COIN-OR::LEMON - Graph Library

source: lemon-1.2/lemon/kruskal.h @ 909:f112c18bc304

Last change on this file since 909:f112c18bc304 was 584:33c6b6e755cd, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Small doc improvements (#263)

File size: 10.3 KB
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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) 2003-2009
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///
34///Kruskal's algorithm to compute a minimum cost spanning tree.
35///
36
37namespace lemon {
38
39  namespace _kruskal_bits {
40
41    // Kruskal for directed graphs.
42
43    template <typename Digraph, typename In, typename Out>
44    typename disable_if<lemon::UndirectedTagIndicator<Digraph>,
45                       typename In::value_type::second_type >::type
46    kruskal(const Digraph& digraph, const In& in, Out& out,dummy<0> = 0) {
47      typedef typename In::value_type::second_type Value;
48      typedef typename Digraph::template NodeMap<int> IndexMap;
49      typedef typename Digraph::Node Node;
50
51      IndexMap index(digraph);
52      UnionFind<IndexMap> uf(index);
53      for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
54        uf.insert(it);
55      }
56
57      Value tree_value = 0;
58      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
59        if (uf.join(digraph.target(it->first),digraph.source(it->first))) {
60          out.set(it->first, true);
61          tree_value += it->second;
62        }
63        else {
64          out.set(it->first, false);
65        }
66      }
67      return tree_value;
68    }
69
70    // Kruskal for undirected graphs.
71
72    template <typename Graph, typename In, typename Out>
73    typename enable_if<lemon::UndirectedTagIndicator<Graph>,
74                       typename In::value_type::second_type >::type
75    kruskal(const Graph& graph, const In& in, Out& out,dummy<1> = 1) {
76      typedef typename In::value_type::second_type Value;
77      typedef typename Graph::template NodeMap<int> IndexMap;
78      typedef typename Graph::Node Node;
79
80      IndexMap index(graph);
81      UnionFind<IndexMap> uf(index);
82      for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
83        uf.insert(it);
84      }
85
86      Value tree_value = 0;
87      for (typename In::const_iterator it = in.begin(); it != in.end(); ++it) {
88        if (uf.join(graph.u(it->first),graph.v(it->first))) {
89          out.set(it->first, true);
90          tree_value += it->second;
91        }
92        else {
93          out.set(it->first, false);
94        }
95      }
96      return tree_value;
97    }
98
99
100    template <typename Sequence>
101    struct PairComp {
102      typedef typename Sequence::value_type Value;
103      bool operator()(const Value& left, const Value& right) {
104        return left.second < right.second;
105      }
106    };
107
108    template <typename In, typename Enable = void>
109    struct SequenceInputIndicator {
110      static const bool value = false;
111    };
112
113    template <typename In>
114    struct SequenceInputIndicator<In,
115      typename exists<typename In::value_type::first_type>::type> {
116      static const bool value = true;
117    };
118
119    template <typename In, typename Enable = void>
120    struct MapInputIndicator {
121      static const bool value = false;
122    };
123
124    template <typename In>
125    struct MapInputIndicator<In,
126      typename exists<typename In::Value>::type> {
127      static const bool value = true;
128    };
129
130    template <typename In, typename Enable = void>
131    struct SequenceOutputIndicator {
132      static const bool value = false;
133    };
134
135    template <typename Out>
136    struct SequenceOutputIndicator<Out,
137      typename exists<typename Out::value_type>::type> {
138      static const bool value = true;
139    };
140
141    template <typename Out, typename Enable = void>
142    struct MapOutputIndicator {
143      static const bool value = false;
144    };
145
146    template <typename Out>
147    struct MapOutputIndicator<Out,
148      typename exists<typename Out::Value>::type> {
149      static const bool value = true;
150    };
151
152    template <typename In, typename InEnable = void>
153    struct KruskalValueSelector {};
154
155    template <typename In>
156    struct KruskalValueSelector<In,
157      typename enable_if<SequenceInputIndicator<In>, void>::type>
158    {
159      typedef typename In::value_type::second_type Value;
160    };
161
162    template <typename In>
163    struct KruskalValueSelector<In,
164      typename enable_if<MapInputIndicator<In>, void>::type>
165    {
166      typedef typename In::Value Value;
167    };
168
169    template <typename Graph, typename In, typename Out,
170              typename InEnable = void>
171    struct KruskalInputSelector {};
172
173    template <typename Graph, typename In, typename Out,
174              typename InEnable = void>
175    struct KruskalOutputSelector {};
176
