, excess.get(w)-flow.get(e));
jacint@78: 		  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;
jacint@78: 		  if (excess.get(w)==0) { break;}
jacint@78: 		} //if (flow.get(e) > excess.get(v)) 
jacint@78: 	      } //if(level.get(w)==level.get(v)+1)
jacint@78: 	      
jacint@78: 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@78: 	      //std::cout << "Leveldecrease of Node " << w << " to " << newlevel << std::endl; 
jacint@78: 
jacint@78: 	    } //if (flow.get(e)>0)
jacint@78: 
jacint@78: 	  } //for in-Edge
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: 	  /*
jacint@78: 	    Relabel
jacint@78: 	  */
jacint@78: 	  if (excess.get(w)>0) {
jacint@78: 	    /*Now newlevel <= n*/
jacint@78: 
jacint@78: 	    int l=level.get(w);	        //l is the old level of w.
jacint@78: 	    --numb[l];
jacint@78: 	   
jacint@78: 	    if (newlevel == n) {
jacint@78: 	      level.set(w,n);
jacint@78: 	      
jacint@78: 	    } else {
jacint@78: 	      
jacint@78: 	      if (numb[l]) {
jacint@78: 		/*If the level of w remains nonempty.*/
jacint@78: 		
jacint@78: 		level.set(w,++newlevel);
jacint@78: 		++numb[newlevel];
jacint@78: 		stack[newlevel].push(w);
jacint@78: 		b=newlevel;
jacint@78: 	      } else { 
jacint@78: 		/*If the level of w gets empty.*/
jacint@78: 	      
jacint@78: 		for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid() ; ++v) {
jacint@78: 		  if (level.get(v) >= l ) { 
jacint@78: 		    level.set(v,n);  
jacint@78: 		  }
jacint@78: 		}
jacint@78: 		
jacint@78: 		for (int i=l+1 ; i!=n ; ++i) numb[i]=0; 
jacint@78: 	      } //if (numb[l])
jacint@78: 	
jacint@78: 	    } // if (newlevel = n)
jacint@78: 	 
jacint@78: 	  } // if (excess.get(w)>0)
jacint@78: 
jacint@78: 
jacint@78: 	} //else
jacint@78:        
jacint@78:       } //while(b)
jacint@78: 
jacint@78:       value=excess.get(t);
jacint@78:       /*Max flow value.*/
jacint@78:       
jacint@78: 
jacint@78: 
jacint@78:       /*
jacint@78: 	We find an empty level, e. The Nodes above this level give 
jacint@78: 	a minimum cut.
jacint@78:       */
jacint@78:       
jacint@78:       int e=1;
jacint@78:       
jacint@78:       while(e) {
jacint@78: 	if(numb[e]) ++e;
jacint@78: 	else break;
jacint@78:       } 
jacint@78:       for (EachNodeIt v=G.template first<EachNodeIt>(); v.valid(); ++v) {
jacint@78: 	if (level.get(v) > e) mincutvector.set(v, true);
jacint@78:       }
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@78:     */
jacint@78:     
jacint@78:     typename Graph::NodeMap<bool> mincut() {
jacint@78:       return mincutvector;
jacint@78:     }
jacint@78:     
jacint@78: 
jacint@78:   };
jacint@78: }//namespace marci
jacint@78: #endif 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: 
jacint@78: