- Gamma distributon random variable.
- Test file for random.h
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2007
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
32 #include <lemon/error.h>
36 namespace _radix_sort_bits {
38 template <typename Value>
40 const Value& operator()(const Value& val) {
47 template <typename Value, typename Iterator, typename Functor>
48 Iterator radixSortPartition(Iterator first, Iterator last,
49 Functor functor, Value mask) {
50 while (first != last && !(functor(*first) & mask)) {
57 while (first != last && (functor(*last) & mask)) {
63 std::iter_swap(first, last);
65 if (!(first < last)) {
69 while (!(functor(*first) & mask)) {
73 while (functor(*last) & mask) {
76 if (!(first < last)) {
79 std::iter_swap(first, last);
84 template <typename Iterator, typename Functor>
85 Iterator radixSortSignPartition(Iterator first, Iterator last,
87 while (first != last && functor(*first) < 0) {
94 while (first != last && functor(*last) >= 0) {
100 std::iter_swap(first, last);
102 if (!(first < last)) {
106 while (functor(*first) < 0) {
110 while (functor(*last) >= 0) {
113 if (!(first < last)) {
116 std::iter_swap(first, last);
121 template <typename Value, typename Iterator, typename Functor>
122 void radixIntroSort(Iterator first, Iterator last,
123 Functor functor, Value mask) {
124 while (mask != 0 && last - first > 1) {
125 Iterator cut = radixSortPartition(first, last, functor, mask);
127 radixIntroSort(first, cut, functor, mask);
132 template <typename Value, typename Iterator, typename Functor>
133 void radixSignedSort(Iterator first, Iterator last, Functor functor) {
134 Iterator cut = radixSortSignPartition(first, last, functor);
140 mask = ~0; max_digit = 0;
141 for (it = first; it != cut; ++it) {
142 while ((mask & functor(*it)) != mask) {
147 radixIntroSort(first, cut, functor, 1 << max_digit);
149 mask = 0; max_digit = 0;
150 for (it = cut; it != last; ++it) {
151 while ((mask | functor(*it)) != mask) {
153 mask <<= 1; mask |= 1;
156 radixIntroSort(cut, last, functor, 1 << max_digit);
159 template <typename Value, typename Iterator, typename Functor>
160 void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
166 for (it = first; it != last; ++it) {
167 while ((mask | functor(*it)) != mask) {
169 mask <<= 1; mask |= 1;
172 radixIntroSort(first, last, functor, 1 << max_digit);
175 namespace _radix_sort_bits {
177 template <typename Value,
178 bool sign = std::numeric_limits<Value>::is_signed >
179 struct RadixSortSelector {
180 template <typename Iterator, typename Functor>
181 static void sort(Iterator first, Iterator last, Functor functor) {
182 radixSignedSort<Value>(first, last, functor);
186 template <typename Value>
187 struct RadixSortSelector<Value, false> {
188 template <typename Iterator, typename Functor>
189 static void sort(Iterator first, Iterator last, Functor functor) {
190 radixUnsignedSort<Value>(first, last, functor);
198 /// \brief Sorts the stl compatible range into ascending order.
200 /// The \c radixSort sorts the stl compatible range into ascending order.
201 /// The radix sort algorithm can sort the items which mapped to an
202 /// integer by the adaptable unary function \c functor and the order
203 /// will be ascending by these mapped values. As function specialization
204 /// there is possible to use a normal function as the functor object
205 /// or if the functor is not given it will use an identity function instead.
207 /// This implemented radix sort is a special quick sort which pivot value
208 /// is choosen to partite the items on the next bit. This way, let be
209 /// \c c the maximal capacity and \c n the number of the items in
210 /// the container, the time complexity of the algorithm
211 /// \f$ O(\log(c)n) \f$ and the additional space complexity is
212 /// \f$ O(\log(c)) \f$.
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 which
217 /// maps the items to any integer type which can be wheter signed or
219 template <typename Iterator, typename Functor>
220 void radixSort(Iterator first, Iterator last, Functor functor) {
221 using namespace _radix_sort_bits;
222 typedef typename Functor::result_type Value;
223 RadixSortSelector<Value>::sort(first, last, functor);
226 template <typename Iterator, typename Value, typename Key>
227 void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
228 using namespace _radix_sort_bits;
229 RadixSortSelector<Value>::sort(first, last, functor);
232 template <typename Iterator, typename Value, typename Key>
233 void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
234 using namespace _radix_sort_bits;
235 RadixSortSelector<Value>::sort(first, last, functor);
238 template <typename Iterator, typename Value, typename Key>
239 void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
240 using namespace _radix_sort_bits;
241 RadixSortSelector<Value>::sort(first, last, functor);
244 template <typename Iterator, typename Value, typename Key>
245 void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
246 using namespace _radix_sort_bits;
247 RadixSortSelector<Value>::sort(first, last, functor);
250 template <typename Iterator>
251 void radixSort(Iterator first, Iterator last) {
252 using namespace _radix_sort_bits;
253 typedef typename std::iterator_traits<Iterator>::value_type Value;
254 RadixSortSelector<Value>::sort(first, last, Identity<Value>());
257 template <typename Value>
258 unsigned char valueByte(Value value, int byte) {
259 return value >> (std::numeric_limits<unsigned char>::digits * byte);
262 template <typename Functor, typename Key>
263 void counterIntroSort(Key *first, Key *last, Key *target,
264 int byte, Functor functor) {
266 unsigned(std::numeric_limits<unsigned char>::max()) + 1;
267 std::vector<int> counter(size);
268 for (int i = 0; i < size; ++i) {
272 while (first != last) {
273 ++counter[valueByte(functor(*first), byte)];
277 for (int i = 0; i < size; ++i) {
283 target[counter[valueByte(functor(*it), byte)]++] = *it;
