/* -*- 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