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 HYPERCUBE_GRAPH_H |
---|
20 | #define HYPERCUBE_GRAPH_H |
---|
21 | |
---|
22 | #include <vector> |
---|
23 | #include <lemon/core.h> |
---|
24 | #include <lemon/assert.h> |
---|
25 | #include <lemon/bits/graph_extender.h> |
---|
26 | |
---|
27 | ///\ingroup graphs |
---|
28 | ///\file |
---|
29 | ///\brief HypercubeGraph class. |
---|
30 | |
---|
31 | namespace lemon { |
---|
32 | |
---|
33 | class HypercubeGraphBase { |
---|
34 | |
---|
35 | public: |
---|
36 | |
---|
37 | typedef HypercubeGraphBase Graph; |
---|
38 | |
---|
39 | class Node; |
---|
40 | class Edge; |
---|
41 | class Arc; |
---|
42 | |
---|
43 | public: |
---|
44 | |
---|
45 | HypercubeGraphBase() {} |
---|
46 | |
---|
47 | protected: |
---|
48 | |
---|
49 | void construct(int dim) { |
---|
50 | LEMON_ASSERT(dim >= 1, "The number of dimensions must be at least 1."); |
---|
51 | _dim = dim; |
---|
52 | _node_num = 1 << dim; |
---|
53 | _edge_num = dim * (1 << (dim-1)); |
---|
54 | } |
---|
55 | |
---|
56 | public: |
---|
57 | |
---|
58 | typedef True NodeNumTag; |
---|
59 | typedef True EdgeNumTag; |
---|
60 | typedef True ArcNumTag; |
---|
61 | |
---|
62 | int nodeNum() const { return _node_num; } |
---|
63 | int edgeNum() const { return _edge_num; } |
---|
64 | int arcNum() const { return 2 * _edge_num; } |
---|
65 | |
---|
66 | int maxNodeId() const { return _node_num - 1; } |
---|
67 | int maxEdgeId() const { return _edge_num - 1; } |
---|
68 | int maxArcId() const { return 2 * _edge_num - 1; } |
---|
69 | |
---|
70 | static Node nodeFromId(int id) { return Node(id); } |
---|
71 | static Edge edgeFromId(int id) { return Edge(id); } |
---|
72 | static Arc arcFromId(int id) { return Arc(id); } |
---|
73 | |
---|
74 | static int id(Node node) { return node._id; } |
---|
75 | static int id(Edge edge) { return edge._id; } |
---|
76 | static int id(Arc arc) { return arc._id; } |
---|
77 | |
---|
78 | Node u(Edge edge) const { |
---|
79 | int base = edge._id & ((1 << (_dim-1)) - 1); |
---|
80 | int k = edge._id >> (_dim-1); |
---|
81 | return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)); |
---|
82 | } |
---|
83 | |
---|
84 | Node v(Edge edge) const { |
---|
85 | int base = edge._id & ((1 << (_dim-1)) - 1); |
---|
86 | int k = edge._id >> (_dim-1); |
---|
87 | return ((base >> k) << (k+1)) | (base & ((1 << k) - 1)) | (1 << k); |
---|
88 | } |
---|
89 | |
---|
90 | Node source(Arc arc) const { |
---|
91 | return (arc._id & 1) == 1 ? u(arc) : v(arc); |
---|
92 | } |
---|
93 | |
---|
94 | Node target(Arc arc) const { |
---|
95 | return (arc._id & 1) == 1 ? v(arc) : u(arc); |
---|
96 | } |
---|
97 | |
---|
98 | typedef True FindEdgeTag; |
---|
99 | typedef True FindArcTag; |
---|
100 | |
---|
101 | Edge findEdge(Node u, Node v, Edge prev = INVALID) const { |
---|
102 | if (prev != INVALID) return INVALID; |
---|
103 | int d = u._id ^ v._id; |
---|
104 | int k = 0; |
---|
105 | if (d == 0) return INVALID; |
---|
106 | for ( ; (d & 1) == 0; d >>= 1) ++k; |
---|
107 | if (d >> 1 != 0) return INVALID; |
---|
108 | return (k << (_dim-1)) | ((u._id >> (k+1)) << k) | |
---|
109 | (u._id & ((1 << k) - 1)); |
---|
110 | } |
---|
111 | |
---|
112 | Arc findArc(Node u, Node v, Arc prev = INVALID) const { |
---|
113 | Edge edge = findEdge(u, v, prev); |
---|
114 | if (edge == INVALID) return INVALID; |
---|
115 | int k = edge._id >> (_dim-1); |
---|
116 | return ((u._id >> k) & 1) == 1 ? edge._id << 1 : (edge._id << 1) | 1; |
---|
117 | } |
---|
118 | |
---|
119 | class Node { |
---|
120 | friend class HypercubeGraphBase; |
---|
121 | |
---|
122 | protected: |
---|
123 | int _id; |
---|
124 | Node(int id) : _id(id) {} |
---|
125 | public: |
---|
126 | Node() {} |
---|
127 | Node (Invalid) : _id(-1) {} |
---|
128 | bool operator==(const Node node) const {return _id == node._id;} |
