lemon/kruskal.h
changeset 215 17c644f5f98d
parent 194 74cd0c58b348
child 216 6d7bfcf5b48e
equal deleted inserted replaced
3:6dee89ef8800 4:4e2e1b412334
     1 /* -*- C++ -*-
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     4  *
     5  * Copyright (C) 2003-2008
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     8  *
    43 
    43 
    44     // Kruskal for directed graphs.
    44     // Kruskal for directed graphs.
    45 
    45 
    46     template <typename Digraph, typename In, typename Out>
    46     template <typename Digraph, typename In, typename Out>
    47     typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
    47     typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
    48 		       typename In::value_type::second_type >::type
    48                        typename In::value_type::second_type >::type
    49     kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
    49     kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
    50       typedef typename In::value_type::second_type Value;
    50       typedef typename In::value_type::second_type Value;
    51       typedef typename Digraph::template NodeMap<int> IndexMap;
    51       typedef typename Digraph::template NodeMap<int> IndexMap;
    52       typedef typename Digraph::Node Node;
    52       typedef typename Digraph::Node Node;
    53       
    53 
    54       IndexMap index(digraph);
    54       IndexMap index(digraph);
    55       UnionFind<IndexMap> uf(index);
    55       UnionFind<IndexMap> uf(index);
    56       for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
    56       for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
    57         uf.insert(it);
    57         uf.insert(it);
    58       }
    58       }
    59       
    59 
    60       Value tree_value = 0;
    60       Value tree_value = 0;
    61       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
    61       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
    62         if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
    62         if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
    63           out.set(it->first, true);
    63           out.set(it->first, true);
    64           tree_value += it->second;
    64           tree_value += it->second;
    72 
    72 
    73     // Kruskal for undirected graphs.
    73     // Kruskal for undirected graphs.
    74 
    74 
    75     template <typename Graph, typename In, typename Out>
    75     template <typename Graph, typename In, typename Out>
    76     typename enable_if<lemon::UndirectedTagIndicator<Graph>,
    76     typename enable_if<lemon::UndirectedTagIndicator<Graph>,
    77 		       typename In::value_type::second_type >::type
    77                        typename In::value_type::second_type >::type
    78     kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
    78     kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
    79       typedef typename In::value_type::second_type Value;
    79       typedef typename In::value_type::second_type Value;
    80       typedef typename Graph::template NodeMap<int> IndexMap;
    80       typedef typename Graph::template NodeMap<int> IndexMap;
    81       typedef typename Graph::Node Node;
    81       typedef typename Graph::Node Node;
    82       
    82 
    83       IndexMap index(graph);
    83       IndexMap index(graph);
    84       UnionFind<IndexMap> uf(index);
    84       UnionFind<IndexMap> uf(index);
    85       for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
    85       for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
    86         uf.insert(it);
    86         uf.insert(it);
    87       }
    87       }
    88       
    88 
    89       Value tree_value = 0;
    89       Value tree_value = 0;
    90       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
    90       for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
    91         if (uf.join(graph.u(it->first),graph.v(it->first))) {
    91         if (uf.join(graph.u(it->first),graph.v(it->first))) {
    92           out.set(it->first, true);
    92           out.set(it->first, true);
    93           tree_value += it->second;
    93           tree_value += it->second;
   102 
   102 
   103     template <typename Sequence>
   103     template <typename Sequence>
   104     struct PairComp {
   104     struct PairComp {
   105       typedef typename Sequence::value_type Value;
   105       typedef typename Sequence::value_type Value;
   106       bool operator()(const Value& left, const Value& right) {
   106       bool operator()(const Value& left, const Value& right) {
   107 	return left.second < right.second;
   107         return left.second < right.second;
   108       }
   108       }
   109     };
   109     };
   110 
   110 
   111     template <typename In, typename Enable = void>
   111     template <typename In, typename Enable = void>
   112     struct SequenceInputIndicator {
   112     struct SequenceInputIndicator {
   113       static const bool value = false;