288 template <typename Functor, typename Key>
289 void signedCounterIntroSort(Key *first, Key *last, Key *target,
290 int byte, Functor functor) {
292 unsigned(std::numeric_limits<unsigned char>::max()) + 1;
293 std::vector<int> counter(size);
294 for (int i = 0; i < size; ++i) {
298 while (first != last) {
299 counter[valueByte(functor(*first), byte)]++;
303 for (int i = size / 2; i < size; ++i) {
308 for (int i = 0; i < size / 2; ++i) {
314 target[counter[valueByte(functor(*it), byte)]++] = *it;
320 template <typename Value, typename Iterator, typename Functor>
321 void counterSignedSort(Iterator first, Iterator last, Functor functor) {
322 if (first == last) return;
323 typedef typename std::iterator_traits<Iterator>::value_type Key;
324 typedef std::allocator<Key> Allocator;
327 int length = std::distance(first, last);
328 Key* buffer = allocator.allocate(2 * length);
331 std::copy(first, last, buffer);
332 for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
334 counterIntroSort(buffer, buffer + length, buffer + length,
337 counterIntroSort(buffer + length, buffer + 2 * length, buffer,
343 signedCounterIntroSort(buffer, buffer + length, buffer + length,
344 sizeof(Value) - 1, functor);
345 std::copy(buffer + length, buffer + 2 * length, first);
347 signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer,
348 sizeof(Value) - 1, functor);
349 std::copy(buffer, buffer + length, first);
352 allocator.deallocate(buffer, 2 * length);
355 allocator.deallocate(buffer, 2 * length);
358 template <typename Value, typename Iterator, typename Functor>
359 void counterUnsignedSort(Iterator first, Iterator last, Functor functor) {
360 if (first == last) return;
361 typedef typename std::iterator_traits<Iterator>::value_type Key;
362 typedef std::allocator<Key> Allocator;
365 int length = std::distance(first, last);
366 Key *buffer = allocator.allocate(2 * length);
369 std::copy(first, last, buffer);
370 for (int i = 0; i < int(sizeof(Value)); ++i) {
372 counterIntroSort(buffer, buffer + length,
373 buffer + length, i, functor);
375 counterIntroSort(buffer + length, buffer + 2 * length,
381 std::copy(buffer, buffer + length, first);
383 std::copy(buffer + length, buffer + 2 * length, first);
386 allocator.deallocate(buffer, 2 * length);
389 allocator.deallocate(buffer, 2 * length);
392 namespace _radix_sort_bits {
394 template <typename Value,
395 bool sign = std::numeric_limits<Value>::is_signed >
396 struct CounterSortSelector {
397 template <typename Iterator, typename Functor>
398 static void sort(Iterator first, Iterator last, Functor functor) {
399 counterSignedSort<Value>(first, last, functor);
403 template <typename Value>
404 struct CounterSortSelector<Value, false> {
405 template <typename Iterator, typename Functor>
406 static void sort(Iterator first, Iterator last, Functor functor) {
407 counterUnsignedSort<Value>(first, last, functor);
415 /// \brief Sorts stable the stl compatible range into ascending order.
417 /// The \c counterSort sorts the stl compatible range into ascending order.
418 /// The counter sort algorithm can sort the items which mapped to an
419 /// integer by the adaptable unary function \c functor and the order
420 /// will be ascending by these mapped values. As function specialization
421 /// there is possible to use a normal function as the functor object
422 /// or if the functor is not given it will use an identity function instead.
424 /// This implemented counter sort use a radix forward sort on the bytes of
425 /// the integer. The algorithm can sort the items on a given byte.
426 /// First time it counts how many times occurs a byte value in the container.
427 /// By the occurence number it is possible to copy the container
428 /// in the right order in \c O(n) time. The algorithm sorts the container
429 /// by each bytes in forward direction which sorts the container by the
430 /// whole value. This way, let be \c c the maximal capacity of the integer
431 /// type and \c n the number of the items in
432 /// the container, the time complexity of the algorithm \f$ O(\log(c)n) \f$
433 /// and the additional space complexity is \f$ O(n) \f$.
435 /// This sorting algorithm is stable so the order of two equal element
436 /// stay in the same order.
438 /// \param first The begin of the given range.
439 /// \param last The end of the given range.
440 /// \param functor An adaptible unary function or a normal function which
441 /// maps the items to any integer type which can be wheter signed or
443 template <typename Iterator, typename Functor>
444 void counterSort(Iterator first, Iterator last, Functor functor) {
445 using namespace _radix_sort_bits;
446 typedef typename Functor::result_type Value;
447 CounterSortSelector<Value>::sort(first, last, functor);
450 template <typename Iterator, typename Value, typename Key>
451 void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {
452 using namespace _radix_sort_bits;
453 CounterSortSelector<Value>::sort(first, last, functor);
456 template <typename Iterator, typename Value, typename Key>
457 void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
458 using namespace _radix_sort_bits;
459 CounterSortSelector<Value>::sort(first, last, functor);
462 template <typename Iterator, typename Value, typename Key>
463 void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
464 using namespace _radix_sort_bits;
465 CounterSortSelector<Value>::sort(first, last, functor);
468 template <typename Iterator, typename Value, typename Key>
469 void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
470 using namespace _radix_sort_bits;
471 CounterSortSelector<Value>::sort(first, last, functor);
474 template <typename Iterator>
475 void counterSort(Iterator first, Iterator last) {
476 using namespace _radix_sort_bits;
477 typedef typename std::iterator_traits<Iterator>::value_type Value;
478 CounterSortSelector<Value>::sort(first, last, Identity<Value>());