COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/kruskal.h @ 209:765619b7cbb2

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 spanning tree
36///
37///Kruskal's algorithm to compute a minimum cost spanning tree.
38///
39
40namespace 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 LoggerBoolMap<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 algorithm to find a minimum cost spanning tree of
255  /// a graph.
256  ///
257  /// This function runs Kruskal's algorithm to find a minimum cost
258  /// spanning tree.
259  /// Due to some C++ hacking, it accepts various input and output types.
260  ///
261  /// \param g The graph the algorithm runs on.
262  /// It can be either \ref concepts::Digraph "directed" or
263  /// \ref concepts::Graph "undirected".
264  /// If the graph is directed, the algorithm consider it to be
265  /// undirected by disregarding the direction of the arcs.
266  ///
267  /// \param in This object is used to describe the arc/edge costs.
268  /// It can be one of the following choices.
269  /// - An STL compatible 'Forward Container' with
270  /// <tt>std::pair<GR::Arc,X></tt> or
271  /// <tt>std::pair<GR::Edge,X></tt> as its <tt>value_type</tt>, where
272  /// \c X is the type of the costs. The pairs indicates the arcs/edges
273  /// along with the assigned cost. <em>They must be in a
274  /// cost-ascending order.</em>
275  /// - Any readable arc/edge map. The values of the map indicate the
276  /// arc/edge costs.
277  ///
278  /// \retval out Here we also have a choice.
279  /// - It can be a writable \c bool arc/edge map. After running the
280  /// algorithm it will contain the found minimum cost spanning
281  /// tree: the value of an arc/edge will be set to \c true if it belongs
282  /// to the tree, otherwise it will be set to \c false. The value of
283  /// each arc/edge will be set exactly once.
284  /// - It can also be an iteraror of an STL Container with
285  /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
286  /// <tt>value_type</tt>.  The algorithm copies the elements of the
287  /// found tree into this sequence.  For example, if we know that the
288  /// spanning tree of the graph \c g has say 53 arcs, then we can
289  /// put its arcs into an STL vector \c tree with a code like this.
290  ///\code
291  /// std::vector<Arc> tree(53);
292  /// kruskal(g,cost,tree.begin());
293  ///\endcode
294  /// Or if we don't know in advance the size of the tree, we can
295  /// write this.
296  ///\code
297  /// std::vector<Arc> tree;
298  /// kruskal(g,cost,std::back_inserter(tree));
299  ///\endcode
300  ///
301  /// \return The total cost of the found spanning tree.
302  ///
303  /// \warning If Kruskal runs on an be consistent of using the same
304  /// Arc type for input and output.
305  ///
306
307#ifdef DOXYGEN
308  template <class Graph, class In, class Out>
309  Value kruskal(GR const& g, const In& in, Out& out)
310#else
311  template <class Graph, class In, class Out>
312  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
313  kruskal(const Graph& graph, const In& in, Out& out)
314#endif
315  {
316    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
317      kruskal(graph, in, out);
318  }
319
320
321
322
323  template <class Graph, class In, class Out>
324  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
325  kruskal(const Graph& graph, const In& in, const Out& out)
326  {
327    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
328      kruskal(graph, in, out);
329  }
330
331} //namespace lemon
332
333#endif //LEMON_KRUSKAL_H
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