Aliases added to some graphToEps() named params.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
19 #ifndef LEMON_KRUSKAL_H
20 #define LEMON_KRUSKAL_H
24 #include <lemon/unionfind.h>
25 // #include <lemon/graph_utils.h>
26 #include <lemon/maps.h>
28 // #include <lemon/radix_sort.h>
30 #include <lemon/bits/utility.h>
31 #include <lemon/bits/traits.h>
35 ///\brief Kruskal's algorithm to compute a minimum cost tree
37 ///Kruskal's algorithm to compute a minimum cost tree.
42 namespace _kruskal_bits {
44 // Kruskal for directed graphs.
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;
54 IndexMap index(digraph);
55 UnionFind<IndexMap> uf(index);
56 for (typename Digraph::NodeIt it(digraph); it != INVALID; ++it) {
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;
67 out.set(it->first, false);
73 // Kruskal for undirected graphs.
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;
83 IndexMap index(graph);
84 UnionFind<IndexMap> uf(index);
85 for (typename Graph::NodeIt it(graph); it != INVALID; ++it) {
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;
96 out.set(it->first, false);
103 template <typename Sequence>
105 typedef typename Sequence::value_type Value;
106 bool operator()(const Value& left, const Value& right) {
107 return left.second < right.second;
111 template <typename In, typename Enable = void>
112 struct SequenceInputIndicator {
113 static const bool value = false;
116 template <typename In>
117 struct SequenceInputIndicator<In,
118 typename exists<typename In::value_type::first_type>::type> {
119 static const bool value = true;
122 template <typename In, typename Enable = void>
123 struct MapInputIndicator {
124 static const bool value = false;
127 template <typename In>
128 struct MapInputIndicator<In,
129 typename exists<typename In::Value>::type> {
130 static const bool value = true;
133 template <typename In, typename Enable = void>
134 struct SequenceOutputIndicator {
135 static const bool value = false;
138 template <typename Out>
139 struct SequenceOutputIndicator<Out,
140 typename exists<typename Out::value_type>::type> {
141 static const bool value = true;
144 template <typename Out, typename Enable = void>
145 struct MapOutputIndicator {
146 static const bool value = false;
149 template <typename Out>
150 struct MapOutputIndicator<Out,
151 typename exists<typename Out::Value>::type> {
152 static const bool value = true;
155 template <typename In, typename InEnable = void>
156 struct KruskalValueSelector {};
158 template <typename In>
159 struct KruskalValueSelector<In,
160 typename enable_if<SequenceInputIndicator<In>, void>::type>
162 typedef typename In::value_type::second_type Value;
165 template <typename In>
166 struct KruskalValueSelector<In,
167 typename enable_if<MapInputIndicator<In>, void>::type>
169 typedef typename In::Value Value;
172 template <typename Graph, typename In, typename Out,
173 typename InEnable = void>
174 struct KruskalInputSelector {};
176 template <typename Graph, typename In, typename Out,
177 typename InEnable = void>
178 struct KruskalOutputSelector {};
180 template <typename Graph, typename In, typename Out>
181 struct KruskalInputSelector<Graph, In, Out,
182 typename enable_if<SequenceInputIndicator<In>, void>::type >
184 typedef typename In::value_type::second_type Value;
186 static Value kruskal(const Graph& graph, const In& in, Out& out) {
187 return KruskalOutputSelector<Graph, In, Out>::
188 kruskal(graph, in, out);
193 template <typename Graph, typename In, typename Out>
194 struct KruskalInputSelector<Graph, In, Out,
195 typename enable_if<MapInputIndicator<In>, void>::type >
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;
205 for (MapArcIt it(graph); it != INVALID; ++it) {
206 seq.push_back(std::make_pair(it, in[it]));
209 std::sort(seq.begin(), seq.end(), PairComp<Sequence>());
210 return KruskalOutputSelector<Graph, Sequence, Out>::
211 kruskal(graph, seq, out);
215 template <typename Graph, typename In, typename Out>
216 struct KruskalOutputSelector<Graph, In, Out,
217 typename enable_if<SequenceOutputIndicator<Out>, void>::type >
219 typedef typename In::value_type::second_type Value;
221 static Value kruskal(const Graph& graph, const In& in, Out& out) {
222 typedef StoreBoolMap<Out> Map;
224 return _kruskal_bits::kruskal(graph, in, map);
229 template <typename Graph, typename In, typename Out>
230 struct KruskalOutputSelector<Graph, In, Out,
231 typename enable_if<MapOutputIndicator<Out>, void>::type >
233 typedef typename In::value_type::second_type Value;
235 static Value kruskal(const Graph& graph, const In& in, Out& out) {
236 return _kruskal_bits::kruskal(graph, in, out);
242 /// \ingroup spantree
244 /// \brief Kruskal's algorithm to find a minimum cost tree of a graph.
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.
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.
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.
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.
278 /// std::vector<Arc> tree(53);
279 /// kruskal(g,cost,tree.begin());
281 /// Or if we don't know in advance the size of the tree, we can
283 ///\code std::vector<Arc> tree;
284 /// kruskal(g,cost,std::back_inserter(tree));
287 /// \return The total cost of the found tree.
289 /// \warning If kruskal runs on an be consistent of using the same
290 /// Arc type for input and output.
294 template <class Graph, class In, class Out>
295 Value kruskal(GR const& g, const In& in, Out& out)
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)
302 return _kruskal_bits::KruskalInputSelector<Graph, In, Out>::
303 kruskal(graph, in, out);
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)
313 return _kruskal_bits::KruskalInputSelector<Graph, In, const Out>::
314 kruskal(graph, in, out);
319 #endif //LEMON_KRUSKAL_H