/* -*- 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

///

/// 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 the STL compatible range into ascending

  /// order.  The radix sort algorithm can sort the items which mapped

  /// to an integer with an adaptable unary function \c functor and the

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

  /// specialization it is possible to use a normal function instead

  /// of 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. Therefore, let be \c c the maximal capacity and \c n the

  /// number of the items in the container, the time complexity of the

  /// algorithm is \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 either

  /// 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>());

  }

  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 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);

    }

    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 with an adaptable unary function \c functor

  /// and the order will be ascending by these mapped values. As

  /// function specialization it is possible to use a normal function

  /// instead of the functor object or if the functor is not given it

  /// will use an identity function instead.

  ///

  /// The implemented counter sort 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 occurs a byte value

  /// in the containerm, and with the occurence number the container

  /// can be copied to an other in asceding order in \c O(n) time.

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

  /// complexity is \f$ O(n) \f$.

  ///

  /// The sorting algorithm is stable, i.e. the order of two equal

  /// element remains the same.

  ///

  /// \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.

  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