lemon/kruskal.h
changeset 1549 8bf39d55b1db
parent 1449 ac7e995e47e2
child 1555 48769ac7ec32
equal deleted inserted replaced
1:cd6f5a0541cd 2:590638a192ed
    43   /// @{
    43   /// @{
    44 
    44 
    45   /// Kruskal's algorithm to find a minimum cost tree of a graph.
    45   /// Kruskal's algorithm to find a minimum cost tree of a graph.
    46 
    46 
    47   /// This function runs Kruskal's algorithm to find a minimum cost tree.
    47   /// This function runs Kruskal's algorithm to find a minimum cost tree.
    48   /// \param G The graph the algorithm runs on. The algorithm considers the
    48   /// \param g The graph the algorithm runs on. The algorithm considers the
    49   /// graph to be undirected, the direction of the edges are not used.
    49   /// graph to be undirected, the direction of the edges are not used.
    50   ///
    50   ///
    51   /// \param in This object is used to describe the edge costs. It must
    51   /// \param in This object is used to describe the edge costs. It must
    52   /// be an STL compatible 'Forward Container'
    52   /// be an STL compatible 'Forward Container'
    53   /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>,
    53   /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>,
    74   /// <tt>Edge</tt>s belonging to a certain <tt>UndirEdge</tt>.
    74   /// <tt>Edge</tt>s belonging to a certain <tt>UndirEdge</tt>.
    75   /// (\ref kruskalEdgeMap() and \ref KruskalMapInput are kind enough to do so.)
    75   /// (\ref kruskalEdgeMap() and \ref KruskalMapInput are kind enough to do so.)
    76 
    76 
    77   template <class GR, class IN, class OUT>
    77   template <class GR, class IN, class OUT>
    78   typename IN::value_type::second_type
    78   typename IN::value_type::second_type
    79   kruskal(GR const& G, IN const& in, 
    79   kruskal(GR const& g, IN const& in, 
    80 		 OUT& out)
    80 		 OUT& out)
    81   {
    81   {
    82     typedef typename IN::value_type::second_type EdgeCost;
    82     typedef typename IN::value_type::second_type EdgeCost;
    83     typedef typename GR::template NodeMap<int> NodeIntMap;
    83     typedef typename GR::template NodeMap<int> NodeIntMap;
    84     typedef typename GR::Node Node;
    84     typedef typename GR::Node Node;
    85 
    85 
    86     NodeIntMap comp(G, -1);
    86     NodeIntMap comp(g, -1);
    87     UnionFind<Node,NodeIntMap> uf(comp); 
    87     UnionFind<Node,NodeIntMap> uf(comp); 
    88       
    88       
    89     EdgeCost tot_cost = 0;
    89     EdgeCost tot_cost = 0;
    90     for (typename IN::const_iterator p = in.begin(); 
    90     for (typename IN::const_iterator p = in.begin(); 
    91 	 p!=in.end(); ++p ) {
    91 	 p!=in.end(); ++p ) {
    92       if ( uf.join(G.target((*p).first),
    92       if ( uf.join(g.target((*p).first),
    93 		   G.source((*p).first)) ) {
    93 		   g.source((*p).first)) ) {
    94 	out.set((*p).first, true);
    94 	out.set((*p).first, true);
    95 	tot_cost += (*p).second;
    95 	tot_cost += (*p).second;
    96       }
    96       }
    97       else {
    97       else {
    98 	out.set((*p).first, false);
    98 	out.set((*p).first, false);
   107 
   107 
   108   /// Helper class for calling kruskal with output maps constructed
   108   /// Helper class for calling kruskal with output maps constructed
   109   /// on-the-fly.
   109   /// on-the-fly.
   110   ///
   110   ///
   111   /// A typical examle is the following call:
   111   /// A typical examle is the following call:
   112   /// <tt>kruskal(G, some_input, makeSequenceOutput(iterator))</tt>.
   112   /// <tt>kruskal(g, some_input, makeSequenceOutput(iterator))</tt>.
   113   /// Here, the third argument is a temporary object (which wraps around an
   113   /// Here, the third argument is a temporary object (which wraps around an
   114   /// iterator with a writable bool map interface), and thus by rules of C++
   114   /// iterator with a writable bool map interface), and thus by rules of C++
   115   /// is a \c const object. To enable call like this exist this class and
   115   /// is a \c const object. To enable call like this exist this class and
   116   /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt>
   116   /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt>
   117   /// third argument.
   117   /// third argument.
   128   };
   128   };
   129 
   129 
   130   template <class GR, class IN, class OUT>
   130   template <class GR, class IN, class OUT>
   131   inline
   131   inline
   132   typename IN::value_type::second_type
   132   typename IN::value_type::second_type
   133   kruskal(GR const& G, IN const& edges, OUT const& out_map)
   133   kruskal(GR const& g, IN const& edges, OUT const& out_map)
   134   {
   134   {
   135     NonConstMapWr<OUT> map_wr(out_map);
   135     NonConstMapWr<OUT> map_wr(out_map);
   136     return kruskal(G, edges, map_wr);
   136     return kruskal(g, edges, map_wr);
   137   }  
   137   }  
   138 
   138 
   139   /* ** ** Input-objects ** ** */
   139   /* ** ** Input-objects ** ** */
   140 
   140 
   141   /// Kruskal's input source.
