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source: lemon/lemon/radix_sort.h @ 1270:dceba191c00d

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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) 2003-2013
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 RADIX_SORT_H
20#define RADIX_SORT_H
21
22/// \ingroup auxalg
23/// \file
24/// \brief Radix sort
25///
26/// Linear time sorting algorithms
27
28#include <vector>
29#include <limits>
30#include <iterator>
31#include <algorithm>
32
33namespace lemon {
34
35  namespace _radix_sort_bits {
36
37    template <typename Iterator>
38    bool unitRange(Iterator first, Iterator last) {
39      ++first;
40      return first == last;
41    }
42
43    template <typename Value>
44    struct Identity {
45      const Value& operator()(const Value& val) {
46        return val;
47      }
48    };
49
50
51    template <typename Value, typename Iterator, typename Functor>
52    Iterator radixSortPartition(Iterator first, Iterator last,
53                                Functor functor, Value mask) {
54      while (first != last && !(functor(*first) & mask)) {
55        ++first;
56      }
57      if (first == last) {
58        return first;
59      }
60      --last;
61      while (first != last && (functor(*last) & mask)) {
62        --last;
63      }
64      if (first == last) {
65        return first;
66      }
67      std::iter_swap(first, last);
68      ++first;
69      while (true) {
70        while (!(functor(*first) & mask)) {
71          ++first;
72        }
73        --last;
74        while (functor(*last) & mask) {
75          --last;
76        }
77        if (unitRange(last, first)) {
78          return first;
79        }
80        std::iter_swap(first, last);
81        ++first;
82      }
83    }
84
85    template <typename Iterator, typename Functor>
86    Iterator radixSortSignPartition(Iterator first, Iterator last,
87                                    Functor functor) {
88      while (first != last && functor(*first) < 0) {
89        ++first;
90      }
91      if (first == last) {
92        return first;
93      }
94      --last;
95      while (first != last && functor(*last) >= 0) {
96        --last;
97      }
98      if (first == last) {
99        return first;
100      }
101      std::iter_swap(first, last);
102      ++first;
103      while (true) {
104        while (functor(*first) < 0) {
105          ++first;
106        }
107        --last;
108        while (functor(*last) >= 0) {
109          --last;
110        }
111        if (unitRange(last, first)) {
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 && first != last && !unitRange(first, last)) {
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
133      Iterator cut = radixSortSignPartition(first, last, functor);
134
135      Value mask;
136      int max_digit;
137      Iterator it;
138
139      mask = ~0; max_digit = 0;
140      for (it = first; it != cut; ++it) {
141        while ((mask & functor(*it)) != mask) {
142          ++max_digit;
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        while ((mask | functor(*it)) != mask) {
151          ++max_digit;
152          mask <<= 1; 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        while ((mask | functor(*it)) != mask) {
167          ++max_digit;
168          mask <<= 1; mask |= 1;
169        }
170      }
171      radixIntroSort(first, last, functor, 1 << max_digit);
172    }
173
174
175    template <typename Value,
176              bool sign = std::numeric_limits<Value>::is_signed >
177    struct RadixSortSelector {
178      template <typename Iterator, typename Functor>
179      static void sort(Iterator first, Iterator last, Functor functor) {
180        radixSignedSort<Value>(first, last, functor);
181      }
182    };
183
184    template <typename Value>
185    struct RadixSortSelector<Value, false> {
186      template <typename Iterator, typename Functor>
187      static void sort(Iterator first, Iterator last, Functor functor) {
188        radixUnsignedSort<Value>(first, last, functor);
189      }
190    };
191
192  }
193
194  /// \ingroup auxalg
195  ///
196  /// \brief Sorts the STL compatible range into ascending order.
197  ///
198  /// The \c radixSort sorts an STL compatible range into ascending
199  /// order.  The radix sort algorithm can sort items which are mapped
200  /// to integers with an adaptable unary function \c functor and the
201  /// order will be ascending according to these mapped values.
202  ///
203  /// It is also possible to use a normal function instead
204  /// of the functor object. If the functor is not given it will use
205  /// the identity function instead.
206  ///
207  /// This is a special quick sort algorithm where the pivot
208  /// values to split the items are choosen to be 2<sup>k</sup>
209  /// for each \c k.
210  /// Therefore, the time complexity of the algorithm is O(log(c)*n) and
211  /// it uses O(log(c)) additional space, where \c c is the maximal value
212  /// and \c n is the number of the items in the container.
213  ///
214  /// \param first The begin of the given range.
215  /// \param last The end of the given range.
216  /// \param functor An adaptible unary function or a normal function
217  /// which maps the items to any integer type which can be either
218  /// signed or unsigned.
