1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/radix_sort.h Fri Oct 17 23:55:18 2008 +0200
1.3 @@ -0,0 +1,484 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2008
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef RADIX_SORT_H
1.23 +#define RADIX_SORT_H
1.24 +
1.25 +/// \ingroup auxalg
1.26 +/// \file
1.27 +/// \brief Radix sort
1.28 +///
1.29 +/// Linear time sorting algorithms
1.30 +
1.31 +#include <vector>
1.32 +#include <limits>
1.33 +#include <iterator>
1.34 +#include <algorithm>
1.35 +
1.36 +namespace lemon {
1.37 +
1.38 + namespace _radix_sort_bits {
1.39 +
1.40 + template <typename Value>
1.41 + struct Identity {
1.42 + const Value& operator()(const Value& val) {
1.43 + return val;
1.44 + }
1.45 + };
1.46 +
1.47 +
1.48 + template <typename Value, typename Iterator, typename Functor>
1.49 + Iterator radixSortPartition(Iterator first, Iterator last,
1.50 + Functor functor, Value mask) {
1.51 + while (first != last && !(functor(*first) & mask)) {
1.52 + ++first;
1.53 + }
1.54 + if (first == last) {
1.55 + return first;
1.56 + }
1.57 + --last;
1.58 + while (first != last && (functor(*last) & mask)) {
1.59 + --last;
1.60 + }
1.61 + if (first == last) {
1.62 + return first;
1.63 + }
1.64 + std::iter_swap(first, last);
1.65 + ++first;
1.66 + if (!(first < last)) {
1.67 + return first;
1.68 + }
1.69 + while (true) {
1.70 + while (!(functor(*first) & mask)) {
1.71 + ++first;
1.72 + }
1.73 + --last;
1.74 + while (functor(*last) & mask) {
1.75 + --last;
1.76 + }
1.77 + if (!(first < last)) {
1.78 + return first;
1.79 + }
1.80 + std::iter_swap(first, last);
1.81 + ++first;
1.82 + }
1.83 + }
1.84 +
1.85 + template <typename Iterator, typename Functor>
1.86 + Iterator radixSortSignPartition(Iterator first, Iterator last,
1.87 + Functor functor) {
1.88 + while (first != last && functor(*first) < 0) {
1.89 + ++first;
1.90 + }
1.91 + if (first == last) {
1.92 + return first;
1.93 + }
1.94 + --last;
1.95 + while (first != last && functor(*last) >= 0) {
1.96 + --last;
1.97 + }
1.98 + if (first == last) {
1.99 + return first;
1.100 + }
1.101 + std::iter_swap(first, last);
1.102 + ++first;
1.103 + if (!(first < last)) {
1.104 + return first;
1.105 + }
1.106 + while (true) {
1.107 + while (functor(*first) < 0) {
1.108 + ++first;
1.109 + }
1.110 + --last;
1.111 + while (functor(*last) >= 0) {
1.112 + --last;
1.113 + }
1.114 + if (!(first < last)) {
1.115 + return first;
1.116 + }
1.117 + std::iter_swap(first, last);
1.118 + ++first;
1.119 + }
1.120 + }
1.121 +
1.122 + template <typename Value, typename Iterator, typename Functor>
1.123 + void radixIntroSort(Iterator first, Iterator last,
1.124 + Functor functor, Value mask) {
1.125 + while (mask != 0 && last - first > 1) {
1.126 + Iterator cut = radixSortPartition(first, last, functor, mask);
1.127 + mask >>= 1;
1.128 + radixIntroSort(first, cut, functor, mask);
1.129 + first = cut;
1.130 + }
1.131 + }
1.132 +
1.133 + template <typename Value, typename Iterator, typename Functor>
1.134 + void radixSignedSort(Iterator first, Iterator last, Functor functor) {
1.135 +
1.136 + Iterator cut = radixSortSignPartition(first, last, functor);
1.137 +
1.138 + Value mask;
1.139 + int max_digit;
1.140 + Iterator it;
1.141 +
1.142 + mask = ~0; max_digit = 0;
1.143 + for (it = first; it != cut; ++it) {
1.144 + while ((mask & functor(*it)) != mask) {
1.145 + ++max_digit;
1.146 + mask <<= 1;
1.147 + }
1.148 + }
1.149 + radixIntroSort(first, cut, functor, 1 << max_digit);
1.150 +
1.151 + mask = 0; max_digit = 0;
1.152 + for (it = cut; it != last; ++it) {
1.153 + while ((mask | functor(*it)) != mask) {
1.154 + ++max_digit;
1.155 + mask <<= 1; mask |= 1;
1.156 + }
1.157 + }
1.158 + radixIntroSort(cut, last, functor, 1 << max_digit);
1.159 + }
1.160 +
1.161 + template <typename Value, typename Iterator, typename Functor>
1.162 + void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
1.163 +
1.164 + Value mask = 0;
1.165 + int max_digit = 0;
1.166 +
1.167 + Iterator it;
1.168 + for (it = first; it != last; ++it) {
1.169 + while ((mask | functor(*it)) != mask) {
1.170 + ++max_digit;
