/* -*- 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_GREEDY_TSP_H

#define LEMON_GREEDY_TSP_H

/// \ingroup tsp

/// \file

/// \brief Greedy algorithm for symmetric TSP

#include <vector>

#include <algorithm>

#include <lemon/full_graph.h>

#include <lemon/unionfind.h>

namespace lemon {

  /// \brief Greedy algorithm for symmetric TSP.

  ///

  /// GreedyTsp implements the greedy heuristic for solving

  /// symmetric \ref tsp "TSP".

  ///

  /// This algorithm is quite similar to the \ref NearestNeighborTsp

  /// "nearest neighbor" heuristic, but it maintains a set of disjoint paths.

  /// At each step, the shortest possible edge is added to these paths

  /// as long as it does not create a cycle of less than n edges and it does

  /// not increase the degree of any node above two.

  ///

  /// This method runs in O(n<sup>2</sup>log(n)) time.

  /// It quickly finds an effectively short tour for most TSP

  /// instances, but in special cases, it could yield a really bad

  /// (or even the worst) solution.

  ///

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

  template <typename CM>

  class GreedyTsp

  {

    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<Node> _path;

    private:

      // Functor class to compare edges by their costs

      class EdgeComp {

      private:

        const CostMap &_cost;

      public:

        EdgeComp(const CostMap &cost) : _cost(cost) {}

        bool operator()(const Edge &a, const Edge &b) const {

          return _cost[a] < _cost[b];

        }

      };

    public:

      /// \brief Constructor

      ///

      /// Constructor.

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

      /// \param cost The cost map.

      GreedyTsp(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;

        }

        std::vector<int> plist;

        plist.resize(_gr.nodeNum()*2, -1);

        std::vector<Edge> sorted_edges;

        sorted_edges.reserve(_gr.edgeNum());

        for (EdgeIt e(_gr); e != INVALID; ++e)

          sorted_edges.push_back(e);

        std::sort(sorted_edges.begin(), sorted_edges.end(), EdgeComp(_cost));

        FullGraph::NodeMap<int> item_int_map(_gr);

        UnionFind<FullGraph::NodeMap<int> > union_find(item_int_map);

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

          union_find.insert(n);

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

        int nodesNum = 0, i = 0;

        while (nodesNum != _gr.nodeNum()-1) {

          Edge e = sorted_edges[i++];

          Node u = _gr.u(e),

               v = _gr.v(e);

          if (degree[u] <= 1 && degree[v] <= 1) {

            if (union_find.join(u, v)) {

              const int uid = _gr.id(u),

                        vid = _gr.id(v);

              plist[uid*2 + degree[u]] = vid;

              plist[vid*2 + degree[v]] = uid;

              ++degree[u];

              ++degree[v];

              ++nodesNum;

            }

          }

        }

        for (int i=0, n=-1; i<_gr.nodeNum()*2; ++i) {

          if (plist[i] == -1) {

            if (n==-1) {

              n = i;

            } else {

              plist[n] = i/2;

              plist[i] = n/2;

              break;

            }

          }

        }

        for (int i=0, next=0, last=-1; i!=_gr.nodeNum(); ++i) {

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

          if (plist[2*next] != last) {

            last = next;

            next = plist[2*next];

          } else {

            last = next;

            next = plist[2*next+1];

          }

        }

        _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 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()));

        }

      }

      /// @}

  };

}; // namespace lemon

#endif