alpar@906: /* -*- C++ -*-
alpar@921:  * src/lemon/kruskal.h - Part of LEMON, a generic C++ optimization library
alpar@906:  *
alpar@1164:  * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@906:  * (Egervary Combinatorial Optimization Research Group, EGRES).
alpar@906:  *
alpar@906:  * Permission to use, modify and distribute this software is granted
alpar@906:  * provided that this copyright notice appears in all copies. For
alpar@906:  * precise terms see the accompanying LICENSE file.
alpar@906:  *
alpar@906:  * This software is provided "AS IS" with no warranty of any kind,
alpar@906:  * express or implied, and with no claim as to its suitability for any
alpar@906:  * purpose.
alpar@906:  *
alpar@906:  */
alpar@906: 
alpar@921: #ifndef LEMON_KRUSKAL_H
alpar@921: #define LEMON_KRUSKAL_H
alpar@810: 
alpar@810: #include <algorithm>
alpar@921: #include <lemon/unionfind.h>
alpar@810: 
alpar@810: /**
alpar@810: @defgroup spantree Minimum Cost Spanning Tree Algorithms
alpar@810: @ingroup galgs
alpar@810: \brief This group containes the algorithms for finding a minimum cost spanning
alpar@810: tree in a graph
alpar@810: 
alpar@810: This group containes the algorithms for finding a minimum cost spanning
alpar@810: tree in a graph
alpar@810: */
alpar@810: 
alpar@810: ///\ingroup spantree
alpar@810: ///\file
alpar@810: ///\brief Kruskal's algorithm to compute a minimum cost tree
alpar@810: ///
alpar@810: ///Kruskal's algorithm to compute a minimum cost tree.
alpar@810: 
alpar@921: namespace lemon {
alpar@810: 
alpar@810:   /// \addtogroup spantree
alpar@810:   /// @{
alpar@810: 
alpar@810:   /// Kruskal's algorithm to find a minimum cost tree of a graph.
alpar@810: 
alpar@810:   /// This function runs Kruskal's algorithm to find a minimum cost tree.
alpar@810:   /// \param G The graph the algorithm runs on. The algorithm considers the
alpar@810:   /// graph to be undirected, the direction of the edges are not used.
alpar@810:   ///
alpar@810:   /// \param in This object is used to describe the edge costs. It must
alpar@810:   /// be an STL compatible 'Forward Container'
alpar@824:   /// with <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>,
alpar@810:   /// where X is the type of the costs. It must contain every edge in
alpar@810:   /// cost-ascending order.
alpar@810:   ///\par
alpar@810:   /// For the sake of simplicity, there is a helper class KruskalMapInput,
alpar@810:   /// which converts a
alpar@810:   /// simple edge map to an input of this form. Alternatively, you can use
alpar@810:   /// the function \ref kruskalEdgeMap to compute the minimum cost tree if
alpar@810:   /// the edge costs are given by an edge map.
alpar@810:   ///
alpar@810:   /// \retval out This must be a writable \c bool edge map.
alpar@810:   /// After running the algorithm
alpar@810:   /// this will contain the found minimum cost spanning tree: the value of an
alpar@810:   /// edge will be set to \c true if it belongs to the tree, otherwise it will
alpar@810:   /// be set to \c false. The value of each edge will be set exactly once.
alpar@810:   ///
alpar@810:   /// \return The cost of the found tree.
