1 | /* -*- C++ -*- |
---|
2 | * lemon/radix_sort.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 RADIX_SORT_H |
---|
18 | #define RADIX_SORT_H |
---|
19 | |
---|
20 | /// \ingroup auxdat |
---|
21 | /// \file |
---|
22 | /// \brief Radix sort |
---|
23 | /// |
---|
24 | |
---|
25 | #include <vector> |
---|
26 | #include <limits> |
---|
27 | #include <iterator> |
---|
28 | #include <algorithm> |
---|
29 | |
---|
30 | #include <lemon/error.h> |
---|
31 | |
---|
32 | namespace lemon { |
---|
33 | |
---|
34 | namespace _radix_sort_bits { |
---|
35 | |
---|
36 | template <typename Value> |
---|
37 | struct Identity { |
---|
38 | const Value& operator()(const Value& val) { |
---|
39 | return val; |
---|
40 | } |
---|
41 | }; |
---|
42 | |
---|
43 | } |
---|
44 | |
---|
45 | template <typename Value, typename Iterator, typename Functor> |
---|
46 | Iterator radixSortPartition(Iterator first, Iterator last, |
---|
47 | Functor functor, Value mask) { |
---|
48 | while (first != last && !(functor(*first) & mask)) { |
---|
49 | ++first; |
---|
50 | } |
---|
51 | if (first == last) { |
---|
52 | return first; |
---|
53 | } |
---|
54 | --last; |
---|
55 | while (first != last && (functor(*last) & mask)) { |
---|
56 | --last; |
---|
57 | } |
---|
58 | if (first == last) { |
---|
59 | return first; |
---|
60 | } |
---|
61 | std::iter_swap(first, last); |
---|
62 | ++first; |
---|
63 | if (!(first < last)) { |
---|
64 | return first; |
---|
65 | } |
---|
66 | while (true) { |
---|
67 | while (!(functor(*first) & mask)) { |
---|
68 | ++first; |
---|
69 | } |
---|
70 | --last; |
---|
71 | while (functor(*last) & mask) { |
---|
72 | --last; |
---|
73 | } |
---|
74 | if (!(first < last)) { |
---|
75 | return first; |
---|
76 | } |
---|
77 | std::iter_swap(first, last); |
---|
78 | ++first; |
---|
79 | } |
---|
80 | } |
---|
81 | |
---|
82 | template <typename Iterator, typename Functor> |
---|
83 | Iterator radixSortSignPartition(Iterator first, Iterator last, |
---|
84 | Functor functor) { |
---|
85 | while (first != last && functor(*first) < 0) { |
---|
86 | ++first; |
---|
87 | } |
---|
88 | if (first == last) { |
---|
89 | return first; |
---|
90 | } |
---|
91 | --last; |
---|
92 | while (first != last && functor(*last) >= 0) { |
---|
93 | --last; |
---|
94 | } |
---|
95 | if (first == last) { |
---|
96 | return first; |
---|
97 | } |
---|
98 | std::iter_swap(first, last); |
---|
99 | ++first; |
---|
100 | if (!(first < last)) { |
---|
101 | return first; |
---|
102 | } |
---|
103 | while (true) { |
---|
104 | while (functor(*first) < 0) { |
---|
105 | ++first; |
---|
106 | } |
---|
107 | --last; |
---|
108 | while (functor(*last) >= 0) { |
---|
109 | --last; |
---|
110 | } |
---|
111 | if (!(first < last)) { |
---|
112 | return first; |
---|
113 | } |
---|
114 | std::iter_swap(first, last); |
---|
115 | ++first; |
---|
116 | } |
---|
117 | } |
---|
118 | |
---|
119 | template <typename Value, typename Iterator, typename Functor> |
---|
120 | void radixIntroSort(Iterator first, Iterator last, |
---|
121 | Functor functor, Value mask) { |
---|
122 | while (mask != 0 && last - first > 1) { |
---|
123 | Iterator cut = radixSortPartition(first, last, functor, mask); |
---|
124 | mask >>= 1; |
---|
125 | radixIntroSort(first, cut, functor, mask); |
---|
126 | first = cut; |
---|
127 | } |
---|
128 | } |
---|
129 | |
---|
130 | template <typename Value, typename Iterator, typename Functor> |
---|
131 | void radixSignedSort(Iterator first, Iterator last, Functor functor) { |
---|
132 | Iterator cut = radixSortSignPartition(first, last, functor); |
---|
133 | |
---|
134 | Value mask; |
---|
135 | int max_digit; |
---|
136 | Iterator it; |
---|
137 | |
---|
