// -*- c++ -*-

 #ifndef LEMON_MINCOSTFLOW_H

 #define LEMON_MINCOSTFLOW_H

 ///\ingroup galgs

 ///\file

 ///\brief An algorithm for finding the minimum cost flow of given value in an uncapacitated network

 #include <lemon/dijkstra.h>

 #include <lemon/graph_wrapper.h>

 #include <lemon/maps.h>

 #include <vector>

 #include <list>

 #include <values.h>

 #include <lemon/for_each_macros.h>

 #include <lemon/unionfind.h>

 #include <lemon/bin_heap.h>

 #include <bfs_dfs.h>

 namespace lemon {

 /// \addtogroup galgs

 /// @{

   ///\brief Implementation of an algorithm for solving the minimum cost general

   /// flow problem in an uncapacitated network

   /// 

   ///

   /// The class \ref lemon::MinCostFlow "MinCostFlow" implements

   /// an algorithm for solving the following general minimum cost flow problem>

   /// 

   ///

   ///

   /// \warning It is assumed here that the problem has a feasible solution

   ///

   /// The range of the cost (weight) function is nonnegative reals but 

   /// the range of capacity function is the set of nonnegative integers. 

   /// It is not a polinomial time algorithm for counting the minimum cost

   /// maximal flow, since it counts the minimum cost flow for every value 0..M

   /// where \c M is the value of the maximal flow.

   ///

   ///\author Attila Bernath

   template <typename Graph, typename CostMap, typename SupplyDemandMap>

   class MinCostFlow {

     typedef typename CostMap::Value Cost;

     typedef typename SupplyDemandMap::Value SupplyDemand;

     typedef typename Graph::Node Node;

     typedef typename Graph::NodeIt NodeIt;

     typedef typename Graph::Edge Edge;

     typedef typename Graph::OutEdgeIt OutEdgeIt;

     typedef typename Graph::template EdgeMap<SupplyDemand> FlowMap;

     typedef ConstMap<Edge,SupplyDemand> ConstEdgeMap;

     //    typedef ConstMap<Edge,int> ConstMap;

     typedef ResGraphWrapper<const Graph,int,ConstEdgeMap,FlowMap> ResGraph;

     typedef typename ResGraph::Edge ResGraphEdge;

     class ModCostMap {   

       //typedef typename ResGraph::template NodeMap<Cost> NodeMap;

       typedef typename Graph::template NodeMap<Cost> NodeMap;

       const ResGraph& res_graph;

       //      const EdgeIntMap& rev;

       const CostMap &ol;

       const NodeMap &pot;

     public :

       typedef typename CostMap::Key Key;

       typedef typename CostMap::Value Value;

       Value operator[](typename ResGraph::Edge e) const {     

 	if (res_graph.forward(e))

 	  return  ol[e]-(pot[res_graph.target(e)]-pot[res_graph.source(e)]);   

 	else

 	  return -ol[e]-(pot[res_graph.target(e)]-pot[res_graph.source(e)]);   

       }     

       ModCostMap(const ResGraph& _res_graph,

 		   const CostMap &o,  const NodeMap &p) : 

 	res_graph(_res_graph), /*rev(_rev),*/ ol(o), pot(p){}; 

     };//ModCostMap

   protected:

     //Input

     const Graph& graph;

     const CostMap& cost;

     const SupplyDemandMap& supply_demand;//supply or demand of nodes

     //auxiliary variables

     //To store the flow

     FlowMap flow; 

     //To store the potential (dual variables)

     typedef typename Graph::template NodeMap<Cost> PotentialMap;

     PotentialMap potential;

     Cost total_cost;

   public :

    MinCostFlow(Graph& _graph, CostMap& _cost, SupplyDemandMap& _supply_demand):

      graph(_graph), 

      cost(_cost), 

      supply_demand(_supply_demand), 

      flow(_graph), 

      potential(_graph){ }

     ///Runs the algorithm.

     ///Runs the algorithm.

