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

 *

 * 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_MIN_COST_ARBORESCENCE_H

#define LEMON_MIN_COST_ARBORESCENCE_H

///\ingroup spantree

///\file

///\brief Minimum Cost Arborescence algorithm.

#include <vector>

#include <lemon/list_graph.h>

#include <lemon/bin_heap.h>

#include <lemon/assert.h>

namespace lemon {

  /// \brief Default traits class for MinCostArborescence class.

  ///

  /// Default traits class for MinCostArborescence class.

  /// \param _Digraph Digraph type.

  /// \param _CostMap Type of cost map.

  template <class _Digraph, class _CostMap>

  struct MinCostArborescenceDefaultTraits{

    /// \brief The digraph type the algorithm runs on.

    typedef _Digraph Digraph;

    /// \brief The type of the map that stores the arc costs.

    ///

    /// The type of the map that stores the arc costs.

    /// It must meet the \ref concepts::ReadMap "ReadMap" concept.

    typedef _CostMap CostMap;

    /// \brief The value type of the costs.

    ///

    /// The value type of the costs.

    typedef typename CostMap::Value Value;

    /// \brief The type of the map that stores which arcs are in the

    /// arborescence.

    ///

    /// The type of the map that stores which arcs are in the

    /// arborescence.  It must meet the \ref concepts::WriteMap

    /// "WriteMap" concept.  Initially it will be set to false on each

    /// arc. After it will set all arborescence arcs once.

    typedef typename Digraph::template ArcMap<bool> ArborescenceMap;

    /// \brief Instantiates a ArborescenceMap.

    ///

    /// This function instantiates a \ref ArborescenceMap.

    /// \param digraph is the graph, to which we would like to

    /// calculate the ArborescenceMap.

    static ArborescenceMap *createArborescenceMap(const Digraph &digraph){

      return new ArborescenceMap(digraph);

    }

    /// \brief The type of the PredMap

    ///

    /// The type of the PredMap. It is a node map with an arc value type.

    typedef typename Digraph::template NodeMap<typename Digraph::Arc> PredMap;

    /// \brief Instantiates a PredMap.

    ///

    /// This function instantiates a \ref PredMap.

    /// \param _digraph is the digraph, to which we would like to define the

    /// PredMap.

    static PredMap *createPredMap(const Digraph &digraph){

      return new PredMap(digraph);

    }

  };

  /// \ingroup spantree

  ///

  /// \brief %MinCostArborescence algorithm class.

  ///

  /// This class provides an efficient implementation of

  /// %MinCostArborescence algorithm. The arborescence is a tree

  /// which is directed from a given source node of the digraph. One or

  /// more sources should be given for the algorithm and it will calculate

  /// the minimum cost subgraph which are union of arborescences with the

  /// given sources and spans all the nodes which are reachable from the

  /// sources. The time complexity of the algorithm is \f$ O(n^2+e) \f$.

  ///

  /// The algorithm provides also an optimal dual solution, therefore

  /// the optimality of the solution can be checked.

  ///

  /// \param _Digraph The digraph type the algorithm runs on. The default value

  /// is \ref ListDigraph.

  /// \param _CostMap This read-only ArcMap determines the costs of the

  /// arcs. It is read once for each arc, so the map may involve in

  /// relatively time consuming process to compute the arc cost if

  /// it is necessary. The default map type is \ref

  /// concepts::Digraph::ArcMap "Digraph::ArcMap<int>".

  /// \param _Traits Traits class to set various data types used

  /// by the algorithm. The default traits class is

  /// \ref MinCostArborescenceDefaultTraits

  /// "MinCostArborescenceDefaultTraits<_Digraph, _CostMap>".  See \ref

  /// MinCostArborescenceDefaultTraits for the documentation of a

  /// MinCostArborescence traits class.

  ///

  /// \author Balazs Dezso

#ifndef DOXYGEN

  template <typename _Digraph = ListDigraph,

            typename _CostMap = typename _Digraph::template ArcMap<int>,

            typename _Traits =

            MinCostArborescenceDefaultTraits<_Digraph, _CostMap> >

#else

  template <typename _Digraph, typename _CostMap, typedef _Traits>

#endif

  class MinCostArborescence {

  public:

    /// The traits.

    typedef _Traits Traits;

    /// The type of the underlying digraph.

    typedef typename Traits::Digraph Digraph;

    /// The type of the map that stores the arc costs.

    typedef typename Traits::CostMap CostMap;

    ///The type of the costs of the arcs.

    typedef typename Traits::Value Value;

    ///The type of the predecessor map.

