alpar@442: /* -*- mode: C++; indent-tabs-mode: nil; -*-
deba@441:  *
alpar@442:  * This file is a part of LEMON, a generic C++ optimization library.
deba@441:  *
alpar@444:  * Copyright (C) 2003-2009
deba@441:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@441:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@441:  *
deba@441:  * Permission to use, modify and distribute this software is granted
deba@441:  * provided that this copyright notice appears in all copies. For
deba@441:  * precise terms see the accompanying LICENSE file.
deba@441:  *
deba@441:  * This software is provided "AS IS" with no warranty of any kind,
deba@441:  * express or implied, and with no claim as to its suitability for any
deba@441:  * purpose.
deba@441:  *
deba@441:  */
deba@441: 
deba@441: #ifndef RADIX_SORT_H
deba@441: #define RADIX_SORT_H
deba@441: 
deba@441: /// \ingroup auxalg
deba@441: /// \file
deba@441: /// \brief Radix sort
deba@441: ///
deba@441: /// Linear time sorting algorithms
deba@441: 
deba@441: #include <vector>
deba@441: #include <limits>
deba@441: #include <iterator>
deba@441: #include <algorithm>
deba@441: 
deba@441: namespace lemon {
deba@441: 
deba@441:   namespace _radix_sort_bits {
deba@441: 
deba@441:     template <typename Value>
deba@441:     struct Identity {
deba@441:       const Value& operator()(const Value& val) {
alpar@442:         return val;
deba@441:       }
deba@441:     };
deba@441: 
deba@441: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
alpar@442:     Iterator radixSortPartition(Iterator first, Iterator last,
alpar@442:                                 Functor functor, Value mask) {
deba@441:       while (first != last && !(functor(*first) & mask)) {
alpar@442:         ++first;
deba@441:       }
deba@441:       if (first == last) {
alpar@442:         return first;
deba@441:       }
deba@441:       --last;
deba@441:       while (first != last && (functor(*last) & mask)) {
alpar@442:         --last;
deba@441:       }
deba@441:       if (first == last) {
alpar@442:         return first;
deba@441:       }
deba@441:       std::iter_swap(first, last);
deba@441:       ++first;
deba@441:       if (!(first < last)) {
alpar@442:         return first;
deba@441:       }
deba@441:       while (true) {
alpar@442:         while (!(functor(*first) & mask)) {
alpar@442:           ++first;
alpar@442:         }
alpar@442:         --last;
alpar@442:         while (functor(*last) & mask) {
alpar@442:           --last;
alpar@442:         }
alpar@442:         if (!(first < last)) {
alpar@442:           return first;
alpar@442:         }
alpar@442:         std::iter_swap(first, last);
alpar@442:         ++first;
deba@441:       }
deba@441:     }
deba@441: 
deba@441:     template <typename Iterator, typename Functor>
alpar@442:     Iterator radixSortSignPartition(Iterator first, Iterator last,
alpar@442:                                     Functor functor) {
deba@441:       while (first != last && functor(*first) < 0) {
alpar@442:         ++first;
deba@441:       }
deba@441:       if (first == last) {
alpar@442:         return first;
deba@441:       }
deba@441:       --last;
deba@441:       while (first != last && functor(*last) >= 0) {
alpar@442:         --last;
deba@441:       }
deba@441:       if (first == last) {
alpar@442:         return first;
deba@441:       }
deba@441:       std::iter_swap(first, last);
deba@441:       ++first;
deba@441:       if (!(first < last)) {
alpar@442:         return first;
deba@441:       }
deba@441:       while (true) {
alpar@442:         while (functor(*first) < 0) {
alpar@442:           ++first;
alpar@442:         }
alpar@442:         --last;
alpar@442:         while (functor(*last) >= 0) {
alpar@442:           --last;
alpar@442:         }
alpar@442:         if (!(first < last)) {
alpar@442:           return first;
alpar@442:         }
alpar@442:         std::iter_swap(first, last);
alpar@442:         ++first;
deba@441:       }
deba@441:     }
deba@441: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
alpar@442:     void radixIntroSort(Iterator first, Iterator last,
alpar@442:                         Functor functor, Value mask) {
