source: lemon-0.x/lemon/kruskal.h @ 2206:c3ff11b0025c

/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2006
 * 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/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.
///
///\todo The file still needs some clean-up.

namespace lemon {

  /// \addtogroup spantree
  /// @{

  /// 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 concept::Graph "directed" or 
  /// \ref concept::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::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.
  /// - Is 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::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 a 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 cost of the found tree.
  ///
  /// \warning If kruskal is run on an
  /// \ref lemon::concept::UGraph "undirected graph", be sure that the
  /// map storing the tree is also undirected
  /// (e.g. ListUGraph::UEdgeMap<bool>, otherwise the values of the
  /// half of the edges will not be set.
  ///
  /// \todo Discuss the case of undirected graphs: In this case the algorithm
  /// also require <tt>Edge</tt>s instead of <tt>UEdge</tt>s, as some
  /// people would expect. So, one should be careful not to add both of the
  /// <tt>Edge</tt>s belonging to a certain <tt>UEdge</tt>.
  /// (\ref kruskal() and \ref KruskalMapInput are kind enough to do so.)

#ifdef DOXYGEN
  template <class GR, class IN, class OUT>
  typename IN::value_type::second_type
  kruskal(GR const& g, IN const& in, 
          OUT& out)
#else
  template <class GR, class IN, class OUT>
  typename IN::value_type::second_type
  kruskal(GR const& g, IN const& in, 
          OUT& out,
//        typename IN::value_type::first_type = typename GR::Edge()
//        ,typename OUT::Key = OUT::Key()
//        //,typename OUT::Key = typename GR::Edge()
          const typename IN::value_type::first_type * = 
          (const typename IN::value_type::first_type *)(0),
          const typename OUT::Key * = (const typename OUT::Key *)(0)
          )
#endif
  {
    typedef typename IN::value_type::second_type EdgeCost;
    typedef typename GR::template NodeMap<int> NodeIntMap;
    typedef typename GR::Node Node;

    NodeIntMap comp(g);
    UnionFind<Node,NodeIntMap> uf(comp);
    for (typename GR::NodeIt it(g); it != INVALID; ++it) {
      uf.insert(it);
    }
      
    EdgeCost tot_cost = 0;
    for (typename IN::const_iterator p = in.begin(); 
         p!=in.end(); ++p ) {
      if ( uf.join(g.target((*p).first),
                   g.source((*p).first)) ) {
        out.set((*p).first, true);
        tot_cost += (*p).second;
      }
      else {
        out.set((*p).first, false);
      }
    }
    return tot_cost;
  }

 
  /// @}

  
  /* A work-around for running Kruskal with const-reference bool maps... */

  /// Helper class for calling kruskal with "constant" output map.

  /// Helper class for calling kruskal with output maps constructed
  /// on-the-fly.
  ///
  /// A typical examle is the following call:
  /// <tt>kruskal(g, some_input, makeSequenceOutput(iterator))</tt>.
  /// Here, the third argument is a temporary object (which wraps around an
  /// iterator with a writable bool map interface), and thus by rules of C++
  /// is a \c const object. To enable call like this exist this class and
  /// the prototype of the \ref kruskal() function with <tt>const& OUT</tt>
  /// third argument.
  template<class Map>
  class NonConstMapWr {
    const Map &m;
  public:
    typedef typename Map::Key Key;
    typedef typename Map::Value Value;

    NonConstMapWr(const Map &_m) : m(_m) {}

    template<class Key>
    void set(Key const& k, Value const &v) const { m.set(k,v); }
  };

  template <class GR, class IN, class OUT>
  inline
  typename IN::value_type::second_type
  kruskal(GR const& g, IN const& edges, OUT const& out_map,
//        typename IN::value_type::first_type = typename GR::Edge(),
//        typename OUT::Key = GR::Edge()
          const typename IN::value_type::first_type * = 
          (const typename IN::value_type::first_type *)(0),
          const typename OUT::Key * = (const typename OUT::Key *)(0)
          )
  {
    NonConstMapWr<OUT> map_wr(out_map);
    return kruskal(g, edges, map_wr);
  }  

  /* ** ** Input-objects ** ** */

  /// Kruskal's input source.
 
  /// Kruskal's input source.
  ///
  /// In most cases you possibly want to use the \ref kruskal() instead.
  ///
  /// \sa makeKruskalMapInput()
  ///
  ///\param GR The type of the graph the algorithm runs on.
  ///\param Map An edge map containing the cost of the edges.
  ///\par
  ///The cost type can be any type satisfying
  ///the STL 'LessThan comparable'
  ///concept if it also has an operator+() implemented. (It is necessary for
  ///computing the total cost of the tree).
  ///
  template<class GR, class Map>
  class KruskalMapInput
    : public std::vector< std::pair<typename GR::Edge,
                                    typename Map::Value> > {
    
  public:
    typedef std::vector< std::pair<typename GR::Edge,
                                   typename Map::Value> > Parent;
    typedef typename Parent::value_type value_type;

  private:
    class comparePair {
    public:
      bool operator()(const value_type& a,
                      const value_type& b) {
        return a.second < b.second;
      }
    };

    template<class _GR>
    typename enable_if<UndirectedTagIndicator<_GR>,void>::type
    fillWithEdges(const _GR& g, const Map& m,dummy<0> = 0) 
    {
      for(typename GR::UEdgeIt e(g);e!=INVALID;++e) 
        push_back(value_type(g.direct(e, true), m[e]));
    }

    template<class _GR>
    typename disable_if<UndirectedTagIndicator<_GR>,void>::type
    fillWithEdges(const _GR& g, const Map& m,dummy<1> = 1) 
    {
      for(typename GR::EdgeIt e(g);e!=INVALID;++e) 
        push_back(value_type(e, m[e]));
    }
    
    
  public:

    void sort() {
      std::sort(this->begin(), this->end(), comparePair());
    }

    KruskalMapInput(GR const& g, Map const& m) {
      fillWithEdges(g,m); 
      sort();
    }
  };

