lemon/kruskal.h
 author Akos Ladanyi Tue, 22 Apr 2008 22:39:57 +0200 changeset 146 4b42aa24ce12 parent 103 b68a7e348e00 child 167 d57ae6f0a335 permissions -rw-r--r--
Makefile cleanup (see ticket #87)
     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 T>

   216     struct RemoveConst {

   217       typedef T type;

   218     };

   219

   220     template <typename T>

   221     struct RemoveConst<const T> {

   222       typedef T type;

   223     };

   224

   225     template <typename Graph, typename In, typename Out>

   226     struct KruskalOutputSelector<Graph, In, Out,

   227       typename enable_if<SequenceOutputIndicator<Out>, void>::type >

   228     {

   229       typedef typename In::value_type::second_type Value;

   230

   231       static Value kruskal(const Graph& graph, const In& in, Out& out) {

   232         typedef StoreBoolMap<typename RemoveConst<Out>::type> Map;

   233         Map map(out);

   234         return _kruskal_bits::kruskal(graph, in, map);

   235       }

   236

   237     };

   238

   239     template <typename Graph, typename In, typename Out>

   240     struct KruskalOutputSelector<Graph, In, Out,

   241       typename enable_if<MapOutputIndicator<Out>, void>::type >

   242     {

   243       typedef typename In::value_type::second_type Value;

   244

   245       static Value kruskal(const Graph& graph, const In& in, Out& out) {

   246         return _kruskal_bits::kruskal(graph, in, out);

   247       }

   248     };

   249

   250   }

   251

   252   /// \ingroup spantree

   253   ///

   254   /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.

   255   ///

   256   /// This function runs Kruskal's algorithm to find a minimum cost tree.

   257   /// Due to some C++ hacking, it accepts various input and output types.

   258   ///

   259   /// \param g The graph the algorithm runs on.

   260   /// It can be either \ref concepts::Digraph "directed" or

   261   /// \ref concepts::Graph "undirected".

   262   /// If the graph is directed, the algorithm consider it to be

   263   /// undirected by disregarding the direction of the arcs.

   264   ///

   265   /// \param in This object is used to describe the arc costs. It can be one

   266   /// of the following choices.

   267   /// - An STL compatible 'Forward Container' with

   268   /// <tt>std::pair<GR::Edge,X></tt> or

   269   /// <tt>std::pair<GR::Arc,X></tt> as its <tt>value_type</tt>, where

   270   /// \c X is the type of the costs. The pairs indicates the arcs

   271   /// along with the assigned cost. <em>They must be in a

   272   /// cost-ascending order.</em>

   273   /// - Any readable Arc map. The values of the map indicate the arc costs.

   274   ///

   275   /// \retval out Here we also have a choise.

   276   /// - It can be a writable \c bool arc map.  After running the

   277   /// algorithm this will contain the found minimum cost spanning

   278   /// tree: the value of an arc will be set to \c true if it belongs

   279   /// to the tree, otherwise it will be set to \c false. The value of

   280   /// each arc will be set exactly once.

   281   /// - It can also be an iteraror of an STL Container with

   282   /// <tt>GR::Edge</tt> or <tt>GR::Arc</tt> as its

   283   /// <tt>value_type</tt>.  The algorithm copies the elements of the

   284   /// found tree into this sequence.  For example, if we know that the

   285   /// spanning tree of the graph \c g has say 53 arcs, then we can

   286   /// put its arcs into an STL vector \c tree with a code like this.

   287   ///\code

   288   /// std::vector<Arc> tree(53);

   289   /// kruskal(g,cost,tree.begin());

   290   ///\endcode

   291   /// Or if we don't know in advance the size of the tree, we can

   292   /// write this.

   293   ///\code std::vector<Arc> tree;

   294   /// kruskal(g,cost,std::back_inserter(tree));

   295   ///\endcode

   296   ///

   297   /// \return The total cost of the found tree.

   298   ///

   299   /// \warning If kruskal runs on an be consistent of using the same

   300   /// Arc type for input and output.

   301   ///

   302

   303 #ifdef DOXYGEN

   304   template <class Graph, class In, class Out>

   305   Value kruskal(GR const& g, const In& in, Out& out)

   306 #else

   307   template <class Graph, class In, class Out>

   308   inline typename _kruskal_bits::KruskalValueSelector<In>::Value

   309   kruskal(const Graph& graph, const In& in, Out& out)

   310 #endif

   311   {

   312     return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::

   313       kruskal(graph, in, out);

   314   }

   315

   316

   317

   318

   319   template <class Graph, class In, class Out>

   320   inline typename _kruskal_bits::KruskalValueSelector<In>::Value

   321   kruskal(const Graph& graph, const In& in, const Out& out)

   322   {

   323     return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::

   324       kruskal(graph, in, out);

   325   }

   326

   327 } //namespace lemon

   328

   329 #endif //LEMON_KRUSKAL_H