deba@441:       while (mask != 0 && last - first > 1) {
alpar@442:         Iterator cut = radixSortPartition(first, last, functor, mask);
alpar@442:         mask >>= 1;
alpar@442:         radixIntroSort(first, cut, functor, mask);
alpar@442:         first = cut;
deba@441:       }
deba@441:     }
deba@441: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
deba@441:     void radixSignedSort(Iterator first, Iterator last, Functor functor) {
deba@441: 
deba@441:       Iterator cut = radixSortSignPartition(first, last, functor);
deba@441: 
deba@441:       Value mask;
deba@441:       int max_digit;
deba@441:       Iterator it;
deba@441: 
deba@441:       mask = ~0; max_digit = 0;
deba@441:       for (it = first; it != cut; ++it) {
alpar@442:         while ((mask & functor(*it)) != mask) {
alpar@442:           ++max_digit;
alpar@442:           mask <<= 1;
alpar@442:         }
deba@441:       }
deba@441:       radixIntroSort(first, cut, functor, 1 << max_digit);
deba@441: 
deba@441:       mask = 0; max_digit = 0;
deba@441:       for (it = cut; it != last; ++it) {
alpar@442:         while ((mask | functor(*it)) != mask) {
alpar@442:           ++max_digit;
alpar@442:           mask <<= 1; mask |= 1;
alpar@442:         }
deba@441:       }
deba@441:       radixIntroSort(cut, last, functor, 1 << max_digit);
deba@441:     }
deba@441: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
deba@441:     void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
deba@441: 
deba@441:       Value mask = 0;
deba@441:       int max_digit = 0;
deba@441: 
deba@441:       Iterator it;
deba@441:       for (it = first; it != last; ++it) {
alpar@442:         while ((mask | functor(*it)) != mask) {
alpar@442:           ++max_digit;
alpar@442:           mask <<= 1; mask |= 1;
alpar@442:         }
deba@441:       }
deba@441:       radixIntroSort(first, last, functor, 1 << max_digit);
deba@441:     }
deba@441: 
deba@441: 
alpar@442:     template <typename Value,
alpar@442:               bool sign = std::numeric_limits<Value>::is_signed >
deba@441:     struct RadixSortSelector {
deba@441:       template <typename Iterator, typename Functor>
deba@441:       static void sort(Iterator first, Iterator last, Functor functor) {
alpar@442:         radixSignedSort<Value>(first, last, functor);
deba@441:       }
deba@441:     };
deba@441: 
deba@441:     template <typename Value>
deba@441:     struct RadixSortSelector<Value, false> {
deba@441:       template <typename Iterator, typename Functor>
deba@441:       static void sort(Iterator first, Iterator last, Functor functor) {
alpar@442:         radixUnsignedSort<Value>(first, last, functor);
deba@441:       }
deba@441:     };
deba@441: 
deba@441:   }
deba@441: 
deba@441:   /// \ingroup auxalg
deba@441:   ///
deba@441:   /// \brief Sorts the STL compatible range into ascending order.
deba@441:   ///
alpar@442:   /// The \c radixSort sorts an STL compatible range into ascending
alpar@442:   /// order.  The radix sort algorithm can sort items which are mapped
alpar@442:   /// to integers with an adaptable unary function \c functor and the
alpar@442:   /// order will be ascending according to these mapped values.
deba@441:   ///
alpar@442:   /// It is also possible to use a normal function instead
alpar@442:   /// of the functor object. If the functor is not given it will use
alpar@442:   /// the identity function instead.
alpar@442:   ///
alpar@442:   /// This is a special quick sort algorithm where the pivot
kpeter@559:   /// values to split the items are choosen to be 2<sup>k</sup>
kpeter@559:   /// for each \c k.
kpeter@559:   /// Therefore, the time complexity of the algorithm is O(log(c)*n) and
kpeter@559:   /// it uses O(log(c)) additional space, where \c c is the maximal value
kpeter@559:   /// and \c n is the number of the items in the container.
deba@441:   ///
deba@441:   /// \param first The begin of the given range.
deba@441:   /// \param last The end of the given range.
deba@441:   /// \param functor An adaptible unary function or a normal function
deba@441:   /// which maps the items to any integer type which can be either
deba@441:   /// signed or unsigned.
