/* -*- 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