/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2006
 * 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) {
      if ((mask | functor(*it)) != ~0) {
	++max_digit;
	mask <<= 1; 
	mask |= 1;
      }
    }
    radixIntroSort(first, cut, functor, 1 << max_digit);

    mask = ~0; max_digit = 0;
    for (it = cut; it != last; ++it) {
      if (mask & functor(*it)) {
	++max_digit;
	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) {
      if (mask & functor(*it)) {
	++max_digit;
	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 int)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 int)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