/* -*- 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 = static_cast<int>(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