138 | mask = 0; max_digit = 0; |
---|
139 | for (it = first; it != cut; ++it) { |
---|
140 | if ((mask | functor(*it)) != ~0) { |
---|
141 | ++max_digit; |
---|
142 | mask <<= 1; |
---|
143 | mask |= 1; |
---|
144 | } |
---|
145 | } |
---|
146 | radixIntroSort(first, cut, functor, 1 << max_digit); |
---|
147 | |
---|
148 | mask = ~0; max_digit = 0; |
---|
149 | for (it = cut; it != last; ++it) { |
---|
150 | if (mask & functor(*it)) { |
---|
151 | ++max_digit; |
---|
152 | mask <<= 1; |
---|
153 | } |
---|
154 | } |
---|
155 | radixIntroSort(cut, last, functor, 1 << max_digit); |
---|
156 | } |
---|
157 | |
---|
158 | template <typename Value, typename Iterator, typename Functor> |
---|
159 | void radixUnsignedSort(Iterator first, Iterator last, Functor functor) { |
---|
160 | |
---|
161 | Value mask = ~0; |
---|
162 | int max_digit = 0; |
---|
163 | |
---|
164 | Iterator it; |
---|
165 | for (it = first; it != last; ++it) { |
---|
166 | if (mask & functor(*it)) { |
---|
167 | ++max_digit; |
---|
168 | mask <<= 1; |
---|
169 | } |
---|
170 | } |
---|
171 | radixIntroSort(first, last, functor, 1 << max_digit); |
---|
172 | } |
---|
173 | |
---|
174 | namespace _radix_sort_bits { |
---|
175 | |
---|
176 | template <typename Value, |
---|
177 | bool sign = std::numeric_limits<Value>::is_signed > |
---|
178 | struct RadixSortSelector { |
---|
179 | template <typename Iterator, typename Functor> |
---|
180 | static void sort(Iterator first, Iterator last, Functor functor) { |
---|
181 | radixSignedSort<Value>(first, last, functor); |
---|
182 | } |
---|
183 | }; |
---|
184 | |
---|
185 | template <typename Value> |
---|
186 | struct RadixSortSelector<Value, false> { |
---|
187 | template <typename Iterator, typename Functor> |
---|
188 | static void sort(Iterator first, Iterator last, Functor functor) { |
---|
189 | radixUnsignedSort<Value>(first, last, functor); |
---|
190 | } |
---|
191 | }; |
---|
192 | |
---|
193 | } |
---|
194 | |
---|
195 | /// \ingroup auxdat |
---|
196 | /// |
---|
197 | /// \brief Sorts the stl compatible range into ascending order. |
---|
198 | /// |
---|
199 | /// The \c radixSort sorts the stl compatible range into ascending order. |
---|
200 | /// The radix sort algorithm can sort the items which mapped to an |
---|
201 | /// integer by the adaptable unary function \c functor and the order |
---|
202 | /// will be ascending by these mapped values. As function specialization |
---|
203 | /// there is possible to use a normal function as the functor object |
---|
204 | /// or if the functor is not given it will use an identity function instead. |
---|
205 | /// |
---|
206 | /// This implemented radix sort is a special quick sort which pivot value |
---|
207 | /// is choosen to partite the items on the next bit. This way, let be |
---|
208 | /// \c c the maximal capacity and \c n the number of the items in |
---|
209 | /// the container, the time complexity of the algorithm \c O(log(c)*n) |
---|
210 | /// and the additional space complexity is \c O(log(c)). |
---|
211 | /// |
---|
212 | /// \param first The begin of the given range. |
---|
213 | /// \param last The end of the given range. |
---|
214 | /// \param functor An adaptible unary function or a normal function which |
---|
215 | /// maps the items to any integer type which can be wheter signed or |
---|
216 | /// unsigned. |
---|
217 | template <typename Iterator, typename Functor> |
---|
218 | void radixSort(Iterator first, Iterator last, Functor functor) { |
---|
219 | using namespace _radix_sort_bits; |
---|
220 | typedef typename Functor::result_type Value; |
---|
221 | RadixSortSelector<Value>::sort(first, last, functor); |
---|
222 | } |
---|
223 | |
---|
