COIN-OR::LEMON - Graph Library

source: lemon-main/lemon/kruskal.h

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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) 2003-2013
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/maps.h>
26
27#include <lemon/core.h>
28#include <lemon/bits/traits.h>
29
30///\ingroup spantree
31///\file
32///\brief Kruskal's algorithm to compute a minimum cost spanning tree
33
34namespace lemon {
35
36  namespace _kruskal_bits {
37
38    // Kruskal for directed graphs.
39
40    template <typename Digraph, typename In, typename Out>
41    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
42                       typename In::value_type::second_type >::type
43    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
44      typedef typename In::value_type::second_type Value;
45      typedef typename Digraph::template NodeMap<int> IndexMap;
46      typedef typename Digraph::Node Node;
47
48      IndexMap index(digraph);
49      UnionFind<IndexMap> uf(index);
50      for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
51        uf.insert(it);
52      }
53
54      Value tree_value = 0;
55      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
56        if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
57          out.set(it->first, true);
58          tree_value += it->second;
59        }
60        else {
61          out.set(it->first, false);
62        }
63      }
64      return tree_value;
65    }
66
67    // Kruskal for undirected graphs.
68
69    template <typename Graph, typename In, typename Out>
70    typename enable_if<lemon::UndirectedTagIndicator<Graph>,
71                       typename In::value_type::second_type >::type
72    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
73      typedef typename In::value_type::second_type Value;
74      typedef typename Graph::template NodeMap<int> IndexMap;
75      typedef typename Graph::Node Node;
76
77      IndexMap index(graph);
78      UnionFind<IndexMap> uf(index);
79      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
80        uf.insert(it);
81      }
82
83      Value tree_value = 0;
84      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
85        if (uf.join(graph.u(it->first),graph.v(it->first))) {
86          out.set(it->first, true);
87          tree_value += it->second;
88        }
89        else {
90          out.set(it->first, false);
91        }
92      }
93      return tree_value;
94    }
95
96
97    template <typename Sequence>
98    struct PairComp {
99      typedef typename Sequence::value_type Value;
100      bool operator()(const Value& left, const Value& right) {
101        return left.second < right.second;
102      }
103    };
104
105    template <typename In, typename Enable = void>
106    struct SequenceInputIndicator {
107      static const bool value = false;
108    };
109
110    template <typename In>
111    struct SequenceInputIndicator<In,
112      typename exists<typename In::value_type::first_type>::type> {
113      static const bool value = true;
114    };
115
116    template <typename In, typename Enable = void>
117    struct MapInputIndicator {
118      static const bool value = false;
119    };
120
121    template <typename In>
122    struct MapInputIndicator<In,
123      typename exists<typename In::Value>::type> {
124      static const bool value = true;
125    };
126
127    template <typename In, typename Enable = void>
128    struct SequenceOutputIndicator {
129      static const bool value = false;
130    };
131
132    template <typename Out>
133    struct SequenceOutputIndicator<Out,
134      typename exists<typename Out::value_type>::type> {
135      static const bool value = true;
136    };
137
138    template <typename Out, typename Enable = void>
139    struct MapOutputIndicator {
140      static const bool value = false;
141    };
142
143    template <typename Out>
144    struct MapOutputIndicator<Out,
145      typename exists<typename Out::Value>::type> {
146      static const bool value = true;
147    };
148
149    template <typename In, typename InEnable = void>
150    struct KruskalValueSelector {};
151
152    template <typename In>
153    struct KruskalValueSelector<In,
154      typename enable_if<SequenceInputIndicator<In>, void>::type>
155    {
156      typedef typename In::value_type::second_type Value;
157    };
158
159    template <typename In>
160    struct KruskalValueSelector<In,
161      typename enable_if<MapInputIndicator<In>, void>::type>
162    {
163      typedef typename In::Value Value;
164    };
165
166    template <typename Graph, typename In, typename Out,
167              typename InEnable = void>
168    struct KruskalInputSelector {};
169
170    template <typename Graph, typename In, typename Out,
171              typename InEnable = void>
172    struct KruskalOutputSelector {};
173
174    template <typename Graph, typename In, typename Out>
175    struct KruskalInputSelector<Graph, In, Out,
176      typename enable_if<SequenceInputIndicator<In>, void>::type >
177    {
178      typedef typename In::value_type::second_type Value;
179
180      static Value kruskal(const Graph& graph, const In& in, Out& out) {
181        return KruskalOutputSelector<Graph, In, Out>::
182          kruskal(graph, in, out);
183      }
184
185    };
186
