/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

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

  *

  * Copyright (C) 2003-2010

  * 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_INSERTION_TSP_H

 #define LEMON_INSERTION_TSP_H

 /// \ingroup tsp

 /// \file

 /// \brief Insertion algorithm for symmetric TSP

 #include <vector>

 #include <lemon/full_graph.h>

 #include <lemon/maps.h>

 #include <lemon/random.h>

 namespace lemon {

   /// \brief Insertion algorithm for symmetric TSP.

   ///

   /// InsertionTsp implements the insertion heuristic for solving

   /// symmetric \ref tsp "TSP".

   ///

   /// This is a basic TSP heuristic that has many variants.

   /// It starts with a subtour containing a few nodes of the graph and it

   /// iteratively inserts the other nodes into this subtour according to a

   /// certain node selection rule.

   ///

   /// This implementation provides four different node selection rules,

   /// from which the most powerful one is used by default.

   /// For more information, see \ref SelectionRule.

   ///

   /// \tparam CM Type of the cost map.

   template <typename CM>

   class InsertionTsp

   {

     public:

       /// Type of the cost map

       typedef CM CostMap;

       /// Type of the edge costs

       typedef typename CM::Value Cost;

     private:

       GRAPH_TYPEDEFS(FullGraph);

       const FullGraph &_gr;

       const CostMap &_cost;

       std::vector<Node> _notused;

       std::vector<Node> _path;

       Cost _sum;

     public:

       /// \brief Constants for specifying the node selection rule.

       ///

       /// Enum type containing constants for specifying the node selection

       /// rule for the \ref run() function.

       ///

       /// During the algorithm, nodes are selected for addition to the current

       /// subtour according to the applied rule.

       /// In general, the FARTHEST yields the best tours, thus it is the

       /// default option. RANDOM usually gives somewhat worse results, but

       /// it is much faster than the others and it is the most robust.

       ///

       /// The desired selection rule can be specified as a parameter of the

       /// \ref run() function.

       enum SelectionRule {

         /// An unvisited node having minimum distance from the current

         /// subtour is selected at each step.

         /// The algorithm runs in O(n<sup>3</sup>) time using this

         /// selection rule.

         NEAREST,

         /// An unvisited node having maximum distance from the current

         /// subtour is selected at each step.

         /// The algorithm runs in O(n<sup>3</sup>) time using this

         /// selection rule.

         FARTHEST,

         /// An unvisited node whose insertion results in the least

         /// increase of the subtour's total cost is selected at each step.

         /// The algorithm runs in O(n<sup>3</sup>) time using this

         /// selection rule.

         CHEAPEST,

         /// An unvisited node is selected randomly without any evaluation

         /// at each step.

         /// The global \ref rnd "random number generator instance" is used.

         /// You can seed it before executing the algorithm, if you

         /// would like to.

         /// The algorithm runs in O(n<sup>2</sup>) time using this

         /// selection rule.

         RANDOM

       };

     public:

       /// \brief Constructor

       ///

       /// Constructor.

       /// \param gr The \ref FullGraph "full graph" the algorithm runs on.

       /// \param cost The cost map.

       InsertionTsp(const FullGraph &gr, const CostMap &cost)

         : _gr(gr), _cost(cost) {}

       /// \name Execution Control

       /// @{

       /// \brief Runs the algorithm.

       ///

       /// This function runs the algorithm.

       ///

       /// \param rule The node selection rule. For more information, see

       /// \ref SelectionRule.

       ///

       /// \return The total cost of the found tour.

       Cost run(SelectionRule rule = FARTHEST) {

         _path.clear();

         if (_gr.nodeNum() == 0) return _sum = 0;

         else if (_gr.nodeNum() == 1) {

           _path.push_back(_gr(0));

           return _sum = 0;

         }

         switch (rule) {

           case NEAREST:

             init(true);

             start<NearestSelection, DefaultInsertion>();

             break;

           case FARTHEST:

             init(false);

             start<FarthestSelection, DefaultInsertion>();

             break;

           case CHEAPEST:

             init(true);

             start<CheapestSelection, CheapestInsertion>();

             break;

           case RANDOM:

             init(true);

             start<RandomSelection, DefaultInsertion>();

             break;

         }

         return _sum;

       }

       /// @}

       /// \name Query Functions

       /// @{

       /// \brief The total cost of the found tour.

