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quicksort.h

/*
 *  Copyright 2002 Adrian Thurston <adriant@ragel.ca>
 */

/*  This file is part of Aapl.
 *
 *  Aapl is free software; you can redistribute it and/or modify it under the
 *  terms of the GNU Lesser General Public License as published by the Free
 *  Software Foundation; either version 2.1 of the License, or (at your option)
 *  any later version.
 *
 *  Aapl is distributed in the hope that it will be useful, but WITHOUT ANY
 *  WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 *  FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public License for
 *  more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with Aapl; if not, write to the Free Software Foundation, Inc., 59
 *  Temple Place, Suite 330, Boston, MA 02111-1307 USA
 */

#ifndef _AAPL_QUICKSORT_H
#define _AAPL_QUICKSORT_H

#include "insertsort.h"

#ifdef AAPL_NAMESPACE
namespace Aapl {
#endif

/**
 * \addtogroup sort 
 * @{
 */

/** 
 * \class QuickSort
 * \brief Quick sort an array of data.
 *
 * QuickSort can be used to sort any array of objects of type T provided a
 * compare class is given. QuickSort is in-place. It does not require any
 * temporary storage.
 *
 * Objects are not made aware that they are being moved around in memory.
 * Assignment operators, constructors and destructors are never invoked by the
 * sort.
 *
 * QuickSort runs in O(n*log(n)) time in the average case. It is faster than
 * mergsort in the average case because it does less moving of data. The
 * performance of quicksort depends mostly on the choice of pivot. This
 * implementation picks the pivot as the median of first, middle, last. This
 * choice of pivot avoids the O(n^2) worst case for input already sorted, but
 * it is still possible to encounter the O(n^2) worst case. For example an
 * array of identical elements will run in O(n^2)
 *
 * QuickSort is not a stable sort. Elements with the same key will not have
 * their relative ordering preserved.  QuickSort switches to an InsertSort
 * when the size of the array being sorted is small. This happens when
 * directly sorting a small array or when QuickSort calls iteself recursively
 * on a small portion of a larger array.
 */

/*@}*/

/* QuickSort. */
00066 template <class T, class Compare> class QuickSort : 
            public InsertSort<T, Compare>
{
public:
      /* Sorting interface routine. */
      void sort(T *data, long len);

private:
      /* Recursive worker. */
      void doSort(T *start, T *end);
      T *partition(T *start, T *end);
      inline T *median(T *start, T *end);
};

#define _QS_INSERTION_THRESH 16

/* Finds the median of start, middle, end. */
template <class T, class Compare> T *QuickSort<T,Compare>::
		median(T *start, T *end)
{
      T *pivot, *mid = start + (end-start)/2;

      /* CChoose the pivot. */
      if ( compare(*start, *mid) < 0  ) {
            if ( compare(*mid, *end) < 0 )
                  pivot = mid;
            else if ( compare(*start, *end) < 0 )
                  pivot = end;
            else
                  pivot = start;
      }
      else if ( compare(*start, *end) < 0 )
            pivot = start;
      else if ( compare(*mid, *end) < 0 )
            pivot = end;
      else
            pivot = mid;

      return pivot;
}

template <class T, class Compare> T *QuickSort<T,Compare>::
		partition(T *start, T *end)
{
      /* Use the median of start, middle, end as the pivot. First save
       * it off then move the last element to the free spot. */
      char pcPivot[sizeof(T)];
      T *pivot = median(start, end);

      memcpy( pcPivot, pivot, sizeof(T) );
      if ( pivot != end )
            memcpy( pivot, end, sizeof(T) );

      T *first = start-1;
      T *last = end;
      pivot = (T*) pcPivot;

      /* Shuffle element to the correct side of the pivot, ending
       * up with the free spot where the pivot will go. */
      while ( true ) {
            /* Throw one element ahead to the free spot at last. */
            while ( true ) {
                  first += 1;
                  if ( first == last )
                        goto done;
                  if ( compare( *first, *pivot ) > 0 ) {
                        memcpy(last, first, sizeof(T));
                        break;
                  }
            }

            /* Throw one element back to the free spot at first. */
            while ( true ) {
                  last -= 1;
                  if ( last == first )
                        goto done;
                  if ( compare( *last, *pivot ) < 0 ) {
                        memcpy(first, last, sizeof(T));
                        break;
                  }
            }
      }
done:
      /* Put the pivot into the middle spot for it. */
      memcpy( first, pivot, sizeof(T) );
      return first;
}


template< class T, class Compare> void QuickSort<T,Compare>::
		doSort(T *start, T *end)
{
      long len = end - start + 1;
      if ( len > _QS_INSERTION_THRESH ) {
            /* Use quicksort. */
            T *pivot = partition( start, end );
            doSort(start, pivot-1);
            doSort(pivot+1, end);
      } 
      else if ( len > 1 ) {
            /* Array is small, use insertion sort. */
            InsertSort<T, Compare>::sort( start, len );
      }
}

/**
 * \brief Quick sort an array of data.
 */
template< class T, class Compare> 
00175       void QuickSort<T,Compare>::sort(T *data, long len)
{
      /* Call recursive worker. */
      doSort(data, data+len-1);
}

#ifdef AAPL_NAMESPACE
}
#endif

#endif /* _AAPL_QUICKSORT_H */

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