jacint@21: /*
jacint@21: preflow_push_max_flow_hh
jacint@21: by jacint. 
jacint@21: Runs a preflow push algorithm with the modification, 
jacint@21: that we do not push on nodes with level at least n. 
jacint@21: Moreover, if a level gets empty, we put all nodes above that
jacint@21: level to level n. Hence, in the end, we arrive at a maximum preflow 
jacint@21: with value of a max flow value. An empty level gives a minimum cut.
jacint@21: 
jacint@21: Member functions:
jacint@21: 
jacint@21: void run() : runs the algorithm
jacint@21: 
jacint@21:   The following functions should be used after run() was already run.
jacint@21: 
jacint@21: T maxflow() : returns the value of a maximum flow
jacint@21: 
jacint@21: node_property_vector<graph_type, bool> mincut(): returns a 
jacint@21:      characteristic vector of a minimum cut.
jacint@21: */
jacint@21: 
jacint@21: #ifndef PREFLOW_PUSH_MAX_FLOW_HH
jacint@21: #define PREFLOW_PUSH_MAX_FLOW_HH
jacint@21: 
jacint@21: #include <algorithm>
jacint@21: #include <vector>
jacint@21: #include <stack>
jacint@21: 
jacint@21: #include <marci_list_graph.hh>
jacint@21: #include <marci_graph_traits.hh>
jacint@21: #include <marci_property_vector.hh>
jacint@21: #include <reverse_bfs.hh>
jacint@21: 
jacint@21: 
jacint@21: namespace marci {
jacint@21: 
jacint@21:   template <typename graph_type, typename T>
jacint@21:   class preflow_push_max_flow {
jacint@21:     
jacint@21:     typedef typename graph_traits<graph_type>::node_iterator node_iterator;
jacint@21:     typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;
jacint@21:     typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;
jacint@21:     typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;
jacint@21:     
jacint@21:     graph_type& G;
jacint@21:     node_iterator s;
jacint@21:     node_iterator t;
jacint@21:     edge_property_vector<graph_type, T>& capacity; 
jacint@21:     T value;
jacint@21:     node_property_vector<graph_type, bool> mincutvector;    
jacint@21: 
jacint@21: 
jacint@21:      
jacint@21:   public:
jacint@21:         
jacint@21:     preflow_push_max_flow(graph_type& _G, node_iterator _s, node_iterator _t, edge_property_vector<graph_type, T>& _capacity) : G(_G), s(_s), t(_t), capacity(_capacity), mincutvector(_G, false) { }
jacint@21: 
jacint@21: 
jacint@21:     /*
jacint@21:       The run() function runs a modified version of the highest label preflow-push, which only 
jacint@21:       finds a maximum preflow, hence giving the value of a maximum flow.
jacint@21:     */
jacint@21:     void run() {
jacint@21:  
jacint@21:       edge_property_vector<graph_type, T> flow(G, 0);         //the flow value, 0 everywhere  
jacint@21:       node_property_vector<graph_type, int> level(G);         //level of node
jacint@21:       node_property_vector<graph_type, T> excess(G);          //excess of node
jacint@21:             
jacint@21:       int n=number_of(G.first_node());                        //number of nodes 
jacint@21:       int b=n-2; 
jacint@21:       /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/
jacint@21:       
jacint@21:       std::vector<int> numb(n);                                //The number of nodes on level i < n.
jacint@21: 
jacint@21:       std::vector<std::stack<node_iterator> > stack(2*n-1);    //Stack of the active nodes in level i.
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21:       /*Reverse_bfs from t, to find the starting level.*/
jacint@21: 
jacint@21:       reverse_bfs<list_graph> bfs(G, t);
jacint@21:       bfs.run();
jacint@30:       for(each_node_iterator v=G.first_node(); v.valid(); ++v) 
jacint@21: 	{
jacint@21: 	  int dist=bfs.dist(v);
jacint@21: 	  level.put(v, dist); 
jacint@21: 	  ++numb[dist];
jacint@21: 	}
jacint@21: 
jacint@21:       /*The level of s is fixed to n*/ 
jacint@21:       level.put(s,n);
jacint@21: 
jacint@21: 
jacint@21:       /* Starting flow. It is everywhere 0 at the moment. */
jacint@21:      
jacint@30:       for(out_edge_iterator i=G.first_out_edge(s); i.valid(); ++i) 
jacint@21: 	{
jacint@21: 	  node_iterator w=G.head(i);
jacint@21: 	  flow.put(i, capacity.get(i)); 
jacint@21: 	  stack[bfs.dist(w)].push(w); 
jacint@21: 	  excess.put(w, capacity.get(i));
jacint@21: 	}
jacint@21: 
jacint@21: 
jacint@21:       /* 
jacint@21: 	 End of preprocessing 
jacint@21:       */
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21:       /*
jacint@21: 	Push/relabel on the highest level active nodes.
