/*

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.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.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.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.valid(); ++e) 

	  for(in_edge_iterator e=G.first_in_edge(w); e.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.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.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