lemon/kruskal.h
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 20 Mar 2008 23:06:35 +0000
changeset 106 9ba2d265e191
child 136 b82dc494bafc
permissions -rw-r--r--
Merge
     1 /* -*- C++ -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library
     4  *
     5  * Copyright (C) 2003-2008
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 #ifndef LEMON_KRUSKAL_H
    20 #define LEMON_KRUSKAL_H
    21 
    22 #include <algorithm>
    23 #include <vector>
    24 #include <lemon/unionfind.h>
    25 // #include <lemon/graph_utils.h>
    26 #include <lemon/maps.h>
    27 
    28 // #include <lemon/radix_sort.h>
    29 
    30 #include <lemon/bits/utility.h>
    31 #include <lemon/bits/traits.h>
    32 
    33 ///\ingroup spantree
    34 ///\file
    35 ///\brief Kruskal's algorithm to compute a minimum cost tree
    36 ///
    37 ///Kruskal's algorithm to compute a minimum cost tree.
    38 ///
    39 
    40 namespace lemon {
    41 
    42   namespace _kruskal_bits {
    43 
    44     // Kruskal for directed graphs.
    45 
    46     template <typename Digraph, typename In, typename Out>
    47     typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
    48 		       typename In::value_type::second_type >::type
    49     kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
    50       typedef typename In::value_type::second_type Value;
    51       typedef typename Digraph::template NodeMap<int> IndexMap;
    52       typedef typename Digraph::Node Node;
    53       
    54       IndexMap index(digraph);
    55       UnionFind<IndexMap> uf(index);
    56       for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
    57         uf.insert(it);
    58       }
    59       
    60       Value tree_value = 0;
    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))) {
    63           out.set(it->first, true);
    64           tree_value += it->second;
    65         }
    66         else {
    67           out.set(it->first, false);
    68         }
    69       }
    70       return tree_value;
    71     }
    72 
    73     // Kruskal for undirected graphs.
    74 
    75     template <typename Graph, typename In, typename Out>
    76     typename enable_if<lemon::UndirectedTagIndicator<Graph>,
    77 		       typename In::value_type::second_type >::type
    78     kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
    79       typedef typename In::value_type::second_type Value;
    80       typedef typename Graph::template NodeMap<int> IndexMap;
    81       typedef typename Graph::Node Node;
    82       
    83       IndexMap index(graph);
    84       UnionFind<IndexMap> uf(index);
    85       for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
    86         uf.insert(it);
    87       }
    88       
    89       Value tree_value = 0;
    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))) {
    92           out.set(it->first, true);
    93           tree_value += it->second;
    94         }
    95         else {
    96           out.set(it->first, false);
    97         }
    98       }
    99       return tree_value;
   100     }
   101 
   102 
   103     template <typename Sequence>
   104     struct PairComp {
   105       typedef typename Sequence::value_type Value;
   106       bool operator()(const Value& left, const Value& right) {
   107 	return left.second < right.second;
   108       }
   109     };
   110 
   111     template <typename In, typename Enable = void>
   112     struct SequenceInputIndicator {
   113       static const bool value = false;
   114     };
   115 
   116     template <typename In>
   117     struct SequenceInputIndicator<In, 
   118       typename exists<typename In::value_type::first_type>::type> {
   119       static const bool value = true;
   120     };
   121 
   122     template <typename In, typename Enable = void>
   123     struct MapInputIndicator {
   124       static const bool value = false;
   125     };
   126 
   127     template <typename In>
   128     struct MapInputIndicator<In, 
   129       typename exists<typename In::Value>::type> {
   130       static const bool value = true;
   131     };
   132 
   133     template <typename In, typename Enable = void>
   134     struct SequenceOutputIndicator {
   135       static const bool value = false;
   136     };
   137  
   138     template <typename Out>
   139     struct SequenceOutputIndicator<Out, 
   140       typename exists<typename Out::value_type>::type> {
   141       static const bool value = true;
   142     };
   143 
   144     template <typename Out, typename Enable = void>
   145     struct MapOutputIndicator {
   146       static const bool value = false;
   147     };
   148 
   149     template <typename Out>
   150     struct MapOutputIndicator<Out, 
   151       typename exists<typename Out::Value>::type> {
   152       static const bool value = true;
   153     };
   154 
   155     template <typename In, typename InEnable = void>
   156     struct KruskalValueSelector {};
   157 
   158     template <typename In>
   159     struct KruskalValueSelector<In,
   160       typename enable_if<SequenceInputIndicator<In>, void>::type> 
   161     {
   162       typedef typename In::value_type::second_type Value;
   163     };    
   164 
   165     template <typename In>
   166     struct KruskalValueSelector<In,
   167       typename enable_if<MapInputIndicator<In>, void>::type> 
   168     {
   169       typedef typename In::Value Value;
   170     };    
   171     
   172     template <typename Graph, typename In, typename Out,
   173               typename InEnable = void>
   174     struct KruskalInputSelector {};
   175 
   176     template <typename Graph, typename In, typename Out,
   177               typename InEnable = void>
   178     struct KruskalOutputSelector {};
   179     
   180     template <typename Graph, typename In, typename Out>
