1 | /* -*- C++ -*- |
---|
2 | * lemon/hypercube_graph.h - Part of LEMON, a generic C++ optimization library |
---|
3 | * |
---|
4 | * Copyright (C) 2005 Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
5 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
6 | * |
---|
7 | * Permission to use, modify and distribute this software is granted |
---|
8 | * provided that this copyright notice appears in all copies. For |
---|
9 | * precise terms see the accompanying LICENSE file. |
---|
10 | * |
---|
11 | * This software is provided "AS IS" with no warranty of any kind, |
---|
12 | * express or implied, and with no claim as to its suitability for any |
---|
13 | * purpose. |
---|
14 | * |
---|
15 | */ |
---|
16 | |
---|
17 | #ifndef HYPERCUBE_GRAPH_H |
---|
18 | #define HYPERCUBE_GRAPH_H |
---|
19 | |
---|
20 | #include <iostream> |
---|
21 | #include <vector> |
---|
22 | #include <lemon/invalid.h> |
---|
23 | #include <lemon/utility.h> |
---|
24 | #include <lemon/error.h> |
---|
25 | |
---|
26 | #include <lemon/bits/iterable_graph_extender.h> |
---|
27 | #include <lemon/bits/alteration_notifier.h> |
---|
28 | #include <lemon/bits/default_map.h> |
---|
29 | #include <lemon/bits/graph_extender.h> |
---|
30 | |
---|
31 | ///\ingroup graphs |
---|
32 | ///\file |
---|
33 | ///\brief HyperCubeGraph class. |
---|
34 | |
---|
35 | namespace lemon { |
---|
36 | |
---|
37 | /// \brief Base graph for HyperCubeGraph. |
---|
38 | /// |
---|
39 | /// Base graph for hyper-cube graph. It describes some member functions |
---|
40 | /// which can be used in the HyperCubeGraph. |
---|
41 | /// |
---|
42 | /// \warning Always use the HyperCubeGraph instead of this. |
---|
43 | /// \see HyperCubeGraph |
---|
44 | class HyperCubeGraphBase { |
---|
45 | |
---|
46 | public: |
---|
47 | |
---|
48 | typedef HyperCubeGraphBase Graph; |
---|
49 | |
---|
50 | class Node; |
---|
51 | class Edge; |
---|
52 | |
---|
53 | public: |
---|
54 | |
---|
55 | HyperCubeGraphBase() {} |
---|
56 | |
---|
57 | protected: |
---|
58 | |
---|
59 | /// \brief Creates a hypercube graph with the given size. |
---|
60 | /// |
---|
61 | /// Creates a hypercube graph with the given size. |
---|
62 | void construct(int dim) { |
---|
63 | _dim = dim; |
---|
64 | _nodeNum = 1 << dim; |
---|
65 | } |
---|
66 | |
---|
67 | public: |
---|
68 | |
---|
69 | |
---|
70 | typedef True NodeNumTag; |
---|
71 | typedef True EdgeNumTag; |
---|
72 | |
---|
73 | ///Number of nodes. |
---|
74 | int nodeNum() const { return _nodeNum; } |
---|
75 | ///Number of edges. |
---|
76 | int edgeNum() const { return _nodeNum * _dim; } |
---|
77 | |
---|
78 | /// Maximum node ID. |
---|
79 | |
---|
80 | /// Maximum node ID. |
---|
81 | ///\sa id(Node) |
---|
82 | int maxNodeId() const { return nodeNum() - 1; } |
---|
83 | /// Maximum edge ID. |
---|
84 | |
---|
85 | /// Maximum edge ID. |
---|
86 | ///\sa id(Edge) |
---|
87 | int maxEdgeId() const { return edgeNum() - 1; } |
---|
88 | |
---|
89 | /// \brief Gives back the source node of an edge. |
---|
90 | /// |
---|
91 | /// Gives back the source node of an edge. |
---|
92 | Node source(Edge e) const { |
---|
93 | return e.id / _dim; |
---|
94 | } |
---|
95 | |
---|
96 | /// \brief Gives back the target node of an edge. |
---|
97 | /// |
---|
98 | /// Gives back the target node of an edge. |
---|
99 | Node target(Edge e) const { |
---|
100 | return (e.id / _dim) ^ ( 1 << (e.id % _dim)); |
---|
101 | } |
---|
102 | |
---|
103 | /// Node ID. |
---|
104 | |
---|
105 | /// The ID of a valid Node is a nonnegative integer not greater than |
---|
106 | /// \ref maxNodeId(). The range of the ID's is not surely continuous |
---|
107 | /// and the greatest node ID can be actually less then \ref maxNodeId(). |
---|
108 | /// |
---|
109 | /// The ID of the \ref INVALID node is -1. |
---|
110 | ///\return The ID of the node \c v. |
---|
111 | |
---|
112 | static int id(Node v) { return v.id; } |
---|
113 | /// Edge ID. |
---|
114 | |
---|
115 | /// The ID of a valid Edge is a nonnegative integer not greater than |
---|
116 | /// \ref maxEdgeId(). The range of the ID's is not surely continuous |
---|
117 | /// and the greatest edge ID can be actually less then \ref maxEdgeId(). |