---|
129 | bool operator!=(const Node node) const {return _id != node._id;} |
---|
130 | bool operator<(const Node node) const {return _id < node._id;} |
---|
131 | }; |
---|
132 | |
---|
133 | class Edge { |
---|
134 | friend class HypercubeGraphBase; |
---|
135 | friend class Arc; |
---|
136 | |
---|
137 | protected: |
---|
138 | int _id; |
---|
139 | |
---|
140 | Edge(int id) : _id(id) {} |
---|
141 | |
---|
142 | public: |
---|
143 | Edge() {} |
---|
144 | Edge (Invalid) : _id(-1) {} |
---|
145 | bool operator==(const Edge edge) const {return _id == edge._id;} |
---|
146 | bool operator!=(const Edge edge) const {return _id != edge._id;} |
---|
147 | bool operator<(const Edge edge) const {return _id < edge._id;} |
---|
148 | }; |
---|
149 | |
---|
150 | class Arc { |
---|
151 | friend class HypercubeGraphBase; |
---|
152 | |
---|
153 | protected: |
---|
154 | int _id; |
---|
155 | |
---|
156 | Arc(int id) : _id(id) {} |
---|
157 | |
---|
158 | public: |
---|
159 | Arc() {} |
---|
160 | Arc (Invalid) : _id(-1) {} |
---|
161 | operator Edge() const { return _id != -1 ? Edge(_id >> 1) : INVALID; } |
---|
162 | bool operator==(const Arc arc) const {return _id == arc._id;} |
---|
163 | bool operator!=(const Arc arc) const {return _id != arc._id;} |
---|
164 | bool operator<(const Arc arc) const {return _id < arc._id;} |
---|
165 | }; |
---|
166 | |
---|
167 | void first(Node& node) const { |
---|
168 | node._id = _node_num - 1; |
---|
169 | } |
---|
170 | |
---|
171 | static void next(Node& node) { |
---|
172 | --node._id; |
---|
173 | } |
---|
174 | |
---|
175 | void first(Edge& edge) const { |
---|
176 | edge._id = _edge_num - 1; |
---|
177 | } |
---|
178 | |
---|
179 | static void next(Edge& edge) { |
---|
180 | --edge._id; |
---|
181 | } |
---|
182 | |
---|
183 | void first(Arc& arc) const { |
---|
184 | arc._id = 2 * _edge_num - 1; |
---|
185 | } |
---|
186 | |
---|
187 | static void next(Arc& arc) { |
---|
188 | --arc._id; |
---|
189 | } |
---|
190 | |
---|
191 | void firstInc(Edge& edge, bool& dir, const Node& node) const { |
---|
192 | edge._id = node._id >> 1; |
---|
193 | dir = (node._id & 1) == 0; |
---|
194 | } |
---|
195 | |
---|
196 | void nextInc(Edge& edge, bool& dir) const { |
---|
197 | Node n = dir ? u(edge) : v(edge); |
---|
198 | int k = (edge._id >> (_dim-1)) + 1; |
---|
199 | if (k < _dim) { |
---|
200 | edge._id = (k << (_dim-1)) | |
---|
201 | ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1)); |
---|
202 | dir = ((n._id >> k) & 1) == 0; |
---|
203 | } else { |
---|
204 | edge._id = -1; |
---|
205 | dir = true; |
---|
206 | } |
---|
207 | } |
---|
208 | |
---|
209 | void firstOut(Arc& arc, const Node& node) const { |
---|
210 | arc._id = ((node._id >> 1) << 1) | (~node._id & 1); |
---|
211 | } |
---|
212 | |
---|
213 | void nextOut(Arc& arc) const { |
---|
214 | Node n = (arc._id & 1) == 1 ? u(arc) : v(arc); |
---|
215 | int k = (arc._id >> _dim) + 1; |
---|
216 | if (k < _dim) { |
---|
217 | arc._id = (k << (_dim-1)) | |
---|
218 | ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1)); |
---|
219 | arc._id = (arc._id << 1) | (~(n._id >> k) & 1); |
---|
220 | } else { |
---|
221 | arc._id = -1; |
---|
222 | } |
---|
223 | } |
---|
224 | |
---|
225 | void firstIn(Arc& arc, const Node& node) const { |
---|
226 | arc._id = ((node._id >> 1) << 1) | (node._id & 1); |
---|
227 | } |
---|
228 | |
---|
229 | void nextIn(Arc& arc) const { |
---|
230 | Node n = (arc._id & 1) == 1 ? v(arc) : u(arc); |
---|
231 | int k = (arc._id >> _dim) + 1; |
---|
232 | if (k < _dim) { |
---|
233 | arc._id = (k << (_dim-1)) | |
---|
234 | ((n._id >> (k+1)) << k) | (n._id & ((1 << k) - 1)); |
---|
235 | arc._id = (arc._id << 1) | ((n._id >> k) & 1); |
---|
236 | } else { |
---|
237 | arc._id = -1; |
---|
238 | } |
---|
239 | } |