   113       static const bool value = false;
   114     };
   114     };
   115 
   115 
   116     template <typename In>
   116     template <typename In>
   117     struct SequenceInputIndicator<In, 
   117     struct SequenceInputIndicator<In,
   118       typename exists<typename In::value_type::first_type>::type> {
   118       typename exists<typename In::value_type::first_type>::type> {
   119       static const bool value = true;
   119       static const bool value = true;
   120     };
   120     };
   121 
   121 
   122     template <typename In, typename Enable = void>
   122     template <typename In, typename Enable = void>
   123     struct MapInputIndicator {
   123     struct MapInputIndicator {
   124       static const bool value = false;
   124       static const bool value = false;
   125     };
   125     };
   126 
   126 
   127     template <typename In>
   127     template <typename In>
   128     struct MapInputIndicator<In, 
   128     struct MapInputIndicator<In,
   129       typename exists<typename In::Value>::type> {
   129       typename exists<typename In::Value>::type> {
   130       static const bool value = true;
   130       static const bool value = true;
   131     };
   131     };
   132 
   132 
   133     template <typename In, typename Enable = void>
   133     template <typename In, typename Enable = void>
   134     struct SequenceOutputIndicator {
   134     struct SequenceOutputIndicator {
   135       static const bool value = false;
   135       static const bool value = false;
   136     };
   136     };
   137  
   137 
   138     template <typename Out>
   138     template <typename Out>
   139     struct SequenceOutputIndicator<Out, 
   139     struct SequenceOutputIndicator<Out,
   140       typename exists<typename Out::value_type>::type> {
   140       typename exists<typename Out::value_type>::type> {
   141       static const bool value = true;
   141       static const bool value = true;
   142     };
   142     };
   143 
   143 
   144     template <typename Out, typename Enable = void>
   144     template <typename Out, typename Enable = void>
   145     struct MapOutputIndicator {
   145     struct MapOutputIndicator {
   146       static const bool value = false;
   146       static const bool value = false;
   147     };
   147     };
   148 
   148 
   149     template <typename Out>
   149     template <typename Out>
   150     struct MapOutputIndicator<Out, 
   150     struct MapOutputIndicator<Out,
   151       typename exists<typename Out::Value>::type> {
   151       typename exists<typename Out::Value>::type> {
   152       static const bool value = true;
   152       static const bool value = true;
   153     };
   153     };
   154 
   154 
   155     template <typename In, typename InEnable = void>
   155     template <typename In, typename InEnable = void>
   156     struct KruskalValueSelector {};
   156     struct KruskalValueSelector {};
   157 
   157 
   158     template <typename In>
   158     template <typename In>
   159     struct KruskalValueSelector<In,
   159     struct KruskalValueSelector<In,
   160       typename enable_if<SequenceInputIndicator<In>, void>::type> 
   160       typename enable_if<SequenceInputIndicator<In>, void>::type>
   161     {
   161     {
   162       typedef typename In::value_type::second_type Value;
   162       typedef typename In::value_type::second_type Value;
   163     };    
   163     };
   164 
   164 
   165     template <typename In>
   165     template <typename In>
   166     struct KruskalValueSelector<In,
   166     struct KruskalValueSelector<In,
   167       typename enable_if<MapInputIndicator<In>, void>::type> 
   167       typename enable_if<MapInputIndicator<In>, void>::type>
   168     {
   168     {
   169       typedef typename In::Value Value;
   169       typedef typename In::Value Value;
   170     };    
   170     };
   171     
   171 
   172     template <typename Graph, typename In, typename Out,
   172     template <typename Graph, typename In, typename Out,
   173               typename InEnable = void>
   173               typename InEnable = void>
   174     struct KruskalInputSelector {};
   174     struct KruskalInputSelector {};
   175 
   175 
   176     template <typename Graph, typename In, typename Out,
   176     template <typename Graph, typename In, typename Out,
   177               typename InEnable = void>
   177               typename InEnable = void>
   178     struct KruskalOutputSelector {};
   178     struct KruskalOutputSelector {};
   179     
   179 
   180     template <typename Graph, typename In, typename Out>
   180     template <typename Graph, typename In, typename Out>
   181     struct KruskalInputSelector<Graph, In, Out,
   181     struct KruskalInputSelector<Graph, In, Out,
   182       typename enable_if<SequenceInputIndicator<In>, void>::type > 
   182       typename enable_if<SequenceInputIndicator<In>, void>::type >
   183     {
   183     {
   184       typedef typename In::value_type::second_type Value;
