/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * 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 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;

       if (!(first < last)) {

         return first;

       }

       while (true) {

         while (!(functor(*first) & mask)) {

           ++first;

         }

         --last;

         while (functor(*last) & mask) {

           --last;

         }

         if (!(first < last)) {

           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;

       if (!(first < last)) {

         return first;

       }

       while (true) {

         while (functor(*first) < 0) {

           ++first;

         }

         --last;

         while (functor(*last) >= 0) {

           --last;

         }

         if (!(first < last)) {

           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 && last - first > 1) {

         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