219  ///
220  /// \sa stableRadixSort()
221  template <typename Iterator, typename Functor>
222  void radixSort(Iterator first, Iterator last, Functor functor) {
223    using namespace _radix_sort_bits;
224    typedef typename Functor::result_type Value;
225    RadixSortSelector<Value>::sort(first, last, functor);
226  }
227
228  template <typename Iterator, typename Value, typename Key>
229  void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
230    using namespace _radix_sort_bits;
231    RadixSortSelector<Value>::sort(first, last, functor);
232  }
233
234  template <typename Iterator, typename Value, typename Key>
235  void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
236    using namespace _radix_sort_bits;
237    RadixSortSelector<Value>::sort(first, last, functor);
238  }
239
240  template <typename Iterator, typename Value, typename Key>
241  void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
242    using namespace _radix_sort_bits;
243    RadixSortSelector<Value>::sort(first, last, functor);
244  }
245
246  template <typename Iterator, typename Value, typename Key>
247  void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
248    using namespace _radix_sort_bits;
249    RadixSortSelector<Value>::sort(first, last, functor);
250  }
251
252  template <typename Iterator>
253  void radixSort(Iterator first, Iterator last) {
254    using namespace _radix_sort_bits;
255    typedef typename std::iterator_traits<Iterator>::value_type Value;
256    RadixSortSelector<Value>::sort(first, last, Identity<Value>());
257  }
258
259  namespace _radix_sort_bits {
260
261    template <typename Value>
262    unsigned char valueByte(Value value, int byte) {
263      return value >> (std::numeric_limits<unsigned char>::digits * byte);
264    }
265
266    template <typename Functor, typename Key>
267    void stableRadixIntroSort(Key *first, Key *last, Key *target,
268                              int byte, Functor functor) {
269      const int size =
270        unsigned(std::numeric_limits<unsigned char>::max()) + 1;
271      std::vector<int> counter(size);
272      for (int i = 0; i < size; ++i) {
273        counter[i] = 0;
274      }
275      Key *it = first;
276      while (first != last) {
277        ++counter[valueByte(functor(*first), byte)];
278        ++first;
279      }
280      int prev, num = 0;
281      for (int i = 0; i < size; ++i) {
282        prev = num;
283        num += counter[i];
284        counter[i] = prev;
285      }
286      while (it != last) {
287        target[counter[valueByte(functor(*it), byte)]++] = *it;
288        ++it;
289      }
290    }
291
292    template <typename Functor, typename Key>
293    void signedStableRadixIntroSort(Key *first, Key *last, Key *target,
294                                    int byte, Functor functor) {
295      const int size =
296        unsigned(std::numeric_limits<unsigned char>::max()) + 1;
297      std::vector<int> counter(size);
298      for (int i = 0; i < size; ++i) {
299        counter[i] = 0;
300      }
301      Key *it = first;
302      while (first != last) {
303        counter[valueByte(functor(*first), byte)]++;
304        ++first;
305      }
306      int prev, num = 0;
307      for (int i = size / 2; i < size; ++i) {
308        prev = num;
309        num += counter[i];
310        counter[i] = prev;
311      }
312      for (int i = 0; i < size / 2; ++i) {
313        prev = num;
314        num += counter[i];
315        counter[i] = prev;
316      }
317      while (it != last) {
318        target[counter[valueByte(functor(*it), byte)]++] = *it;
319        ++it;
320      }
321    }
322
323
324    template <typename Value, typename Iterator, typename Functor>
325    void stableRadixSignedSort(Iterator first, Iterator last, Functor functor) {
326      if (first == last) return;
327      typedef typename std::iterator_traits<Iterator>::value_type Key;
328      typedef std::allocator<Key> Allocator;
329      Allocator allocator;
330
331      int length = std::distance(first, last);
332      Key* buffer = allocator.allocate(2 * length);
333      try {
334        bool dir = true;
335        std::copy(first, last, buffer);
336        for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
337          if (dir) {
338            stableRadixIntroSort(buffer, buffer + length, buffer + length,
339                                 i, functor);
340          } else {
341            stableRadixIntroSort(buffer + length, buffer + 2 * length, buffer,
342                                 i, functor);
343          }
344          dir = !dir;
345        }
346        if (dir) {
347          signedStableRadixIntroSort(buffer, buffer + length, buffer + length,
348                                     sizeof(Value) - 1, functor);
349          std::copy(buffer + length, buffer + 2 * length, first);
350        }        else {
351          signedStableRadixIntroSort(buffer + length, buffer + 2 * length,
352                                     buffer, sizeof(Value) - 1, functor);
353          std::copy(buffer, buffer + length, first);
354        }
355      } catch (...) {