   141   /// Kruskal's input source.
   173       }
   173       }
   174     };
   174     };
   175 
   175 
   176     template<class _GR>
   176     template<class _GR>
   177     typename enable_if<typename _GR::UndirTag,void>::type
   177     typename enable_if<typename _GR::UndirTag,void>::type
   178     fillWithEdges(const _GR& G, const Map& m,dummy<0> = 0) 
   178     fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0) 
   179     {
   179     {
   180       for(typename GR::UndirEdgeIt e(G);e!=INVALID;++e) 
   180       for(typename GR::UndirEdgeIt e(g);e!=INVALID;++e) 
   181 	push_back(value_type(typename GR::Edge(e,true), m[e]));
   181 	push_back(value_type(typename GR::Edge(e,true), m[e]));
   182     }
   182     }
   183 
   183 
   184     template<class _GR>
   184     template<class _GR>
   185     typename disable_if<typename _GR::UndirTag,void>::type
   185     typename disable_if<typename _GR::UndirTag,void>::type
   186     fillWithEdges(const _GR& G, const Map& m,dummy<1> = 1) 
   186     fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1) 
   187     {
   187     {
   188       for(typename GR::EdgeIt e(G);e!=INVALID;++e) 
   188       for(typename GR::EdgeIt e(g);e!=INVALID;++e) 
   189 	push_back(value_type(e, m[e]));
   189 	push_back(value_type(e, m[e]));
   190     }
   190     }
   191     
   191     
   192     
   192     
   193   public:
   193   public:
   194 
   194 
   195     void sort() {
   195     void sort() {
   196       std::sort(this->begin(), this->end(), comparePair());
   196       std::sort(this->begin(), this->end(), comparePair());
   197     }
   197     }
   198 
   198 
   199     KruskalMapInput(GR const& G, Map const& m) {
   199     KruskalMapInput(GR const& g, Map const& m) {
   200       fillWithEdges(G,m); 
   200       fillWithEdges(g,m); 
   201       sort();
   201       sort();
   202     }
   202     }
   203   };
   203   };
   204 
   204 
   205   /// Creates a KruskalMapInput object for \ref kruskal()
   205   /// Creates a KruskalMapInput object for \ref kruskal()
   209   /// to explicitly give the type of the parameters.
   209   /// to explicitly give the type of the parameters.
   210   ///
   210   ///
   211   /// In most cases you possibly
   211   /// In most cases you possibly
   212   /// want to use the function kruskalEdgeMap() instead.
   212   /// want to use the function kruskalEdgeMap() instead.
   213   ///
   213   ///
   214   ///\param G The type of the graph the algorithm runs on.
   214   ///\param g The type of the graph the algorithm runs on.
   215   ///\param m An edge map containing the cost of the edges.
   215   ///\param m An edge map containing the cost of the edges.
   216   ///\par
   216   ///\par
   217   ///The cost type can be any type satisfying the
   217   ///The cost type can be any type satisfying the
   218   ///STL 'LessThan Comparable'
   218   ///STL 'LessThan Comparable'
   219   ///concept if it also has an operator+() implemented. (It is necessary for
   219   ///concept if it also has an operator+() implemented. (It is necessary for
   221   ///
   221   ///
   222   ///\return An appropriate input source for \ref kruskal().
   222   ///\return An appropriate input source for \ref kruskal().
   223   ///
   223   ///
   224   template<class GR, class Map>
   224   template<class GR, class Map>
   225   inline
   225   inline
   226   KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &G,const Map &m)
   226   KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m)
   227   {
   227   {
   228     return KruskalMapInput<GR,Map>(G,m);
   228     return KruskalMapInput<GR,Map>(g,m);
   229   }
   229   }
   230   
   230   
   231   
   231   
   232 
   232 
   233   /* ** ** Output-objects: simple writable bool maps ** ** */
   233   /* ** ** Output-objects: simple writable bool maps ** ** */
   289   /// Input is from an edge map, output is a plain bool map.
   289   /// Input is from an edge map, output is a plain bool map.
   290   ///
   290   ///
   291   /// Wrapper function to kruskal().
   291   /// Wrapper function to kruskal().
   292   /// Input is from an edge map, output is a plain bool map.
   292   /// Input is from an edge map, output is a plain bool map.
   293   ///
   293   ///
   294   ///\param G The type of the graph the algorithm runs on.
   294   ///\param g The type of the graph the algorithm runs on.
   295   ///\param in An edge map containing the cost of the edges.
   295   ///\param in An edge map containing the cost of the edges.