1.171 + mask <<= 1; mask |= 1;
1.172 + }
1.173 + }
1.174 + radixIntroSort(first, last, functor, 1 << max_digit);
1.175 + }
1.176 +
1.177 +
1.178 + template <typename Value,
1.179 + bool sign = std::numeric_limits<Value>::is_signed >
1.180 + struct RadixSortSelector {
1.181 + template <typename Iterator, typename Functor>
1.182 + static void sort(Iterator first, Iterator last, Functor functor) {
1.183 + radixSignedSort<Value>(first, last, functor);
1.184 + }
1.185 + };
1.186 +
1.187 + template <typename Value>
1.188 + struct RadixSortSelector<Value, false> {
1.189 + template <typename Iterator, typename Functor>
1.190 + static void sort(Iterator first, Iterator last, Functor functor) {
1.191 + radixUnsignedSort<Value>(first, last, functor);
1.192 + }
1.193 + };
1.194 +
1.195 + }
1.196 +
1.197 + /// \ingroup auxalg
1.198 + ///
1.199 + /// \brief Sorts the STL compatible range into ascending order.
1.200 + ///
1.201 + /// The \c radixSort sorts the STL compatible range into ascending
1.202 + /// order. The radix sort algorithm can sort the items which mapped
1.203 + /// to an integer with an adaptable unary function \c functor and the
1.204 + /// order will be ascending by these mapped values. As function
1.205 + /// specialization it is possible to use a normal function instead
1.206 + /// of the functor object or if the functor is not given it will use
1.207 + /// an identity function instead.
1.208 + ///
1.209 + /// This implemented radix sort is a special quick sort which pivot
1.210 + /// value is choosen to partite the items on the next
1.211 + /// bit. Therefore, let be \c c the maximal capacity and \c n the
1.212 + /// number of the items in the container, the time complexity of the
1.213 + /// algorithm is \f$ O(\log(c)n) \f$ and the additional space
1.214 + /// complexity is \f$ O(\log(c)) \f$.
1.215 + ///
1.216 + /// \param first The begin of the given range.
1.217 + /// \param last The end of the given range.
1.218 + /// \param functor An adaptible unary function or a normal function
1.219 + /// which maps the items to any integer type which can be either
1.220 + /// signed or unsigned.
1.221 + template <typename Iterator, typename Functor>
1.222 + void radixSort(Iterator first, Iterator last, Functor functor) {
1.223 + using namespace _radix_sort_bits;
1.224 + typedef typename Functor::result_type Value;
1.225 + RadixSortSelector<Value>::sort(first, last, functor);
1.226 + }
1.227 +
1.228 + template <typename Iterator, typename Value, typename Key>
1.229 + void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
1.230 + using namespace _radix_sort_bits;
1.231 + RadixSortSelector<Value>::sort(first, last, functor);
1.232 + }
1.233 +
1.234 + template <typename Iterator, typename Value, typename Key>
1.235 + void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
1.236 + using namespace _radix_sort_bits;
1.237 + RadixSortSelector<Value>::sort(first, last, functor);
1.238 + }
1.239 +
1.240 + template <typename Iterator, typename Value, typename Key>
1.241 + void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
1.242 + using namespace _radix_sort_bits;
1.243 + RadixSortSelector<Value>::sort(first, last, functor);
1.244 + }
1.245 +
1.246 + template <typename Iterator, typename Value, typename Key>
1.247 + void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
1.248 + using namespace _radix_sort_bits;
1.249 + RadixSortSelector<Value>::sort(first, last, functor);
1.250 + }
1.251 +
1.252 + template <typename Iterator>
1.253 + void radixSort(Iterator first, Iterator last) {
1.254 + using namespace _radix_sort_bits;
1.255 + typedef typename std::iterator_traits<Iterator>::value_type Value;
1.256 + RadixSortSelector<Value>::sort(first, last, Identity<Value>());
1.257 + }
1.258 +
1.259 + namespace _radix_sort_bits {
1.260 +
1.261 + template <typename Value>
1.262 + unsigned char valueByte(Value value, int byte) {
1.263 + return value >> (std::numeric_limits<unsigned char>::digits * byte);
1.264 + }
1.265 +
1.266 + template <typename Functor, typename Key>
1.267 + void counterIntroSort(Key *first, Key *last, Key *target,
1.268 + int byte, Functor functor) {
1.269 + const int size =
1.270 + unsigned(std::numeric_limits<unsigned char>::max()) + 1;
1.271 + std::vector<int> counter(size);
1.272 + for (int i = 0; i < size; ++i) {
1.273 + counter[i] = 0;
1.274 + }
1.275 + Key *it = first;
1.276 + while (first != last) {
1.277 + ++counter[valueByte(functor(*first), byte)];
1.278 + ++first;
1.279 + }
1.280 + int prev, num = 0;
1.281 + for (int i = 0; i < size; ++i) {
1.282 + prev = num;
1.283 + num += counter[i];
1.284 + counter[i] = prev;
1.285 + }
1.286 + while (it != last) {
1.287 + target[counter[valueByte(functor(*it), byte)]++] = *it;
1.288 + ++it;
1.289 + }
1.290 + }
1.291 +
1.292 + template <typename Functor, typename Key>
1.293 + void signedCounterIntroSort(Key *first, Key *last, Key *target,
1.294 + int byte, Functor functor) {
1.295 + const int size =
1.296 + unsigned(std::numeric_limits<unsigned char>::max()) + 1;
1.297 + std::vector<int> counter(size);
1.298 + for (int i = 0; i < size; ++i) {
1.299 + counter[i] = 0;
1.300 + }
1.301 + Key *it = first;
1.302 + while (first != last) {
1.303 + counter[valueByte(functor(*first), byte)]++;
1.304 + ++first;
1.305 + }
1.306 + int prev, num = 0;
1.307 + for (int i = size / 2; i < size; ++i) {
1.308 + prev = num;
1.309 + num += counter[i];
1.310 + counter[i] = prev;
1.311 + }
1.312 + for (int i = 0; i < size / 2; ++i) {
1.313 + prev = num;
1.314 + num += counter[i];
1.315 + counter[i] = prev;
1.316 + }
1.317 + while (it != last) {
1.318 + target[counter[valueByte(functor(*it), byte)]++] = *it;
1.319 + ++it;
1.320 + }
1.321 + }
1.322 +
1.323 +
1.324 + template <typename Value, typename Iterator, typename Functor>
1.325 + void counterSignedSort(Iterator first, Iterator last, Functor functor) {
1.326 + if (first == last) return;
1.327 + typedef typename std::iterator_traits<Iterator>::value_type Key;
1.328 + typedef std::allocator<Key> Allocator;
1.329 + Allocator allocator;
1.330 +
1.331 + int length = std::distance(first, last);
1.332 + Key* buffer = allocator.allocate(2 * length);
1.333 + try {
1.334 + bool dir = true;
1.335 + std::copy(first, last, buffer);
1.336 + for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
1.337 + if (dir) {
1.338 + counterIntroSort(buffer, buffer + length, buffer + length,
1.339 + i, functor);
1.340 + } else {
1.341 + counterIntroSort(buffer + length, buffer + 2 * length, buffer,
1.342 + i, functor);
1.343 + }
1.344 + dir = !dir;
1.345 + }
1.346 + if (dir) {
1.347 + signedCounterIntroSort(buffer, buffer + length, buffer + length,
1.348 + sizeof(Value) - 1, functor);
1.349 + std::copy(buffer + length, buffer + 2 * length, first);
1.350 + } else {
1.351 + signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer,
1.352 + sizeof(Value) - 1, functor);
1.353 + std::copy(buffer, buffer + length, first);
1.354 + }
1.355 + } catch (...) {
1.356 + allocator.deallocate(buffer, 2 * length);
1.357 + throw;
1.358 + }
1.359 + allocator.deallocate(buffer, 2 * length);
1.360 + }
1.361 +
1.362 + template <typename Value, typename Iterator, typename Functor>
1.363 + void counterUnsignedSort(Iterator first, Iterator last, Functor functor) {
1.364 + if (first == last) return;
1.365 + typedef typename std::iterator_traits<Iterator>::value_type Key;
1.366 + typedef std::allocator<Key> Allocator;
1.367 + Allocator allocator;
1.368 +
1.369 + int length = std::distance(first, last);
1.370 + Key *buffer = allocator.allocate(2 * length);
1.371 + try {
1.372 + bool dir = true;
1.373 + std::copy(first, last, buffer);
1.374 + for (int i = 0; i < int(sizeof(Value)); ++i) {
1.375 + if (dir) {
1.376 + counterIntroSort(buffer, buffer + length,
1.377 + buffer + length, i, functor);
1.378 + } else {
1.379 + counterIntroSort(buffer + length, buffer + 2 * length,
1.380 + buffer, i, functor);
1.381 + }
1.382 + dir = !dir;
1.383 + }
1.384 + if (dir) {
1.385 + std::copy(buffer, buffer + length, first);
1.386 + } else {
1.387 + std::copy(buffer + length, buffer + 2 * length, first);
1.388 + }
1.389 + } catch (...) {
1.390 + allocator.deallocate(buffer, 2 * length);
1.391 + throw;
1.392 + }
1.393 + allocator.deallocate(buffer, 2 * length);
1.394 + }
1.395 +
1.396 +
1.397 +
1.398 + template <typename Value,
1.399 + bool sign = std::numeric_limits<Value>::is_signed >
1.400 + struct CounterSortSelector {
1.401 + template <typename Iterator, typename Functor>
1.402 + static void sort(Iterator first, Iterator last, Functor functor) {
1.403 + counterSignedSort<Value>(first, last, functor);
1.404 + }
1.405 + };
1.406 +
1.407 + template <typename Value>
1.408 + struct CounterSortSelector<Value, false> {
1.409 + template <typename Iterator, typename Functor>
1.410 + static void sort(Iterator first, Iterator last, Functor functor) {
1.411 + counterUnsignedSort<Value>(first, last, functor);
1.412 + }
1.413 + };
1.414 +
1.415 + }
1.416 +
1.417 + /// \ingroup auxalg
1.418 + ///
1.419 + /// \brief Sorts stable the STL compatible range into ascending order.
1.420 + ///
1.421 + /// The \c counterSort sorts the STL compatible range into ascending
1.422 + /// order. The counter sort algorithm can sort the items which
1.423 + /// mapped to an integer with an adaptable unary function \c functor
1.424 + /// and the order will be ascending by these mapped values. As
1.425 + /// function specialization it is possible to use a normal function
1.426 + /// instead of the functor object or if the functor is not given it
1.427 + /// will use an identity function instead.
1.428 + ///
1.429 + /// The implemented counter sort use a radix forward sort on the
1.430 + /// bytes of the integer number. The algorithm sorts the items
1.431 + /// byte-by-byte, first it counts how many times occurs a byte value
1.432 + /// in the containerm, and with the occurence number the container
1.433 + /// can be copied to an other in asceding order in \c O(n) time.
1.434 + /// Let be \c c the maximal capacity of the integer type and \c n
1.435 + /// the number of the items in the container, the time complexity of
1.436 + /// the algorithm is \f$ O(\log(c)n) \f$ and the additional space
1.437 + /// complexity is \f$ O(n) \f$.
1.438 + ///
1.439 + /// The sorting algorithm is stable, i.e. the order of two equal
1.440 + /// element remains the same.
1.441 + ///
1.442 + /// \param first The begin of the given range.
1.443 + /// \param last The end of the given range.
1.444 + /// \param functor An adaptible unary function or a normal function
1.445 + /// which maps the items to any integer type which can be either
1.446 + /// signed or unsigned.
1.447 + template <typename Iterator, typename Functor>
1.448 + void counterSort(Iterator first, Iterator last, Functor functor) {
1.449 + using namespace _radix_sort_bits;
1.450 + typedef typename Functor::result_type Value;
1.451 + CounterSortSelector<Value>::sort(first, last, functor);
1.452 + }
1.453 +
1.454 + template <typename Iterator, typename Value, typename Key>
1.455 + void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {
1.456 + using namespace _radix_sort_bits;
1.457 + CounterSortSelector<Value>::sort(first, last, functor);
1.458 + }
1.459 +
1.460 + template <typename Iterator, typename Value, typename Key>
1.461 + void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
1.462 + using namespace _radix_sort_bits;
1.463 + CounterSortSelector<Value>::sort(first, last, functor);
1.464 + }
1.465 +
1.466 + template <typename Iterator, typename Value, typename Key>
1.467 + void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
1.468 + using namespace _radix_sort_bits;
1.469 + CounterSortSelector<Value>::sort(first, last, functor);
1.470 + }
1.471 +
1.472 + template <typename Iterator, typename Value, typename Key>
1.473 + void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
1.474 + using namespace _radix_sort_bits;
1.475 + CounterSortSelector<Value>::sort(first, last, functor);
1.476 + }
1.477 +
1.478 + template <typename Iterator>
1.479 + void counterSort(Iterator first, Iterator last) {
1.480 + using namespace _radix_sort_bits;
1.481 + typedef typename std::iterator_traits<Iterator>::value_type Value;
1.482 + CounterSortSelector<Value>::sort(first, last, Identity<Value>());
1.483 + }
1.484 +
1.485 +}
1.486 +
1.487 +#endif