177    template <typename Graph, typename In, typename Out>
178    struct KruskalInputSelector<Graph, In, Out,
179      typename enable_if<SequenceInputIndicator<In>, void>::type >
180    {
181      typedef typename In::value_type::second_type Value;
182
183      static Value kruskal(const Graph& graph, const In& in, Out& out) {
184        return KruskalOutputSelector<Graph, In, Out>::
185          kruskal(graph, in, out);
186      }
187
188    };
189
190    template <typename Graph, typename In, typename Out>
191    struct KruskalInputSelector<Graph, In, Out,
192      typename enable_if<MapInputIndicator<In>, void>::type >
193    {
194      typedef typename In::Value Value;
195      static Value kruskal(const Graph& graph, const In& in, Out& out) {
196        typedef typename In::Key MapArc;
197        typedef typename In::Value Value;
198        typedef typename ItemSetTraits<Graph, MapArc>::ItemIt MapArcIt;
199        typedef std::vector<std::pair<MapArc, Value> > Sequence;
200        Sequence seq;
201
202        for (MapArcIt it(graph); it != INVALID; ++it) {
203          seq.push_back(std::make_pair(it, in[it]));
204        }
205
206        std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
207        return KruskalOutputSelector<Graph, Sequence, Out>::
208          kruskal(graph, seq, out);
209      }
210    };
211
212    template <typename T>
213    struct RemoveConst {
214      typedef T type;
215    };
216
217    template <typename T>
218    struct RemoveConst<const T> {
219      typedef T type;
220    };
221
222    template <typename Graph, typename In, typename Out>
223    struct KruskalOutputSelector<Graph, In, Out,
224      typename enable_if<SequenceOutputIndicator<Out>, void>::type >
225    {
226      typedef typename In::value_type::second_type Value;
227
228      static Value kruskal(const Graph& graph, const In& in, Out& out) {
229        typedef LoggerBoolMap<typename RemoveConst<Out>::type> Map;
230        Map map(out);
231        return _kruskal_bits::kruskal(graph, in, map);
232      }
233
234    };
235
236    template <typename Graph, typename In, typename Out>
237    struct KruskalOutputSelector<Graph, In, Out,
238      typename enable_if<MapOutputIndicator<Out>, void>::type >
239    {
240      typedef typename In::value_type::second_type Value;
241
242      static Value kruskal(const Graph& graph, const In& in, Out& out) {
243        return _kruskal_bits::kruskal(graph, in, out);
244      }
245    };
246
247  }
248
249  /// \ingroup spantree
250  ///
251  /// \brief Kruskal's algorithm for finding a minimum cost spanning tree of
252  /// a graph.
253  ///
254  /// This function runs Kruskal's algorithm to find a minimum cost
255  /// spanning tree of a graph.
256  /// Due to some C++ hacking, it accepts various input and output types.
257  ///
258  /// \param g The graph the algorithm runs on.
259  /// It can be either \ref concepts::Digraph "directed" or
260  /// \ref concepts::Graph "undirected".
261  /// If the graph is directed, the algorithm consider it to be
262  /// undirected by disregarding the direction of the arcs.
263  ///
264  /// \param in This object is used to describe the arc/edge costs.
265  /// It can be one of the following choices.
266  /// - An STL compatible 'Forward Container' with
267  /// <tt>std::pair<GR::Arc,C></tt> or
268  /// <tt>std::pair<GR::Edge,C></tt> as its <tt>value_type</tt>, where
269  /// \c C is the type of the costs. The pairs indicates the arcs/edges
270  /// along with the assigned cost. <em>They must be in a
271  /// cost-ascending order.</em>
272  /// - Any readable arc/edge map. The values of the map indicate the
273  /// arc/edge costs.
274  ///
275  /// \retval out Here we also have a choice.
276  /// - It can be a writable arc/edge map with \c bool value type. After
277  /// running the algorithm it will contain the found minimum cost spanning
278  /// tree: the value of an arc/edge 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/edge will be set exactly once.
281  /// - It can also be an iteraror of an STL Container with
282  /// <tt>GR::Arc</tt> or <tt>GR::Edge</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
294  /// std::vector<Arc> tree;
295  /// kruskal(g,cost,std::back_inserter(tree));
296  ///\endcode
297  ///
298  /// \return The total cost of the found spanning tree.
299  ///
300  /// \note If the input graph is not (weakly) connected, a spanning
301  /// forest is calculated instead of a spanning tree.
302
303#ifdef DOXYGEN
304  template <typename Graph, typename In, typename Out>
305  Value kruskal(const Graph& 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  template <class Graph, class In, class Out>
318  inline typename _kruskal_bits::KruskalValueSelector<In>::Value
319  kruskal(const Graph& graph, const In& in, const Out& out)
320  {
321    return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
322      kruskal(graph, in, out);
323  }
324
325} //namespace lemon
326
327#endif //LEMON_KRUSKAL_H
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