    typedef typename Traits::PredMap PredMap;

    ///The type of the map that stores which arcs are in the arborescence.

    typedef typename Traits::ArborescenceMap ArborescenceMap;

    typedef MinCostArborescence Create;

  private:

    TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);

    struct CostArc {

      Arc arc;

      Value value;

      CostArc() {}

      CostArc(Arc _arc, Value _value) : arc(_arc), value(_value) {}

    };

    const Digraph *_digraph;

    const CostMap *_cost;

    PredMap *_pred;

    bool local_pred;

    ArborescenceMap *_arborescence;

    bool local_arborescence;

    typedef typename Digraph::template ArcMap<int> ArcOrder;

    ArcOrder *_arc_order;

    typedef typename Digraph::template NodeMap<int> NodeOrder;

    NodeOrder *_node_order;

    typedef typename Digraph::template NodeMap<CostArc> CostArcMap;

    CostArcMap *_cost_arcs;

    struct StackLevel {

      std::vector<CostArc> arcs;

      int node_level;

    };

    std::vector<StackLevel> level_stack;

    std::vector<Node> queue;

    typedef std::vector<typename Digraph::Node> DualNodeList;

    DualNodeList _dual_node_list;

    struct DualVariable {

      int begin, end;

      Value value;

      DualVariable(int _begin, int _end, Value _value)

        : begin(_begin), end(_end), value(_value) {}

    };

    typedef std::vector<DualVariable> DualVariables;

    DualVariables _dual_variables;

    typedef typename Digraph::template NodeMap<int> HeapCrossRef;

    HeapCrossRef *_heap_cross_ref;

    typedef BinHeap<int, HeapCrossRef> Heap;

    Heap *_heap;

  protected:

    MinCostArborescence() {}

  private:

    void createStructures() {

      if (!_pred) {

        local_pred = true;

        _pred = Traits::createPredMap(*_digraph);

      }

      if (!_arborescence) {

        local_arborescence = true;

        _arborescence = Traits::createArborescenceMap(*_digraph);

      }

      if (!_arc_order) {

        _arc_order = new ArcOrder(*_digraph);

      }

      if (!_node_order) {

        _node_order = new NodeOrder(*_digraph);

      }

      if (!_cost_arcs) {

        _cost_arcs = new CostArcMap(*_digraph);

      }

      if (!_heap_cross_ref) {

        _heap_cross_ref = new HeapCrossRef(*_digraph, -1);

      }

      if (!_heap) {

        _heap = new Heap(*_heap_cross_ref);

      }

    }

    void destroyStructures() {

      if (local_arborescence) {

        delete _arborescence;

      }

      if (local_pred) {

        delete _pred;

      }

      if (_arc_order) {

        delete _arc_order;

      }

      if (_node_order) {

        delete _node_order;

      }

      if (_cost_arcs) {

        delete _cost_arcs;

      }

      if (_heap) {

        delete _heap;

      }

      if (_heap_cross_ref) {

        delete _heap_cross_ref;

      }

    }

    Arc prepare(Node node) {

      std::vector<Node> nodes;

      (*_node_order)[node] = _dual_node_list.size();

      StackLevel level;

      level.node_level = _dual_node_list.size();

      _dual_node_list.push_back(node);

      for (InArcIt it(*_digraph, node); it != INVALID; ++it) {

        Arc arc = it;

        Node source = _digraph->source(arc);

        Value value = (*_cost)[it];

        if (source == node || (*_node_order)[source] == -3) continue;

        if ((*_cost_arcs)[source].arc == INVALID) {

          (*_cost_arcs)[source].arc = arc;

          (*_cost_arcs)[source].value = value;

          nodes.push_back(source);

        } else {

          if ((*_cost_arcs)[source].value > value) {

            (*_cost_arcs)[source].arc = arc;

            (*_cost_arcs)[source].value = value;

          }

        }

      }

      CostArc minimum = (*_cost_arcs)[nodes[0]];

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

        if ((*_cost_arcs)[nodes[i]].value < minimum.value) {

          minimum = (*_cost_arcs)[nodes[i]];

        }

      }

      _arc_order->set(minimum.arc, _dual_variables.size());

      DualVariable var(_dual_node_list.size() - 1,

                       _dual_node_list.size(), minimum.value);

      _dual_variables.push_back(var);

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

        (*_cost_arcs)[nodes[i]].value -= minimum.value;

        level.arcs.push_back((*_cost_arcs)[nodes[i]]);

        (*_cost_arcs)[nodes[i]].arc = INVALID;