alpar@442:   ///
deba@443:   /// \sa stableRadixSort()
deba@441:   template <typename Iterator, typename Functor>
deba@441:   void radixSort(Iterator first, Iterator last, Functor functor) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     typedef typename Functor::result_type Value;
deba@441:     RadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@441:   void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     RadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@441:   void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     RadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@441:   void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     RadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@441:   void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     RadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator>
deba@441:   void radixSort(Iterator first, Iterator last) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@441:     RadixSortSelector<Value>::sort(first, last, Identity<Value>());
deba@441:   }
deba@441: 
deba@441:   namespace _radix_sort_bits {
deba@441: 
deba@441:     template <typename Value>
deba@441:     unsigned char valueByte(Value value, int byte) {
deba@441:       return value >> (std::numeric_limits<unsigned char>::digits * byte);
deba@441:     }
deba@441: 
deba@441:     template <typename Functor, typename Key>
deba@443:     void stableRadixIntroSort(Key *first, Key *last, Key *target,
deba@443:                               int byte, Functor functor) {
alpar@442:       const int size =
alpar@442:         unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@441:       std::vector<int> counter(size);
deba@441:       for (int i = 0; i < size; ++i) {
alpar@442:         counter[i] = 0;
deba@441:       }
deba@441:       Key *it = first;
deba@441:       while (first != last) {
alpar@442:         ++counter[valueByte(functor(*first), byte)];
alpar@442:         ++first;
deba@441:       }
deba@441:       int prev, num = 0;
deba@441:       for (int i = 0; i < size; ++i) {
alpar@442:         prev = num;
alpar@442:         num += counter[i];
alpar@442:         counter[i] = prev;
deba@441:       }
deba@441:       while (it != last) {
alpar@442:         target[counter[valueByte(functor(*it), byte)]++] = *it;
alpar@442:         ++it;
deba@441:       }
deba@441:     }
deba@441: 
deba@441:     template <typename Functor, typename Key>
deba@443:     void signedStableRadixIntroSort(Key *first, Key *last, Key *target,
deba@443:                                     int byte, Functor functor) {
alpar@442:       const int size =
alpar@442:         unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@441:       std::vector<int> counter(size);
deba@441:       for (int i = 0; i < size; ++i) {
alpar@442:         counter[i] = 0;
deba@441:       }
deba@441:       Key *it = first;
deba@441:       while (first != last) {
alpar@442:         counter[valueByte(functor(*first), byte)]++;
alpar@442:         ++first;
deba@441:       }
deba@441:       int prev, num = 0;
deba@441:       for (int i = size / 2; i < size; ++i) {
alpar@442:         prev = num;
alpar@442:         num += counter[i];
alpar@442:         counter[i] = prev;
deba@441:       }
deba@441:       for (int i = 0; i < size / 2; ++i) {
alpar@442:         prev = num;
alpar@442:         num += counter[i];
alpar@442:         counter[i] = prev;
deba@441:       }
deba@441:       while (it != last) {
alpar@442:         target[counter[valueByte(functor(*it), byte)]++] = *it;
alpar@442:         ++it;
deba@441:       }
deba@441:     }
deba@441: 
alpar@442: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
deba@443:     void stableRadixSignedSort(Iterator first, Iterator last, Functor functor) {
deba@441:       if (first == last) return;
deba@441:       typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@441:       typedef std::allocator<Key> Allocator;
deba@441:       Allocator allocator;
deba@441: 
deba@441:       int length = std::distance(first, last);
deba@441:       Key* buffer = allocator.allocate(2 * length);
deba@441:       try {
alpar@442:         bool dir = true;
alpar@442:         std::copy(first, last, buffer);
alpar@442:         for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
alpar@442:           if (dir) {
deba@443:             stableRadixIntroSort(buffer, buffer + length, buffer + length,
deba@443:                                  i, functor);
alpar@442:           } else {
deba@443:             stableRadixIntroSort(buffer + length, buffer + 2 * length, buffer,
deba@443:                                  i, functor);
alpar@442:           }
alpar@442:           dir = !dir;
alpar@442:         }
alpar@442:         if (dir) {
deba@443:           signedStableRadixIntroSort(buffer, buffer + length, buffer + length,
deba@443:                                      sizeof(Value) - 1, functor);
alpar@442:           std::copy(buffer + length, buffer + 2 * length, first);
alpar@442:         }        else {
alpar@444:           signedStableRadixIntroSort(buffer + length, buffer + 2 * length,
deba@443:                                      buffer, sizeof(Value) - 1, functor);
alpar@442:           std::copy(buffer, buffer + length, first);
alpar@442:         }
deba@441:       } catch (...) {
alpar@442:         allocator.deallocate(buffer, 2 * length);
alpar@442:         throw;
deba@441:       }