jacint@21:       */
jacint@21: 	
jacint@21:       /*While there exists an active node.*/
jacint@21:       while (b) { 
jacint@21: 
jacint@21: 	/*We decrease the bound if there is no active node of level b.*/
jacint@21: 	if (stack[b].empty()) {
jacint@21: 	  --b;
jacint@21: 	} else {
jacint@21: 
jacint@21: 	  node_iterator w=stack[b].top();    //w is the highest label active node.
jacint@21: 	  stack[b].pop();                    //We delete w from the stack.
jacint@21: 	
jacint@21: 	  int newlevel=2*n-2;                //In newlevel we maintain the next level of w.
jacint@21: 	
jacint@30: 	  for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) {
jacint@21: 	    node_iterator v=G.head(e);
jacint@21: 	    /*e is the edge wv.*/
jacint@21: 
jacint@21: 	    if (flow.get(e)<capacity.get(e)) {              
jacint@21: 	      /*e is an edge of the residual graph */
jacint@21: 
jacint@21: 	      if(level.get(w)==level.get(v)+1) {      
jacint@21: 		/*Push is allowed now*/
jacint@21: 
jacint@21: 		if (capacity.get(e)-flow.get(e) > excess.get(w)) {       
jacint@21: 		  /*A nonsaturating push.*/
jacint@21: 		  
jacint@21: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@21: 		  /*v becomes active.*/
jacint@21: 		  
jacint@21: 		  flow.put(e, flow.get(e)+excess.get(w));
jacint@21: 		  excess.put(v, excess.get(v)+excess.get(w));
jacint@21: 		  excess.put(w,0);
jacint@21: 		  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;
jacint@21: 		  break; 
jacint@21: 		} else { 
jacint@21: 		  /*A saturating push.*/
jacint@21: 
jacint@21: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@21: 		  /*v becomes active.*/
jacint@21: 
jacint@21: 		  excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e));
jacint@21: 		  excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e));
jacint@21: 		  flow.put(e, capacity.get(e));
jacint@21: 		  //std::cout << w <<" " << v <<" elore elen sat pump "   << std::endl;
jacint@21: 		  if (excess.get(w)==0) break; 
jacint@21: 		  /*If w is not active any more, then we go on to the next node.*/
jacint@21: 		  
jacint@21: 		} // if (capacity.get(e)-flow.get(e) > excess.get(w))
jacint@21: 	      } // if (level.get(w)==level.get(v)+1)
jacint@21: 	    
jacint@21: 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@21: 	    
jacint@21: 	    } //if (flow.get(e)<capacity.get(e))
jacint@21: 	 
jacint@30: 	  } //for(out_edge_iterator e=G.first_out_edge(w); e.valid(); ++e) 
jacint@21: 	  
jacint@21: 
jacint@21: 
jacint@30: 	  for(in_edge_iterator e=G.first_in_edge(w); e.valid(); ++e) {
jacint@21: 	    node_iterator v=G.tail(e);
jacint@21: 	    /*e is the edge vw.*/
jacint@21: 
jacint@21: 	    if (excess.get(w)==0) break;
jacint@21: 	    /*It may happen, that w became inactive in the first 'for' cycle.*/		
jacint@21:   
jacint@21: 	    if(flow.get(e)>0) {             
jacint@21: 	      /*e is an edge of the residual graph */
jacint@21: 
jacint@21: 	      if(level.get(w)==level.get(v)+1) {  
jacint@21: 		/*Push is allowed now*/
jacint@21: 		
jacint@21: 		if (flow.get(e) > excess.get(w)) { 
jacint@21: 		  /*A nonsaturating push.*/
jacint@21: 		  
jacint@21: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@21: 		  /*v becomes active.*/
jacint@21: 
jacint@21: 		  flow.put(e, flow.get(e)-excess.get(w));
jacint@21: 		  excess.put(v, excess.get(v)+excess.get(w));
jacint@21: 		  excess.put(w,0);
jacint@21: 		  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;