224 | template <typename Iterator, typename Value, typename Key> |
---|
225 | void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) { |
---|
226 | using namespace _radix_sort_bits; |
---|
227 | RadixSortSelector<Value>::sort(first, last, functor); |
---|
228 | } |
---|
229 | |
---|
230 | template <typename Iterator, typename Value, typename Key> |
---|
231 | void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) { |
---|
232 | using namespace _radix_sort_bits; |
---|
233 | RadixSortSelector<Value>::sort(first, last, functor); |
---|
234 | } |
---|
235 | |
---|
236 | template <typename Iterator, typename Value, typename Key> |
---|
237 | void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) { |
---|
238 | using namespace _radix_sort_bits; |
---|
239 | RadixSortSelector<Value>::sort(first, last, functor); |
---|
240 | } |
---|
241 | |
---|
242 | template <typename Iterator, typename Value, typename Key> |
---|
243 | void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) { |
---|
244 | using namespace _radix_sort_bits; |
---|
245 | RadixSortSelector<Value>::sort(first, last, functor); |
---|
246 | } |
---|
247 | |
---|
248 | template <typename Iterator> |
---|
249 | void radixSort(Iterator first, Iterator last) { |
---|
250 | using namespace _radix_sort_bits; |
---|
251 | typedef typename std::iterator_traits<Iterator>::value_type Value; |
---|
252 | RadixSortSelector<Value>::sort(first, last, Identity<Value>()); |
---|
253 | } |
---|
254 | |
---|
255 | template <typename Value> |
---|
256 | unsigned char valueByte(Value value, int byte) { |
---|
257 | return *((unsigned char *)(&value) + byte); |
---|
258 | } |
---|
259 | |
---|
260 | template <typename Functor, typename Key> |
---|
261 | void counterIntroSort(Key *first, Key *last, Key *target, |
---|
262 | int byte, Functor functor) { |
---|
263 | const int size = |
---|
264 | (unsigned int)std::numeric_limits<unsigned char>::max() + 1; |
---|
265 | int counter[size]; |
---|
266 | for (int i = 0; i < size; ++i) { |
---|
267 | counter[i] = 0; |
---|
268 | } |
---|
269 | Key *it = first; |
---|
270 | while (first != last) { |
---|
271 | ++counter[valueByte(functor(*first), byte)]; |
---|
272 | ++first; |
---|
273 | } |
---|
274 | int prev, num = 0; |
---|
275 | for (int i = 0; i < size; ++i) { |
---|
276 | prev = num; |
---|
277 | num += counter[i]; |
---|
278 | counter[i] = prev; |
---|
279 | } |
---|
280 | while (it != last) { |
---|
281 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
---|
282 | ++it; |
---|
283 | } |
---|
284 | } |
---|
285 | |
---|
286 | template <typename Functor, typename Key> |
---|
287 | void signedCounterIntroSort(Key *first, Key *last, Key *target, |
---|
288 | int byte, Functor functor) { |
---|
289 | const int size = |
---|
290 | (unsigned int)std::numeric_limits<unsigned char>::max() + 1; |
---|
291 | int counter[size]; |
---|
292 | for (int i = 0; i < size; ++i) { |
---|
293 | counter[i] = 0; |
---|
294 | } |
---|
295 | Key *it = first; |
---|
296 | while (first != last) { |
---|
297 | counter[valueByte(functor(*first), byte)]++; |
---|
298 | ++first; |
---|
299 | } |
---|
300 | int prev, num = 0; |
---|
301 | for (int i = size / 2; i < size; ++i) { |
---|
302 | prev = num; |
---|
303 | num += counter[i]; |
---|
304 | counter[i] = prev; |
---|
305 | } |
---|
306 | for (int i = 0; i < size / 2; ++i) { |
---|
307 | prev = num; |
---|
308 | num += counter[i]; |
---|
309 | counter[i] = prev; |
---|
310 | } |
---|
311 | while (it != last) { |
---|
312 | target[counter[valueByte(functor(*it), byte)]++] = *it; |
---|
313 | ++it; |
---|
314 | } |
---|
315 | } |
---|
316 | |
---|
317 | |
---|
318 | template <typename Value, typename Iterator, typename Functor> |
---|
