/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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_STEINER_H

#define LEMON_STEINER_H

///\ingroup approx

///\file

///\brief Algorithm for the 2-approximation of Steiner Tree problem.

///

#include <lemon/smart_graph.h>

#include <lemon/graph_utils.h>

#include <lemon/error.h>

#include <lemon/ugraph_adaptor.h>

#include <lemon/maps.h>

#include <lemon/dijkstra.h>

#include <lemon/prim.h>

namespace lemon {

  /// \ingroup approx

  /// \brief Algorithm for the 2-approximation of Steiner Tree problem

  ///

  /// The Steiner-tree problem is the next: Given a connected

  /// undirected graph, a cost function on the edges and a subset of

  /// the nodes. Construct a tree with minimum cost which covers the

  /// given subset of the nodes. The problem is NP-hard moreover

  /// it is APX-complete too.

  ///

  /// Mehlhorn's approximation algorithm is implemented in this class,

  /// which gives a 2-approximation for the Steiner-tree problem. The

  /// algorithm's time complexity is O(nlog(n)+e).

  template <typename UGraph,

            typename CostMap = typename UGraph:: template UEdgeMap<double> >

  class SteinerTree {

  public:

    UGRAPH_TYPEDEFS(typename UGraph);

    typedef typename CostMap::Value Value;

  private:

    class CompMap {

    public:

      typedef Node Key;

      typedef Edge Value;

    private:

      const UGraph& _graph;

      typename UGraph::template NodeMap<int> _comp;

    public:

      CompMap(const UGraph& graph) : _graph(graph), _comp(graph) {}

      void set(const Node& node, const Edge& edge) {

        if (edge != INVALID) {

          _comp.set(node, _comp[_graph.source(edge)]);

        } else {

          _comp.set(node, -1);

        }

      }

      int comp(const Node& node) const { return _comp[node]; }

      void comp(const Node& node, int value) { _comp.set(node, value); }

    };

    typedef typename UGraph::template NodeMap<Edge> PredMap;

    typedef ForkWriteMap<PredMap, CompMap> ForkedMap;

    struct External {

      int source, target;

      UEdge uedge;

      Value value;

      External(int s, int t, const UEdge& e, const Value& v)

        : source(s), target(t), uedge(e), value(v) {}

    };

    struct ExternalLess {

      bool operator()(const External& left, const External& right) const {

        return (left.source < right.source) || 

          (left.source == right.source && left.target < right.target);

      }

    };

    typedef typename UGraph::template NodeMap<bool> FilterMap;

    typedef typename UGraph::template UEdgeMap<bool> TreeMap;

    const UGraph& _graph;

    const CostMap& _cost;

    typename Dijkstra<UGraph, CostMap>::

    template DefPredMap<ForkedMap>::Create _dijkstra;

    PredMap* _pred;

    CompMap* _comp;

    ForkedMap* _forked;

    int _terminal_num;

    FilterMap *_filter;

    TreeMap *_tree;

    Value _value;

  public:

    /// \brief Constructor

    /// Constructor

    ///

    SteinerTree(const UGraph &graph, const CostMap &cost)

      : _graph(graph), _cost(cost), _dijkstra(graph, _cost), 

        _pred(0), _comp(0), _forked(0), _filter(0), _tree(0) {}

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures.

    void init() {

      if (!_pred) _pred = new PredMap(_graph);

      if (!_comp) _comp = new CompMap(_graph);

      if (!_forked) _forked = new ForkedMap(*_pred, *_comp);

      if (!_filter) _filter = new FilterMap(_graph);

      if (!_tree) _tree = new TreeMap(_graph);

      _dijkstra.predMap(*_forked);

      _dijkstra.init();

      _terminal_num = 0;

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

        _filter->set(it, false);

      }

    }

    /// \brief Adds a new terminal node.

    ///

    /// Adds a new terminal node to the Steiner-tree problem.

    void addTerminal(const Node& node) {

      if (!_dijkstra.reached(node)) {

        _dijkstra.addSource(node);

        _comp->comp(node, _terminal_num);

        ++_terminal_num;

      }

    }

    /// \brief Executes the algorithm.

    ///

    /// Executes the algorithm.

    ///

    /// \pre init() must be called and at least some nodes should be

    /// added with addTerminal() before using this function.

