deba@1833: /* -*- C++ -*-
deba@1833: *
alpar@1956: * This file is a part of LEMON, a generic C++ optimization library
alpar@1956: *
alpar@2391: * Copyright (C) 2003-2007
alpar@1956: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@1833: * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@1833: *
deba@1833: * Permission to use, modify and distribute this software is granted
deba@1833: * provided that this copyright notice appears in all copies. For
deba@1833: * precise terms see the accompanying LICENSE file.
deba@1833: *
deba@1833: * This software is provided "AS IS" with no warranty of any kind,
deba@1833: * express or implied, and with no claim as to its suitability for any
deba@1833: * purpose.
deba@1833: *
deba@1833: */
deba@1833:
deba@1833: #ifndef RADIX_SORT_H
deba@1833: #define RADIX_SORT_H
deba@1833:
deba@2084: /// \ingroup auxalg
deba@1833: /// \file
deba@1833: /// \brief Radix sort
deba@1833: ///
deba@1833:
deba@1833: #include <vector>
deba@1833: #include <limits>
deba@1833: #include <iterator>
deba@1833: #include <algorithm>
deba@1833:
deba@1833: #include <lemon/error.h>
deba@1833:
deba@1833: namespace lemon {
deba@1833:
deba@1833: namespace _radix_sort_bits {
deba@1833:
deba@1833: template <typename Value>
deba@1833: struct Identity {
deba@1833: const Value& operator()(const Value& val) {
deba@1833: return val;
deba@1833: }
deba@1833: };
deba@1833:
deba@1833: }
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: Iterator radixSortPartition(Iterator first, Iterator last,
deba@1833: Functor functor, Value mask) {
deba@1833: while (first != last && !(functor(*first) & mask)) {
deba@1833: ++first;
deba@1833: }
deba@1833: if (first == last) {
deba@1833: return first;
deba@1833: }
deba@1833: --last;
deba@1833: while (first != last && (functor(*last) & mask)) {
deba@1833: --last;
deba@1833: }
deba@1833: if (first == last) {
deba@1833: return first;
deba@1833: }
deba@1833: std::iter_swap(first, last);
deba@1833: ++first;
deba@1833: if (!(first < last)) {
deba@1833: return first;
deba@1833: }
deba@1833: while (true) {
deba@1833: while (!(functor(*first) & mask)) {
deba@1833: ++first;
deba@1833: }
deba@1833: --last;
deba@1833: while (functor(*last) & mask) {
deba@1833: --last;
deba@1833: }
deba@1833: if (!(first < last)) {
deba@1833: return first;
deba@1833: }
deba@1833: std::iter_swap(first, last);
deba@1833: ++first;
deba@1833: }
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Functor>
deba@1833: Iterator radixSortSignPartition(Iterator first, Iterator last,
deba@1833: Functor functor) {
deba@1833: while (first != last && functor(*first) < 0) {
deba@1833: ++first;
deba@1833: }
deba@1833: if (first == last) {
deba@1833: return first;
deba@1833: }
deba@1833: --last;
deba@1833: while (first != last && functor(*last) >= 0) {
deba@1833: --last;
deba@1833: }
deba@1833: if (first == last) {
deba@1833: return first;
deba@1833: }
deba@1833: std::iter_swap(first, last);
deba@1833: ++first;
deba@1833: if (!(first < last)) {
deba@1833: return first;
deba@1833: }
deba@1833: while (true) {
deba@1833: while (functor(*first) < 0) {
deba@1833: ++first;
deba@1833: }
deba@1833: --last;
deba@1833: while (functor(*last) >= 0) {
deba@1833: --last;
deba@1833: }
deba@1833: if (!(first < last)) {
deba@1833: return first;
deba@1833: }
deba@1833: std::iter_swap(first, last);
deba@1833: ++first;
deba@1833: }
deba@1833: }
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: void radixIntroSort(Iterator first, Iterator last,
deba@1833: Functor functor, Value mask) {
deba@1833: while (mask != 0 && last - first > 1) {
deba@1833: Iterator cut = radixSortPartition(first, last, functor, mask);
deba@1833: mask >>= 1;
deba@1833: radixIntroSort(first, cut, functor, mask);
deba@1833: first = cut;
deba@1833: }
deba@1833: }
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: void radixSignedSort(Iterator first, Iterator last, Functor functor) {
deba@1833: Iterator cut = radixSortSignPartition(first, last, functor);
deba@1833:
deba@1833: Value mask;
deba@1833: int max_digit;
deba@1833: Iterator it;
deba@1833:
deba@1833: mask = 0; max_digit = 0;
deba@1833: for (it = first; it != cut; ++it) {
deba@1833: if ((mask | functor(*it)) != ~0) {
deba@1833: ++max_digit;
deba@1833: mask <<= 1;
deba@1833: mask |= 1;
deba@1833: }
deba@1833: }
deba@1833: radixIntroSort(first, cut, functor, 1 << max_digit);
deba@1833:
deba@1833: mask = ~0; max_digit = 0;
deba@1833: for (it = cut; it != last; ++it) {
deba@1833: if (mask & functor(*it)) {
deba@1833: ++max_digit;
deba@1833: mask <<= 1;
deba@1833: }
deba@1833: }
deba@1833: radixIntroSort(cut, last, functor, 1 << max_digit);
deba@1833: }
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
deba@1833:
deba@1833: Value mask = ~0;
deba@1833: int max_digit = 0;
deba@1833:
deba@1833: Iterator it;
deba@1833: for (it = first; it != last; ++it) {
deba@1833: if (mask & functor(*it)) {
deba@1833: ++max_digit;
deba@1833: mask <<= 1;
deba@1833: }
deba@1833: }
deba@1833: radixIntroSort(first, last, functor, 1 << max_digit);
deba@1833: }
deba@1833:
deba@1833: namespace _radix_sort_bits {
deba@1833:
deba@1833: template <typename Value,
deba@1833: bool sign = std::numeric_limits<Value>::is_signed >
deba@1833: struct RadixSortSelector {
deba@1833: template <typename Iterator, typename Functor>
deba@1833: static void sort(Iterator first, Iterator last, Functor functor) {
deba@1833: radixSignedSort<Value>(first, last, functor);
deba@1833: }
deba@1833: };
deba@1833:
deba@1833: template <typename Value>
deba@1833: struct RadixSortSelector<Value, false> {
deba@1833: template <typename Iterator, typename Functor>
deba@1833: static void sort(Iterator first, Iterator last, Functor functor) {
deba@1833: radixUnsignedSort<Value>(first, last, functor);
deba@1833: }
deba@1833: };
deba@1833:
deba@1833: }
deba@1833:
deba@2084: /// \ingroup auxalg
deba@1833: ///
deba@1833: /// \brief Sorts the stl compatible range into ascending order.
deba@1833: ///
deba@1833: /// The \c radixSort sorts the stl compatible range into ascending order.
deba@1833: /// The radix sort algorithm can sort the items which mapped to an
deba@1833: /// integer by the adaptable unary function \c functor and the order
deba@1833: /// will be ascending by these mapped values. As function specialization
deba@1833: /// there is possible to use a normal function as the functor object
deba@1833: /// or if the functor is not given it will use an identity function instead.
deba@1833: ///
deba@1833: /// This implemented radix sort is a special quick sort which pivot value
deba@1833: /// is choosen to partite the items on the next bit. This way, let be
deba@1833: /// \c c the maximal capacity and \c n the number of the items in
deba@2042: /// the container, the time complexity of the algorithm
deba@2042: /// \f$ O(\log(c)n) \f$ and the additional space complexity is
deba@2042: /// \f$ O(\log(c)) \f$.
deba@1833: ///
deba@1833: /// \param first The begin of the given range.
deba@1833: /// \param last The end of the given range.
deba@1833: /// \param functor An adaptible unary function or a normal function which
deba@1833: /// maps the items to any integer type which can be wheter signed or
deba@1833: /// unsigned.
deba@1833: template <typename Iterator, typename Functor>
deba@1833: void radixSort(Iterator first, Iterator last, Functor functor) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: typedef typename Functor::result_type Value;
deba@1833: RadixSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: RadixSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: RadixSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: RadixSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: RadixSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator>
deba@1833: void radixSort(Iterator first, Iterator last) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@1833: RadixSortSelector<Value>::sort(first, last, Identity<Value>());
deba@1833: }
deba@1833:
deba@1833: template <typename Value>
deba@1833: unsigned char valueByte(Value value, int byte) {
deba@1844: return value >> (std::numeric_limits<unsigned char>::digits * byte);
deba@1833: }
deba@1833:
deba@1833: template <typename Functor, typename Key>
deba@1833: void counterIntroSort(Key *first, Key *last, Key *target,
deba@1833: int byte, Functor functor) {
deba@1833: const int size =
deba@2386: unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@1979: std::vector<int> counter(size);
deba@1833: for (int i = 0; i < size; ++i) {
deba@1833: counter[i] = 0;
deba@1833: }
deba@1833: Key *it = first;
deba@1833: while (first != last) {
deba@1833: ++counter[valueByte(functor(*first), byte)];
deba@1833: ++first;
deba@1833: }
deba@1833: int prev, num = 0;
deba@1833: for (int i = 0; i < size; ++i) {
deba@1833: prev = num;
deba@1833: num += counter[i];
deba@1833: counter[i] = prev;
deba@1833: }
deba@1833: while (it != last) {
deba@1833: target[counter[valueByte(functor(*it), byte)]++] = *it;
deba@1833: ++it;
deba@1833: }
deba@1833: }
deba@1833:
deba@1833: template <typename Functor, typename Key>
deba@1833: void signedCounterIntroSort(Key *first, Key *last, Key *target,
deba@1833: int byte, Functor functor) {
deba@1833: const int size =
deba@2386: unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@1979: std::vector<int> counter(size);
deba@1833: for (int i = 0; i < size; ++i) {
deba@1833: counter[i] = 0;
deba@1833: }
deba@1833: Key *it = first;
deba@1833: while (first != last) {
deba@1833: counter[valueByte(functor(*first), byte)]++;
deba@1833: ++first;
deba@1833: }
deba@1833: int prev, num = 0;
deba@1833: for (int i = size / 2; i < size; ++i) {
deba@1833: prev = num;
deba@1833: num += counter[i];
deba@1833: counter[i] = prev;
deba@1833: }
deba@1833: for (int i = 0; i < size / 2; ++i) {
deba@1833: prev = num;
deba@1833: num += counter[i];
deba@1833: counter[i] = prev;
deba@1833: }
deba@1833: while (it != last) {
deba@1833: target[counter[valueByte(functor(*it), byte)]++] = *it;
deba@1833: ++it;
deba@1833: }
deba@1833: }
deba@1833:
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: void counterSignedSort(Iterator first, Iterator last, Functor functor) {
deba@1904: if (first == last) return;
deba@1833: typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@1833: typedef std::allocator<Key> Allocator;
deba@1833: Allocator allocator;
deba@1833:
deba@1833: int length = std::distance(first, last);
deba@2033: Key* buffer = allocator.allocate(2 * length);
deba@1833: try {
deba@1833: bool dir = true;
deba@1833: std::copy(first, last, buffer);
deba@2386: for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
deba@1833: if (dir) {
deba@1833: counterIntroSort(buffer, buffer + length, buffer + length,
deba@1833: i, functor);
deba@1833: } else {
deba@1833: counterIntroSort(buffer + length, buffer + 2 * length, buffer,
deba@1833: i, functor);
deba@1833: }
deba@1833: dir = !dir;
deba@1833: }
deba@1833: if (dir) {
deba@1833: signedCounterIntroSort(buffer, buffer + length, buffer + length,
deba@1833: sizeof(Value) - 1, functor);
deba@1833: std::copy(buffer + length, buffer + 2 * length, first);
deba@1833: } else {
deba@1833: signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer,
deba@1833: sizeof(Value) - 1, functor);
deba@1833: std::copy(buffer, buffer + length, first);
deba@1833: }
deba@1833: } catch (...) {
deba@1833: allocator.deallocate(buffer, 2 * length);
deba@1833: throw;
deba@1833: }
deba@1833: allocator.deallocate(buffer, 2 * length);
deba@1833: }
deba@1833:
deba@1833: template <typename Value, typename Iterator, typename Functor>
deba@1833: void counterUnsignedSort(Iterator first, Iterator last, Functor functor) {
deba@1904: if (first == last) return;
deba@1833: typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@1833: typedef std::allocator<Key> Allocator;
deba@1833: Allocator allocator;
deba@1833:
deba@1833: int length = std::distance(first, last);
deba@2033: Key *buffer = allocator.allocate(2 * length);
deba@1833: try {
deba@1833: bool dir = true;
deba@1833: std::copy(first, last, buffer);
deba@2386: for (int i = 0; i < int(sizeof(Value)); ++i) {
deba@1833: if (dir) {
deba@2033: counterIntroSort(buffer, buffer + length,
deba@2033: buffer + length, i, functor);
deba@1833: } else {
deba@2033: counterIntroSort(buffer + length, buffer + 2 * length,
deba@2033: buffer, i, functor);
deba@1833: }
deba@1833: dir = !dir;
deba@1833: }
deba@1833: if (dir) {
deba@1833: std::copy(buffer, buffer + length, first);
deba@1833: } else {
deba@1833: std::copy(buffer + length, buffer + 2 * length, first);
deba@1833: }
deba@1833: } catch (...) {
deba@1833: allocator.deallocate(buffer, 2 * length);
deba@1833: throw;
deba@1833: }
deba@1833: allocator.deallocate(buffer, 2 * length);
deba@1833: }
deba@1833:
deba@1833: namespace _radix_sort_bits {
deba@1833:
deba@1833: template <typename Value,
deba@1833: bool sign = std::numeric_limits<Value>::is_signed >
deba@1833: struct CounterSortSelector {
deba@1833: template <typename Iterator, typename Functor>
deba@1833: static void sort(Iterator first, Iterator last, Functor functor) {
deba@1833: counterSignedSort<Value>(first, last, functor);
deba@1833: }
deba@1833: };
deba@1833:
deba@1833: template <typename Value>
deba@1833: struct CounterSortSelector<Value, false> {
deba@1833: template <typename Iterator, typename Functor>
deba@1833: static void sort(Iterator first, Iterator last, Functor functor) {
deba@1833: counterUnsignedSort<Value>(first, last, functor);
deba@1833: }
deba@1833: };
deba@1833:
deba@1833: }
deba@1833:
deba@2084: /// \ingroup auxalg
deba@1833: ///
deba@1833: /// \brief Sorts stable the stl compatible range into ascending order.
deba@1833: ///
deba@1833: /// The \c counterSort sorts the stl compatible range into ascending order.
deba@1833: /// The counter sort algorithm can sort the items which mapped to an
deba@1833: /// integer by the adaptable unary function \c functor and the order
deba@1833: /// will be ascending by these mapped values. As function specialization
deba@1833: /// there is possible to use a normal function as the functor object
deba@1833: /// or if the functor is not given it will use an identity function instead.
deba@1833: ///
deba@1833: /// This implemented counter sort use a radix forward sort on the bytes of
deba@1833: /// the integer. The algorithm can sort the items on a given byte.
deba@1833: /// First time it counts how many times occurs a byte value in the container.
deba@1833: /// By the occurence number it is possible to copy the container
deba@1833: /// in the right order in \c O(n) time. The algorithm sorts the container
deba@1833: /// by each bytes in forward direction which sorts the container by the
deba@1844: /// whole value. This way, let be \c c the maximal capacity of the integer
deba@1844: /// type and \c n the number of the items in
deba@2042: /// the container, the time complexity of the algorithm \f$ O(\log(c)n) \f$
deba@2042: /// and the additional space complexity is \f$ O(n) \f$.
deba@1833: ///
deba@1833: /// This sorting algorithm is stable so the order of two equal element
deba@1833: /// stay in the same order.
deba@1833: ///
deba@1833: /// \param first The begin of the given range.
deba@1833: /// \param last The end of the given range.
deba@1833: /// \param functor An adaptible unary function or a normal function which
deba@1833: /// maps the items to any integer type which can be wheter signed or
deba@1833: /// unsigned.
deba@1833: template <typename Iterator, typename Functor>
deba@1833: void counterSort(Iterator first, Iterator last, Functor functor) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: typedef typename Functor::result_type Value;
deba@1833: CounterSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: CounterSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: CounterSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: CounterSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator, typename Value, typename Key>
deba@1833: void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: CounterSortSelector<Value>::sort(first, last, functor);
deba@1833: }
deba@1833:
deba@1833: template <typename Iterator>
deba@1833: void counterSort(Iterator first, Iterator last) {
deba@1833: using namespace _radix_sort_bits;
deba@1833: typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@1833: CounterSortSelector<Value>::sort(first, last, Identity<Value>());
deba@1833: }
deba@1833:
deba@1833: }
deba@1833:
deba@1833:
deba@1833:
deba@1833: #endif