/* -*- C++ -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library

  *

  * Copyright (C) 2003-2008

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_CSP_H

 #define LEMON_CSP_H

 ///\ingroup approx

 ///\file

 ///\brief Algorithm for the Resource Constrained Shortest Path problem.

 ///

 #include <lemon/list_graph.h>

 #include <lemon/graph_utils.h>

 #include <lemon/error.h>

 #include <lemon/maps.h>

 #include <lemon/tolerance.h>

 #include <lemon/dijkstra.h>

 #include <lemon/path.h>

 #include <lemon/counter.h>

 namespace lemon {

   ///\ingroup approx

   ///

   ///\brief Algorithms for the Resource Constrained Shortest Path Problem

   ///

   ///The Resource Constrained Shortest (Least Cost) Path problem is the

   ///following. We are given a directed graph with two additive weightings

   ///on the edges, referred as \e cost and \e delay. In addition,

   ///a source and a destination node \e s and \e t and a delay

   ///constraint \e D is given. A path \e p is called \e feasible

   ///if <em>delay(p)\<=D</em>. Then, the task is to find the least cost

   ///feasible path.

   ///

   template<class Graph,

 	   class CM=typename Graph:: template EdgeMap<double>,

 	   class DM=CM>

   class ConstrainedShortestPath 

   {

   public:

     GRAPH_TYPEDEFS(typename Graph);

     typedef SimplePath<Graph> Path;

   private:

     const Graph &_g;

     Tolerance<double> tol;

     const CM &_cost;

     const DM &_delay;

     class CoMap 

     {

       const CM &_cost;

       const DM &_delay;

       double _lambda;

     public:

       typedef typename CM::Key Key;

       typedef double Value;

       CoMap(const CM &c, const DM &d) :_cost(c), _delay(d), _lambda(0) {}

       double lambda() const { return _lambda; }

       void lambda(double l)  { _lambda=l; }

       Value operator[](Key &e) const 

       {

 	return _cost[e]+_lambda*_delay[e];

       }

     };

     CoMap _co_map;

     Dijkstra<Graph, CoMap> _dij;

   public:

     /// \brief Constructor

     ///Constructor

     ///

     ConstrainedShortestPath(const Graph &g, const CM &ct, const DM &dl)

       : _g(g), _cost(ct), _delay(dl),

 	_co_map(ct, dl), _dij(_g,_co_map) {}

     ///Compute the cost of a path

     double cost(const Path &p) const

     {

       double s=0;

       //      Path r;  

       for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_cost[e];

       return s;

     }

     ///Compute the delay of a path

     double delay(const Path &p) const

     {

       double s=0;

       for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_delay[e];

       return s;

     }

     ///Runs the LARAC algorithm

     ///This function runs a Lagrange relaxation based heuristic to find

     ///a delay constrained least cost path.

     ///\param s source node

     ///\param t target node

     ///\param delta upper bound on the delta

     ///\retval lo_bo a lower bound on the optimal solution

     ///\return the found path or an empty 

     Path larac(Node s, Node t, double delta, double &lo_bo) 

     {

       double lambda=0;

       double cp,cq,dp,dq,cr,dr;

       Path p;

       Path q;

       Path r;

       {

 	Dijkstra<Graph,CM> dij(_g,_cost);

 	dij.run(s,t);

 	if(!dij.reached(t)) return Path();

 	p=dij.path(t);

 	cp=cost(p);

 	dp=delay(p);

       }

       if(delay(p)<=delta) return p;

       {

 	Dijkstra<Graph,DM> dij(_g,_delay);

 	dij.run(s,t);

 	q=dij.path(t);

 	cq=cost(q);

 	dq=delay(q);

       }

       if(delay(q)>delta) return Path();

       while (true) {

 	lambda=(cp-cq)/(dq-dp);

 	_co_map.lambda(lambda);

 	_dij.run(s,t);

 	r=_dij.path(t);

 	cr=cost(r);

 	dr=delay(r);

 	if(!tol.less(cr+lambda*dr,cp+lambda*dp)) {

 	  lo_bo=cq+lambda*(dq-delta);

 	  return q;

 	}

 	else if(tol.less(dr,delta)) 

 	  {

 	    q=r;

 	    cq=cr;

 	    dq=dr;

 	  }

 	else if(tol.less(delta,dr))

 	  {

 	    p=r;

 	    cp=cr;

 	    dp=dr;

 	  }

 	else return r;

       }

     }

   };

 } //END OF NAMESPACE LEMON

 #endif