356        allocator.deallocate(buffer, 2 * length);
357        throw;
358      }
359      allocator.deallocate(buffer, 2 * length);
360    }
361
362    template <typename Value, typename Iterator, typename Functor>
363    void stableRadixUnsignedSort(Iterator first, Iterator last,
364                                 Functor functor) {
365      if (first == last) return;
366      typedef typename std::iterator_traits<Iterator>::value_type Key;
367      typedef std::allocator<Key> Allocator;
368      Allocator allocator;
369
370      int length = std::distance(first, last);
371      Key *buffer = allocator.allocate(2 * length);
372      try {
373        bool dir = true;
374        std::copy(first, last, buffer);
375        for (int i = 0; i < int(sizeof(Value)); ++i) {
376          if (dir) {
377            stableRadixIntroSort(buffer, buffer + length,
378                                 buffer + length, i, functor);
379          } else {
380            stableRadixIntroSort(buffer + length, buffer + 2 * length,
381                                 buffer, i, functor);
382          }
383          dir = !dir;
384        }
385        if (dir) {
386          std::copy(buffer, buffer + length, first);
387        }        else {
388          std::copy(buffer + length, buffer + 2 * length, first);
389        }
390      } catch (...) {
391        allocator.deallocate(buffer, 2 * length);
392        throw;
393      }
394      allocator.deallocate(buffer, 2 * length);
395    }
396
397
398
399    template <typename Value,
400              bool sign = std::numeric_limits<Value>::is_signed >
401    struct StableRadixSortSelector {
402      template <typename Iterator, typename Functor>
403      static void sort(Iterator first, Iterator last, Functor functor) {
404        stableRadixSignedSort<Value>(first, last, functor);
405      }
406    };
407
408    template <typename Value>
409    struct StableRadixSortSelector<Value, false> {
410      template <typename Iterator, typename Functor>
411      static void sort(Iterator first, Iterator last, Functor functor) {
412        stableRadixUnsignedSort<Value>(first, last, functor);
413      }
414    };
415
416  }
417
418  /// \ingroup auxalg
419  ///
420  /// \brief Sorts the STL compatible range into ascending order in a stable
421  /// way.
422  ///
423  /// This function sorts an STL compatible range into ascending
424  /// order according to an integer mapping in the same as radixSort() does.
425  ///
426  /// This sorting algorithm is stable, i.e. the order of two equal
427  /// elements remains the same after the sorting.
428  ///
429  /// This sort algorithm  use a radix forward sort on the
430  /// bytes of the integer number. The algorithm sorts the items
431  /// byte-by-byte. First, it counts how many times a byte value occurs
432  /// in the container, then it copies the corresponding items to
433  /// another container in asceding order in O(n) time.
434  ///
435  /// The time complexity of the algorithm is O(log(c)*n) and
436  /// it uses O(n) additional space, where \c c is the
437  /// maximal value and \c n is the number of the items in the
438  /// container.
439  ///
440
441  /// \param first The begin of the given range.
442  /// \param last The end of the given range.
443  /// \param functor An adaptible unary function or a normal function
444  /// which maps the items to any integer type which can be either
445  /// signed or unsigned.
446  /// \sa radixSort()
447  template <typename Iterator, typename Functor>
448  void stableRadixSort(Iterator first, Iterator last, Functor functor) {
449    using namespace _radix_sort_bits;
450    typedef typename Functor::result_type Value;
451    StableRadixSortSelector<Value>::sort(first, last, functor);
452  }
453
454  template <typename Iterator, typename Value, typename Key>
455  void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
456    using namespace _radix_sort_bits;
457    StableRadixSortSelector<Value>::sort(first, last, functor);
458  }
459
460  template <typename Iterator, typename Value, typename Key>
461  void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
462    using namespace _radix_sort_bits;
463    StableRadixSortSelector<Value>::sort(first, last, functor);
464  }
465
466  template <typename Iterator, typename Value, typename Key>
467  void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
468    using namespace _radix_sort_bits;
469    StableRadixSortSelector<Value>::sort(first, last, functor);
470  }
471
472  template <typename Iterator, typename Value, typename Key>
473  void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
474    using namespace _radix_sort_bits;
475    StableRadixSortSelector<Value>::sort(first, last, functor);
476  }
477
478  template <typename Iterator>
479  void stableRadixSort(Iterator first, Iterator last) {
480    using namespace _radix_sort_bits;
481    typedef typename std::iterator_traits<Iterator>::value_type Value;
482    StableRadixSortSelector<Value>::sort(first, last, Identity<Value>());
483  }
484
485}
486
487#endif
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