/* -*- C++ -*-

 *

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

 *

 * Copyright (C) 2003-2008

 * 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

///

#include <vector>

#include <limits>

#include <iterator>

#include <algorithm>

#include <lemon/error.h>

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);

  }

  namespace _radix_sort_bits {

    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 the stl compatible range into ascending order.

  /// The radix sort algorithm can sort the items which mapped to an

  /// integer by the adaptable unary function \c functor and the order

  /// will be ascending by these mapped values. As function specialization

  /// there is possible to use a normal function as the functor object

  /// or if the functor is not given it will use an identity function instead.

  ///

  /// This implemented radix sort is a special quick sort which pivot value

  /// is choosen to partite the items on the next bit. This way, let be

  /// \c c the maximal capacity and \c n the number of the items in

  /// the container, the time complexity of the algorithm 

  /// \f$ O(\log(c)n) \f$ and the additional space complexity is 

  /// \f$ O(\log(c)) \f$.

  ///

  /// \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 wheter signed or 

  /// unsigned.

  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>());

  }

  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 counterIntroSort(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 signedCounterIntroSort(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 counterSignedSort(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) {

	  counterIntroSort(buffer, buffer + length, buffer + length, 

			   i, functor);

	} else {

	  counterIntroSort(buffer + length, buffer + 2 * length, buffer, 

			   i, functor);

	}

	dir = !dir;

      }

      if (dir) {

	signedCounterIntroSort(buffer, buffer + length, buffer + length, 

			       sizeof(Value) - 1, functor);

	std::copy(buffer + length, buffer + 2 * length, first);

      }	else {

	signedCounterIntroSort(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 counterUnsignedSort(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) {

	  counterIntroSort(buffer, buffer + length, 

                           buffer + length, i, functor);

	} else {

	  counterIntroSort(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);

  }

  namespace _radix_sort_bits {

    template <typename Value, 

	      bool sign = std::numeric_limits<Value>::is_signed >

    struct CounterSortSelector {

      template <typename Iterator, typename Functor>

      static void sort(Iterator first, Iterator last, Functor functor) {

	counterSignedSort<Value>(first, last, functor);

      }

    };

    template <typename Value>

    struct CounterSortSelector<Value, false> {

      template <typename Iterator, typename Functor>

      static void sort(Iterator first, Iterator last, Functor functor) {

	counterUnsignedSort<Value>(first, last, functor);

      }

    };

  }

  /// \ingroup auxalg

  ///

  /// \brief Sorts stable the stl compatible range into ascending order.

  ///

  /// The \c counterSort sorts the stl compatible range into ascending order.

  /// The counter sort algorithm can sort the items which mapped to an

  /// integer by the adaptable unary function \c functor and the order

  /// will be ascending by these mapped values. As function specialization

  /// there is possible to use a normal function as the functor object

  /// or if the functor is not given it will use an identity function instead.

  ///

  /// This implemented counter sort use a radix forward sort on the bytes of

  /// the integer. The algorithm can sort the items on a given byte. 

  /// First time it counts how many times occurs a byte value in the container.

  /// By the occurence number it is possible to copy the container

  /// in the right order in \c O(n) time. The algorithm sorts the container

  /// by each bytes in forward direction which sorts the container by the

  /// whole value. This way, let be \c c the maximal capacity of the integer 

  /// type and \c n the number of the items in

  /// the container, the time complexity of the algorithm \f$ O(\log(c)n) \f$

  /// and the additional space complexity is \f$ O(n) \f$.

  ///

  /// This sorting algorithm is stable so the order of two equal element

  /// stay in the same order.

  ///

  /// \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 wheter signed or 

  /// unsigned.

  template <typename Iterator, typename Functor>

  void counterSort(Iterator first, Iterator last, Functor functor) {

    using namespace _radix_sort_bits;

    typedef typename Functor::result_type Value;

    CounterSortSelector<Value>::sort(first, last, functor);

  }

  template <typename Iterator, typename Value, typename Key>

  void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {

    using namespace _radix_sort_bits;

    CounterSortSelector<Value>::sort(first, last, functor);

  }

  template <typename Iterator, typename Value, typename Key>

  void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {

    using namespace _radix_sort_bits;

    CounterSortSelector<Value>::sort(first, last, functor);

  }

  template <typename Iterator, typename Value, typename Key>

  void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {

    using namespace _radix_sort_bits;

    CounterSortSelector<Value>::sort(first, last, functor);

  }

  template <typename Iterator, typename Value, typename Key>

  void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {

    using namespace _radix_sort_bits;

    CounterSortSelector<Value>::sort(first, last, functor);

  }

  template <typename Iterator>

  void counterSort(Iterator first, Iterator last) {

    using namespace _radix_sort_bits;

    typedef typename std::iterator_traits<Iterator>::value_type Value;

    CounterSortSelector<Value>::sort(first, last, Identity<Value>());

  }

}

#endif