       ///

       /// This function returns the total cost of the found tour.

       ///

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

       Cost tourCost() const {

         return _sum;

       }

       /// \brief Returns a const reference to the node sequence of the

       /// found tour.

       ///

       /// This function returns a const reference to the internal structure

       /// that stores the node sequence of the found tour.

       ///

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

       const std::vector<Node>& tourNodes() const {

         return _path;

       }

       /// \brief Gives back the node sequence of the found tour.

       ///

       /// This function copies the node sequence of the found tour into

       /// the given standard container.

       ///

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

       template <typename Container>

       void tourNodes(Container &container) const {

         container.assign(_path.begin(), _path.end());

       }

       /// \brief Gives back the found tour as a path.

       ///

       /// This function copies the found tour as a list of arcs/edges into

       /// the given \ref concept::Path "path structure".

       ///

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

       template <typename Path>

       void tour(Path &path) const {

         path.clear();

         for (int i = 0; i < int(_path.size()) - 1; ++i) {

           path.addBack(_gr.arc(_path[i], _path[i+1]));

         }

         if (int(_path.size()) >= 2) {

           path.addBack(_gr.arc(_path.back(), _path.front()));

         }

       }

       /// @}

     private:

       // Initializes the algorithm

       void init(bool min) {

         Edge min_edge = min ? mapMin(_gr, _cost) : mapMax(_gr, _cost);

         _path.clear();

         _path.push_back(_gr.u(min_edge));

         _path.push_back(_gr.v(min_edge));

         _notused.clear();

         for (NodeIt n(_gr); n!=INVALID; ++n) {

           if (n != _gr.u(min_edge) && n != _gr.v(min_edge)) {

             _notused.push_back(n);

           }

         }

         _sum = _cost[min_edge] * 2;

       }

       // Executes the algorithm

       template <class SelectionFunctor, class InsertionFunctor>

       void start() {

         SelectionFunctor selectNode(_gr, _cost, _path, _notused);

         InsertionFunctor insertNode(_gr, _cost, _path, _sum);

         for (int i=0; i<_gr.nodeNum()-2; ++i) {

           insertNode.insert(selectNode.select());

         }

         _sum = _cost[_gr.edge(_path.back(), _path.front())];

         for (int i = 0; i < int(_path.size())-1; ++i) {

           _sum += _cost[_gr.edge(_path[i], _path[i+1])];

         }

       }

       // Implementation of the nearest selection rule

       class NearestSelection {

         public:

           NearestSelection(const FullGraph &gr, const CostMap &cost,

                            std::vector<Node> &path, std::vector<Node> &notused)

             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}

           Node select() const {

             Cost insert_val = 0;

             int insert_node = -1;

             for (unsigned int i=0; i<_notused.size(); ++i) {

               Cost min_val = _cost[_gr.edge(_notused[i], _path[0])];

               int min_node = 0;

               for (unsigned int j=1; j<_path.size(); ++j) {

                 Cost curr = _cost[_gr.edge(_notused[i], _path[j])];

                 if (min_val > curr) {

                     min_val = curr;

                     min_node = j;

                 }

               }

               if (insert_val > min_val || insert_node == -1) {

                 insert_val = min_val;

                 insert_node = i;

               }

             }

             Node n = _notused[insert_node];

             _notused.erase(_notused.begin()+insert_node);

             return n;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_path;

           std::vector<Node> &_notused;

       };

       // Implementation of the farthest selection rule

       class FarthestSelection {

         public:

           FarthestSelection(const FullGraph &gr, const CostMap &cost,

                             std::vector<Node> &path, std::vector<Node> &notused)

