/* -*- 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_CHRISTOFIDES_TSP_H

#define LEMON_CHRISTOFIDES_TSP_H

/// \ingroup tsp

/// \file

/// \brief Christofides algorithm for symmetric TSP

#include <lemon/full_graph.h>

#include <lemon/smart_graph.h>

#include <lemon/kruskal.h>

#include <lemon/matching.h>

#include <lemon/euler.h>

namespace lemon {

  /// \ingroup tsp

  ///

  /// \brief Christofides algorithm for symmetric TSP.

  ///

  /// ChristofidesTsp implements Christofides' heuristic for solving

  /// symmetric \ref tsp "TSP".

  ///

  /// This a well-known approximation method for the TSP problem with

  /// metric cost function.

  /// It has a guaranteed approximation factor of 3/2 (i.e. it finds a tour

  /// whose total cost is at most 3/2 of the optimum), but it usually

  /// provides better solutions in practice.

  /// This implementation runs in O(n<sup>3</sup>log(n)) time.

  ///

  /// The algorithm starts with a \ref spantree "minimum cost spanning tree" and

  /// finds a \ref MaxWeightedPerfectMatching "minimum cost perfect matching"

  /// in the subgraph induced by the nodes that have odd degree in the

  /// spanning tree.

  /// Finally, it constructs the tour from the \ref EulerIt "Euler traversal"

  /// of the union of the spanning tree and the matching.

  /// During this last step, the algorithm simply skips the visited nodes

  /// (i.e. creates shortcuts) assuming that the triangle inequality holds

  /// for the cost function.

  ///

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

  ///

  /// \warning CM::Value must be a signed number type.

  template <typename CM>

  class ChristofidesTsp

  {

    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> _path;

      Cost _sum;

    public:

      /// \brief Constructor

      ///

      /// Constructor.

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

      /// \param cost The cost map.

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

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

      /// \name Execution Control

      /// @{

      /// \brief Runs the algorithm.

      ///

      /// This function runs the algorithm.

      ///

      /// \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))];

        }

        // Compute min. cost spanning tree

        std::vector<Edge> tree;

        kruskal(_gr, _cost, std::back_inserter(tree));

        FullGraph::NodeMap<int> deg(_gr, 0);

        for (int i = 0; i != int(tree.size()); ++i) {

          Edge e = tree[i];

          ++deg[_gr.u(e)];

          ++deg[_gr.v(e)];

        }

        // Copy the induced subgraph of odd nodes

        std::vector<Node> odd_nodes;

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

          if (deg[u] % 2 == 1) odd_nodes.push_back(u);

        }

        SmartGraph sgr;

        SmartGraph::EdgeMap<Cost> scost(sgr);

        for (int i = 0; i != int(odd_nodes.size()); ++i) {

          sgr.addNode();

        }

        for (int i = 0; i != int(odd_nodes.size()); ++i) {

          for (int j = 0; j != int(odd_nodes.size()); ++j) {

            if (j == i) continue;

            SmartGraph::Edge e =

              sgr.addEdge(sgr.nodeFromId(i), sgr.nodeFromId(j));

            scost[e] = -_cost[_gr.edge(odd_nodes[i], odd_nodes[j])];

          }

        }

        // Compute min. cost perfect matching

        MaxWeightedPerfectMatching<SmartGraph, SmartGraph::EdgeMap<Cost> >

          mwpm(sgr, scost);

        mwpm.run();

        for (SmartGraph::EdgeIt e(sgr); e != INVALID; ++e) {

          if (mwpm.matching(e)) {

            tree.push_back( _gr.edge(odd_nodes[sgr.id(sgr.u(e))],

                                     odd_nodes[sgr.id(sgr.v(e))]) );

          }

        }

        // Join the spanning tree and the matching

        sgr.clear();

        for (int i = 0; i != _gr.nodeNum(); ++i) {

          sgr.addNode();

        }

        for (int i = 0; i != int(tree.size()); ++i) {

          int ui = _gr.id(_gr.u(tree[i])),

              vi = _gr.id(_gr.v(tree[i]));

          sgr.addEdge(sgr.nodeFromId(ui), sgr.nodeFromId(vi));

        }

        // Compute the tour from the Euler traversal

        SmartGraph::NodeMap<bool> visited(sgr, false);

        for (EulerIt<SmartGraph> e(sgr); e != INVALID; ++e) {

          SmartGraph::Node n = sgr.target(e);

          if (!visited[n]) {

            _path.push_back(_gr(sgr.id(n)));

            visited[n] = true;

          }

        }

        _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;

      }

      /// @}

      /// \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()));

        }

      }

      /// @}

  };

}; // namespace lemon

#endif