187    template <typename Graph, typename In, typename Out>
188    struct KruskalInputSelector<Graph, In, Out,
189      typename enable_if<MapInputIndicator<In>, void>::type >
190    {
191      typedef typename In::Value Value;
192      static Value kruskal(const Graph& graph, const In& in, Out& out) {
193        typedef typename In::Key MapArc;
194        typedef typename In::Value Value;
195        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
196        typedef std::vector<std::pair<MapArc, Value> > Sequence;
197        Sequence seq;
198
199        for (MapArcIt it(graph); it != INVALID; ++it) {
200          seq.push_back(std::make_pair(it, in[it]));
201        }
202
203        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
204        return KruskalOutputSelector<Graph, Sequence, Out>::
205          kruskal(graph, seq, out);
206      }
207    };
208
209    template <typename T>
210    struct RemoveConst {
211      typedef T type;
212    };
213
214    template <typename T>
215    struct RemoveConst<const T> {
216      typedef T type;
217    };
218
219    template <typename Graph, typename In, typename Out>
220    struct KruskalOutputSelector<Graph, In, Out,
221      typename enable_if<SequenceOutputIndicator<Out>, void>::type >
222    {
223      typedef typename In::value_type::second_type Value;
224
225      static Value kruskal(const Graph& graph, const In& in, Out& out) {
226        typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
227        Map map(out);
228        return _kruskal_bits::kruskal(graph, in, map);
229      }
230
231    };
232
233    template <typename Graph, typename In, typename Out>
234    struct KruskalOutputSelector<Graph, In, Out,
235      typename enable_if<MapOutputIndicator<Out>, void>::type >
236    {
237      typedef typename In::value_type::second_type Value;
238
239      static Value kruskal(const Graph& graph, const In& in, Out& out) {
240        return _kruskal_bits::kruskal(graph, in, out);
241      }
242    };
243
244  }
245
246  /// \ingroup spantree
247  ///
248  /// \brief Kruskal's algorithm for finding a minimum cost spanning tree of
249  /// a graph.
250  ///
251  /// This function runs Kruskal's algorithm to find a minimum cost
252  /// spanning tree of a graph.
253  /// Due to some C++ hacking, it accepts various input and output types.
254  ///
255  /// \param g The graph the algorithm runs on.
256  /// It can be either \ref concepts::Digraph "directed" or
257  /// \ref concepts::Graph "undirected".
258  /// If the graph is directed, the algorithm consider it to be
259  /// undirected by disregarding the direction of the arcs.
260  ///
261  /// \param in This object is used to describe the arc/edge costs.
262  /// It can be one of the following choices.
263  /// - An STL compatible 'Forward Container' with
264  /// <tt>std::pair<GR::Arc,C></tt> or
265  /// <tt>std::pair<GR::Edge,C></tt> as its <tt>value_type</tt>, where
266  /// \c C is the type of the costs. The pairs indicates the arcs/edges
267  /// along with the assigned cost. <em>They must be in a
268  /// cost-ascending order.</em>
269  /// - Any readable arc/edge map. The values of the map indicate the
270  /// arc/edge costs.
271  ///
272  /// \retval out Here we also have a choice.
273  /// - It can be a writable arc/edge map with \c bool value type. After
274  /// running the algorithm it will contain the found minimum cost spanning
275  /// tree: the value of an arc/edge will be set to \c true if it belongs
276  /// to the tree, otherwise it will be set to \c false. The value of
277  /// each arc/edge will be set exactly once.
278  /// - It can also be an iteraror of an STL Container with
279  /// <tt>GR::Arc</tt> or <tt>GR::Edge</tt> as its
280  /// <tt>value_type</tt>.  The algorithm copies the elements of the
281  /// found tree into this sequence.  For example, if we know that the
282  /// spanning tree of the graph \c g has say 53 arcs, then we can
283  /// put its arcs into an STL vector \c tree with a code like this.
284  ///\code
285  /// std::vector<Arc> tree(53);
286  /// kruskal(g,cost,tree.begin());
287  ///\endcode
288  /// Or if we don't know in advance the size of the tree, we can
289  /// write this.
290  ///\code
291  /// std::vector<Arc> tree;
292  /// kruskal(g,cost,std::back_inserter(tree));
293  ///\endcode
294  ///
295  /// \return The total cost of the found spanning tree.
296  ///
297  /// \note If the input graph is not (weakly) connected, a spanning
298  /// forest is calculated instead of a spanning tree.
299
300#ifdef DOXYGEN
301  template <typename Graph, typename In, typename Out>
302  Value kruskal(const Graph& g, const In& in, Out& out)
303#else
304  template <class Graph, class In, class Out>
305  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
306  kruskal(const Graph& graph, const In& in, Out& out)
307#endif
308  {
309    return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
310      kruskal(graph, in, out);
311  }
312
313
314  template <class Graph, class In, class Out>
315  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
316  kruskal(const Graph& graph, const In& in, const Out& out)
317  {
318    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
319      kruskal(graph, in, out);
320  }
321
322} //namespace lemon
323
324#endif //LEMON_KRUSKAL_H
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