     ///\todo May be it does make sense to be able to start with a nonzero 

     /// feasible primal-dual solution pair as well.

     void run() {

       //To store excess-deficit values

       SupplyDemandMap excess_deficit(graph);

       //Resetting variables from previous runs

       //total_cost = 0;

       typedef typename Graph::template NodeMap<int> HeapMap;

       typedef BinHeap< Node, SupplyDemand, typename Graph::template NodeMap<int>,

 	std::greater<SupplyDemand> > 	HeapType;

       //A heap for the excess nodes

       HeapMap excess_nodes_map(graph,-1);

       HeapType excess_nodes(excess_nodes_map);

       //A heap for the deficit nodes

       HeapMap deficit_nodes_map(graph,-1);

       HeapType deficit_nodes(deficit_nodes_map);

       //A container to store nonabundant arcs

       std::list<Edge> nonabundant_arcs;

       FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){

 	flow.set(e,0);

 	nonabundant_arcs.push_back(e);

       }

       //Initial value for delta

       SupplyDemand delta = 0;

       typedef UnionFindEnum<Node, Graph::template NodeMap> UFE;

       //A union-find structure to store the abundant components

       typename UFE::MapType abund_comp_map(graph);

       UFE abundant_components(abund_comp_map);

       FOR_EACH_LOC(typename Graph::NodeIt, n, graph){

        	excess_deficit.set(n,supply_demand[n]);

 	//A supply node

 	if (excess_deficit[n] > 0){

 	  excess_nodes.push(n,excess_deficit[n]);

 	}

 	//A demand node

 	if (excess_deficit[n] < 0){

 	  deficit_nodes.push(n, - excess_deficit[n]);

 	}

 	//Finding out starting value of delta

 	if (delta < abs(excess_deficit[n])){

 	  delta = abs(excess_deficit[n]);

 	}

 	//Initialize the copy of the Dijkstra potential to zero

 	potential.set(n,0);

 	//Every single point is an abundant component initially 

 	abundant_components.insert(n);

       }

       //It'll be allright as an initial value, though this value 

       //can be the maximum deficit here

       SupplyDemand max_excess = delta;

       ///\bug This is a serious cheat here, before we have an uncapacitated ResGraph

       ConstEdgeMap const_inf_map(MAXINT);

       //We need a residual graph which is uncapacitated

       ResGraph res_graph(graph, const_inf_map, flow);

       //An EdgeMap to tell which arcs are abundant

       typename Graph::template EdgeMap<bool> abundant_arcs(graph);

       //Let's construct the sugraph consisting only of the abundant edges

       typedef ConstMap< typename Graph::Node, bool > ConstNodeMap;

       ConstNodeMap const_true_map(true);

       typedef SubGraphWrapper< const Graph, ConstNodeMap, 

 	 typename Graph::template EdgeMap<bool> > 

 	AbundantGraph;

       AbundantGraph abundant_graph(graph, const_true_map, abundant_arcs );

       //Let's construct the residual graph for the abundant graph

       typedef ResGraphWrapper<const AbundantGraph,int,ConstEdgeMap,FlowMap> 

 	ResAbGraph;

       //Again uncapacitated

       ResAbGraph res_ab_graph(abundant_graph, const_inf_map, flow);

       //We need things for the bfs

       typename ResAbGraph::template NodeMap<bool> bfs_reached(res_ab_graph);

       typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge> 

 	bfs_pred(res_ab_graph); 

       NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy;

       //Teszt celbol:

       //BfsIterator<ResAbGraph, typename ResAbGraph::template NodeMap<bool> > 

       //izebize(res_ab_graph, bfs_reached);

       //We want to run bfs-es (more) on this graph 'res_ab_graph'

       Bfs < const ResAbGraph , 

 	typename ResAbGraph::template NodeMap<bool>, 

 	typename ResAbGraph::template NodeMap<typename ResAbGraph::Edge>,

 	NullMap<typename ResAbGraph::Node, int> > 

 	bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy);

       /*This is what Marci wants for a bfs

 	template <typename Graph, 

 	    typename ReachedMap=typename Graph::template NodeMap<bool>, 

 	    typename PredMap

 	    =typename Graph::template NodeMap<typename Graph::Edge>, 

 	    typename DistMap=typename Graph::template NodeMap<int> > 

 	    class Bfs : public BfsIterator<Graph, ReachedMap> {

        */

       ModCostMap mod_cost(res_graph, cost, potential);