---|
240 | |
---|
241 | static bool direction(Arc arc) { |
---|
242 | return (arc._id & 1) == 1; |
---|
243 | } |
---|
244 | |
---|
245 | static Arc direct(Edge edge, bool dir) { |
---|
246 | return Arc((edge._id << 1) | (dir ? 1 : 0)); |
---|
247 | } |
---|
248 | |
---|
249 | int dimension() const { |
---|
250 | return _dim; |
---|
251 | } |
---|
252 | |
---|
253 | bool projection(Node node, int n) const { |
---|
254 | return static_cast<bool>(node._id & (1 << n)); |
---|
255 | } |
---|
256 | |
---|
257 | int dimension(Edge edge) const { |
---|
258 | return edge._id >> (_dim-1); |
---|
259 | } |
---|
260 | |
---|
261 | int dimension(Arc arc) const { |
---|
262 | return arc._id >> _dim; |
---|
263 | } |
---|
264 | |
---|
265 | int index(Node node) const { |
---|
266 | return node._id; |
---|
267 | } |
---|
268 | |
---|
269 | Node operator()(int ix) const { |
---|
270 | return Node(ix); |
---|
271 | } |
---|
272 | |
---|
273 | private: |
---|
274 | int _dim; |
---|
275 | int _node_num, _edge_num; |
---|
276 | }; |
---|
277 | |
---|
278 | |
---|
279 | typedef GraphExtender<HypercubeGraphBase> ExtendedHypercubeGraphBase; |
---|
280 | |
---|
281 | /// \ingroup graphs |
---|
282 | /// |
---|
283 | /// \brief Hypercube graph class |
---|
284 | /// |
---|
285 | /// This class implements a special graph type. The nodes of the graph |
---|
286 | /// are indiced with integers with at most \c dim binary digits. |
---|
287 | /// Two nodes are connected in the graph if and only if their indices |
---|
288 | /// differ only on one position in the binary form. |
---|
289 | /// |
---|
290 | /// \note The type of the indices is chosen to \c int for efficiency |
---|
291 | /// reasons. Thus the maximum dimension of this implementation is 26 |
---|
292 | /// (assuming that the size of \c int is 32 bit). |
---|
293 | /// |
---|
294 | /// This graph type is fully conform to the \ref concepts::Graph |
---|
295 | /// "Graph" concept, and it also has an important extra feature |
---|
296 | /// that its maps are real \ref concepts::ReferenceMap |
---|
297 | /// "reference map"s. |
---|
298 | class HypercubeGraph : public ExtendedHypercubeGraphBase { |
---|
299 | public: |
---|
300 | |
---|
301 | typedef ExtendedHypercubeGraphBase Parent; |
---|
302 | |
---|
303 | /// \brief Constructs a hypercube graph with \c dim dimensions. |
---|
304 | /// |
---|
305 | /// Constructs a hypercube graph with \c dim dimensions. |
---|
306 | HypercubeGraph(int dim) { construct(dim); } |
---|
307 | |
---|
308 | /// \brief The number of dimensions. |
---|
309 | /// |
---|
310 | /// Gives back the number of dimensions. |
---|
311 | int dimension() const { |
---|
312 | return Parent::dimension(); |
---|
313 | } |
---|
314 | |
---|
315 | /// \brief Returns \c true if the n'th bit of the node is one. |
---|
316 | /// |
---|
317 | /// Returns \c true if the n'th bit of the node is one. |
---|
318 | bool projection(Node node, int n) const { |
---|
319 | return Parent::projection(node, n); |
---|
320 | } |
---|
321 | |
---|
322 | /// \brief The dimension id of an edge. |
---|
323 | /// |
---|
324 | /// Gives back the dimension id of the given edge. |
---|
325 | /// It is in the [0..dim-1] range. |
---|
326 | int dimension(Edge edge) const { |
---|
327 | return Parent::dimension(edge); |
---|
328 | } |
---|
329 | |
---|
330 | /// \brief The dimension id of an arc. |
---|
331 | /// |
---|
332 | /// Gives back the dimension id of the given arc. |
---|
333 | /// It is in the [0..dim-1] range. |
---|
334 | int dimension(Arc arc) const { |
---|
335 | return Parent::dimension(arc); |
---|
336 | } |
---|
337 | |
---|
338 | /// \brief The index of a node. |
---|
339 | /// |
---|
340 | /// Gives back the index of the given node. |
---|
341 | /// The lower bits of the integer describes the node. |
---|
342 | int index(Node node) const { |
