# HG changeset patch
# User jacint
# Date 1074634030 0
# Node ID 181b37336b2915aca8115b0456c66ebfcda3bcf6
# Parent  bf088f14b87a35bbd293fc506b1757206d5548af
A max flow algorithm counting only the max flow value

diff -r bf088f14b87a -r 181b37336b29 src/work/preflow_push_max_flow.hh
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/work/preflow_push_max_flow.hh	Tue Jan 20 21:27:10 2004 +0000
@@ -0,0 +1,315 @@
+/*
+preflow_push_max_flow_hh
+by jacint. 
+Runs a preflow push algorithm with the modification, 
+that we do not push on nodes with level at least n. 
+Moreover, if a level gets empty, we put all nodes above that
+level to level n. Hence, in the end, we arrive at a maximum preflow 
+with value of a max flow value. An empty level gives a minimum cut.
+
+Member functions:
+
+void run() : runs the algorithm
+
+  The following functions should be used after run() was already run.
+
+T maxflow() : returns the value of a maximum flow
+
+node_property_vector<graph_type, bool> mincut(): returns a 
+     characteristic vector of a minimum cut.
+*/
+
+#ifndef PREFLOW_PUSH_MAX_FLOW_HH
+#define PREFLOW_PUSH_MAX_FLOW_HH
+
+#include <algorithm>
+#include <vector>
+#include <stack>
+
+#include <marci_list_graph.hh>
+#include <marci_graph_traits.hh>
+#include <marci_property_vector.hh>
+#include <reverse_bfs.hh>
+
+
+namespace marci {
+
+  template <typename graph_type, typename T>
+  class preflow_push_max_flow {
+    
+    typedef typename graph_traits<graph_type>::node_iterator node_iterator;
+    typedef typename graph_traits<graph_type>::each_node_iterator each_node_iterator;
+    typedef typename graph_traits<graph_type>::out_edge_iterator out_edge_iterator;
+    typedef typename graph_traits<graph_type>::in_edge_iterator in_edge_iterator;
+    
+    graph_type& G;
+    node_iterator s;
+    node_iterator t;
+    edge_property_vector<graph_type, T>& capacity; 
+    T value;
+    node_property_vector<graph_type, bool> mincutvector;    
+
+
+     
+  public:
+        
+    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) { }
+
+
+    /*
+      The run() function runs a modified version of the highest label preflow-push, which only 
+      finds a maximum preflow, hence giving the value of a maximum flow.
+    */
+    void run() {
+ 
+      edge_property_vector<graph_type, T> flow(G, 0);         //the flow value, 0 everywhere  
+      node_property_vector<graph_type, int> level(G);         //level of node
+      node_property_vector<graph_type, T> excess(G);          //excess of node
+            
+      int n=number_of(G.first_node());                        //number of nodes 
+      int b=n-2; 
+      /*b is a bound on the highest level of an active node. In the beginning it is at most n-2.*/
+      
+      std::vector<int> numb(n);                                //The number of nodes on level i < n.
+
+      std::vector<std::stack<node_iterator> > stack(2*n-1);    //Stack of the active nodes in level i.
+
+
+
+      /*Reverse_bfs from t, to find the starting level.*/
+
+      reverse_bfs<list_graph> bfs(G, t);
+      bfs.run();
+      for(each_node_iterator v=G.first_node(); v.is_valid(); ++v) 
+	{
+	  int dist=bfs.dist(v);
+	  level.put(v, dist); 
+	  ++numb[dist];
+	}
+
+      /*The level of s is fixed to n*/ 
+      level.put(s,n);
+
+
+      /* Starting flow. It is everywhere 0 at the moment. */
+     
+      for(out_edge_iterator i=G.first_out_edge(s); i.is_valid(); ++i) 
+	{
+	  node_iterator w=G.head(i);
+	  flow.put(i, capacity.get(i)); 
+	  stack[bfs.dist(w)].push(w); 
+	  excess.put(w, capacity.get(i));
+	}
+
+
+      /* 
+	 End of preprocessing 
+      */
+
+
+
+
+      /*
+	Push/relabel on the highest level active nodes.
+      */
+	
+      /*While there exists an active node.*/
+      while (b) { 
+
+	/*We decrease the bound if there is no active node of level b.*/
+	if (stack[b].empty()) {
+	  --b;
+	} else {
+
+	  node_iterator w=stack[b].top();    //w is the highest label active node.
+	  stack[b].pop();                    //We delete w from the stack.
+	
+	  int newlevel=2*n-2;                //In newlevel we maintain the next level of w.