      }

      level_stack.push_back(level);

      return minimum.arc;

    }

    Arc contract(Node node) {

      int node_bottom = bottom(node);

      std::vector<Node> nodes;

      while (!level_stack.empty() &&

             level_stack.back().node_level >= node_bottom) {

        for (int i = 0; i < int(level_stack.back().arcs.size()); ++i) {

          Arc arc = level_stack.back().arcs[i].arc;

          Node source = _digraph->source(arc);

          Value value = level_stack.back().arcs[i].value;

          if ((*_node_order)[source] >= node_bottom) continue;

          if ((*_cost_arcs)[source].arc == INVALID) {

            (*_cost_arcs)[source].arc = arc;

            (*_cost_arcs)[source].value = value;

            nodes.push_back(source);

          } else {

            if ((*_cost_arcs)[source].value > value) {

              (*_cost_arcs)[source].arc = arc;

              (*_cost_arcs)[source].value = value;

            }

          }

        }

        level_stack.pop_back();

      }

      CostArc minimum = (*_cost_arcs)[nodes[0]];

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

        if ((*_cost_arcs)[nodes[i]].value < minimum.value) {

          minimum = (*_cost_arcs)[nodes[i]];

        }

      }

      _arc_order->set(minimum.arc, _dual_variables.size());

      DualVariable var(node_bottom, _dual_node_list.size(), minimum.value);

      _dual_variables.push_back(var);

      StackLevel level;

      level.node_level = node_bottom;

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

        (*_cost_arcs)[nodes[i]].value -= minimum.value;

        level.arcs.push_back((*_cost_arcs)[nodes[i]]);

        (*_cost_arcs)[nodes[i]].arc = INVALID;

      }

      level_stack.push_back(level);

      return minimum.arc;

    }

    int bottom(Node node) {

      int k = level_stack.size() - 1;

      while (level_stack[k].node_level > (*_node_order)[node]) {

        --k;

      }

      return level_stack[k].node_level;

    }

    void finalize(Arc arc) {

      Node node = _digraph->target(arc);

      _heap->push(node, (*_arc_order)[arc]);

      _pred->set(node, arc);

      while (!_heap->empty()) {

        Node source = _heap->top();

        _heap->pop();

        _node_order->set(source, -1);

        for (OutArcIt it(*_digraph, source); it != INVALID; ++it) {

          if ((*_arc_order)[it] < 0) continue;

          Node target = _digraph->target(it);

          switch(_heap->state(target)) {

          case Heap::PRE_HEAP:

            _heap->push(target, (*_arc_order)[it]);

            _pred->set(target, it);

            break;

          case Heap::IN_HEAP:

            if ((*_arc_order)[it] < (*_heap)[target]) {

              _heap->decrease(target, (*_arc_order)[it]);

              _pred->set(target, it);

            }

            break;

          case Heap::POST_HEAP:

            break;

          }

        }

        _arborescence->set((*_pred)[source], true);

      }

    }

  public:

    /// \name Named template parameters

    /// @{

    template <class T>

    struct DefArborescenceMapTraits : public Traits {

      typedef T ArborescenceMap;

      static ArborescenceMap *createArborescenceMap(const Digraph &)

      {

        LEMON_ASSERT(false, "ArborescenceMap is not initialized");

        return 0; // ignore warnings

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for

    /// setting ArborescenceMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting

    /// ArborescenceMap type

    template <class T>

    struct DefArborescenceMap

      : public MinCostArborescence<Digraph, CostMap,

                                   DefArborescenceMapTraits<T> > {

    };

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Digraph &)

      {

        LEMON_ASSERT(false, "PredMap is not initialized");

      }

    };

    /// \brief \ref named-templ-param "Named parameter" for

    /// setting PredMap type

    ///

    /// \ref named-templ-param "Named parameter" for setting

    /// PredMap type

    template <class T>

    struct DefPredMap

      : public MinCostArborescence<Digraph, CostMap, DefPredMapTraits<T> > {

    };

    /// @}

    /// \brief Constructor.

    ///

    /// \param _digraph The digraph the algorithm will run on.

    /// \param _cost The cost map used by the algorithm.

    MinCostArborescence(const Digraph& digraph, const CostMap& cost)

      : _digraph(&digraph), _cost(&cost), _pred(0), local_pred(false),

        _arborescence(0), local_arborescence(false),

        _arc_order(0), _node_order(0), _cost_arcs(0),

        _heap_cross_ref(0), _heap(0) {}

    /// \brief Destructor.

    ~MinCostArborescence() {

      destroyStructures();

    }

    /// \brief Sets the arborescence map.

