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+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2013
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef RADIX_SORT_H
+#define RADIX_SORT_H
+
+/// \ingroup auxalg
+/// \file
+/// \brief Radix sort
+///
+/// Linear time sorting algorithms
+
+#include <vector>
+#include <limits>
+#include <iterator>
+#include <algorithm>
+
+namespace lemon {
+
+ namespace _radix_sort_bits {
+
+ template <typename Iterator>
+ bool unitRange(Iterator first, Iterator last) {
+ ++first;
+ return first == last;
+ }
+
+ template <typename Value>
+ struct Identity {
+ const Value& operator()(const Value& val) {
+ return val;
+ }
+ };
+
+
+ template <typename Value, typename Iterator, typename Functor>
+ Iterator radixSortPartition(Iterator first, Iterator last,
+ Functor functor, Value mask) {
+ while (first != last && !(functor(*first) & mask)) {
+ ++first;
+ }
+ if (first == last) {
+ return first;
+ }
+ --last;
+ while (first != last && (functor(*last) & mask)) {
+ --last;
+ }
+ if (first == last) {
+ return first;
+ }
+ std::iter_swap(first, last);
+ ++first;
+ while (true) {
+ while (!(functor(*first) & mask)) {
+ ++first;
+ }
+ --last;
+ while (functor(*last) & mask) {
+ --last;
+ }
+ if (unitRange(last, first)) {
+ return first;
+ }
+ std::iter_swap(first, last);
+ ++first;
+ }
+ }
+
+ template <typename Iterator, typename Functor>
+ Iterator radixSortSignPartition(Iterator first, Iterator last,
+ Functor functor) {
+ while (first != last && functor(*first) < 0) {
+ ++first;
+ }
+ if (first == last) {
+ return first;
+ }
+ --last;
+ while (first != last && functor(*last) >= 0) {
+ --last;
+ }
+ if (first == last) {
+ return first;
+ }
+ std::iter_swap(first, last);
+ ++first;
+ while (true) {
+ while (functor(*first) < 0) {
+ ++first;
+ }
+ --last;
+ while (functor(*last) >= 0) {
+ --last;
+ }
+ if (unitRange(last, first)) {
+ return first;
+ }
+ std::iter_swap(first, last);
+ ++first;
+ }
+ }
+
+ template <typename Value, typename Iterator, typename Functor>
+ void radixIntroSort(Iterator first, Iterator last,
+ Functor functor, Value mask) {
+ while (mask != 0 && first != last && !unitRange(first, last)) {
+ Iterator cut = radixSortPartition(first, last, functor, mask);
+ mask >>= 1;
+ radixIntroSort(first, cut, functor, mask);
+ first = cut;
+ }
+ }
+
+ template <typename Value, typename Iterator, typename Functor>
+ void radixSignedSort(Iterator first, Iterator last, Functor functor) {
+
+ Iterator cut = radixSortSignPartition(first, last, functor);
+
+ Value mask;
+ int max_digit;
+ Iterator it;
+
+ mask = ~0; max_digit = 0;
+ for (it = first; it != cut; ++it) {
+ while ((mask & functor(*it)) != mask) {
+ ++max_digit;
+ mask <<= 1;
+ }
+ }
+ radixIntroSort(first, cut, functor, 1 << max_digit);
+
+ mask = 0; max_digit = 0;
+ for (it = cut; it != last; ++it) {
+ while ((mask | functor(*it)) != mask) {
+ ++max_digit;
+ mask <<= 1; mask |= 1;
+ }
+ }
+ radixIntroSort(cut, last, functor, 1 << max_digit);
+ }
+
+ template <typename Value, typename Iterator, typename Functor>
+ void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
+
+ Value mask = 0;
+ int max_digit = 0;
+
+ Iterator it;
+ for (it = first; it != last; ++it) {
+ while ((mask | functor(*it)) != mask) {
+ ++max_digit;
+ mask <<= 1; mask |= 1;
+ }
+ }
+ radixIntroSort(first, last, functor, 1 << max_digit);
+ }
+
+
+ template <typename Value,
+ bool sign = std::numeric_limits<Value>::is_signed >
+ struct RadixSortSelector {
+ template <typename Iterator, typename Functor>
+ static void sort(Iterator first, Iterator last, Functor functor) {
+ radixSignedSort<Value>(first, last, functor);
+ }
+ };
+
+ template <typename Value>
+ struct RadixSortSelector<Value, false> {
+ template <typename Iterator, typename Functor>
+ static void sort(Iterator first, Iterator last, Functor functor) {
+ radixUnsignedSort<Value>(first, last, functor);
+ }
+ };
+
+ }
+
+ /// \ingroup auxalg
+ ///
+ /// \brief Sorts the STL compatible range into ascending order.
+ ///
+ /// The \c radixSort sorts an STL compatible range into ascending
+ /// order. The radix sort algorithm can sort items which are mapped
+ /// to integers with an adaptable unary function \c functor and the
+ /// order will be ascending according to these mapped values.
+ ///
+ /// It is also possible to use a normal function instead
+ /// of the functor object. If the functor is not given it will use
+ /// the identity function instead.
+ ///
+ /// This is a special quick sort algorithm where the pivot
+ /// values to split the items are choosen to be 2<sup>k</sup>
+ /// for each \c k.
+ /// Therefore, the time complexity of the algorithm is O(log(c)*n) and
+ /// it uses O(log(c)) additional space, where \c c is the maximal value
+ /// and \c n is the number of the items in the container.
+ ///
+ /// \param first The begin of the given range.
+ /// \param last The end of the given range.
+ /// \param functor An adaptible unary function or a normal function
+ /// which maps the items to any integer type which can be either
+ /// signed or unsigned.
+ ///
+ /// \sa stableRadixSort()
+ template <typename Iterator, typename Functor>
+ void radixSort(Iterator first, Iterator last, Functor functor) {
+ using namespace _radix_sort_bits;
+ typedef typename Functor::result_type Value;
+ RadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
+ using namespace _radix_sort_bits;
+ RadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
+ using namespace _radix_sort_bits;
+ RadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
+ using namespace _radix_sort_bits;
+ RadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
+ using namespace _radix_sort_bits;
+ RadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator>
+ void radixSort(Iterator first, Iterator last) {
+ using namespace _radix_sort_bits;
+ typedef typename std::iterator_traits<Iterator>::value_type Value;
+ RadixSortSelector<Value>::sort(first, last, Identity<Value>());
+ }
+
+ namespace _radix_sort_bits {
+
+ template <typename Value>
+ unsigned char valueByte(Value value, int byte) {
+ return value >> (std::numeric_limits<unsigned char>::digits * byte);
+ }
+
+ template <typename Functor, typename Key>
+ void stableRadixIntroSort(Key *first, Key *last, Key *target,
+ int byte, Functor functor) {
+ const int size =
+ unsigned(std::numeric_limits<unsigned char>::max()) + 1;
+ std::vector<int> counter(size);
+ for (int i = 0; i < size; ++i) {
+ counter[i] = 0;
+ }
+ Key *it = first;
+ while (first != last) {
+ ++counter[valueByte(functor(*first), byte)];
+ ++first;
+ }
+ int prev, num = 0;
+ for (int i = 0; i < size; ++i) {
+ prev = num;
+ num += counter[i];
+ counter[i] = prev;
+ }
+ while (it != last) {
+ target[counter[valueByte(functor(*it), byte)]++] = *it;
+ ++it;
+ }
+ }
+
+ template <typename Functor, typename Key>
+ void signedStableRadixIntroSort(Key *first, Key *last, Key *target,
+ int byte, Functor functor) {
+ const int size =
+ unsigned(std::numeric_limits<unsigned char>::max()) + 1;
+ std::vector<int> counter(size);
+ for (int i = 0; i < size; ++i) {
+ counter[i] = 0;
+ }
+ Key *it = first;
+ while (first != last) {
+ counter[valueByte(functor(*first), byte)]++;
+ ++first;
+ }
+ int prev, num = 0;
+ for (int i = size / 2; i < size; ++i) {
+ prev = num;
+ num += counter[i];
+ counter[i] = prev;
+ }
+ for (int i = 0; i < size / 2; ++i) {
+ prev = num;
+ num += counter[i];
+ counter[i] = prev;
+ }
+ while (it != last) {
+ target[counter[valueByte(functor(*it), byte)]++] = *it;
+ ++it;
+ }
+ }
+
+
+ template <typename Value, typename Iterator, typename Functor>
+ void stableRadixSignedSort(Iterator first, Iterator last, Functor functor) {
+ if (first == last) return;
+ typedef typename std::iterator_traits<Iterator>::value_type Key;
+ typedef std::allocator<Key> Allocator;
+ Allocator allocator;
+
+ int length = std::distance(first, last);
+ Key* buffer = allocator.allocate(2 * length);
+ try {
+ bool dir = true;
+ std::copy(first, last, buffer);
+ for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
+ if (dir) {
+ stableRadixIntroSort(buffer, buffer + length, buffer + length,
+ i, functor);
+ } else {
+ stableRadixIntroSort(buffer + length, buffer + 2 * length, buffer,
+ i, functor);
+ }
+ dir = !dir;
+ }
+ if (dir) {
+ signedStableRadixIntroSort(buffer, buffer + length, buffer + length,
+ sizeof(Value) - 1, functor);
+ std::copy(buffer + length, buffer + 2 * length, first);
+ } else {
+ signedStableRadixIntroSort(buffer + length, buffer + 2 * length,
+ buffer, sizeof(Value) - 1, functor);
+ std::copy(buffer, buffer + length, first);
+ }
+ } catch (...) {
+ allocator.deallocate(buffer, 2 * length);
+ throw;
+ }
+ allocator.deallocate(buffer, 2 * length);
+ }
+
+ template <typename Value, typename Iterator, typename Functor>
+ void stableRadixUnsignedSort(Iterator first, Iterator last,
+ Functor functor) {
+ if (first == last) return;
+ typedef typename std::iterator_traits<Iterator>::value_type Key;
+ typedef std::allocator<Key> Allocator;
+ Allocator allocator;
+
+ int length = std::distance(first, last);
+ Key *buffer = allocator.allocate(2 * length);
+ try {
+ bool dir = true;
+ std::copy(first, last, buffer);
+ for (int i = 0; i < int(sizeof(Value)); ++i) {
+ if (dir) {
+ stableRadixIntroSort(buffer, buffer + length,
+ buffer + length, i, functor);
+ } else {
+ stableRadixIntroSort(buffer + length, buffer + 2 * length,
+ buffer, i, functor);
+ }
+ dir = !dir;
+ }
+ if (dir) {
+ std::copy(buffer, buffer + length, first);
+ } else {
+ std::copy(buffer + length, buffer + 2 * length, first);
+ }
+ } catch (...) {
+ allocator.deallocate(buffer, 2 * length);
+ throw;
+ }
+ allocator.deallocate(buffer, 2 * length);
+ }
+
+
+
+ template <typename Value,
+ bool sign = std::numeric_limits<Value>::is_signed >
+ struct StableRadixSortSelector {
+ template <typename Iterator, typename Functor>
+ static void sort(Iterator first, Iterator last, Functor functor) {
+ stableRadixSignedSort<Value>(first, last, functor);
+ }
+ };
+
+ template <typename Value>
+ struct StableRadixSortSelector<Value, false> {
+ template <typename Iterator, typename Functor>
+ static void sort(Iterator first, Iterator last, Functor functor) {
+ stableRadixUnsignedSort<Value>(first, last, functor);
+ }
+ };
+
+ }
+
+ /// \ingroup auxalg
+ ///
+ /// \brief Sorts the STL compatible range into ascending order in a stable
+ /// way.
+ ///
+ /// This function sorts an STL compatible range into ascending
+ /// order according to an integer mapping in the same as radixSort() does.
+ ///
+ /// This sorting algorithm is stable, i.e. the order of two equal
+ /// elements remains the same after the sorting.
+ ///
+ /// This sort algorithm use a radix forward sort on the
+ /// bytes of the integer number. The algorithm sorts the items
+ /// byte-by-byte. First, it counts how many times a byte value occurs
+ /// in the container, then it copies the corresponding items to
+ /// another container in asceding order in O(n) time.
+ ///
+ /// The time complexity of the algorithm is O(log(c)*n) and
+ /// it uses O(n) additional space, where \c c is the
+ /// maximal value and \c n is the number of the items in the
+ /// container.
+ ///
+
+ /// \param first The begin of the given range.
+ /// \param last The end of the given range.
+ /// \param functor An adaptible unary function or a normal function
+ /// which maps the items to any integer type which can be either
+ /// signed or unsigned.
+ /// \sa radixSort()
+ template <typename Iterator, typename Functor>
+ void stableRadixSort(Iterator first, Iterator last, Functor functor) {
+ using namespace _radix_sort_bits;
+ typedef typename Functor::result_type Value;
+ StableRadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
+ using namespace _radix_sort_bits;
+ StableRadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
+ using namespace _radix_sort_bits;
+ StableRadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
+ using namespace _radix_sort_bits;
+ StableRadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator, typename Value, typename Key>
+ void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
+ using namespace _radix_sort_bits;
+ StableRadixSortSelector<Value>::sort(first, last, functor);
+ }
+
+ template <typename Iterator>
+ void stableRadixSort(Iterator first, Iterator last) {
+ using namespace _radix_sort_bits;
+ typedef typename std::iterator_traits<Iterator>::value_type Value;
+ StableRadixSortSelector<Value>::sort(first, last, Identity<Value>());
+ }
+
+}
+
+#endif
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