+	
+	  for(out_edge_iterator e=G.first_out_edge(w); e.is_valid(); ++e) {
+	    node_iterator v=G.head(e);
+	    /*e is the edge wv.*/
+
+	    if (flow.get(e)<capacity.get(e)) {              
+	      /*e is an edge of the residual graph */
+
+	      if(level.get(w)==level.get(v)+1) {      
+		/*Push is allowed now*/
+
+		if (capacity.get(e)-flow.get(e) > excess.get(w)) {       
+		  /*A nonsaturating push.*/
+		  
+		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
+		  /*v becomes active.*/
+		  
+		  flow.put(e, flow.get(e)+excess.get(w));
+		  excess.put(v, excess.get(v)+excess.get(w));
+		  excess.put(w,0);
+		  //std::cout << w << " " << v <<" elore elen nonsat pump "  << std::endl;
+		  break; 
+		} else { 
+		  /*A saturating push.*/
+
+		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
+		  /*v becomes active.*/
+
+		  excess.put(v, excess.get(v)+capacity.get(e)-flow.get(e));
+		  excess.put(w, excess.get(w)-capacity.get(e)+flow.get(e));
+		  flow.put(e, capacity.get(e));
+		  //std::cout << w <<" " << v <<" elore elen sat pump "   << std::endl;
+		  if (excess.get(w)==0) break; 
+		  /*If w is not active any more, then we go on to the next node.*/
+		  
+		} // if (capacity.get(e)-flow.get(e) > excess.get(w))
+	      } // if (level.get(w)==level.get(v)+1)
+	    
+	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
+	    
+	    } //if (flow.get(e)<capacity.get(e))
+	 
+	  } //for(out_edge_iterator e=G.first_out_edge(w); e.is_valid(); ++e) 
+	  
+
+
+	  for(in_edge_iterator e=G.first_in_edge(w); e.is_valid(); ++e) {
+	    node_iterator v=G.tail(e);
+	    /*e is the edge vw.*/
+
+	    if (excess.get(w)==0) break;
+	    /*It may happen, that w became inactive in the first 'for' cycle.*/		
+  
+	    if(flow.get(e)>0) {             
+	      /*e is an edge of the residual graph */
+
+	      if(level.get(w)==level.get(v)+1) {  
+		/*Push is allowed now*/
+		
+		if (flow.get(e) > excess.get(w)) { 
+		  /*A nonsaturating push.*/
+		  
+		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
+		  /*v becomes active.*/
+
+		  flow.put(e, flow.get(e)-excess.get(w));
+		  excess.put(v, excess.get(v)+excess.get(w));
+		  excess.put(w,0);
+		  //std::cout << v << " " << w << " vissza elen nonsat pump "     << std::endl;
+		  break; 
+		} else {                                               
+		  /*A saturating push.*/
+		  
+		  if (excess.get(v)==0 && v != s) stack[level.get(v)].push(v); 
+		  /*v becomes active.*/
+		  
+		  flow.put(e,0);
+		  excess.put(v, excess.get(v)+flow.get(e));
+		  excess.put(w, excess.get(w)-flow.get(e));
+		  //std::cout << v <<" " << w << " vissza elen sat pump "     << std::endl;
+		  if (excess.get(w)==0) { break;}
+		} //if (flow.get(e) > excess.get(v)) 
+	      } //if(level.get(w)==level.get(v)+1)
+	      
+	      else {newlevel = newlevel < level.get(v) ? newlevel : level.get(v);}
+	      //std::cout << "Leveldecrease of node " << w << " to " << newlevel << std::endl; 
+
+	    } //if (flow.get(e)>0)
+
+	  } //for in-edge
+
+
+
+
+	  /*
+	    Relabel
+	  */
+	  if (excess.get(w)>0) {
+	    /*Now newlevel <= n*/
+
+	    int l=level.get(w);	        //l is the old level of w.
+	    --numb[l];
+	   
+	    if (newlevel == n) {
+	      level.put(w,n);
+	      
+	    } else {
+	      
+	      if (numb[l]) {
+		/*If the level of w remains nonempty.*/
+		
+		level.put(w,++newlevel);
+		++numb[newlevel];
+		stack[newlevel].push(w);
+		b=newlevel;
+	      } else { 
+		/*If the level of w gets empty.*/
+	      
+		for (each_node_iterator v=G.first_node() ; v.is_valid() ; ++v) {
+		  if (level.get(v) >= l ) { 
+		    level.put(v,n);  
+		  }
+		}
+		
+		for (int i=l+1 ; i!=n ; ++i) numb[i]=0; 
+	      } //if (numb[l])
+	
+	    } // if (newlevel = n)
+	 
+	  } // if (excess.get(w)>0)
+
+
+	} //else
+       
+      } //while(b)
+
+      value=excess.get(t);
+      /*Max flow value.*/
+      
+
+
+      /*
+	We find an empty level, e. The nodes above this level give 
+	a minimum cut.
+      */
+      
+      int e=1;
+      
+      while(e) {
+	if(numb[e]) ++e;
+	else break;
+      } 
+      for (each_node_iterator v=G.first_node(); v.is_valid(); ++v) {
+	if (level.get(v) > e) mincutvector.put(v, true);
+      }
+      
+
+    } // void run()
+
+
+
+    /*
+      Returns the maximum value of a flow.
+     */
+
+    T maxflow() {
+      return value;
+    }
+
+
+
+    /*
+      Returns a minimum cut.
+    */
+    
+    node_property_vector<graph_type, bool> mincut() {
+      return mincutvector;
+    }
+    
+
+  };
+}//namespace marci
+#endif 
+
+
+
+
+