alpar@810: 
alpar@824:   template <class GR, class IN, class OUT>
alpar@824:   typename IN::value_type::second_type
alpar@824:   kruskal(GR const& G, IN const& in, 
alpar@824: 		 OUT& out)
alpar@810:   {
alpar@824:     typedef typename IN::value_type::second_type EdgeCost;
alpar@824:     typedef typename GR::template NodeMap<int> NodeIntMap;
alpar@824:     typedef typename GR::Node Node;
alpar@810: 
alpar@810:     NodeIntMap comp(G, -1);
alpar@810:     UnionFind<Node,NodeIntMap> uf(comp); 
alpar@810:       
alpar@810:     EdgeCost tot_cost = 0;
alpar@824:     for (typename IN::const_iterator p = in.begin(); 
alpar@810: 	 p!=in.end(); ++p ) {
alpar@986:       if ( uf.join(G.target((*p).first),
alpar@986: 		   G.source((*p).first)) ) {
alpar@810: 	out.set((*p).first, true);
alpar@810: 	tot_cost += (*p).second;
alpar@810:       }
alpar@810:       else {
alpar@810: 	out.set((*p).first, false);
alpar@810:       }
alpar@810:     }
alpar@810:     return tot_cost;
alpar@810:   }
alpar@810: 
alpar@810:   /* A work-around for running Kruskal with const-reference bool maps... */
alpar@810: 
klao@885:   /// Helper class for calling kruskal with "constant" output map.
klao@885: 
klao@885:   /// Helper class for calling kruskal with output maps constructed
klao@885:   /// on-the-fly.
alpar@810:   ///
klao@885:   /// A typical examle is the following call:
klao@885:   /// <tt>kruskal(G, some_input, makeSequenceOutput(iterator))</tt>.
klao@885:   /// Here, the third argument is a temporary object (which wraps around an
klao@885:   /// iterator with a writable bool map interface), and thus by rules of C++
klao@885:   /// is a \c const object. To enable call like this exist this class and
klao@885:   /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt>
klao@885:   /// third argument.
alpar@824:   template<class Map>
alpar@810:   class NonConstMapWr {
alpar@810:     const Map &m;
alpar@810:   public:
alpar@987:     typedef typename Map::Value Value;
alpar@810: 
alpar@810:     NonConstMapWr(const Map &_m) : m(_m) {}
alpar@810: 
alpar@987:     template<class Key>
alpar@987:     void set(Key const& k, Value const &v) const { m.set(k,v); }
alpar@810:   };
alpar@810: 
alpar@824:   template <class GR, class IN, class OUT>
alpar@810:   inline
klao@885:   typename IN::value_type::second_type
klao@885:   kruskal(GR const& G, IN const& edges, OUT const& out_map)
alpar@810:   {
alpar@824:     NonConstMapWr<OUT> map_wr(out_map);
alpar@810:     return kruskal(G, edges, map_wr);
alpar@810:   }  
alpar@810: 
alpar@810:   /* ** ** Input-objects ** ** */
alpar@810: 
alpar@810:   /// Kruskal input source.
alpar@810: 
alpar@810:   /// Kruskal input source.
alpar@810:   ///
alpar@810:   /// In most cases you possibly want to use the \ref kruskalEdgeMap() instead.
alpar@810:   ///
alpar@810:   /// \sa makeKruskalMapInput()
alpar@810:   ///
alpar@824:   ///\param GR The type of the graph the algorithm runs on.
alpar@810:   ///\param Map An edge map containing the cost of the edges.
alpar@810:   ///\par
alpar@810:   ///The cost type can be any type satisfying
alpar@810:   ///the STL 'LessThan comparable'
alpar@810:   ///concept if it also has an operator+() implemented. (It is necessary for
alpar@810:   ///computing the total cost of the tree).
alpar@810:   ///
alpar@824:   template<class GR, class Map>
alpar@810:   class KruskalMapInput
alpar@824:     : public std::vector< std::pair<typename GR::Edge,
alpar@987: 				    typename Map::Value> > {
alpar@810:     
alpar@810:   public:
alpar@824:     typedef std::vector< std::pair<typename GR::Edge,
alpar@987: 				   typename Map::Value> > Parent;
alpar@810:     typedef typename Parent::value_type value_type;
alpar@810: 
alpar@810:   private:
alpar@810:     class comparePair {
alpar@810:     public:
alpar@810:       bool operator()(const value_type& a,
alpar@810: 		      const value_type& b) {
alpar@810: 	return a.second < b.second;
alpar@810:       }
alpar@810:     };
alpar@810: 
alpar@810:   public:
alpar@810: 
alpar@810:     void sort() {
alpar@810:       std::sort(this->begin(), this->end(), comparePair());
alpar@810:     }
alpar@810: 
alpar@824:     KruskalMapInput(GR const& G, Map const& m) {
alpar@824:       typedef typename GR::EdgeIt EdgeIt;
alpar@810:       
klao@885:       for(EdgeIt e(G);e!=INVALID;++e) push_back(value_type(e, m[e]));
alpar@810:       sort();
alpar@810:     }
alpar@810:   };
alpar@810: 
alpar@810:   /// Creates a KruskalMapInput object for \ref kruskal()
alpar@810: 
alpar@810:   /// It makes is easier to use 
alpar@810:   /// \ref KruskalMapInput by making it unnecessary 
alpar@810:   /// to explicitly give the type of the parameters.