  /// Creates a KruskalMapInput object for \ref kruskal()

  /// It makes easier to use 
  /// \ref KruskalMapInput by making it unnecessary 
  /// to explicitly give the type of the parameters.
  ///
  /// In most cases you possibly
  /// want to use \ref kruskal() instead.
  ///
  ///\param g The type of the graph the algorithm runs on.
  ///\param m An edge map containing the cost of the edges.
  ///\par
  ///The cost type can be any type satisfying the
  ///STL 'LessThan Comparable'
  ///concept if it also has an operator+() implemented. (It is necessary for
  ///computing the total cost of the tree).
  ///
  ///\return An appropriate input source for \ref kruskal().
  ///
  template<class GR, class Map>
  inline
  KruskalMapInput<GR,Map> makeKruskalMapInput(const GR &g,const Map &m)
  {
    return KruskalMapInput<GR,Map>(g,m);
  }
  
  

  /* ** ** Output-objects: simple writable bool maps ** ** */
  


  /// A writable bool-map that makes a sequence of "true" keys

  /// A writable bool-map that creates a sequence out of keys that receives
  /// the value "true".
  ///
  /// \sa makeKruskalSequenceOutput()
  ///
  /// Very often, when looking for a min cost spanning tree, we want as
  /// output a container containing the edges of the found tree. For this
  /// purpose exist this class that wraps around an STL iterator with a
  /// writable bool map interface. When a key gets value "true" this key
  /// is added to sequence pointed by the iterator.
  ///
  /// A typical usage:
  ///\code
  /// std::vector<Graph::Edge> v;
  /// kruskal(g, input, makeKruskalSequenceOutput(back_inserter(v)));
  ///\endcode
  /// 
  /// For the most common case, when the input is given by a simple edge
  /// map and the output is a sequence of the tree edges, a special
  /// wrapper function exists: \ref kruskalEdgeMap_IteratorOut().
  ///
  /// \warning Not a regular property map, as it doesn't know its Key

  template<class Iterator>
  class KruskalSequenceOutput {
    mutable Iterator it;

  public:
    typedef typename std::iterator_traits<Iterator>::value_type Key;
    typedef bool Value;

    KruskalSequenceOutput(Iterator const &_it) : it(_it) {}

    template<typename Key>
    void set(Key const& k, bool v) const { if(v) {*it=k; ++it;} }
  };

  template<class Iterator>
  inline
  KruskalSequenceOutput<Iterator>
  makeKruskalSequenceOutput(Iterator it) {
    return KruskalSequenceOutput<Iterator>(it);
  }



  /* ** ** Wrapper funtions ** ** */

//   \brief Wrapper function to kruskal().
//   Input is from an edge map, output is a plain bool map.
//  
//   Wrapper function to kruskal().
//   Input is from an edge map, output is a plain bool map.
//  
//   \param g The type of the graph the algorithm runs on.
//   \param in An edge map containing the cost of the edges.
//   \par
//   The cost type can be any type satisfying the
//   STL 'LessThan Comparable'
//   concept if it also has an operator+() implemented. (It is necessary for
//   computing the total cost of the tree).
//  
//   \retval out This must 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.
//  
//   \return The cost of the found tree.

  template <class GR, class IN, class RET>
  inline
  typename IN::Value
  kruskal(GR const& g,
          IN const& in,
          RET &out,
          //      typename IN::Key = typename GR::Edge(),
          //typename IN::Key = typename IN::Key (),
          //      typename RET::Key = typename GR::Edge()
          const typename IN::Key *  = (const typename IN::Key *)(0),
          const typename RET::Key * = (const typename RET::Key *)(0)
          )
  {
    return kruskal(g,
                   KruskalMapInput<GR,IN>(g,in),
                   out);
  }

//   \brief Wrapper function to kruskal().
//   Input is from an edge map, output is an STL Sequence.
//  
//   Wrapper function to kruskal().
//   Input is from an edge map, output is an STL Sequence.
//  
//   \param g The type of the graph the algorithm runs on.
//   \param in An edge map containing the cost of the edges.
//   \par
//   The cost type can be any type satisfying the
//   STL 'LessThan Comparable'
//   concept if it also has an operator+() implemented. (It is necessary for
//   computing the total cost of the tree).
//  
//   \retval out This must be an iteraror of an STL Container with
//   <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 a 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 cost of the found tree.
//  
//   \bug its name does not follow the coding style.

  template <class GR, class IN, class RET>
  inline
  typename IN::Value
  kruskal(const GR& g,
          const IN& in,
          RET out,
          const typename RET::value_type * = 
          (const typename RET::value_type *)(0)
          )
  {
    KruskalSequenceOutput<RET> _out(out);
    return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out);
  }
 
  template <class GR, class IN, class RET>
  inline
  typename IN::Value
  kruskal(const GR& g,
          const IN& in,
          RET *out
          )
  {
    KruskalSequenceOutput<RET*> _out(out);
    return kruskal(g, KruskalMapInput<GR,IN>(g, in), _out);
  }
 
  /// @}

} //namespace lemon

#endif //LEMON_KRUSKAL_H