   184       typedef typename In::value_type::second_type Value;
   185 
   185 
   186       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   186       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   187         return KruskalOutputSelector<Graph, In, Out>::
   187         return KruskalOutputSelector<Graph, In, Out>::
   190 
   190 
   191     };
   191     };
   192 
   192 
   193     template <typename Graph, typename In, typename Out>
   193     template <typename Graph, typename In, typename Out>
   194     struct KruskalInputSelector<Graph, In, Out,
   194     struct KruskalInputSelector<Graph, In, Out,
   195       typename enable_if<MapInputIndicator<In>, void>::type > 
   195       typename enable_if<MapInputIndicator<In>, void>::type >
   196     {
   196     {
   197       typedef typename In::Value Value;
   197       typedef typename In::Value Value;
   198       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   198       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   199         typedef typename In::Key MapArc;
   199         typedef typename In::Key MapArc;
   200         typedef typename In::Value Value;
   200         typedef typename In::Value Value;
   201         typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
   201         typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
   202         typedef std::vector<std::pair<MapArc, Value> > Sequence;
   202         typedef std::vector<std::pair<MapArc, Value> > Sequence;
   203         Sequence seq;
   203         Sequence seq;
   204         
   204 
   205         for (MapArcIt it(graph); it != INVALID; ++it) {
   205         for (MapArcIt it(graph); it != INVALID; ++it) {
   206           seq.push_back(std::make_pair(it, in[it]));
   206           seq.push_back(std::make_pair(it, in[it]));
   207         }
   207         }
   208 
   208 
   209         std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
   209         std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
   222       typedef T type;
   222       typedef T type;
   223     };
   223     };
   224 
   224 
   225     template <typename Graph, typename In, typename Out>
   225     template <typename Graph, typename In, typename Out>
   226     struct KruskalOutputSelector<Graph, In, Out,
   226     struct KruskalOutputSelector<Graph, In, Out,
   227       typename enable_if<SequenceOutputIndicator<Out>, void>::type > 
   227       typename enable_if<SequenceOutputIndicator<Out>, void>::type >
   228     {
   228     {
   229       typedef typename In::value_type::second_type Value;
   229       typedef typename In::value_type::second_type Value;
   230 
   230 
   231       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   231       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   232         typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
   232         typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
   236 
   236 
   237     };
   237     };
   238 
   238 
   239     template <typename Graph, typename In, typename Out>
   239     template <typename Graph, typename In, typename Out>
   240     struct KruskalOutputSelector<Graph, In, Out,
   240     struct KruskalOutputSelector<Graph, In, Out,
   241       typename enable_if<MapOutputIndicator<Out>, void>::type > 
   241       typename enable_if<MapOutputIndicator<Out>, void>::type >
   242     {
   242     {
   243       typedef typename In::value_type::second_type Value;
   243       typedef typename In::value_type::second_type Value;
   244 
   244 
   245       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   245       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   246         return _kruskal_bits::kruskal(graph, in, out);
   246         return _kruskal_bits::kruskal(graph, in, out);
   252   /// \ingroup spantree
   252   /// \ingroup spantree
   253   ///
   253   ///
   254   /// \brief Kruskal algorithm to find a minimum cost spanning tree of
   254   /// \brief Kruskal algorithm to find a minimum cost spanning tree of
   255   /// a graph.
   255   /// a graph.
   256   ///
   256   ///
   257   /// This function runs Kruskal's algorithm to find a minimum cost 
   257   /// This function runs Kruskal's algorithm to find a minimum cost
   258   /// spanning tree.
   258   /// spanning tree.
   259   /// Due to some C++ hacking, it accepts various input and output types.
   259   /// Due to some C++ hacking, it accepts various input and output types.
   260   ///
   260   ///
   261   /// \param g The graph the algorithm runs on.
   261   /// \param g The graph the algorithm runs on.
   262   /// It can be either \ref concepts::Digraph "directed" or 
   262   /// It can be either \ref concepts::Digraph "directed" or
   263   /// \ref concepts::Graph "undirected".
   263   /// \ref concepts::Graph "undirected".
   264   /// If the graph is directed, the algorithm consider it to be 
   264   /// If the graph is directed, the algorithm consider it to be
   265   /// undirected by disregarding the direction of the arcs.
