/* -*- 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_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>

namespace lemon {

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

  /// 

  /// Default traits class of MinCostArborescence class.

  /// \param _Graph Graph type.

  /// \param _CostMap Type of cost map.

  template <class _Graph, class _CostMap>

  struct MinCostArborescenceDefaultTraits{

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

    typedef _Graph Graph;

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

    ///

    /// The type of the map that stores the edge 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 edges are 

    /// in the arborescence.

    ///

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

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

    /// Initially it will be set to false on each edge. After it

    /// will set all arborescence edges once.

    typedef typename Graph::template EdgeMap<bool> ArborescenceMap; 

    /// \brief Instantiates a ArborescenceMap.

    ///

    /// This function instantiates a \ref ArborescenceMap. 

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

    /// ArborescenceMap.

    static ArborescenceMap *createArborescenceMap(const Graph &_graph){

      return new ArborescenceMap(_graph);

    }

    /// \brief The type of the PredMap

    ///

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

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

    /// \brief Instantiates a PredMap.

    ///

    /// This function instantiates a \ref PredMap. 

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

    /// PredMap.

    static PredMap *createPredMap(const Graph &_graph){

      return new PredMap(_graph);

    }

  };

  /// \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 graph. 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 to arborescence

  /// that way the optimality of the solution can be proofed easily.

  ///

  /// \param _Graph The graph type the algorithm runs on. The default value

  /// is \ref ListGraph. The value of _Graph is not used directly by

  /// MinCostArborescence, it is only passed to 

  /// \ref MinCostArborescenceDefaultTraits.

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

  /// edges. It is read once for each edge, so the map may involve in

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

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

  /// concepts::Graph::EdgeMap "Graph::EdgeMap<int>".  The value

  /// of _CostMap is not used directly by MinCostArborescence, 

  /// it is only passed to \ref MinCostArborescenceDefaultTraits.  

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

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

  /// \ref MinCostArborescenceDefaultTraits

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

  /// MinCostArborescenceDefaultTraits for the documentation of a 

  /// MinCostArborescence traits class.

  ///

  /// \author Balazs Dezso

#ifndef DOXYGEN

  template <typename _Graph = ListGraph, 

            typename _CostMap = typename _Graph::template EdgeMap<int>,

            typename _Traits = 

            MinCostArborescenceDefaultTraits<_Graph, _CostMap> >

#else 

  template <typename _Graph, typename _CostMap, typedef _Traits>

#endif

  class MinCostArborescence {

  public:

    /// \brief \ref Exception for uninitialized parameters.

    ///

    /// This error represents problems in the initialization

    /// of the parameters of the algorithms.    

    class UninitializedParameter : public lemon::UninitializedParameter {

    public:

      virtual const char* what() const throw() {

	return "lemon::MinCostArborescence::UninitializedParameter";

      }

    };

    /// The traits.

    typedef _Traits Traits;

    /// The type of the underlying graph.

    typedef typename Traits::Graph Graph;

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

    typedef typename Traits::CostMap CostMap;

    ///The type of the costs of the edges.

    typedef typename Traits::Value Value;

    ///The type of the predecessor map.

    typedef typename Traits::PredMap PredMap;

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

    typedef typename Traits::ArborescenceMap ArborescenceMap;

  protected:

    typedef typename Graph::Node Node;

    typedef typename Graph::Edge Edge;

    typedef typename Graph::NodeIt NodeIt;

    typedef typename Graph::EdgeIt EdgeIt;

    typedef typename Graph::InEdgeIt InEdgeIt;

    typedef typename Graph::OutEdgeIt OutEdgeIt;

    struct CostEdge {

      Edge edge;

      Value value;

      CostEdge() {}

      CostEdge(Edge _edge, Value _value) : edge(_edge), value(_value) {}

    };

    const Graph *graph;

    const CostMap *cost;

    PredMap *_pred;

    bool local_pred;

    ArborescenceMap *_arborescence;

    bool local_arborescence;

    typedef typename Graph::template EdgeMap<int> EdgeOrder;

    EdgeOrder *_edge_order;

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

    NodeOrder *_node_order;

    typedef typename Graph::template NodeMap<CostEdge> CostEdgeMap;