       Dijkstra<ResGraph, ModCostMap> dijkstra(res_graph, mod_cost);

       //We will use the number of the nodes of the graph often

       int number_of_nodes = graph.nodeNum();

       while (max_excess > 0){

 	//Reset delta if still too big

 	if (8*number_of_nodes*max_excess <= delta){

 	  delta = max_excess;

 	}

 	/*

 	 * Beginning of the delta scaling phase 

 	*/

 	//Merge and stuff

 	{

 	  SupplyDemand buf=8*number_of_nodes*delta;

 	  typename std::list<Edge>::iterator i = nonabundant_arcs.begin();

 	  while ( i != nonabundant_arcs.end() ){

 	    if (flow[*i]>=buf){

 	      Node a = abundant_components.find(res_graph.target(*i));

 	      Node b = abundant_components.find(res_graph.source(*i));

 	      //Merge

 	      if (a != b){

 		abundant_components.join(a,b);

 		//We want to push the smaller

 		//Which has greater absolut value excess/deficit

 		Node root=(abs(excess_deficit[a])>abs(excess_deficit[b]))?a:b;

 		//Which is the other

 		Node non_root = ( a == root ) ? b : a ;

 		abundant_components.makeRep(root);

 		SupplyDemand qty_to_augment = abs(excess_deficit[non_root]); 

 		//Push the positive value

 		if (excess_deficit[non_root] < 0)

 		  swap(root, non_root);

 		//If the non_root node has excess/deficit at all

 		if (qty_to_augment>0){

 		  //Find path and augment

 		  bfs.run(typename AbundantGraph::Node(non_root));

 		  //root should be reached

 		  //Augmenting on the found path

 		  Node n=root;

 		  ResGraphEdge e;

 		  while (n!=non_root){

 		    e = bfs_pred[n];

 		    n = res_graph.source(e);

 		    res_graph.augment(e,qty_to_augment);

 		  }

 		  //We know that non_root had positive excess

 		  excess_nodes.set(non_root,

 				   excess_nodes[non_root] - qty_to_augment);

 		  //But what about root node

 		  //It might have been positive and so became larger

 		  if (excess_deficit[root]>0){

 		    excess_nodes.set(root, 

 				     excess_nodes[root] + qty_to_augment);

 		  }

 		  else{

 		    //Or negative but not turned into positive

 		    deficit_nodes.set(root, 

 				      deficit_nodes[root] - qty_to_augment);

 		  }

 		  //Update the excess_deficit map

 		  excess_deficit[non_root] -= qty_to_augment;

 		  excess_deficit[root] += qty_to_augment;

 		}

 	      }

 	      //What happens to i?

 	      //Marci and Zsolt says I shouldn't do such things

 	      nonabundant_arcs.erase(i++);

 	      abundant_arcs[*i] = true;

 	    }

 	    else

 	      ++i;

 	  }

 	}

 	Node s = excess_nodes.top(); 

 	max_excess = excess_nodes[s];

 	Node t = deficit_nodes.top(); 

 	if (max_excess < deficit_nodes[t]){

 	  max_excess = deficit_nodes[t];

 	}

 	while(max_excess > (number_of_nodes-1)*delta/number_of_nodes){

 	  //s es t valasztasa

 	  //Dijkstra part	

 	  dijkstra.run(s);

 	  /*We know from theory that t can be reached

 	  if (!dijkstra.reached(t)){

 	    //There are no k paths from s to t

 	    break;

 	  };

 	  */

 	  //We have to change the potential

 	  FOR_EACH_LOC(typename ResGraph::NodeIt, n, res_graph){

 	    potential[n] += dijkstra.distMap()[n];

 	  }

 	  //Augmenting on the sortest path

 	  Node n=t;

 	  ResGraphEdge e;

 	  while (n!=s){

 	    e = dijkstra.pred(n);

 	    n = dijkstra.predNode(n);

 	    res_graph.augment(e,delta);

 	    /*

 	    //Let's update the total cost

 	    if (res_graph.forward(e))

 	      total_cost += cost[e];

 	    else 

 	      total_cost -= cost[e];	    