   265   /// undirected by disregarding the direction of the arcs.
   266   ///
   266   ///
   267   /// \param in This object is used to describe the arc/edge costs. 
   267   /// \param in This object is used to describe the arc/edge costs.
   268   /// It can be one of the following choices.
   268   /// It can be one of the following choices.
   269   /// - An STL compatible 'Forward Container' with
   269   /// - An STL compatible 'Forward Container' with
   270   /// <tt>std::pair<GR::Arc,X></tt> or
   270   /// <tt>std::pair<GR::Arc,X></tt> or
   271   /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where
   271   /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where
   272   /// \c X is the type of the costs. The pairs indicates the arcs/edges
   272   /// \c X is the type of the costs. The pairs indicates the arcs/edges
   273   /// along with the assigned cost. <em>They must be in a
   273   /// along with the assigned cost. <em>They must be in a
   274   /// cost-ascending order.</em>
   274   /// cost-ascending order.</em>
   275   /// - Any readable arc/edge map. The values of the map indicate the 
   275   /// - Any readable arc/edge map. The values of the map indicate the
   276   /// arc/edge costs.
   276   /// arc/edge costs.
   277   ///
   277   ///
   278   /// \retval out Here we also have a choice.
   278   /// \retval out Here we also have a choice.
   279   /// - It can be a writable \c bool arc/edge map. After running the
   279   /// - It can be a writable \c bool arc/edge map. After running the
   280   /// algorithm it will contain the found minimum cost spanning
   280   /// algorithm it will contain the found minimum cost spanning
   290   ///\code
   290   ///\code
   291   /// std::vector<Arc> tree(53);
   291   /// std::vector<Arc> tree(53);
   292   /// kruskal(g,cost,tree.begin());
   292   /// kruskal(g,cost,tree.begin());
   293   ///\endcode
   293   ///\endcode
   294   /// Or if we don't know in advance the size of the tree, we can
   294   /// Or if we don't know in advance the size of the tree, we can
   295   /// write this.  
   295   /// write this.
   296   ///\code
   296   ///\code
   297   /// std::vector<Arc> tree;
   297   /// std::vector<Arc> tree;
   298   /// kruskal(g,cost,std::back_inserter(tree)); 
   298   /// kruskal(g,cost,std::back_inserter(tree));
   299   ///\endcode
   299   ///\endcode
   300   ///
   300   ///
   301   /// \return The total cost of the found spanning tree.
   301   /// \return The total cost of the found spanning tree.
   302   ///
   302   ///
   303   /// \warning If Kruskal runs on an be consistent of using the same
   303   /// \warning If Kruskal runs on an be consistent of using the same
   305   ///
   305   ///
   306 
   306 
   307 #ifdef DOXYGEN
   307 #ifdef DOXYGEN
   308   template <class Graph, class In, class Out>
   308   template <class Graph, class In, class Out>
   309   Value kruskal(GR const& g, const In& in, Out& out)
   309   Value kruskal(GR const& g, const In& in, Out& out)
   310 #else 
   310 #else
   311   template <class Graph, class In, class Out>
   311   template <class Graph, class In, class Out>
   312   inline typename _kruskal_bits::KruskalValueSelector<In>::Value 
   312   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
   313   kruskal(const Graph& graph, const In& in, Out& out) 
   313   kruskal(const Graph& graph, const In& in, Out& out)
   314 #endif
   314 #endif
   315   {
   315   {
   316     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
   316     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
   317       kruskal(graph, in, out);
   317       kruskal(graph, in, out);
   318   }
   318   }
   319 
   319 
   320  
   320 
   321   
   321 
   322 
   322 
   323   template <class Graph, class In, class Out>
   323   template <class Graph, class In, class Out>
   324   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
   324   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
   325   kruskal(const Graph& graph, const In& in, const Out& out)
   325   kruskal(const Graph& graph, const In& in, const Out& out)
   326   {
   326   {
   327     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
   327     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
   328       kruskal(graph, in, out);
   328       kruskal(graph, in, out);
   329   }  
   329   }
   330 
   330 
   331 } //namespace lemon
   331 } //namespace lemon
   332 
   332 
   333 #endif //LEMON_KRUSKAL_H
   333 #endif //LEMON_KRUSKAL_H