alpar@810:   ///
alpar@810:   /// In most cases you possibly
alpar@810:   /// want to use the function kruskalEdgeMap() instead.
alpar@810:   ///
alpar@810:   ///\param G The type of the graph the algorithm runs on.
alpar@810:   ///\param m An edge map containing the cost of the edges.
alpar@810:   ///\par
alpar@810:   ///The cost type can be any type satisfying the
alpar@810:   ///STL 'LessThan Comparable'
alpar@810:   ///concept if it also has an operator+() implemented. (It is necessary for
alpar@810:   ///computing the total cost of the tree).
alpar@810:   ///
alpar@810:   ///\return An appropriate input source for \ref kruskal().
alpar@810:   ///
alpar@824:   template<class GR, class Map>
alpar@810:   inline
alpar@824:   KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &G,const Map &m)
alpar@810:   {
alpar@824:     return KruskalMapInput<GR,Map>(G,m);
alpar@810:   }
alpar@810:   
alpar@810:   
klao@885: 
klao@885:   /* ** ** Output-objects: simple writable bool maps ** ** */
alpar@810:   
klao@885: 
klao@885: 
alpar@810:   /// A writable bool-map that makes a sequence of "true" keys
alpar@810: 
alpar@810:   /// A writable bool-map that creates a sequence out of keys that receives
alpar@810:   /// the value "true".
klao@885:   ///
klao@885:   /// \sa makeKruskalSequenceOutput()
klao@885:   ///
klao@885:   /// Very often, when looking for a min cost spanning tree, we want as
klao@885:   /// output a container containing the edges of the found tree. For this
klao@885:   /// purpose exist this class that wraps around an STL iterator with a
klao@885:   /// writable bool map interface. When a key gets value "true" this key
klao@885:   /// is added to sequence pointed by the iterator.
klao@885:   ///
klao@885:   /// A typical usage:
klao@885:   /// \code
klao@885:   /// std::vector<Graph::Edge> v;
klao@885:   /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v)));
klao@885:   /// \endcode
klao@885:   /// 
klao@885:   /// For the most common case, when the input is given by a simple edge
klao@885:   /// map and the output is a sequence of the tree edges, a special
klao@885:   /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut().
klao@885:   ///
alpar@987:   /// \warning Not a regular property map, as it doesn't know its Key
klao@885: 
alpar@824:   template<class Iterator>
klao@885:   class KruskalSequenceOutput {
alpar@810:     mutable Iterator it;
alpar@810: 
alpar@810:   public:
alpar@987:     typedef bool Value;
alpar@810: 
klao@885:     KruskalSequenceOutput(Iterator const &_it) : it(_it) {}
alpar@810: 
alpar@987:     template<typename Key>
alpar@987:     void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} }
alpar@810:   };
alpar@810: 
alpar@824:   template<class Iterator>
alpar@810:   inline
klao@885:   KruskalSequenceOutput<Iterator>
klao@885:   makeKruskalSequenceOutput(Iterator it) {
klao@885:     return KruskalSequenceOutput<Iterator>(it);
alpar@810:   }
alpar@810: 
klao@885: 
klao@885: 
alpar@810:   /* ** ** Wrapper funtions ** ** */
alpar@810: 
alpar@810: 
klao@885: 
alpar@810:   /// \brief Wrapper function to kruskal().
alpar@810:   /// Input is from an edge map, output is a plain bool map.
alpar@810:   ///
alpar@810:   /// Wrapper function to kruskal().