---|
343 | return Parent::index(node); |
---|
344 | } |
---|
345 | |
---|
346 | /// \brief Gives back a node by its index. |
---|
347 | /// |
---|
348 | /// Gives back a node by its index. |
---|
349 | Node operator()(int ix) const { |
---|
350 | return Parent::operator()(ix); |
---|
351 | } |
---|
352 | |
---|
353 | /// \brief Number of nodes. |
---|
354 | int nodeNum() const { return Parent::nodeNum(); } |
---|
355 | /// \brief Number of edges. |
---|
356 | int edgeNum() const { return Parent::edgeNum(); } |
---|
357 | /// \brief Number of arcs. |
---|
358 | int arcNum() const { return Parent::arcNum(); } |
---|
359 | |
---|
360 | /// \brief Linear combination map. |
---|
361 | /// |
---|
362 | /// This map makes possible to give back a linear combination |
---|
363 | /// for each node. It works like the \c std::accumulate function, |
---|
364 | /// so it accumulates the \c bf binary function with the \c fv first |
---|
365 | /// value. The map accumulates only on that positions (dimensions) |
---|
366 | /// where the index of the node is one. The values that have to be |
---|
367 | /// accumulated should be given by the \c begin and \c end iterators |
---|
368 | /// and the length of this range should be equal to the dimension |
---|
369 | /// number of the graph. |
---|
370 | /// |
---|
371 | ///\code |
---|
372 | /// const int DIM = 3; |
---|
373 | /// HypercubeGraph graph(DIM); |
---|
374 | /// dim2::Point<double> base[DIM]; |
---|
375 | /// for (int k = 0; k < DIM; ++k) { |
---|
376 | /// base[k].x = rnd(); |
---|
377 | /// base[k].y = rnd(); |
---|
378 | /// } |
---|
379 | /// HypercubeGraph::HyperMap<dim2::Point<double> > |
---|
380 | /// pos(graph, base, base + DIM, dim2::Point<double>(0.0, 0.0)); |
---|
381 | ///\endcode |
---|
382 | /// |
---|
383 | /// \see HypercubeGraph |
---|
384 | template <typename T, typename BF = std::plus<T> > |
---|
385 | class HyperMap { |
---|
386 | public: |
---|
387 | |
---|
388 | /// \brief The key type of the map |
---|
389 | typedef Node Key; |
---|
390 | /// \brief The value type of the map |
---|
391 | typedef T Value; |
---|
392 | |
---|
393 | /// \brief Constructor for HyperMap. |
---|
394 | /// |
---|
395 | /// Construct a HyperMap for the given graph. The values that have |
---|
396 | /// to be accumulated should be given by the \c begin and \c end |
---|
397 | /// iterators and the length of this range should be equal to the |
---|
398 | /// dimension number of the graph. |
---|
399 | /// |
---|
400 | /// This map accumulates the \c bf binary function with the \c fv |
---|
401 | /// first value on that positions (dimensions) where the index of |
---|
402 | /// the node is one. |
---|
403 | template <typename It> |
---|
404 | HyperMap(const Graph& graph, It begin, It end, |
---|
405 | T fv = 0, const BF& bf = BF()) |
---|
406 | : _graph(graph), _values(begin, end), _first_value(fv), _bin_func(bf) |
---|
407 | { |
---|
408 | LEMON_ASSERT(_values.size() == graph.dimension(), |
---|
409 | "Wrong size of range"); |
---|
410 | } |
---|
411 | |
---|
412 | /// \brief The partial accumulated value. |
---|
413 | /// |
---|
414 | /// Gives back the partial accumulated value. |
---|
415 | Value operator[](const Key& k) const { |
---|
416 | Value val = _first_value; |
---|
417 | int id = _graph.index(k); |
---|
418 | int n = 0; |
---|
419 | while (id != 0) { |
---|
420 | if (id & 1) { |
---|
421 | val = _bin_func(val, _values[n]); |
---|
422 | } |
---|
423 | id >>= 1; |
---|
424 | ++n; |
---|
425 | } |
---|
426 | return val; |
---|
427 | } |
---|
428 | |
---|
429 | private: |
---|
430 | const Graph& _graph; |
---|
431 | std::vector<T> _values; |
---|
432 | T _first_value; |
---|
433 | BF _bin_func; |
---|
434 | }; |
---|
435 | |
---|
436 | }; |
---|
437 | |
---|
438 | } |
---|
439 | |
---|
440 | #endif |
---|