    ///

    /// This method constructs an approximation of the Steiner-Tree.

    void start() {

      _dijkstra.start();

      std::vector<External> externals;

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

        Node s = _graph.source(it);

        Node t = _graph.target(it);

        if (_comp->comp(s) == _comp->comp(t)) continue;

        Value cost = _dijkstra.dist(s) + _dijkstra.dist(t) + _cost[it];

        if (_comp->comp(s) < _comp->comp(t)) {

          externals.push_back(External(_comp->comp(s), _comp->comp(t), 

                                       it, cost));

        } else {

          externals.push_back(External(_comp->comp(t), _comp->comp(s), 

                                       it, cost));

        }

      }

      std::sort(externals.begin(), externals.end(), ExternalLess());

      SmartUGraph aux_graph;

      std::vector<SmartUGraph::Node> aux_nodes;

      for (int i = 0; i < _terminal_num; ++i) {

        aux_nodes.push_back(aux_graph.addNode());

      }

      SmartUGraph::UEdgeMap<Value> aux_cost(aux_graph);

      SmartUGraph::UEdgeMap<UEdge> cross(aux_graph);

      {

        int i = 0;

        while (i < int(externals.size())) {

          int sn = externals[i].source;

          int tn = externals[i].target;

          Value ev = externals[i].value;

          UEdge ee = externals[i].uedge;

          ++i;

          while (i < int(externals.size()) && 

                 sn == externals[i].source && tn == externals[i].target) {

            if (externals[i].value < ev) {

              ev = externals[i].value;

              ee = externals[i].uedge;

            }

            ++i;

          }

          SmartUGraph::UEdge ne = 

            aux_graph.addEdge(aux_nodes[sn], aux_nodes[tn]);

          aux_cost.set(ne, ev);

          cross.set(ne, ee);

        }

      }

      std::vector<SmartUGraph::UEdge> aux_tree_edges;

      BackInserterBoolMap<std::vector<SmartUGraph::UEdge> >

        aux_tree_map(aux_tree_edges);

      prim(aux_graph, aux_cost, aux_tree_map);

      for (std::vector<SmartUGraph::UEdge>::iterator 

             it = aux_tree_edges.begin(); it != aux_tree_edges.end(); ++it) {

        Node node;

        node = _graph.source(cross[*it]);

        while (node != INVALID && !(*_filter)[node]) {

          _filter->set(node, true);

          node = (*_pred)[node] != INVALID ? 

            _graph.source((*_pred)[node]) : INVALID;

        }

        node = _graph.target(cross[*it]);

        while (node != INVALID && !(*_filter)[node]) {

          _filter->set(node, true);

          node = (*_pred)[node] != INVALID ? 

            _graph.source((*_pred)[node]) : INVALID;

        }

      }

      _value = prim(nodeSubUGraphAdaptor(_graph, *_filter), _cost, *_tree);

    }

    /// \brief Checks if an edge is in the Steiner-tree or not.

    ///

    /// Checks if an edge is in the Steiner-tree or not.

    /// \param e is the edge that will be checked

    /// \return \c true if e is in the Steiner-tree, \c false otherwise

    bool tree(UEdge e){

      return (*_tree)[e];

    }

    /// \brief Checks if the node is in the Steiner-tree or not.

    ///

    /// Checks if a node is in the Steiner-tree or not.

    /// \param n is the node that will be checked

    /// \return \c true if n is in the Steiner-tree, \c false otherwise

    bool tree(Node n){

      return (*_filter)[n];

    }

    /// \brief Checks if the node is a Steiner-node.

    ///

    /// Checks if the node is a Steiner-node (i.e. a tree node but

    /// not terminal).

    /// \param n is the node that will be checked

    /// \return \c true if n is a Steiner-node, \c false otherwise

    bool steiner(Node n){

      return (*_filter)[n] && (*_pred)[n] != INVALID;

    }

    /// \brief Checks if the node is a terminal.

    ///

    /// Checks if the node is a terminal.

    /// \param n is the node that will be checked

    /// \return \c true if n is a terminal, \c false otherwise

    bool terminal(Node n){

      return _dijkstra.reached(n) && (*_pred)[n] == INVALID;

    }

    /// \brief The total cost of the tree

    ///

    /// The total cost of the constructed tree. The calculated value does

    /// not exceed the double of the optimal value.

    Value treeValue() const {

      return _value;

    }

  };

} //END OF NAMESPACE LEMON

#endif