/* -*- 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