---|
118 | /// |
---|
119 | /// The ID of the \ref INVALID edge is -1. |
---|
120 | ///\return The ID of the edge \c e. |
---|
121 | static int id(Edge e) { return e.id; } |
---|
122 | |
---|
123 | static Node nodeFromId(int id) { return Node(id);} |
---|
124 | |
---|
125 | static Edge edgeFromId(int id) { return Edge(id);} |
---|
126 | |
---|
127 | class Node { |
---|
128 | friend class HyperCubeGraphBase; |
---|
129 | |
---|
130 | protected: |
---|
131 | int id; |
---|
132 | Node(int _id) { id = _id;} |
---|
133 | public: |
---|
134 | Node() {} |
---|
135 | Node (Invalid) { id = -1; } |
---|
136 | bool operator==(const Node node) const {return id == node.id;} |
---|
137 | bool operator!=(const Node node) const {return id != node.id;} |
---|
138 | bool operator<(const Node node) const {return id < node.id;} |
---|
139 | }; |
---|
140 | |
---|
141 | class Edge { |
---|
142 | friend class HyperCubeGraphBase; |
---|
143 | |
---|
144 | protected: |
---|
145 | int id; |
---|
146 | |
---|
147 | Edge(int _id) : id(_id) {} |
---|
148 | |
---|
149 | public: |
---|
150 | Edge() { } |
---|
151 | Edge (Invalid) { id = -1; } |
---|
152 | bool operator==(const Edge edge) const {return id == edge.id;} |
---|
153 | bool operator!=(const Edge edge) const {return id != edge.id;} |
---|
154 | bool operator<(const Edge edge) const {return id < edge.id;} |
---|
155 | }; |
---|
156 | |
---|
157 | void first(Node& node) const { |
---|
158 | node.id = nodeNum() - 1; |
---|
159 | } |
---|
160 | |
---|
161 | static void next(Node& node) { |
---|
162 | --node.id; |
---|
163 | } |
---|
164 | |
---|
165 | void first(Edge& edge) const { |
---|
166 | edge.id = edgeNum() - 1; |
---|
167 | } |
---|
168 | |
---|
169 | static void next(Edge& edge) { |
---|
170 | --edge.id; |
---|
171 | } |
---|
172 | |
---|
173 | void firstOut(Edge& edge, const Node& node) const { |
---|
174 | edge.id = node.id * _dim; |
---|
175 | } |
---|
176 | |
---|
177 | void nextOut(Edge& edge) const { |
---|
178 | ++edge.id; |
---|
179 | if (edge.id % _dim == 0) edge.id = -1; |
---|
180 | } |
---|
181 | |
---|
182 | void firstIn(Edge& edge, const Node& node) const { |
---|
183 | edge.id = (node.id ^ 1) * _dim; |
---|
184 | } |
---|
185 | |
---|
186 | void nextIn(Edge& edge) const { |
---|
187 | int cnt = edge.id % _dim; |
---|
188 | if ((cnt + 1) % _dim == 0) { |
---|
189 | edge.id = -1; |
---|
190 | } else { |
---|
191 | edge.id = ((edge.id / _dim) ^ ((1 << cnt) * 3)) * _dim + cnt + 1; |
---|
192 | } |
---|
193 | } |
---|
194 | |
---|
195 | /// \brief Gives back the number of the dimensions. |
---|
196 | /// |
---|
197 | /// Gives back the number of the dimensions. |
---|
198 | int dimension() const { |
---|
199 | return _dim; |
---|
200 | } |
---|
201 | |
---|
202 | /// \brief Returns true if the n'th bit of the node is one. |
---|
203 | /// |
---|
204 | /// Returns true if the n'th bit of the node is one. |
---|
205 | bool projection(Node node, int n) const { |
---|
206 | return (bool)(node.id & (1 << n)); |
---|
207 | } |
---|
208 | |
---|
209 | /// \brief The dimension id of the edge. |
---|
210 | /// |
---|
211 | /// It returns the dimension id of the edge. It can |
---|
212 | /// be in the ${0, 1, dim-1}$ intervall. |
---|
213 | int dimension(Edge edge) const { |
---|
214 | return edge.id % _dim; |
---|
215 | } |
---|
216 | |
---|
217 | /// \brief Gives back the index of the node. |
---|
218 | /// |
---|
219 | /// Gives back the index of the node. The lower bits of the |
---|
220 | /// integer describe the node. |
---|
221 | int index(Node node) const { |
---|
222 | return node.id; |
---|
223 | } |
---|
224 | |
---|
225 | /// \brief Gives back the node by its index. |
---|
226 | /// |
---|
227 | /// Gives back the node by its index. |
---|
228 | Node node(int index) const { |
---|
229 | return Node(index); |
---|
230 | } |
---|
231 | |
---|
232 | private: |
---|
233 | int _dim, _nodeNum; |
---|
234 | }; |
---|
235 | |
---|
236 | |
---|
237 | typedef StaticMappableGraphExtender< |
---|
238 | IterableGraphExtender< |
---|
239 | AlterableGraphExtender< |
---|
240 | GraphExtender< |
---|
241 | HyperCubeGraphBase> > > > ExtendedHyperCubeGraphBase; |
---|