    ///

    /// Sets the arborescence map.

    /// \return \c (*this)

    MinCostArborescence& arborescenceMap(ArborescenceMap& m) {

      if (local_arborescence) {

        delete _arborescence;

      }

      local_arborescence = false;

      _arborescence = &m;

      return *this;

    }

    /// \brief Sets the arborescence map.

    ///

    /// Sets the arborescence map.

    /// \return \c (*this)

    MinCostArborescence& predMap(PredMap& m) {

      if (local_pred) {

        delete _pred;

      }

      local_pred = false;

      _pred = &m;

      return *this;

    }

    /// \name Query Functions

    /// The result of the %MinCostArborescence algorithm can be obtained

    /// using these functions.\n

    /// Before the use of these functions,

    /// either run() or start() must be called.

    /// @{

    /// \brief Returns a reference to the arborescence map.

    ///

    /// Returns a reference to the arborescence map.

    const ArborescenceMap& arborescenceMap() const {

      return *_arborescence;

    }

    /// \brief Returns true if the arc is in the arborescence.

    ///

    /// Returns true if the arc is in the arborescence.

    /// \param arc The arc of the digraph.

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

    bool arborescence(Arc arc) const {

      return (*_pred)[_digraph->target(arc)] == arc;

    }

    /// \brief Returns a reference to the pred map.

    ///

    /// Returns a reference to the pred map.

    const PredMap& predMap() const {

      return *_pred;

    }

    /// \brief Returns the predecessor arc of the given node.

    ///

    /// Returns the predecessor arc of the given node.

    Arc pred(Node node) const {

      return (*_pred)[node];

    }

    /// \brief Returns the cost of the arborescence.

    ///

    /// Returns the cost of the arborescence.

    Value arborescenceValue() const {

      Value sum = 0;

      for (ArcIt it(*_digraph); it != INVALID; ++it) {

        if (arborescence(it)) {

          sum += (*_cost)[it];

        }

      }

      return sum;

    }

    /// \brief Indicates that a node is reachable from the sources.

    ///

    /// Indicates that a node is reachable from the sources.

    bool reached(Node node) const {

      return (*_node_order)[node] != -3;

    }

    /// \brief Indicates that a node is processed.

    ///

    /// Indicates that a node is processed. The arborescence path exists

    /// from the source to the given node.

    bool processed(Node node) const {

      return (*_node_order)[node] == -1;

    }

    /// \brief Returns the number of the dual variables in basis.

    ///

    /// Returns the number of the dual variables in basis.

    int dualNum() const {

      return _dual_variables.size();

    }

    /// \brief Returns the value of the dual solution.

    ///

    /// Returns the value of the dual solution. It should be

    /// equal to the arborescence value.

    Value dualValue() const {

      Value sum = 0;

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

        sum += _dual_variables[i].value;

      }

      return sum;

    }

    /// \brief Returns the number of the nodes in the dual variable.

    ///

    /// Returns the number of the nodes in the dual variable.

    int dualSize(int k) const {

      return _dual_variables[k].end - _dual_variables[k].begin;

    }

    /// \brief Returns the value of the dual variable.

    ///

    /// Returns the the value of the dual variable.

    const Value& dualValue(int k) const {

      return _dual_variables[k].value;

    }

    /// \brief Lemon iterator for get a dual variable.

    ///

    /// Lemon iterator for get a dual variable. This class provides

    /// a common style lemon iterator which gives back a subset of

    /// the nodes.

    class DualIt {

    public:

      /// \brief Constructor.

      ///

      /// Constructor for get the nodeset of the variable.

      DualIt(const MinCostArborescence& algorithm, int variable)

        : _algorithm(&algorithm)

      {

        _index = _algorithm->_dual_variables[variable].begin;

        _last = _algorithm->_dual_variables[variable].end;

      }

      /// \brief Conversion to node.

      ///

      /// Conversion to node.

      operator Node() const {

        return _algorithm->_dual_node_list[_index];

      }

      /// \brief Increment operator.

      ///

      /// Increment operator.

      DualIt& operator++() {

        ++_index;

        return *this;

      }

      /// \brief Validity checking

      ///

      /// Checks whether the iterator is invalid.

      bool operator==(Invalid) const {

        return _index == _last;

      }

      /// \brief Validity checking

      ///

      /// Checks whether the iterator is valid.

      bool operator!=(Invalid) const {

        return _index != _last;

      }

    private:

      const MinCostArborescence* _algorithm;

      int _index, _last;

    };

    /// @}

    /// \name Execution control

    /// The simplest way to execute the algorithm is to use

    /// one of the member functions called \c run(...). \n

    /// If you need more control on the execution,

    /// first you must call \ref init(), then you can add several

    /// source nodes with \ref addSource().

