// -*- c++ -*-

#ifndef HUGO_MINLENGTHPATHS_H

#define HUGO_MINLENGTHPATHS_H

///\file

///\brief An algorithm for finding k paths of minimal total length.

#include <iostream>

#include <dijkstra.h>

#include <graph_wrapper.h>

#include <maps.h>

#include <vector>

namespace hugo {

  ///\brief Implementation of an algorithm for finding k paths between 2 nodes 

  /// of minimal total length 

  ///

  /// The class \ref hugo::MinLengthPaths "MinLengthPaths" implements

  /// an algorithm which finds k edge-disjoint paths

  /// from a given source node to a given target node in an

  /// edge-weighted directed graph having minimal total weigth (length).

  template <typename Graph, typename LengthMap>

  class MinLengthPaths {

    typedef typename LengthMap::ValueType Length;

    typedef typename Graph::Node Node;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    typedef typename Graph::EdgeMap<int> EdgeIntMap;

    typedef ConstMap<Edge,int> ConstMap;

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

    class ModLengthMap {   

      typedef typename ResGraphType::NodeMap<Length> NodeMap;

      const ResGraphType& G;

      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 ( (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)] ) <0 ){

	//  std::cout<<"Negative length!!"<<std::endl;

	//}

	return (1-2*rev[e])*ol[e]-(pot[G.head(e)]-pot[G.tail(e)]);   

      }     

      ModLengthMap(const ResGraphType& _G, const EdgeIntMap& _rev, 

		   const LengthMap &o,  const NodeMap &p) : 

	G(_G), rev(_rev), ol(o), pot(p){}; 

    };

    const Graph& G;

    const LengthMap& length;

    //auxiliary variables

    //The value is 1 iff the edge is reversed. 

    //If the algorithm has finished, the edges of the seeked paths are 

    //exactly those that are reversed 

    EdgeIntMap reversed; 

    //Container to store found paths

    std::vector< std::vector<Edge> > paths;

  public :

    MinLengthPaths(Graph& _G, LengthMap& _length) : G(_G), 

      length(_length), reversed(_G)/*, dijkstra_dist(_G)*/{ }

    ///Runs the algorithm

    ///Returns k if there are at least k edge-disjoint paths from s to t.

    ///Otherwise it returns the number of edge-disjoint paths from s to t.

    int run(Node s, Node t, int k) {

      ConstMap const1map(1);

      //We need a residual graph, in which some of the edges are reversed

      ResGraphType res_graph(G, reversed, const1map);

      //Initialize the copy of the Dijkstra potential to zero

      typename ResGraphType::NodeMap<Length> dijkstra_dist(res_graph);

      ModLengthMap mod_length(res_graph, reversed, length, dijkstra_dist);

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

      int i;

      for (i=0; i<k; ++i){

	dijkstra.run(s);

	if (!dijkstra.reached(t)){

	  //There are no k paths from s to t

	  break;

	};

	{

	  //We have to copy the potential

	  typename ResGraphType::NodeIt n;

	  for ( res_graph.first(n) ; res_graph.valid(n) ; res_graph.next(n) ) {

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

	  }

	}

	//Reversing the sortest path

	Node n=t;

	Edge e;

	while (n!=s){

	  e = dijkstra.pred(n);

	  n = dijkstra.predNode(n);

	  reversed[e] = 1-reversed[e];

	}

      }

      //Let's find the paths

      //We put the paths into vectors (just for now). In the meantime we lose 

      //the information stored in 'reversed'

      //We suppose the lengths to be positive now.

      paths.clear();

      paths.resize(k);

      for (int j=0; j<i; ++j){

	Node n=s;

	OutEdgeIt e;

	while (n!=t){

	  G.first(e,n);

	  while (!reversed[e]){

	    G.next(e);

	  }

	  n = G.head(e);

	  paths[j].push_back(e);

	  reversed[e] = 1-reversed[e];

	}

      }

      return i;

    }

  }; //class MinLengthPaths

} //namespace hugo

#endif //HUGO_MINLENGTHPATHS_H