242 | |
---|
243 | /// \ingroup graphs |
---|
244 | /// |
---|
245 | /// \brief HyperCube graph class |
---|
246 | /// |
---|
247 | /// This class implements a special graph type. The nodes of the |
---|
248 | /// graph can be indiced with integers with at most \c dim binary length. |
---|
249 | /// Two nodes are connected in the graph if the indices differ only |
---|
250 | /// on one position in the binary form. |
---|
251 | /// |
---|
252 | /// \note The type of the \c ids is chosen to \c int because efficiency |
---|
253 | /// reasons. This way the maximal dimension of this implementation |
---|
254 | /// is 26. |
---|
255 | /// |
---|
256 | /// The graph type is fully conform to the \ref concept::StaticGraph |
---|
257 | /// concept but it does not conform to the \ref concept::UndirGraph. |
---|
258 | /// |
---|
259 | /// \see HyperCubeGraphBase |
---|
260 | /// \author Balazs Dezso |
---|
261 | class HyperCubeGraph : public ExtendedHyperCubeGraphBase { |
---|
262 | public: |
---|
263 | |
---|
264 | /// \brief Construct a graph with \c dim dimension. |
---|
265 | /// |
---|
266 | /// Construct a graph with \c dim dimension. |
---|
267 | HyperCubeGraph(int dim) { construct(dim); } |
---|
268 | |
---|
269 | /// \brief Linear combination map. |
---|
270 | /// |
---|
271 | /// It makes possible to give back a linear combination |
---|
272 | /// for each node. This function works like the \c std::accumulate |
---|
273 | /// so it accumulates the \c bf binary function with the \c fv |
---|
274 | /// first value. The map accumulates only on that dimensions where |
---|
275 | /// the node's index is one. The accumulated values should be |
---|
276 | /// given by the \c begin and \c end iterators and this range's length |
---|
277 | /// should be the dimension number of the graph. |
---|
278 | /// |
---|
279 | /// \code |
---|
280 | /// const int DIM = 3; |
---|
281 | /// HyperCubeGraph graph(DIM); |
---|
282 | /// xy<double> base[DIM]; |
---|
283 | /// for (int k = 0; k < DIM; ++k) { |
---|
284 | /// base[k].x = rand() / (RAND_MAX + 1.0); |
---|
285 | /// base[k].y = rand() / (RAND_MAX + 1.0); |
---|
286 | /// } |
---|
287 | /// HyperCubeGraph::HyperMap<xy<double> > |
---|
288 | /// pos(graph, base, base + DIM, xy<double>(0.0, 0.0)); |
---|
289 | /// \endcode |
---|
290 | /// |
---|
291 | /// \see HyperCubeGraph |
---|
292 | template <typename T, typename BF = std::plus<T> > |
---|
293 | class HyperMap { |
---|
294 | public: |
---|
295 | |
---|
296 | typedef Node Key; |
---|
297 | typedef T Value; |
---|
298 | |
---|
299 | |
---|
300 | /// \brief Constructor for HyperMap. |
---|
301 | /// |
---|
302 | /// Construct a HyperMap for the given graph. The accumulated values |
---|
303 | /// should be given by the \c begin and \c end iterators and this |
---|
304 | /// range's length should be the dimension number of the graph. |
---|
305 | /// |
---|
306 | /// This function accumulates the \c bf binary function with |
---|
307 | /// the \c fv first value. The map accumulates only on that dimensions |
---|
308 | /// where the node's index is one. |
---|
309 | template <typename It> |
---|
310 | HyperMap(const Graph& graph, It begin, It end, |
---|
311 | T fv = 0.0, const BF& bf = BF()) |
---|
312 | : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf) { |
---|
313 | LEMON_ASSERT(_values.size() != graph.dimension(), |
---|
314 | "Wrong size of dimension"); |
---|
315 | } |
---|
316 | |
---|
317 | /// \brief Gives back the partial accumulated value. |
---|
318 | /// |
---|
319 | /// Gives back the partial accumulated value. |
---|
320 | Value operator[](Key k) const { |
---|
321 | Value val = _first_value; |
---|
322 | int id = _graph.index(k); |
---|
323 | int n = 0; |
---|
324 | while (id != 0) { |
---|
325 | if (id & 1) { |
---|
326 | val = _bin_func(_values[n], _first_value); |
---|
327 | } |
---|
328 | id >>= 1; |
---|
329 | ++n; |
---|
330 | } |
---|
331 | return val; |
---|
332 | } |
---|
333 | |
---|
334 | private: |
---|
335 | const Graph& _graph; |
---|
336 | std::vector<T> _values; |
---|
337 | T _first_value; |
---|
338 | BF _bin_func; |
---|
339 | }; |
---|
340 | }; |
---|
341 | } |
---|
342 | #endif |
---|
343 | |
---|