deba@441:       allocator.deallocate(buffer, 2 * length);
deba@441:     }
deba@441: 
deba@441:     template <typename Value, typename Iterator, typename Functor>
alpar@444:     void stableRadixUnsignedSort(Iterator first, Iterator last,
deba@443:                                  Functor functor) {
deba@441:       if (first == last) return;
deba@441:       typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@441:       typedef std::allocator<Key> Allocator;
deba@441:       Allocator allocator;
deba@441: 
deba@441:       int length = std::distance(first, last);
deba@441:       Key *buffer = allocator.allocate(2 * length);
deba@441:       try {
alpar@442:         bool dir = true;
alpar@442:         std::copy(first, last, buffer);
alpar@442:         for (int i = 0; i < int(sizeof(Value)); ++i) {
alpar@442:           if (dir) {
deba@443:             stableRadixIntroSort(buffer, buffer + length,
deba@443:                                  buffer + length, i, functor);
alpar@442:           } else {
deba@443:             stableRadixIntroSort(buffer + length, buffer + 2 * length,
deba@443:                                  buffer, i, functor);
alpar@442:           }
alpar@442:           dir = !dir;
alpar@442:         }
alpar@442:         if (dir) {
alpar@442:           std::copy(buffer, buffer + length, first);
alpar@442:         }        else {
alpar@442:           std::copy(buffer + length, buffer + 2 * length, first);
alpar@442:         }
deba@441:       } catch (...) {
alpar@442:         allocator.deallocate(buffer, 2 * length);
alpar@442:         throw;
deba@441:       }
deba@441:       allocator.deallocate(buffer, 2 * length);
deba@441:     }
deba@441: 
deba@441: 
deba@441: 
alpar@442:     template <typename Value,
alpar@442:               bool sign = std::numeric_limits<Value>::is_signed >
deba@443:     struct StableRadixSortSelector {
deba@441:       template <typename Iterator, typename Functor>
deba@441:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@443:         stableRadixSignedSort<Value>(first, last, functor);
deba@441:       }
deba@441:     };
deba@441: 
deba@441:     template <typename Value>
deba@443:     struct StableRadixSortSelector<Value, false> {
deba@441:       template <typename Iterator, typename Functor>
deba@441:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@443:         stableRadixUnsignedSort<Value>(first, last, functor);
deba@441:       }
deba@441:     };
deba@441: 
deba@441:   }
deba@441: 
deba@441:   /// \ingroup auxalg
deba@441:   ///
alpar@442:   /// \brief Sorts the STL compatible range into ascending order in a stable
alpar@442:   /// way.
deba@441:   ///
alpar@442:   /// This function sorts an STL compatible range into ascending
alpar@442:   /// order according to an integer mapping in the same as radixSort() does.
deba@441:   ///
alpar@442:   /// This sorting algorithm is stable, i.e. the order of two equal
deba@443:   /// elements remains the same after the sorting.
alpar@442:   ///
alpar@442:   /// This sort algorithm  use a radix forward sort on the
deba@441:   /// bytes of the integer number. The algorithm sorts the items
alpar@442:   /// byte-by-byte. First, it counts how many times a byte value occurs
alpar@442:   /// in the container, then it copies the corresponding items to
kpeter@559:   /// another container in asceding order in O(n) time.
deba@441:   ///
kpeter@559:   /// The time complexity of the algorithm is O(log(c)*n) and
kpeter@559:   /// it uses O(n) additional space, where \c c is the
alpar@442:   /// maximal value and \c n is the number of the items in the
alpar@442:   /// container.
deba@441:   ///
alpar@442: 
deba@441:   /// \param first The begin of the given range.
deba@441:   /// \param last The end of the given range.
deba@441:   /// \param functor An adaptible unary function or a normal function
deba@441:   /// which maps the items to any integer type which can be either
deba@441:   /// signed or unsigned.
alpar@442:   /// \sa radixSort()
deba@441:   template <typename Iterator, typename Functor>
deba@443:   void stableRadixSort(Iterator first, Iterator last, Functor functor) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     typedef typename Functor::result_type Value;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@443:   void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@441:     using namespace _radix_sort_bits;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@443:   void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@441:     using namespace _radix_sort_bits;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@443:   void stableRadixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@441:     using namespace _radix_sort_bits;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator, typename Value, typename Key>
deba@443:   void stableRadixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@441:     using namespace _radix_sort_bits;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, functor);
deba@441:   }
deba@441: 
deba@441:   template <typename Iterator>
deba@443:   void stableRadixSort(Iterator first, Iterator last) {
deba@441:     using namespace _radix_sort_bits;
deba@441:     typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@443:     StableRadixSortSelector<Value>::sort(first, last, Identity<Value>());
deba@441:   }
deba@441: 
deba@441: }
deba@441: 
deba@441: #endif