319 | void counterSignedSort(Iterator first, Iterator last, Functor functor) { |
---|
320 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
---|
321 | typedef std::allocator<Key> Allocator; |
---|
322 | Allocator allocator; |
---|
323 | |
---|
324 | int length = std::distance(first, last); |
---|
325 | Key* buffer; |
---|
326 | buffer = allocator.allocate(2 * length); |
---|
327 | try { |
---|
328 | bool dir = true; |
---|
329 | std::copy(first, last, buffer); |
---|
330 | for (int i = 0; i < (int)sizeof(Value) - 1; ++i) { |
---|
331 | if (dir) { |
---|
332 | counterIntroSort(buffer, buffer + length, buffer + length, |
---|
333 | i, functor); |
---|
334 | } else { |
---|
335 | counterIntroSort(buffer + length, buffer + 2 * length, buffer, |
---|
336 | i, functor); |
---|
337 | } |
---|
338 | dir = !dir; |
---|
339 | } |
---|
340 | if (dir) { |
---|
341 | signedCounterIntroSort(buffer, buffer + length, buffer + length, |
---|
342 | sizeof(Value) - 1, functor); |
---|
343 | std::copy(buffer + length, buffer + 2 * length, first); |
---|
344 | } else { |
---|
345 | signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer, |
---|
346 | sizeof(Value) - 1, functor); |
---|
347 | std::copy(buffer, buffer + length, first); |
---|
348 | } |
---|
349 | } catch (...) { |
---|
350 | allocator.deallocate(buffer, 2 * length); |
---|
351 | throw; |
---|
352 | } |
---|
353 | allocator.deallocate(buffer, 2 * length); |
---|
354 | } |
---|
355 | |
---|
356 | template <typename Value, typename Iterator, typename Functor> |
---|
357 | void counterUnsignedSort(Iterator first, Iterator last, Functor functor) { |
---|
358 | typedef typename std::iterator_traits<Iterator>::value_type Key; |
---|
359 | typedef std::allocator<Key> Allocator; |
---|
360 | Allocator allocator; |
---|
361 | |
---|
362 | int length = std::distance(first, last); |
---|
363 | Key *buffer; |
---|
364 | buffer = allocator.allocate(2 * length); |
---|
365 | try { |
---|
366 | bool dir = true; |
---|
367 | std::copy(first, last, buffer); |
---|
368 | for (int i = 0; i < sizeof(Value); ++i) { |
---|
369 | if (dir) { |
---|
370 | counterIntroSort(buffer, buffer + length, buffer + length, |
---|
371 | i, functor); |
---|
372 | } else { |
---|
373 | counterIntroSort(buffer + length, buffer + 2 * length, buffer, |
---|
374 | i, functor); |
---|
375 | } |
---|
376 | dir = !dir; |
---|
377 | } |
---|
378 | if (dir) { |
---|
379 | std::copy(buffer, buffer + length, first); |
---|
380 | } else { |
---|
381 | std::copy(buffer + length, buffer + 2 * length, first); |
---|
382 | } |
---|
383 | } catch (...) { |
---|
384 | allocator.deallocate(buffer, 2 * length); |
---|
385 | throw; |
---|
386 | } |
---|
387 | allocator.deallocate(buffer, 2 * length); |
---|
388 | } |
---|
389 | |
---|
390 | namespace _radix_sort_bits { |
---|
391 | |
---|
392 | template <typename Value, |
---|
393 | bool sign = std::numeric_limits<Value>::is_signed > |
---|
394 | struct CounterSortSelector { |
---|
395 | template <typename Iterator, typename Functor> |
---|
396 | static void sort(Iterator first, Iterator last, Functor functor) { |
---|
397 | counterSignedSort<Value>(first, last, functor); |
---|
398 | } |
---|
399 | }; |
---|
400 | |
---|
401 | template <typename Value> |
---|
402 | struct CounterSortSelector<Value, false> { |
---|
403 | template <typename Iterator, typename Functor> |
---|
404 | static void sort(Iterator first, Iterator last, Functor functor) { |
---|
405 | counterUnsignedSort<Value>(first, last, functor); |
---|
406 | } |
---|
407 | }; |
---|
408 | |
---|
409 | } |
---|
410 | |
---|
411 | /// \ingroup auxdat |
---|
412 | /// |
---|
413 | /// \brief Sorts stable the stl compatible range into ascending order. |