    CostEdgeMap *_cost_edges; 

    struct StackLevel {

      std::vector<CostEdge> edges;

      int node_level;

    };

    std::vector<StackLevel> level_stack;    

    std::vector<Node> queue;

    typedef std::vector<typename Graph::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 Graph::template NodeMap<int> HeapCrossRef;

    HeapCrossRef *_heap_cross_ref;

    typedef BinHeap<int, HeapCrossRef> Heap;

    Heap *_heap;

  public:

    /// \name Named template parameters

    /// @{

    template <class T>

    struct DefArborescenceMapTraits : public Traits {

      typedef T ArborescenceMap;

      static ArborescenceMap *createArborescenceMap(const Graph &)

      {

	throw UninitializedParameter();

      }

    };

    /// \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<Graph, CostMap,

                                   DefArborescenceMapTraits<T> > {

      typedef MinCostArborescence<Graph, CostMap, 

                                   DefArborescenceMapTraits<T> > Create;

    };

    template <class T>

    struct DefPredMapTraits : public Traits {

      typedef T PredMap;

      static PredMap *createPredMap(const Graph &)

      {

	throw UninitializedParameter();

      }

    };

    /// \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<Graph, CostMap, DefPredMapTraits<T> > {

      typedef MinCostArborescence<Graph, CostMap, DefPredMapTraits<T> > Create;

    };

    /// @}

    /// \brief Constructor.

    ///

    /// \param _graph The graph the algorithm will run on.

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

    MinCostArborescence(const Graph& _graph, const CostMap& _cost) 

      : graph(&_graph), cost(&_cost), _pred(0), local_pred(false),

        _arborescence(0), local_arborescence(false), 

        _edge_order(0), _node_order(0), _cost_edges(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 edge is in the arborescence.

    ///

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

    /// \param edge The edge of the graph.

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

    bool arborescence(Edge edge) const {

      return (*_pred)[graph->target(edge)] == edge;

    }

    /// \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 edge of the given node.

    ///

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

    bool 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 (EdgeIt it(*graph); 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 dualSize() 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), _variable(variable) 

      {

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

      }

      /// \brief Invalid constructor.

      ///

      /// Invalid constructor.

      DualIt(Invalid) : _algorithm(0) {}

      /// \brief Conversion to node.

      ///

      /// Conversion to node.

      operator Node() const { 

        return _algorithm ? _algorithm->_dual_node_list[_index] : INVALID;

      }

      /// \brief Increment operator.

      ///

      /// Increment operator.

      DualIt& operator++() {

        ++_index;

        if (_algorithm->_dual_variables[_variable].end == _index) {

          _algorithm = 0;

        }

        return *this; 

      }

      bool operator==(const DualIt& it) const { 

        return static_cast<Node>(*this) == static_cast<Node>(it); 

      }

      bool operator!=(const DualIt& it) const { 

        return static_cast<Node>(*this) != static_cast<Node>(it); 

      }

      bool operator<(const DualIt& it) const { 

        return static_cast<Node>(*this) < static_cast<Node>(it); 

      }

    private:

      const MinCostArborescence* _algorithm;

      int _variable;

      int _index;

    };

    /// @}

    /// \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() {

      initStructures();

      _heap->clear();

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

        (*_cost_edges)[it].edge = INVALID;

        _node_order->set(it, -3); 

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

        _pred->set(it, INVALID);

      }

      for (EdgeIt it(*graph); it != INVALID; ++it) {

        _arborescence->set(it, false);

        _edge_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 (OutEdgeIt it(*graph, node); it != INVALID; ++it) {

          Node target = graph->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) {

        Edge edge = prepare(node);

        Node source = graph->source(edge);

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

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

            edge = contract(source);

          } else {

            edge = prepare(source);

          }

          source = graph->source(edge);

        }

        finalize(edge);

        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();

    }

    ///@}

  protected:

    void initStructures() {

      if (!_pred) {

        local_pred = true;

        _pred = Traits::createPredMap(*graph);

      }

      if (!_arborescence) {

        local_arborescence = true;

        _arborescence = Traits::createArborescenceMap(*graph);

