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extern/quadriflow/3rd/lemon-1.3.1/lemon/radix_sort.h

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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