deba@1833: /* -*- C++ -*-
deba@1833:  *
alpar@1956:  * This file is a part of LEMON, a generic C++ optimization library
alpar@1956:  *
alpar@1956:  * Copyright (C) 2003-2006
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