/* -*- 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 <functional>

 #include <lemon/full_graph.h>

 #include <lemon/maps.h>

 #include <lemon/random.h>

 namespace lemon {

   /// \ingroup tsp

   ///

   /// \brief Insertion algorithm for symmetric TSP.

   ///

   /// InsertionTsp implements the insertion heuristic for solving

   /// symmetric \ref tsp "TSP".

   ///

   /// This is a fast and effective tour construction method 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 method is among the fastest TSP algorithms, and it typically

   /// provides quite good solutions (usually much better than

   /// \ref NearestNeighborTsp and \ref GreedyTsp).

   ///

   /// InsertionTsp implements four different node selection rules,

   /// from which the most effective one (\e farthest \e node \e selection)

   /// is used by default.

   /// With this choice, the algorithm runs in O(n<sup>2</sup>) time.

   /// 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> _tour;

       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.

       /// The FARTHEST method is one of the fastest selection rules, and

       /// it is typically the most effective, thus it is the default

       /// option. The RANDOM rule usually gives slightly worse results,

       /// but it is more 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>2</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>2</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, but in most cases, it is almost as fast as

         /// with other rules.

         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) {

         _tour.clear();

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

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

           _tour.push_back(_gr(0));

           return _sum = 0;

         }

         switch (rule) {

           case NEAREST:

             init(true);

             start<ComparingSelection<std::less<Cost> >,

                   DefaultInsertion>();

             break;

           case FARTHEST:

             init(false);

             start<ComparingSelection<std::greater<Cost> >,

                   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 a vector

       /// 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 _tour;

       }

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

       ///

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

       /// an STL container through the given output iterator. The

       /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>.

       /// For example,

       /// \code

       /// std::vector<FullGraph::Node> nodes(countNodes(graph));

       /// tsp.tourNodes(nodes.begin());

       /// \endcode

       /// or

       /// \code

       /// std::list<FullGraph::Node> nodes;

       /// tsp.tourNodes(std::back_inserter(nodes));

       /// \endcode

       ///

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

       template <typename Iterator>

       void tourNodes(Iterator out) const {

         std::copy(_tour.begin(), _tour.end(), out);

       }

       /// \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 lemon::concepts::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(_tour.size()) - 1; ++i) {

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

         }

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

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

         }

       }

       /// @}

     private:

       // Initializes the algorithm

       void init(bool min) {

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

         _tour.clear();

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

         _tour.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, _tour, _notused);

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

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

           insertNode.insert(selectNode.select());

         }

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

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

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

         }

       }

       // Implementation of the nearest and farthest selection rule

       template <typename Comparator>

       class ComparingSelection {

         public:

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

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

             : _gr(gr), _cost(cost), _tour(tour), _notused(notused),

               _dist(gr, 0), _compare()

           {

             // Compute initial distances for the unused nodes

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

               Node u = _notused[i];

               Cost min_dist = _cost[_gr.edge(u, _tour[0])];

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

                 Cost curr = _cost[_gr.edge(u, _tour[j])];

                 if (curr < min_dist) {

                   min_dist = curr;

                 }

               }

               _dist[u] = min_dist;

             }

           }

           Node select() {

             // Select an used node with minimum distance

             Cost ins_dist = 0;

             int ins_node = -1;

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

               Cost curr = _dist[_notused[i]];

               if (_compare(curr, ins_dist) || ins_node == -1) {

                 ins_dist = curr;

                 ins_node = i;

               }

             }

             // Remove the selected node from the unused vector

             Node sn = _notused[ins_node];

             _notused[ins_node] = _notused.back();

             _notused.pop_back();

             // Update the distances of the remaining nodes

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

               Node u = _notused[i];

               Cost nc = _cost[_gr.edge(sn, u)];

               if (nc < _dist[u]) {

                 _dist[u] = nc;

               }

             }

             return sn;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_tour;

           std::vector<Node> &_notused;

           FullGraph::NodeMap<Cost> _dist;

           Comparator _compare;

       };

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

             : _gr(gr), _cost(cost), _tour(tour), _notused(notused),

               _ins_cost(gr, 0), _ins_pos(gr, -1)

           {

             // Compute insertion cost and position for the unused nodes

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

               Node u = _notused[i];

               Cost min_cost = costDiff(_tour.back(), _tour.front(), u);

               int min_pos = 0;              

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

                 Cost curr_cost = costDiff(_tour[j-1], _tour[j], u);

                 if (curr_cost < min_cost) {

                   min_cost = curr_cost;

                   min_pos = j;

                 }

               }

               _ins_cost[u] = min_cost;

               _ins_pos[u] = min_pos;

             }

           }

           Cost select() {

             // Select an used node with minimum insertion cost

             Cost min_cost = 0;

             int min_node = -1;

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

               Cost curr_cost = _ins_cost[_notused[i]];

               if (curr_cost < min_cost || min_node == -1) {

                 min_cost = curr_cost;

                 min_node = i;

               }

             }

             // Remove the selected node from the unused vector

             Node sn = _notused[min_node];

             _notused[min_node] = _notused.back();

             _notused.pop_back();

             // Insert the selected node into the tour

             const int ipos = _ins_pos[sn];

             _tour.insert(_tour.begin() + ipos, sn);

             // Update the insertion cost and position of the remaining nodes

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

               Node u = _notused[i];

               Cost curr_cost = _ins_cost[u];

               int curr_pos = _ins_pos[u];

               int ipos_prev = ipos == 0 ? _tour.size()-1 : ipos-1;

               int ipos_next = ipos == int(_tour.size())-1 ? 0 : ipos+1;

               Cost nc1 = costDiff(_tour[ipos_prev], _tour[ipos], u);

               Cost nc2 = costDiff(_tour[ipos], _tour[ipos_next], u);

               if (nc1 <= curr_cost || nc2 <= curr_cost) {

                 // A new position is better than the old one

                 if (nc1 <= nc2) {

                   curr_cost = nc1;

                   curr_pos = ipos;

                 } else {

                   curr_cost = nc2;

                   curr_pos = ipos_next;

                 }

               }

               else {

                 if (curr_pos == ipos) {

                   // The minimum should be found again

                   curr_cost = costDiff(_tour.back(), _tour.front(), u);

                   curr_pos = 0;              

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

                     Cost tmp_cost = costDiff(_tour[j-1], _tour[j], u);

                     if (tmp_cost < curr_cost) {

                       curr_cost = tmp_cost;

                       curr_pos = j;

                     }

                   }

                 }

                 else if (curr_pos > ipos) {

                   ++curr_pos;

                 }

               }

               _ins_cost[u] = curr_cost;

               _ins_pos[u] = curr_pos;

             }

             return min_cost;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_tour;

           std::vector<Node> &_notused;

           FullGraph::NodeMap<Cost> _ins_cost;

           FullGraph::NodeMap<int> _ins_pos;

       };

       // 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[index] = _notused.back();

             _notused.pop_back();

             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> &tour, Cost &total_cost) :

             _gr(gr), _cost(cost), _tour(tour), _total(total_cost) {}

           void insert(Node n) const {

             int min = 0;

             Cost min_val =

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

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

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

               if (tmp < min_val) {

                 min = i;

                 min_val = tmp;

               }

             }

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

             _total += min_val;

           }

         private:

           const FullGraph &_gr;

           const CostMap &_cost;

           std::vector<Node> &_tour;

           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