jacint@21: 		  break; 
jacint@21: 		} else {                                               
jacint@21: 		  /*A saturating push.*/
jacint@21: 		  
jacint@21: 		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
jacint@21: 		  /*v becomes active.*/
jacint@21: 		  
jacint@21: 		  flow.put(e,0);
jacint@21: 		  excess.put(v, excess.get(v)+flow.get(e));
jacint@21: 		  excess.put(w, excess.get(w)-flow.get(e));
jacint@21: 		  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;
jacint@21: 		  if (excess.get(w)==0) { break;}
jacint@21: 		} //if (flow.get(e) > excess.get(v)) 
jacint@21: 	      } //if(level.get(w)==level.get(v)+1)
jacint@21: 	      
jacint@21: 	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
jacint@21: 	      //std::cout << "Leveldecrease of node " << w << " to " << newlevel << std::endl; 
jacint@21: 
jacint@21: 	    } //if (flow.get(e)>0)
jacint@21: 
jacint@21: 	  } //for in-edge
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21: 	  /*
jacint@21: 	    Relabel
jacint@21: 	  */
jacint@21: 	  if (excess.get(w)>0) {
jacint@21: 	    /*Now newlevel <= n*/
jacint@21: 
jacint@21: 	    int l=level.get(w);	        //l is the old level of w.
jacint@21: 	    --numb[l];
jacint@21: 	   
jacint@21: 	    if (newlevel == n) {
jacint@21: 	      level.put(w,n);
jacint@21: 	      
jacint@21: 	    } else {
jacint@21: 	      
jacint@21: 	      if (numb[l]) {
jacint@21: 		/*If the level of w remains nonempty.*/
jacint@21: 		
jacint@21: 		level.put(w,++newlevel);
jacint@21: 		++numb[newlevel];
jacint@21: 		stack[newlevel].push(w);
jacint@21: 		b=newlevel;
jacint@21: 	      } else { 
jacint@21: 		/*If the level of w gets empty.*/
jacint@21: 	      
jacint@30: 		for (each_node_iterator v=G.first_node() ; v.valid() ; ++v) {
jacint@21: 		  if (level.get(v) >= l ) { 
jacint@21: 		    level.put(v,n);  
jacint@21: 		  }
jacint@21: 		}
jacint@21: 		
jacint@21: 		for (int i=l+1 ; i!=n ; ++i) numb[i]=0; 
jacint@21: 	      } //if (numb[l])
jacint@21: 	
jacint@21: 	    } // if (newlevel = n)
jacint@21: 	 
jacint@21: 	  } // if (excess.get(w)>0)
jacint@21: 
jacint@21: 
jacint@21: 	} //else
jacint@21:        
jacint@21:       } //while(b)
jacint@21: 
jacint@21:       value=excess.get(t);
jacint@21:       /*Max flow value.*/
jacint@21:       
jacint@21: 
jacint@21: 
jacint@21:       /*
jacint@21: 	We find an empty level, e. The nodes above this level give 
jacint@21: 	a minimum cut.
jacint@21:       */
jacint@21:       
jacint@21:       int e=1;
jacint@21:       
jacint@21:       while(e) {
jacint@21: 	if(numb[e]) ++e;
jacint@21: 	else break;
jacint@21:       } 
jacint@30:       for (each_node_iterator v=G.first_node(); v.valid(); ++v) {
jacint@21: 	if (level.get(v) > e) mincutvector.put(v, true);
jacint@21:       }
jacint@21:       
jacint@21: 
jacint@21:     } // void run()
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21:     /*
jacint@21:       Returns the maximum value of a flow.
jacint@21:      */
jacint@21: 
jacint@21:     T maxflow() {
jacint@21:       return value;
jacint@21:     }
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21:     /*
jacint@21:       Returns a minimum cut.
jacint@21:     */
jacint@21:     
jacint@21:     node_property_vector<graph_type, bool> mincut() {
jacint@21:       return mincutvector;
jacint@21:     }
jacint@21:     
jacint@21: 
jacint@21:   };
jacint@21: }//namespace marci
jacint@21: #endif 
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21: 
jacint@21: