/* -*- 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_KRUSKAL_H

 #define LEMON_KRUSKAL_H

 #include <algorithm>

 #include <vector>

 #include <lemon/unionfind.h>

 #include <lemon/graph_utils.h>

 #include <lemon/maps.h>

 #include <lemon/radix_sort.h>

 #include <lemon/bits/utility.h>

 #include <lemon/bits/traits.h>

 ///\ingroup spantree

 ///\file

 ///\brief Kruskal's algorithm to compute a minimum cost tree

 ///

 ///Kruskal's algorithm to compute a minimum cost tree.

 ///

 namespace lemon {

   namespace _kruskal_bits {

     template <typename Map, typename Comp>

     struct MappedComp {

       typedef typename Map::Key Key;

       const Map& map;

       Comp comp;

       MappedComp(const Map& _map) 

         : map(_map), comp() {}

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

         return comp(map[left], map[right]);

       }

     };

   }

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

   ///

   /// Default traits class of Kruskal class.

   /// \param _UGraph Undirected graph type.

   /// \param _CostMap Type of cost map.

   template <typename _UGraph, typename _CostMap>

   struct KruskalDefaultTraits{

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

     typedef _UGraph UGraph;

     /// \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 type of the cost of the edges.

     typedef typename _CostMap::Value Value;

     /// \brief The type of the map that stores whether an edge is in the

     /// spanning tree or not.

     ///

     /// The type of the map that stores whether an edge is in the

     /// spanning tree or not.

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

     /// \brief Instantiates a TreeMap.

     ///

     /// This function instantiates a \ref TreeMap.

     ///

     /// The first parameter is the graph, to which

     /// we would like to define the \ref TreeMap

     static TreeMap *createTreeMap(const _UGraph& graph){

       return new TreeMap(graph);

     }

     template <typename Iterator>

     static void sort(Iterator begin, Iterator end, const CostMap& cost) {

       _kruskal_bits::MappedComp<CostMap, std::less<Value> > comp(cost);

       std::sort(begin, end, comp);

     }

   };

   ///\ingroup spantree

   ///

   /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.

   ///

   /// This class implements Kruskal's algorithm to find a minimum cost

   /// spanning tree. The 

   ///

   /// \param _UGraph Undirected graph type.

   /// \param _CostMap Type of cost map.

   template <typename _UGraph, typename _CostMap,

             typename _Traits = KruskalDefaultTraits<_UGraph, _CostMap> >

   class Kruskal {

   public:

     typedef _Traits Traits;

     typedef typename _Traits::UGraph UGraph;

     typedef typename _Traits::CostMap CostMap;

     typedef typename _Traits::TreeMap TreeMap;

     typedef typename _Traits::Value Value;

     template <typename Comp>

     struct DefSortCompareTraits : public Traits {

       template <typename Iterator>

       static void sort(Iterator begin, Iterator end, const CostMap& cost) {

         _kruskal_bits::MappedComp<CostMap, Comp> comp(cost, Comp());

         std::sort(begin, end, comp);

       }

     };

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

     /// comparator object of the standard sort

     ///

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

     /// comparator object of the standard sort

     template <typename Comp>

     struct DefSortCompare

       : public Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > {

       typedef Kruskal<UGraph, CostMap, DefSortCompareTraits<Comp> > Create;

     };    

     struct DefRadixSortTraits : public Traits {

       template <typename Iterator>

       static void sort(Iterator begin, Iterator end, const CostMap& cost) {

         radixSort(begin, end, cost);

       }

     };

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

     /// sort function to radix sort

     ///

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

     /// sort function to radix sort. The value type of the cost map should

     /// be integral, of course. 

     struct DefRadixSort

       : public Kruskal<UGraph, CostMap, DefRadixSortTraits> {

       typedef Kruskal<UGraph, CostMap, DefRadixSortTraits> Create;

     };    

     template <class TM>

     struct DefTreeMapTraits : public Traits {

       typedef TM TreeMap;

       static TreeMap *createTreeMap(const UGraph &) {

         throw UninitializedParameter();

       }

     };

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

     /// TreeMap

     ///

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

     ///

     template <class TM>

     struct DefTreeMap

       : public Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > {

       typedef Kruskal< UGraph, CostMap, DefTreeMapTraits<TM> > Create;

     };    

   private:

     typedef typename UGraph::Node Node;

     typedef typename UGraph::NodeIt NodeIt;

     typedef typename UGraph::UEdge UEdge;

     typedef typename UGraph::UEdgeIt UEdgeIt;

     const UGraph& graph;

     const CostMap& cost;

     std::vector<UEdge> edges;

     typedef typename UGraph::template NodeMap<int> UfIndex;

     typedef UnionFind<UfIndex> Uf;

     UfIndex *ufi;

     Uf *uf;

     int index;

     void initStructures() {

       if (!_tree) {

         _tree = Traits::createTreeMap(graph);

         local_tree = true;

       }

       if (!uf) {

         ufi = new typename UGraph::template NodeMap<int>(graph);

         uf = new UnionFind<typename UGraph::template NodeMap<int> >(*ufi);

       }

     }

     void initUnionFind() {

       uf->clear();

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

         uf->insert(it);

       }

     }

     bool local_tree;

     TreeMap* _tree;

   public:

     /// \brief Constructor

     ///

     /// Constructor of the algorithm.

     Kruskal(const UGraph& _graph, const CostMap& _cost) 

       : graph(_graph), cost(_cost),

         ufi(0), uf(0), local_tree(false), _tree(0) {}

     /// \brief Destructor

     ///

     /// Destructor

     ~Kruskal() {

       if (local_tree) {

         delete _tree;

       }

       if (uf) {

         delete uf;

         delete ufi;

       }

     }

     /// \brief Sets the map storing the tree edges.

     ///

     /// Sets the map storing the tree edges.

     /// If you don't use this function before calling \ref run(),

     /// it will allocate one. The destuctor deallocates this

     /// automatically allocated map, of course.

     /// \return \c *this </tt>

     Kruskal& treeMap(TreeMap &m){

       if (local_tree) {

 	delete _tree;

 	local_tree = false;

       }

       _tree = &m;

       return *this;

     }

     /// \brief Initialize the algorithm

     ///

     /// This member function initializes the unionfind data structure

     /// and sorts the edges into ascending order

     void init() {

       initStructures();

       initUnionFind();

       for (UEdgeIt e(graph); e != INVALID; ++e) {

         edges.push_back(e);

         _tree->set(e, false);

       }      

       Traits::sort(edges.begin(), edges.end(), cost); 

       index = 0;

     }

     /// \brief Initialize the algorithm

     ///

     /// This member function initializes the unionfind data structure

     /// and sets the edge order to the given sequence. The given

     /// sequence should be a valid STL range of undirected edges.

     template <typename Iterator>

     void initPresorted(Iterator begin, Iterator end) {

       initStructures();

       initUnionFind();

       edges.clear();

       std::copy(begin, end, std::back_inserter(edges));

       index = 0;

     }

     /// \brief Initialize the algorithm

     ///

     /// This member function initializes the unionfind data structure

     /// and sets the tree to empty. It does not change the order of

     /// the edges, it uses the order of the previous running.

     void reinit() {

       initStructures();

       initUnionFind();

       for (UEdgeIt e(graph); e != INVALID; ++e) {

         _tree->set(e, false);

       }

       index = 0;

     }

     /// \brief Executes the algorithm.

     ///

     /// Executes the algorithm.

     ///

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

     ///

     /// This method runs the %Kruskal algorithm.

     void start() {

       while (index < int(edges.size())) {

         if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) {

           _tree->set(edges[index], true);

         }

         ++index;

       }

     }

     /// \brief Runs the prim algorithm until it find a new tree edge

     ///

     /// Runs the prim algorithm until it find a new tree edge. If it

     /// does not next tree edge in the sequence it gives back \c INVALID.

     UEdge findNextTreeEdge() {

       while (index < int(edges.size())) {

         if (uf->join(graph.target(edges[index]), graph.source(edges[index]))) {

           _tree->set(edges[index], true);

           return edges[index++];

         }        

         ++index;

       }

       return INVALID;

     }

     /// \brief Processes the next edge in the sequence

     ///

     /// Processes the next edge in the sequence.

     ///

     /// \return The prcocessed edge.

     ///

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

     UEdge processNextEdge() {

       UEdge edge = edges[index++];

       processEdge(edge);

       return edge;

     }

     /// \brief Processes an arbitrary edge

     ///

     /// Processes the next edge in the sequence.

     ///

     /// \return True when the edge is a tree edge.

     bool processEdge(const UEdge& edge) {

       if (uf->join(graph.target(edge), graph.source(edge))) {

         _tree->set(edge, true);

         return true;

       } else {

         return false;

       }    

     }

     /// \brief Returns \c false if there are edge to be processed in

     /// sequence

     ///

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

     /// sequence

     bool emptyQueue() {

       return index == int(edges.size());

     }

     /// \brief Returns the next edge to be processed

     ///

     /// Returns the next edge to be processed

     ///

     UEdge nextEdge() const {

       return edges[index];

     }

     /// \brief Runs %Kruskal algorithm.

     ///

     /// This method runs the %Kruskal algorithm in order to compute the

     /// minimum spanning tree (or minimum spanning forest).  The

     /// method also works on graphs that has more than one components.

     /// In this case it computes the minimum spanning forest.

     void run() {

       init();

       start();

     }

     /// \brief Returns a reference to the tree edges map

     ///

     /// Returns a reference to the TreeEdgeMap of the edges of the

     /// minimum spanning tree. The value of the map is \c true only if

     /// the edge is in the minimum spanning tree.

     ///

     const TreeMap &treeMap() const { return *_tree;}

     /// \brief Returns the total cost of the tree

     ///

     /// Returns the total cost of the tree

     Value treeValue() const {

       Value value = 0;

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

         if ((*_tree)[it]) {

           value += cost[it];

         }

       }

       return value;

     }

     /// \brief Returns true when the given edge is tree edge

     ///

     /// Returns true when the given edge is tree edge

     bool tree(UEdge e) const {

       return (*_tree)[e];

     }

   };

   namespace _kruskal_bits {

     template <typename Graph, typename In, typename Out>

     typename In::value_type::second_type

     kruskal(const Graph& graph, const In& in, Out& out) {

       typedef typename In::value_type::second_type Value;

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

       typedef typename Graph::Node Node;

       IndexMap index(graph);

       UnionFind<IndexMap> uf(index);

       for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {

         uf.insert(it);

       }

       Value tree_value = 0;

       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {

         if (uf.join(graph.target(it->first),graph.source(it->first))) {

           out.set(it->first, true);

           tree_value += it->second;

         }

         else {

           out.set(it->first, false);

         }

       }

       return tree_value;

     }

     template <typename Sequence>

     struct PairComp {

       typedef typename Sequence::value_type Value;

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

 	return left.second < right.second;

       }

     };

     template <typename In, typename Enable = void>

     struct SequenceInputIndicator {

       static const bool value = false;

     };

     template <typename In>

     struct SequenceInputIndicator<In, 

       typename exists<typename In::value_type::first_type>::type> {

       static const bool value = true;

     };

     template <typename In, typename Enable = void>

     struct MapInputIndicator {

       static const bool value = false;

     };

     template <typename In>

     struct MapInputIndicator<In, 

       typename exists<typename In::Value>::type> {

       static const bool value = true;

     };

     template <typename In, typename Enable = void>

     struct SequenceOutputIndicator {

       static const bool value = false;

     };

     template <typename Out>

     struct SequenceOutputIndicator<Out, 

       typename exists<typename Out::value_type>::type> {

       static const bool value = true;

     };

     template <typename Out, typename Enable = void>

     struct MapOutputIndicator {

       static const bool value = false;

     };

     template <typename Out>

     struct MapOutputIndicator<Out, 

       typename exists<typename Out::Value>::type> {

       static const bool value = true;

     };

     template <typename In, typename InEnable = void>

     struct KruskalValueSelector {};

     template <typename In>

     struct KruskalValueSelector<In,

       typename enable_if<SequenceInputIndicator<In>, void>::type> 

     {

       typedef typename In::value_type::second_type Value;

     };    

     template <typename In>

     struct KruskalValueSelector<In,

       typename enable_if<MapInputIndicator<In>, void>::type> 

     {

       typedef typename In::Value Value;

     };    

     template <typename Graph, typename In, typename Out,

               typename InEnable = void>

     struct KruskalInputSelector {};

     template <typename Graph, typename In, typename Out,

               typename InEnable = void>

     struct KruskalOutputSelector {};

     template <typename Graph, typename In, typename Out>

     struct KruskalInputSelector<Graph, In, Out,

       typename enable_if<SequenceInputIndicator<In>, void>::type > 

     {

       typedef typename In::value_type::second_type Value;

       static Value kruskal(const Graph& graph, const In& in, Out& out) {

         return KruskalOutputSelector<Graph, In, Out>::

           kruskal(graph, in, out);

       }

     };

     template <typename Graph, typename In, typename Out>

     struct KruskalInputSelector<Graph, In, Out,

       typename enable_if<MapInputIndicator<In>, void>::type > 

     {

       typedef typename In::Value Value;

       static Value kruskal(const Graph& graph, const In& in, Out& out) {

         typedef typename In::Key MapEdge;

         typedef typename In::Value Value;

         typedef typename ItemSetTraits<Graph, MapEdge>::ItemIt MapEdgeIt;

         typedef std::vector<std::pair<MapEdge, Value> > Sequence;

         Sequence seq;

         for (MapEdgeIt it(graph); it != INVALID; ++it) {

           seq.push_back(std::make_pair(it, in[it]));

         }

         std::sort(seq.begin(), seq.end(), PairComp<Sequence>());

         return KruskalOutputSelector<Graph, Sequence, Out>::

           kruskal(graph, seq, out);

       }

     };

     template <typename Graph, typename In, typename Out>

     struct KruskalOutputSelector<Graph, In, Out,

       typename enable_if<SequenceOutputIndicator<Out>, void>::type > 

     {

       typedef typename In::value_type::second_type Value;

       static Value kruskal(const Graph& graph, const In& in, Out& out) {

         typedef StoreBoolMap<Out> Map;

         Map map(out);

         return _kruskal_bits::kruskal(graph, in, map);

       }

     };

     template <typename Graph, typename In, typename Out>

     struct KruskalOutputSelector<Graph, In, Out,

       typename enable_if<MapOutputIndicator<Out>, void>::type > 

     {

       typedef typename In::value_type::second_type Value;

       static Value kruskal(const Graph& graph, const In& in, Out& out) {

         return _kruskal_bits::kruskal(graph, in, out);

       }

     };

   }

   /// \ingroup spantree

   ///

   /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.

   ///

   /// This function runs Kruskal's algorithm to find a minimum cost tree.

   /// Due to hard C++ hacking, it accepts various input and output types.

   ///

   /// \param g The graph the algorithm runs on.

   /// It can be either \ref concepts::Graph "directed" or 

   /// \ref concepts::UGraph "undirected".

   /// If the graph is directed, the algorithm consider it to be 

   /// undirected by disregarding the direction of the edges.

   ///

   /// \param in This object is used to describe the edge costs. It can be one

   /// of the following choices.

   /// - An STL compatible 'Forward Container' with

   /// <tt>std::pair<GR::UEdge,X></tt> or

   /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where

   /// \c X is the type of the costs. The pairs indicates the edges

   /// along with the assigned cost. <em>They must be in a

   /// cost-ascending order.</em>

   /// - Any readable Edge map. The values of the map indicate the edge costs.

   ///

   /// \retval out Here we also have a choise.

   /// - It can be a writable \c bool edge map.  After running the

   /// algorithm this will contain the found minimum cost spanning

   /// tree: the value of an edge will be set to \c true if it belongs

   /// to the tree, otherwise it will be set to \c false. The value of

   /// each edge will be set exactly once.

   /// - It can also be an iteraror of an STL Container with

   /// <tt>GR::UEdge</tt> or <tt>GR::Edge</tt> as its

   /// <tt>value_type</tt>.  The algorithm copies the elements of the

   /// found tree into this sequence.  For example, if we know that the

   /// spanning tree of the graph \c g has say 53 edges, then we can

   /// put its edges into an STL vector \c tree with a code like this.

   ///\code

   /// std::vector<Edge> tree(53);

   /// kruskal(g,cost,tree.begin());

   ///\endcode

   /// Or if we don't know in advance the size of the tree, we can

   /// write this.  

   ///\code std::vector<Edge> tree;

   /// kruskal(g,cost,std::back_inserter(tree)); 

   ///\endcode

   ///

   /// \return The total cost of the found tree.

   ///

   /// \warning If kruskal runs on an be consistent of using the same

   /// Edge type for input and output.

   ///

 #ifdef DOXYGEN

   template <class Graph, class In, class Out>

   Value kruskal(GR const& g, const In& in, Out& out)

 #else 

   template <class Graph, class In, class Out>

   inline typename _kruskal_bits::KruskalValueSelector<In>::Value 

   kruskal(const Graph& graph, const In& in, Out& out) 

 #endif

   {

     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::

       kruskal(graph, in, out);

   }

   template <class Graph, class In, class Out>

   inline typename _kruskal_bits::KruskalValueSelector<In>::Value

   kruskal(const Graph& graph, const In& in, const Out& out)

   {

     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::

       kruskal(graph, in, out);

   }  

 } //namespace lemon

 #endif //LEMON_KRUSKAL_H