      }

      if (!_edge_order) {

        _edge_order = new EdgeOrder(*graph);

      }

      if (!_node_order) {

        _node_order = new NodeOrder(*graph);

      }

      if (!_cost_edges) {

        _cost_edges = new CostEdgeMap(*graph);

      }

      if (!_heap_cross_ref) {

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

      }

      if (!_heap) {

        _heap = new Heap(*_heap_cross_ref);

      }

    }

    void destroyStructures() {

      if (local_arborescence) {

        delete _arborescence;

      }

      if (local_pred) {

        delete _pred;

      }

      if (_edge_order) {

        delete _edge_order;

      }

      if (_node_order) {

        delete _node_order;

      }

      if (_cost_edges) {

        delete _cost_edges;

      }

      if (_heap) {

        delete _heap;

      }

      if (_heap_cross_ref) {

        delete _heap_cross_ref;

      }

    }

    Edge 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 (InEdgeIt it(*graph, node); it != INVALID; ++it) {

        Edge edge = it;

        Node source = graph->source(edge);

        Value value = (*cost)[it];

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

        if ((*_cost_edges)[source].edge == INVALID) {

          (*_cost_edges)[source].edge = edge;

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

          nodes.push_back(source);

        } else {

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

            (*_cost_edges)[source].edge = edge;

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

          }

        }      

      }

      CostEdge minimum = (*_cost_edges)[nodes[0]]; 

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

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

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

        }

      }

      _edge_order->set(minimum.edge, _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_edges)[nodes[i]].value -= minimum.value;

        level.edges.push_back((*_cost_edges)[nodes[i]]);

        (*_cost_edges)[nodes[i]].edge = INVALID;

      }

      level_stack.push_back(level);

      return minimum.edge;

    }

    Edge 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().edges.size()); ++i) {

          Edge edge = level_stack.back().edges[i].edge;

          Node source = graph->source(edge);

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

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

          if ((*_cost_edges)[source].edge == INVALID) {

            (*_cost_edges)[source].edge = edge;

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

            nodes.push_back(source);

          } else {

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

              (*_cost_edges)[source].edge = edge;

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

            }

          }

        }

        level_stack.pop_back();

      }

      CostEdge minimum = (*_cost_edges)[nodes[0]]; 

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

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

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

        }

      }

      _edge_order->set(minimum.edge, _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_edges)[nodes[i]].value -= minimum.value;

        level.edges.push_back((*_cost_edges)[nodes[i]]);

        (*_cost_edges)[nodes[i]].edge = INVALID;

      }

      level_stack.push_back(level);

      return minimum.edge;

    }

    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(Edge edge) {

      Node node = graph->target(edge);

      _heap->push(node, (*_edge_order)[edge]);

      _pred->set(node, edge);

      while (!_heap->empty()) {

        Node source = _heap->top();

        _heap->pop();

        _node_order->set(source, -1);

        for (OutEdgeIt it(*graph, source); it != INVALID; ++it) {

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

          Node target = graph->target(it);

          switch(_heap->state(target)) {

          case Heap::PRE_HEAP:

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

            _pred->set(target, it);

            break;

          case Heap::IN_HEAP:

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

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

              _pred->set(target, it);

            }

            break;

          case Heap::POST_HEAP:

            break;

          }

        }

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

      }

    }

  };

  /// \ingroup spantree

  ///

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

  ///

  /// Function type interface for MinCostArborescence algorithm.

  /// \param graph The Graph that the algorithm runs on.

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

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

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

  /// \return The cost of the arborescence. 

  ///

  /// \sa MinCostArborescence

  template <typename Graph, typename CostMap, typename ArborescenceMap>

  typename CostMap::Value minCostArborescence(const Graph& graph, 

                                              const CostMap& cost,

                                              typename Graph::Node source,

                                              ArborescenceMap& arborescence) {

    typename MinCostArborescence<Graph, CostMap>

      ::template DefArborescenceMap<ArborescenceMap>

      ::Create mca(graph, cost);

    mca.arborescenceMap(arborescence);

    mca.run(source);

    return mca.arborescenceValue();

  }

}

#endif