---|
414 | /// |
---|
415 | /// The \c counterSort sorts the stl compatible range into ascending order. |
---|
416 | /// The counter sort algorithm can sort the items which mapped to an |
---|
417 | /// integer by the adaptable unary function \c functor and the order |
---|
418 | /// will be ascending by these mapped values. As function specialization |
---|
419 | /// there is possible to use a normal function as the functor object |
---|
420 | /// or if the functor is not given it will use an identity function instead. |
---|
421 | /// |
---|
422 | /// This implemented counter sort use a radix forward sort on the bytes of |
---|
423 | /// the integer. The algorithm can sort the items on a given byte. |
---|
424 | /// First time it counts how many times occurs a byte value in the container. |
---|
425 | /// By the occurence number it is possible to copy the container |
---|
426 | /// in the right order in \c O(n) time. The algorithm sorts the container |
---|
427 | /// by each bytes in forward direction which sorts the container by the |
---|
428 | /// whole value. This way, let be |
---|
429 | /// \c c the maximal capacity and \c n the number of the items in |
---|
430 | /// the container, the time complexity of the algorithm \c O(log(c)*n) |
---|
431 | /// and the additional space complexity is \c O(n). |
---|
432 | /// |
---|
433 | /// This sorting algorithm is stable so the order of two equal element |
---|
434 | /// stay in the same order. |
---|
435 | /// |
---|
436 | /// \param first The begin of the given range. |
---|
437 | /// \param last The end of the given range. |
---|
438 | /// \param functor An adaptible unary function or a normal function which |
---|
439 | /// maps the items to any integer type which can be wheter signed or |
---|
440 | /// unsigned. |
---|
441 | template <typename Iterator, typename Functor> |
---|
442 | void counterSort(Iterator first, Iterator last, Functor functor) { |
---|
443 | using namespace _radix_sort_bits; |
---|
444 | typedef typename Functor::result_type Value; |
---|
445 | CounterSortSelector<Value>::sort(first, last, functor); |
---|
446 | } |
---|
447 | |
---|
448 | template <typename Iterator, typename Value, typename Key> |
---|
449 | void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) { |
---|
450 | using namespace _radix_sort_bits; |
---|
451 | CounterSortSelector<Value>::sort(first, last, functor); |
---|
452 | } |
---|
453 | |
---|
454 | template <typename Iterator, typename Value, typename Key> |
---|
455 | void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) { |
---|
456 | using namespace _radix_sort_bits; |
---|
457 | CounterSortSelector<Value>::sort(first, last, functor); |
---|
458 | } |
---|
459 | |
---|
460 | template <typename Iterator, typename Value, typename Key> |
---|
461 | void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) { |
---|
462 | using namespace _radix_sort_bits; |
---|
463 | CounterSortSelector<Value>::sort(first, last, functor); |
---|
464 | } |
---|
465 | |
---|
466 | template <typename Iterator, typename Value, typename Key> |
---|
467 | void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) { |
---|
468 | using namespace _radix_sort_bits; |
---|
469 | CounterSortSelector<Value>::sort(first, last, functor); |
---|
470 | } |
---|
471 | |
---|
472 | template <typename Iterator> |
---|
473 | void counterSort(Iterator first, Iterator last) { |
---|
474 | using namespace _radix_sort_bits; |
---|
475 | typedef typename std::iterator_traits<Iterator>::value_type Value; |
---|
476 | CounterSortSelector<Value>::sort(first, last, Identity<Value>()); |
---|
477 | } |
---|
478 | |
---|
479 | } |
---|
480 | |
---|
481 | |
---|
482 | |
---|
483 | #endif |
---|