    /// Finally \ref start() will perform the arborescence

    /// computation.

    ///@{

    /// \brief Initializes the internal data structures.

    ///

    /// Initializes the internal data structures.

    ///

    void init() {

      createStructures();

      _heap->clear();

      for (NodeIt it(*_digraph); it != INVALID; ++it) {

        (*_cost_arcs)[it].arc = INVALID;

        _node_order->set(it, -3);

        _heap_cross_ref->set(it, Heap::PRE_HEAP);

        _pred->set(it, INVALID);

      }

      for (ArcIt it(*_digraph); it != INVALID; ++it) {

        _arborescence->set(it, false);

        _arc_order->set(it, -1);

      }

      _dual_node_list.clear();

      _dual_variables.clear();

    }

    /// \brief Adds a new source node.

    ///

    /// Adds a new source node to the algorithm.

    void addSource(Node source) {

      std::vector<Node> nodes;

      nodes.push_back(source);

      while (!nodes.empty()) {

        Node node = nodes.back();

        nodes.pop_back();

        for (OutArcIt it(*_digraph, node); it != INVALID; ++it) {

          Node target = _digraph->target(it);

          if ((*_node_order)[target] == -3) {

            (*_node_order)[target] = -2;

            nodes.push_back(target);

            queue.push_back(target);

          }

        }

      }

      (*_node_order)[source] = -1;

    }

    /// \brief Processes the next node in the priority queue.

    ///

    /// Processes the next node in the priority queue.

    ///

    /// \return The processed node.

    ///

    /// \warning The queue must not be empty!

    Node processNextNode() {

      Node node = queue.back();

      queue.pop_back();

      if ((*_node_order)[node] == -2) {

        Arc arc = prepare(node);

        Node source = _digraph->source(arc);

        while ((*_node_order)[source] != -1) {

          if ((*_node_order)[source] >= 0) {

            arc = contract(source);

          } else {

            arc = prepare(source);

          }

          source = _digraph->source(arc);

        }

        finalize(arc);

        level_stack.clear();

      }

      return node;

    }

    /// \brief Returns the number of the nodes to be processed.

    ///

    /// Returns the number of the nodes to be processed.

    int queueSize() const {

      return queue.size();

    }

    /// \brief Returns \c false if there are nodes to be processed.

    ///

    /// Returns \c false if there are nodes to be processed.

    bool emptyQueue() const {

      return queue.empty();

    }

    /// \brief Executes the algorithm.

    ///

    /// Executes the algorithm.

    ///

    /// \pre init() must be called and at least one node should be added

    /// with addSource() before using this function.

    ///

    ///\note mca.start() is just a shortcut of the following code.

    ///\code

    ///while (!mca.emptyQueue()) {

    ///  mca.processNextNode();

    ///}

    ///\endcode

    void start() {

      while (!emptyQueue()) {

        processNextNode();

      }

    }

    /// \brief Runs %MinCostArborescence algorithm from node \c s.

    ///

    /// This method runs the %MinCostArborescence algorithm from

    /// a root node \c s.

    ///

    /// \note mca.run(s) is just a shortcut of the following code.

    /// \code

    /// mca.init();

    /// mca.addSource(s);

    /// mca.start();

    /// \endcode

    void run(Node node) {

      init();

      addSource(node);

      start();

    }

    ///@}

  };

  /// \ingroup spantree

  ///

  /// \brief Function type interface for MinCostArborescence algorithm.

  ///

  /// Function type interface for MinCostArborescence algorithm.

  /// \param digraph The Digraph that the algorithm runs on.

  /// \param cost The CostMap of the arcs.

  /// \param source The source of the arborescence.

  /// \retval arborescence The bool ArcMap which stores the arborescence.

  /// \return The cost of the arborescence.

  ///

  /// \sa MinCostArborescence

  template <typename Digraph, typename CostMap, typename ArborescenceMap>

  typename CostMap::Value minCostArborescence(const Digraph& digraph,

                                              const CostMap& cost,

                                              typename Digraph::Node source,

                                              ArborescenceMap& arborescence) {

    typename MinCostArborescence<Digraph, CostMap>

      ::template DefArborescenceMap<ArborescenceMap>

      ::Create mca(digraph, cost);

    mca.arborescenceMap(arborescence);

    mca.run(source);

    return mca.arborescenceValue();

  }

}

#endif