alpar@810:   /// Input is from an edge map, output is a plain bool map.
alpar@810:   ///
alpar@810:   ///\param G The type of the graph the algorithm runs on.
alpar@810:   ///\param in An edge map containing the cost of the edges.
alpar@810:   ///\par
alpar@810:   ///The cost type can be any type satisfying the
alpar@810:   ///STL 'LessThan Comparable'
alpar@810:   ///concept if it also has an operator+() implemented. (It is necessary for
alpar@810:   ///computing the total cost of the tree).
alpar@810:   ///
alpar@810:   /// \retval out This must be a writable \c bool edge map.
alpar@810:   /// After running the algorithm
alpar@810:   /// this will contain the found minimum cost spanning tree: the value of an
alpar@810:   /// edge will be set to \c true if it belongs to the tree, otherwise it will
alpar@810:   /// be set to \c false. The value of each edge will be set exactly once.
alpar@810:   ///
alpar@810:   /// \return The cost of the found tree.
alpar@810: 
alpar@824:   template <class GR, class IN, class RET>
alpar@810:   inline
alpar@987:   typename IN::Value
alpar@824:   kruskalEdgeMap(GR const& G,
alpar@824: 		 IN const& in,
alpar@824: 		 RET &out) {
alpar@810:     return kruskal(G,
alpar@824: 		   KruskalMapInput<GR,IN>(G,in),
alpar@810: 		   out);
alpar@810:   }
alpar@810: 
alpar@810:   /// \brief Wrapper function to kruskal().
alpar@810:   /// Input is from an edge map, output is an STL Sequence.
alpar@810:   ///
alpar@810:   /// Wrapper function to kruskal().
alpar@810:   /// Input is from an edge map, output is an STL Sequence.
alpar@810:   ///
alpar@810:   ///\param G The type of the graph the algorithm runs on.
alpar@810:   ///\param in An edge map containing the cost of the edges.
alpar@810:   ///\par
alpar@810:   ///The cost type can be any type satisfying the
alpar@810:   ///STL 'LessThan Comparable'
alpar@810:   ///concept if it also has an operator+() implemented. (It is necessary for
alpar@810:   ///computing the total cost of the tree).
alpar@810:   ///
alpar@810:   /// \retval out This must be an iteraror of an STL Container with
alpar@824:   /// <tt>GR::Edge</tt> as its <tt>value_type</tt>.
alpar@810:   /// The algorithm copies the elements of the found tree into this sequence.
alpar@810:   /// For example, if we know that the spanning tree of the graph \c G has
alpar@810:   /// say 53 edges then
alpar@824:   /// we can put its edges into a STL vector \c tree with a code like this.
alpar@810:   /// \code
alpar@810:   /// std::vector<Edge> tree(53);
alpar@810:   /// kruskalEdgeMap_IteratorOut(G,cost,tree.begin());
alpar@810:   /// \endcode
alpar@810:   /// Or if we don't know in advance the size of the tree, we can write this.
alpar@810:   /// \code
alpar@810:   /// std::vector<Edge> tree;
alpar@810:   /// kruskalEdgeMap_IteratorOut(G,cost,std::back_inserter(tree));
alpar@810:   /// \endcode
alpar@810:   ///
alpar@810:   /// \return The cost of the found tree.
alpar@810:   ///
alpar@810:   /// \bug its name does not follow the coding style.
klao@885: 
alpar@824:   template <class GR, class IN, class RET>
alpar@810:   inline
alpar@987:   typename IN::Value
alpar@824:   kruskalEdgeMap_IteratorOut(const GR& G,
alpar@824: 			     const IN& in,
alpar@824: 			     RET out)
alpar@810:   {
klao@885:     KruskalSequenceOutput<RET> _out(out);
klao@885:     return kruskal(G, KruskalMapInput<GR,IN>(G, in), _out);
alpar@810:   }
alpar@810: 
alpar@810:   /// @}
alpar@810: 
alpar@921: } //namespace lemon
alpar@810: 
alpar@921: #endif //LEMON_KRUSKAL_H