   181     struct KruskalInputSelector<Graph, In, Out,
   182       typename enable_if<SequenceInputIndicator<In>, void>::type > 
   183     {
   184       typedef typename In::value_type::second_type Value;
   185 
   186       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   187         return KruskalOutputSelector<Graph, In, Out>::
   188           kruskal(graph, in, out);
   189       }
   190 
   191     };
   192 
   193     template <typename Graph, typename In, typename Out>
   194     struct KruskalInputSelector<Graph, In, Out,
   195       typename enable_if<MapInputIndicator<In>, void>::type > 
   196     {
   197       typedef typename In::Value Value;
   198       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   199         typedef typename In::Key MapArc;
   200         typedef typename In::Value Value;
   201         typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
   202         typedef std::vector<std::pair<MapArc, Value> > Sequence;
   203         Sequence seq;
   204         
   205         for (MapArcIt it(graph); it != INVALID; ++it) {
   206           seq.push_back(std::make_pair(it, in[it]));
   207         }
   208 
   209         std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
   210         return KruskalOutputSelector<Graph, Sequence, Out>::
   211           kruskal(graph, seq, out);
   212       }
   213     };
   214 
   215     template <typename Graph, typename In, typename Out>
   216     struct KruskalOutputSelector<Graph, In, Out,
   217       typename enable_if<SequenceOutputIndicator<Out>, void>::type > 
   218     {
   219       typedef typename In::value_type::second_type Value;
   220 
   221       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   222         typedef StoreBoolMap<Out> Map;
   223         Map map(out);
   224         return _kruskal_bits::kruskal(graph, in, map);
   225       }
   226 
   227     };
   228 
   229     template <typename Graph, typename In, typename Out>
   230     struct KruskalOutputSelector<Graph, In, Out,
   231       typename enable_if<MapOutputIndicator<Out>, void>::type > 
   232     {
   233       typedef typename In::value_type::second_type Value;
   234 
   235       static Value kruskal(const Graph& graph, const In& in, Out& out) {
   236         return _kruskal_bits::kruskal(graph, in, out);
   237       }
   238     };
   239 
   240   }
   241 
   242   /// \ingroup spantree
   243   ///
   244   /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.
   245   ///
   246   /// This function runs Kruskal's algorithm to find a minimum cost tree.
   247   /// Due to some C++ hacking, it accepts various input and output types.
   248   ///
   249   /// \param g The graph the algorithm runs on.
   250   /// It can be either \ref concepts::Digraph "directed" or 
   251   /// \ref concepts::Graph "undirected".
   252   /// If the graph is directed, the algorithm consider it to be 
   253   /// undirected by disregarding the direction of the arcs.
   254   ///
   255   /// \param in This object is used to describe the arc costs. It can be one
   256   /// of the following choices.
   257   /// - An STL compatible 'Forward Container' with
   258   /// <tt>std::pair<GR::Edge,X></tt> or
   259   /// <tt>std::pair<GR::Arc,X></tt> as its <tt>value_type</tt>, where
   260   /// \c X is the type of the costs. The pairs indicates the arcs
   261   /// along with the assigned cost. <em>They must be in a
   262   /// cost-ascending order.</em>
   263   /// - Any readable Arc map. The values of the map indicate the arc costs.
   264   ///
   265   /// \retval out Here we also have a choise.
   266   /// - It can be a writable \c bool arc map.  After running the
   267   /// algorithm this will contain the found minimum cost spanning
   268   /// tree: the value of an arc will be set to \c true if it belongs
   269   /// to the tree, otherwise it will be set to \c false. The value of
   270   /// each arc will be set exactly once.
   271   /// - It can also be an iteraror of an STL Container with
   272   /// <tt>GR::Edge</tt> or <tt>GR::Arc</tt> as its
   273   /// <tt>value_type</tt>.  The algorithm copies the elements of the
   274   /// found tree into this sequence.  For example, if we know that the
   275   /// spanning tree of the graph \c g has say 53 arcs, then we can
   276   /// put its arcs into an STL vector \c tree with a code like this.
   277   ///\code
   278   /// std::vector<Arc> tree(53);
   279   /// kruskal(g,cost,tree.begin());
   280   ///\endcode
   281   /// Or if we don't know in advance the size of the tree, we can
   282   /// write this.  
   283   ///\code std::vector<Arc> tree;
   284   /// kruskal(g,cost,std::back_inserter(tree)); 
   285   ///\endcode
   286   ///
   287   /// \return The total cost of the found tree.
   288   ///
   289   /// \warning If kruskal runs on an be consistent of using the same
   290   /// Arc type for input and output.
   291   ///
   292 
   293 #ifdef DOXYGEN
   294   template <class Graph, class In, class Out>
   295   Value kruskal(GR const& g, const In& in, Out& out)
   296 #else 
   297   template <class Graph, class In, class Out>
   298   inline typename _kruskal_bits::KruskalValueSelector<In>::Value 
   299   kruskal(const Graph& graph, const In& in, Out& out) 
   300 #endif
   301   {
   302     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
   303       kruskal(graph, in, out);
   304   }
   305 
   306  
   307   
   308 
   309   template <class Graph, class In, class Out>
   310   inline typename _kruskal_bits::KruskalValueSelector<In>::Value
   311   kruskal(const Graph& graph, const In& in, const Out& out)
   312   {
   313     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
   314       kruskal(graph, in, out);
   315   }  
   316 
   317 } //namespace lemon
   318 
   319 #endif //LEMON_KRUSKAL_H