// -*- c++ -*-

#ifndef HUGO_MINCOSTFLOW_H

#define HUGO_MINCOSTFLOW_H

///\ingroup galgs

///\file

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

#include <hugo/dijkstra.h>

#include <hugo/graph_wrapper.h>

#include <hugo/maps.h>

#include <vector>

#include <list>

#include <for_each_macros.h>

#include <hugo/union_find.h>

namespace hugo {

/// \addtogroup galgs

/// @{

  ///\brief Implementation of an algorithm for finding the minimum cost flow 

  /// of given value in an uncapacitated network

  /// 

  ///

  /// The class \ref hugo::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 length (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 LengthMap, typename SupplyDemandMap>

  class MinCostFlow {

    typedef typename LengthMap::ValueType Length;

    typedef typename SupplyDemandMap::ValueType 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<int> EdgeIntMap;

    //    typedef ConstMap<Edge,int> ConstMap;

    typedef ResGraphWrapper<const Graph,int,CapacityMap,EdgeIntMap> ResGraphType;

    typedef typename ResGraphType::Edge ResGraphEdge;

    class ModLengthMap {   

      //typedef typename ResGraphType::template NodeMap<Length> NodeMap;

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

      const ResGraphType& res_graph;

      //      const EdgeIntMap& rev;

      const LengthMap &ol;

      const NodeMap &pot;

    public :

      typedef typename LengthMap::KeyType KeyType;

      typedef typename LengthMap::ValueType ValueType;

      ValueType operator[](typename ResGraphType::Edge e) const {     

	if (res_graph.forward(e))

	  return  ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]);   

	else

	  return -ol[e]-(pot[res_graph.head(e)]-pot[res_graph.tail(e)]);   

      }     

      ModLengthMap(const ResGraphType& _res_graph,

		   const LengthMap &o,  const NodeMap &p) : 

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

    };//ModLengthMap

  protected:

    //Input

    const Graph& graph;

    const LengthMap& length;

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

    //auxiliary variables

    //To store the flow

    EdgeIntMap flow; 

    //To store the potentila (dual variables)

    typename Graph::template NodeMap<Length> potential;

    //To store excess-deficit values

    SupplyDemandMap excess_deficit;

    Length total_length;

  public :

    MinCostFlow(Graph& _graph, LengthMap& _length, SupplyDemandMap& _supply_demand) : graph(_graph), 

      length(_length), 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() {

      //Resetting variables from previous runs

      //total_length = 0;

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

      typedef Heap< 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

      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

      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;

      //ConstMap<Edge,SupplyDemand> ConstEdgeMap;

      //We need a residual graph which is uncapacitated

      ResGraphType res_graph(graph, flow);

      //An EdgeMap to tell which arcs are abundant

      template typename Graph::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< Graph, ConstNodeMap, 

	 template typename Graph::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,CapacityMap,EdgeIntMap> 

	ResAbGraph;

      //Again uncapacitated

      ResAbGraph res_ab_graph(abundant_graph, flow);

      //We need things for the bfs

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

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

	bfs_pred(res_ab_graph); 

      NullMap<typename ResAbGraph::Node, int> bfs_dist_dummy(res_ab_graph);

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

      Bfs < ResAbGraph , 

	typename ResAbGraph::NodeMap<bool>, 

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

	NullMap<typename ResAbGraph::Node, int> > 

	bfs(res_ab_graph, bfs_reached, bfs_pred, bfs_dist_dummy);

      ModLengthMap mod_length(res_graph, length, potential);

      Dijkstra<ResGraphType, ModLengthMap> dijkstra(res_graph, mod_length);

      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;

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

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

	    if (flow[i]>=buf){

	      Node a = abundant_components.find(res_graph.head(i));

	      Node b = abundant_components.find(res_graph.tail(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(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.tail(e);

		    res_graph.augment(e,qty_to_augment);

		  }

		  //We know that non_root had positive excess

		  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[root] += qty_to_augment;

		  }

		  else{

		    //Or negative but not turned into positive

		    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(); 

	SupplyDemand max_excess = excess_nodes[s];

	Node t = deficit_nodes.top(); 

	if (max_excess < deficit_nodes[t]){

	  max_excess = deficit_nodes[t];

	}

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

	  //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 ResGraphType::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 length

	    if (res_graph.forward(e))

	      total_length += length[e];

	    else 

	      total_length -= length[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[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[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 length of the found paths.

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

    Length totalLength(){

      return total_length;

    }

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

    ///be called before using this function.

    const EdgeIntMap &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 EdgeIntMap &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 check optimality, doesn't bother with feasibility

    ///

    ///\todo Is this OK here?

    bool checkComplementarySlackness(){

      Length mod_pot;

      Length fl_e;

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

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

	mod_pot = length[e]-potential[graph.head(e)]+potential[graph.tail(e)];

	fl_e = flow[e];

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

	if (0<fl_e && fl_e<capacity[e]){

	  if (mod_pot != 0)

	    return false;

	}

	else{

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

	    return false;

	  if (mod_pot < 0 && fl_e != capacity[e])

	    return false;

	}

      }

      return true;

    }

  }; //class MinCostFlow

  ///@}

} //namespace hugo

#endif //HUGO_MINCOSTFLOW_H