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

 *

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

 *

 * Copyright (C) 2003-2013

 * 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_OPT2_TSP_H

#define LEMON_OPT2_TSP_H

/// \ingroup tsp

/// \file

/// \brief 2-opt algorithm for symmetric TSP.

#include <vector>

#include <lemon/full_graph.h>

namespace lemon {

  /// \ingroup tsp

  ///

  /// \brief 2-opt algorithm for symmetric TSP.

  ///

  /// Opt2Tsp implements the 2-opt heuristic for solving

  /// symmetric \ref tsp "TSP".

  ///

  /// This algorithm starts with an initial tour and iteratively improves it.

  /// At each step, it removes two edges and the reconnects the created two

  /// paths in the other way if the resulting tour is shorter.

  /// The algorithm finishes when no such 2-opt move can be applied, and so

  /// the tour is 2-optimal.

  ///

  /// If no starting tour is given to the \ref run() function, then the

  /// algorithm uses the node sequence determined by the node IDs.

  /// Oherwise, it starts with the given tour.

  ///

  /// This is a rather slow but effective method.

  /// Its typical usage is the improvement of the result of a fast tour

  /// construction heuristic (e.g. the InsertionTsp algorithm).

  ///

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

  template <typename CM>

  class Opt2Tsp

  {

    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;

      Cost _sum;

      std::vector<int> _plist;

      std::vector<Node> _path;

    public:

      /// \brief Constructor

      ///

      /// Constructor.

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

      /// \param cost The cost map.

      Opt2Tsp(const FullGraph &gr, const CostMap &cost)

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

      /// \name Execution Control

      /// @{

      /// \brief Runs the algorithm from scratch.

      ///

      /// This function runs the algorithm starting from the tour that is

      /// determined by the node ID sequence.

      ///

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

      Cost run() {

        _path.clear();

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

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

          _path.push_back(_gr(0));

          return _sum = 0;

        }

        else if (_gr.nodeNum() == 2) {

          _path.push_back(_gr(0));

          _path.push_back(_gr(1));

          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];

        }

        _plist.resize(2*_gr.nodeNum());

        for (int i = 1; i < _gr.nodeNum()-1; ++i) {

          _plist[2*i] = i-1;

          _plist[2*i+1] = i+1;

        }

        _plist[0] = _gr.nodeNum()-1;

        _plist[1] = 1;

        _plist[2*_gr.nodeNum()-2] = _gr.nodeNum()-2;

        _plist[2*_gr.nodeNum()-1] = 0;

        return start();

      }

      /// \brief Runs the algorithm starting from the given tour.

      ///

      /// This function runs the algorithm starting from the given tour.

      ///

      /// \param tour The tour as a path structure. It must be a

      /// \ref checkPath() "valid path" containing excactly n arcs.

      ///

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

      template <typename Path>

      Cost run(const Path& tour) {

        _path.clear();

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

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

          _path.push_back(_gr(0));

          return _sum = 0;

        }

        else if (_gr.nodeNum() == 2) {

          _path.push_back(_gr(0));

          _path.push_back(_gr(1));

          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];

        }

        _plist.resize(2*_gr.nodeNum());

        typename Path::ArcIt it(tour);

        int first = _gr.id(_gr.source(it)),

            prev = first,

            curr = _gr.id(_gr.target(it)),

            next = -1;

        _plist[2*first+1] = curr;

        for (++it; it != INVALID; ++it) {

          next = _gr.id(_gr.target(it));

          _plist[2*curr] = prev;

          _plist[2*curr+1] = next;

          prev = curr;

          curr = next;

        }

        _plist[2*first] = prev;

        return start();

      }

      /// \brief Runs the algorithm starting from the given tour.

      ///

      /// This function runs the algorithm starting from the given tour

      /// (node sequence).

      ///

      /// \param tour A vector that stores all <tt>Node</tt>s of the graph

      /// in the desired order.

      ///

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

      Cost run(const std::vector<Node>& tour) {

        _path.clear();

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

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

          _path.push_back(_gr(0));

          return _sum = 0;

        }

        else if (_gr.nodeNum() == 2) {

          _path.push_back(_gr(0));

          _path.push_back(_gr(1));

          return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))];

        }

        _plist.resize(2*_gr.nodeNum());

        typename std::vector<Node>::const_iterator it = tour.begin();

        int first = _gr.id(*it),

            prev = first,

            curr = _gr.id(*(++it)),

            next = -1;

        _plist[2*first+1] = curr;

        for (++it; it != tour.end(); ++it) {

          next = _gr.id(*it);

          _plist[2*curr] = prev;

          _plist[2*curr+1] = next;

          prev = curr;

          curr = next;

        }

        _plist[2*first] = curr;

        _plist[2*curr] = prev;

        _plist[2*curr+1] = first;

        return start();

      }

      /// @}

      /// \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 _path;

      }

      /// \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(_path.begin(), _path.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(_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:

      // Iterator class for the linked list storage of the tour

      class PathListIt {

        public:

          PathListIt(const std::vector<int> &pl, int i=0)

            : plist(&pl), act(i), last(pl[2*act]) {}

          PathListIt(const std::vector<int> &pl, int i, int l)

            : plist(&pl), act(i), last(l) {}

          int nextIndex() const {

            return (*plist)[2*act] == last ? 2*act+1 : 2*act;

          }

          int prevIndex() const {

            return (*plist)[2*act] == last ? 2*act : 2*act+1;

          }

          int next() const {

            int x = (*plist)[2*act];

            return x == last ? (*plist)[2*act+1] : x;

          }

          int prev() const {

            return last;

          }

          PathListIt& operator++() {

            int tmp = act;

            act = next();

            last = tmp;

            return *this;

          }

          operator int() const {

            return act;

          }

        private:

          const std::vector<int> *plist;

          int act;

          int last;

      };

      // Checks and applies 2-opt move (if it improves the tour)

      bool checkOpt2(const PathListIt& i, const PathListIt& j) {

        Node u  = _gr.nodeFromId(i),

             un = _gr.nodeFromId(i.next()),

             v  = _gr.nodeFromId(j),

             vn = _gr.nodeFromId(j.next());

        if (_cost[_gr.edge(u, un)] + _cost[_gr.edge(v, vn)] >

            _cost[_gr.edge(u, v)] + _cost[_gr.edge(un, vn)])

        {

          _plist[PathListIt(_plist, i.next(), i).prevIndex()] = j.next();

          _plist[PathListIt(_plist, j.next(), j).prevIndex()] = i.next();

          _plist[i.nextIndex()] = j;

          _plist[j.nextIndex()] = i;

          return true;

        }

        return false;

     }

      // Executes the algorithm from the initial tour

      Cost start() {

      restart_search:

        for (PathListIt i(_plist); true; ++i) {

          PathListIt j = i;

          if (++j == 0 || ++j == 0) break;

          for (; j != 0 && j != i.prev(); ++j) {

            if (checkOpt2(i, j))

              goto restart_search;

          }

        }

        PathListIt i(_plist);

        _path.push_back(_gr.nodeFromId(i));

        for (++i; i != 0; ++i)

          _path.push_back(_gr.nodeFromId(i));

        _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])];

        }

        return _sum;

      }

  };

}; // namespace lemon

#endif