 	    */

 	  }

 	  //Update the excess_deficit map

 	  excess_deficit[s] -= delta;

 	  excess_deficit[t] += delta;

 	  //Update the excess_nodes heap

 	  if (delta > excess_nodes[s]){

 	    if (delta > excess_nodes[s])

 	      deficit_nodes.push(s,delta - excess_nodes[s]);

 	    excess_nodes.pop();

 	  } 

 	  else{

 	    excess_nodes.set(s, excess_nodes[s] - delta);

 	  }

 	  //Update the deficit_nodes heap

 	  if (delta > deficit_nodes[t]){

 	    if (delta > deficit_nodes[t])

 	      excess_nodes.push(t,delta - deficit_nodes[t]);

 	    deficit_nodes.pop();

 	  } 

 	  else{

 	    deficit_nodes.set(t, deficit_nodes[t] - delta);

 	  }

 	  //Dijkstra part ends here

 	  //Choose s and t again

 	  s = excess_nodes.top(); 

 	  max_excess = excess_nodes[s];

 	  t = deficit_nodes.top(); 

 	  if (max_excess < deficit_nodes[t]){

 	    max_excess = deficit_nodes[t];

 	  }

 	}

 	/*

 	 * End of the delta scaling phase 

 	*/

 	//Whatever this means

 	delta = delta / 2;

 	/*This is not necessary here

 	//Update the max_excess

 	max_excess = 0;

 	FOR_EACH_LOC(typename Graph::NodeIt, n, graph){

 	  if (max_excess < excess_deficit[n]){

 	    max_excess = excess_deficit[n];

 	  }

 	}

 	*/

       }//while(max_excess > 0)

       //return i;

     }

     ///This function gives back the total cost of the found paths.

     ///Assumes that \c run() has been run and nothing changed since then.

     Cost totalCost(){

       return total_cost;

     }

     ///Returns a const reference to the EdgeMap \c flow. \pre \ref run() must

     ///be called before using this function.

     const FlowMap &getFlow() const { return flow;}

   ///Returns a const reference to the NodeMap \c potential (the dual solution).

     /// \pre \ref run() must be called before using this function.

     const PotentialMap &getPotential() const { return potential;}

     ///This function checks, whether the given solution is optimal

     ///Running after a \c run() should return with true

     ///In this "state of the art" this only checks optimality, doesn't bother with feasibility

     ///

     ///\todo Is this OK here?

     bool checkComplementarySlackness(){

       Cost mod_pot;

       Cost fl_e;

       FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){

 	//C^{\Pi}_{i,j}

 	mod_pot = cost[e]-potential[graph.target(e)]+potential[graph.source(e)];

 	fl_e = flow[e];

 	//	std::cout << fl_e << std::endl;

 	if (mod_pot > 0 && fl_e != 0)

 	  return false;

       }

       return true;

     }

     /*

     //For testing purposes only

     //Lists the node_properties

     void write_property_vector(const SupplyDemandMap& a,

 			       char* prop_name="property"){

       FOR_EACH_LOC(typename Graph::NodeIt, i, graph){

 	cout<<"Node id.: "<<graph.id(i)<<", "<<prop_name<<" value: "<<a[i]<<endl;

       }

       cout<<endl;

     }

     */

     bool checkFeasibility(){

       SupplyDemandMap supdem(graph);

       FOR_EACH_LOC(typename Graph::EdgeIt, e, graph){

 	if ( flow[e] < 0){

 	  return false;

 	}

 	supdem[graph.source(e)] += flow[e];

 	supdem[graph.target(e)] -= flow[e];

       }

       //write_property_vector(supdem, "supdem");

       //write_property_vector(supply_demand, "supply_demand");

       FOR_EACH_LOC(typename Graph::NodeIt, n, graph){

 	if ( supdem[n] != supply_demand[n]){

 	  //cout<<"Node id.: "<<graph.id(n)<<" : "<<supdem[n]<<", should be: "<<supply_demand[n]<<endl;

 	  return false;

 	}

       }

       return true;

     }

     bool checkOptimality(){

       return checkFeasibility() && checkComplementarySlackness();

     }

   }; //class MinCostFlow

   ///@}

 } //namespace lemon

 #endif //LEMON_MINCOSTFLOW_H