   296   ///\par
   296   ///\par
   297   ///The cost type can be any type satisfying the
   297   ///The cost type can be any type satisfying the
   298   ///STL 'LessThan Comparable'
   298   ///STL 'LessThan Comparable'
   299   ///concept if it also has an operator+() implemented. (It is necessary for
   299   ///concept if it also has an operator+() implemented. (It is necessary for
   308   /// \return The cost of the found tree.
   308   /// \return The cost of the found tree.
   309 
   309 
   310   template <class GR, class IN, class RET>
   310   template <class GR, class IN, class RET>
   311   inline
   311   inline
   312   typename IN::Value
   312   typename IN::Value
   313   kruskalEdgeMap(GR const& G,
   313   kruskalEdgeMap(GR const& g,
   314 		 IN const& in,
   314 		 IN const& in,
   315 		 RET &out) {
   315 		 RET &out) {
   316     return kruskal(G,
   316     return kruskal(g,
   317 		   KruskalMapInput<GR,IN>(G,in),
   317 		   KruskalMapInput<GR,IN>(g,in),
   318 		   out);
   318 		   out);
   319   }
   319   }
   320 
   320 
   321   /// \brief Wrapper function to kruskal().
   321   /// \brief Wrapper function to kruskal().
   322   /// Input is from an edge map, output is an STL Sequence.
   322   /// Input is from an edge map, output is an STL Sequence.
   323   ///
   323   ///
   324   /// Wrapper function to kruskal().
   324   /// Wrapper function to kruskal().
   325   /// Input is from an edge map, output is an STL Sequence.
   325   /// Input is from an edge map, output is an STL Sequence.
   326   ///
   326   ///
   327   ///\param G The type of the graph the algorithm runs on.
   327   ///\param g The type of the graph the algorithm runs on.
   328   ///\param in An edge map containing the cost of the edges.
   328   ///\param in An edge map containing the cost of the edges.
   329   ///\par
   329   ///\par
   330   ///The cost type can be any type satisfying the
   330   ///The cost type can be any type satisfying the
   331   ///STL 'LessThan Comparable'
   331   ///STL 'LessThan Comparable'
   332   ///concept if it also has an operator+() implemented. (It is necessary for
   332   ///concept if it also has an operator+() implemented. (It is necessary for
   333   ///computing the total cost of the tree).
   333   ///computing the total cost of the tree).
   334   ///
   334   ///
   335   /// \retval out This must be an iteraror of an STL Container with
   335   /// \retval out This must be an iteraror of an STL Container with
   336   /// <tt>GR::Edge</tt> as its <tt>value_type</tt>.
   336   /// <tt>GR::Edge</tt> as its <tt>value_type</tt>.
   337   /// The algorithm copies the elements of the found tree into this sequence.
   337   /// The algorithm copies the elements of the found tree into this sequence.
   338   /// For example, if we know that the spanning tree of the graph \c G has
   338   /// For example, if we know that the spanning tree of the graph \c g has
   339   /// say 53 edges then
   339   /// say 53 edges then
   340   /// we can put its edges into a STL vector \c tree with a code like this.
   340   /// we can put its edges into a STL vector \c tree with a code like this.
   341   /// \code
   341   /// \code
   342   /// std::vector<Edge> tree(53);
   342   /// std::vector<Edge> tree(53);
   343   /// kruskalEdgeMap_IteratorOut(G,cost,tree.begin());
   343   /// kruskalEdgeMap_IteratorOut(g,cost,tree.begin());
   344   /// \endcode
   344   /// \endcode
   345   /// Or if we don't know in advance the size of the tree, we can write this.
   345   /// Or if we don't know in advance the size of the tree, we can write this.
   346   /// \code
   346   /// \code
   347   /// std::vector<Edge> tree;
   347   /// std::vector<Edge> tree;
   348   /// kruskalEdgeMap_IteratorOut(G,cost,std::back_inserter(tree));
   348   /// kruskalEdgeMap_IteratorOut(g,cost,std::back_inserter(tree));
   349   /// \endcode
   349   /// \endcode
   350   ///
   350   ///
   351   /// \return The cost of the found tree.
   351   /// \return The cost of the found tree.
   352   ///
   352   ///
   353   /// \bug its name does not follow the coding style.
   353   /// \bug its name does not follow the coding style.
   354 
   354 
   355   template <class GR, class IN, class RET>
   355   template <class GR, class IN, class RET>
   356   inline
   356   inline
   357   typename IN::Value
   357   typename IN::Value
   358   kruskalEdgeMap_IteratorOut(const GR& G,
   358   kruskalEdgeMap_IteratorOut(const GR& g,
   359 			     const IN& in,
   359 			     const IN& in,
   360 			     RET out)
   360 			     RET out)
   361   {
   361   {
   362     KruskalSequenceOutput<RET> _out(out);
   362     KruskalSequenceOutput<RET> _out(out);
   363     return kruskal(G, KruskalMapInput<GR,IN>(G, in), _out);
   363     return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out);
   364   }
   364   }
   365 
   365 
   366   /// @}
   366   /// @}
   367 
   367 
   368 } //namespace lemon
   368 } //namespace lemon