             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}

           Node select() const {

             Cost insert_val = 0;

             int insert_node = -1;

             for (unsigned int i=0; i<_notused.size(); ++i) {

               Cost min_val = _cost[_gr.edge(_notused[i], _path[0])];

               int min_node = 0;

               for (unsigned int j=1; j<_path.size(); ++j) {

                 Cost curr = _cost[_gr.edge(_notused[i], _path[j])];

                 if (min_val > curr) {

                   min_val = curr;

                   min_node = j;

                 }

               }

               if (insert_val < min_val || insert_node == -1) {

                 insert_val = min_val;

                 insert_node = i;

               }

             }

             Node n = _notused[insert_node];

             _notused.erase(_notused.begin()+insert_node);

             return n;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_path;

           std::vector<Node> &_notused;

       };

       // Implementation of the cheapest selection rule

       class CheapestSelection {

         private:

           Cost costDiff(Node u, Node v, Node w) const {

             return

               _cost[_gr.edge(u, w)] +

               _cost[_gr.edge(v, w)] -

               _cost[_gr.edge(u, v)];

           }

         public:

           CheapestSelection(const FullGraph &gr, const CostMap &cost,

                             std::vector<Node> &path, std::vector<Node> &notused)

             : _gr(gr), _cost(cost), _path(path), _notused(notused) {}

           Cost select() const {

             int insert_notused = -1;

             int best_insert_index = -1;

             Cost insert_val = 0;

             for (unsigned int i=0; i<_notused.size(); ++i) {

               int min = i;

               int best_insert_tmp = 0;

               Cost min_val =

                 costDiff(_path.front(), _path.back(), _notused[i]);

               for (unsigned int j=1; j<_path.size(); ++j) {

                 Cost tmp =

                   costDiff(_path[j-1], _path[j], _notused[i]);

                 if (min_val > tmp) {

                   min = i;

                   min_val = tmp;

                   best_insert_tmp = j;

                 }

               }

               if (insert_val > min_val || insert_notused == -1) {

                 insert_notused = min;

                 insert_val = min_val;

                 best_insert_index = best_insert_tmp;

               }

             }

             _path.insert(_path.begin()+best_insert_index,

                          _notused[insert_notused]);

             _notused.erase(_notused.begin()+insert_notused);

             return insert_val;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_path;

           std::vector<Node> &_notused;

       };

       // Implementation of the random selection rule

       class RandomSelection {

         public:

           RandomSelection(const FullGraph &, const CostMap &,

                           std::vector<Node> &, std::vector<Node> &notused)

             : _notused(notused) {}

           Node select() const {

             const int index = rnd[_notused.size()];

             Node n = _notused[index];

             _notused.erase(_notused.begin()+index);

             return n;

           }

         private:

           std::vector<Node> &_notused;

       };

       // Implementation of the default insertion method

       class DefaultInsertion {

         private:

           Cost costDiff(Node u, Node v, Node w) const {

             return

               _cost[_gr.edge(u, w)] +

               _cost[_gr.edge(v, w)] -

               _cost[_gr.edge(u, v)];

           }

         public:

           DefaultInsertion(const FullGraph &gr, const CostMap &cost,

                            std::vector<Node> &path, Cost &total_cost) :

             _gr(gr), _cost(cost), _path(path), _total(total_cost) {}

           void insert(Node n) const {

             int min = 0;

             Cost min_val =

               costDiff(_path.front(), _path.back(), n);

             for (unsigned int i=1; i<_path.size(); ++i) {

               Cost tmp = costDiff(_path[i-1], _path[i], n);

               if (tmp < min_val) {

                 min = i;

                 min_val = tmp;

               }

             }

             _path.insert(_path.begin()+min, n);

             _total += min_val;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_path;

           Cost &_total;

       };

       // Implementation of a special insertion method for the cheapest

       // selection rule

       class CheapestInsertion {

         TEMPLATE_GRAPH_TYPEDEFS(FullGraph);

         public:

           CheapestInsertion(const FullGraph &, const CostMap &,

                             std::vector<Node> &, Cost &total_cost) :

             _total(total_cost) {}

           void insert(Cost diff) const {

             _total += diff;

           }

         private:

           Cost &_total;

       };

   };

 }; // namespace lemon

 #endif