Examples
Example 5. Quicksort
Quicksort is a partition exchange sort first described by C.A.R. Hoare in 1960. The version here is from GNU libc, which implements optimizations suggested by Robert Sedgewick. It has two phases,the partition phase and the sort phase. When the partition falls below a threshold value, then the routine switches to an insertion sort.
Quicksort works well for a variety of different kinds of input data, and is substantially faster than any other sorting method in typical applications. It is in-place, using only a small auxiliary stack, and requires time proportional to N log N on the average to sort N items.
Performance is stated to be: Worst case: Ο(n2), Best case: Ο(n log n) Average case: Ο(n log n)
The qsort() function sorts an array of n elements, each of width bytes in size, where the first element of the array is pointed to by pbase. The compare pointer points to a function, which you supply, that compares two array elements and returns an integer value specifying their relationship. The qsort() function calls the comparison function one or more times during the sort, passing pointers to two array elements on each call. The comparison function must compare the elements and return one of the following values:
- < 0 – element1 less than element2
- 0 – element1 equal to element2
- > 0 – element1 greater than element2
The sorted array elements are stored in increasing order, as returned by the comparison function. To sort reverse order reverse the “greater than” and “less than” logic in the comparison function. If two elements are equal, their order in the sorted array is unspecified.
I modified this implementation to pass the comparator function the size of the elements to be compared.
Type Signature
extern void _quicksort (void *const pbase, size_t total_elems, size_t size, __compar_fn_t2 cmp);
Testing the routine for performance, an array of 10,000, 100-byte entries (1MB) took .05 seconds, on a zEnterprise 114 3.8GHz processor.
/* Copyright (C) 1991,1992,1996,1997,1999,2004 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Written by Douglas C. Schmidt (schmidt@ics.uci.edu).
The GNU C Library 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.
The GNU C Library 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 the GNU C Library; if not, write to the Free
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA. */
/* If you consider tuning this algorithm, you should consult first:
Engineering a sort function; Jon Bentley and M. Douglas McIlroy;
Software - Practice and Experience; Vol. 23 (11), 1249-1265, 1993. */
#include <alloca.h>
#include <limits.h>
#include <stdlib.h>
#include <string.h>
typedef int (*__compar_fn_t2) (const void *, const void *, int) ;
/* Byte-wise swap two items of size SIZE. */
#define SWAP(a, b, size) \
do \
{ \
register size_t __size = (size); \
register char *__a = (a), *__b = (b); \
do \
{ \
char __tmp = *__a; \
*__a++ = *__b; \
*__b++ = __tmp; \
} while (--__size > 0); \
} while (0)
/* Discontinue quicksort algorithm when partition gets below this size.
*/
#define MAX_THRESH 4
/* Stack node declarations used to store unfulfilled partition obligations. */
typedef struct
{
char *lo;
char *hi;
} stack_node;
/* The next 4 #defines implement a very fast in-line stack abstraction.
The stack needs log (total_elements) entries (we could even subtract
log(MAX_THRESH)). Since total_elements has type size_t, we get as
upper bound for log (total_elements):
bits per byte (CHAR_BIT) * sizeof(size_t). */
#define STACK_SIZE (CHAR_BIT * sizeof(size_t))
#define PUSH(low, high) ((void) ((top->lo = (low)), (top->hi = (high)), ++top))
#define POP(low, high) ((void) (--top, (low = top->lo), (high = top->hi)))
#define STACK_NOT_EMPTY (stack < top)
/* Order size using quicksort. This implementation incorporates
four optimizations discussed in Sedgewick:
1. Non-recursive, using an explicit stack of pointers that store the
next array partition to sort. To save time, this maximum amount
of space required to store an array of SIZE_MAX is allocated on the
stack. Assuming a 32-bit (64 bit) integer for size_t, this needs
only 32 * sizeof(stack_node) == 256 bytes (for 64 bit: 1024 bytes).
2. Chose the pivot element using a median-of-three decision tree.
This reduces the probability of selecting a bad pivot value and
eliminates certain extraneous comparisons.
3. Only quicksorts TOTAL_ELEMS / MAX_THRESH partitions, leaving
insertion sort to order the MAX_THRESH items within each partition.
This is a big win, since insertion sort is faster for small, mostly
sorted array segments.
4. The larger of the two sub-partitions is always pushed onto the
stack first, with the algorithm then concentrating on the
smaller partition. This guarantees no more than log (total_elems)
stack size is needed (actually O(1) in this case) */
/*
/*
The qsort() function overwrites the contents of the array with the sorted elements.
*/
void _quicksort (void *const pbase, size_t total_elems, size_t size,
__compar_fn_t2 cmp)
{
register char *base_ptr = (char *) pbase;
const size_t max_thresh = MAX_THRESH * size;
if (total_elems == 0)
/* Avoid lossage with unsigned arithmetic below. */
return;
if (total_elems > MAX_THRESH)
{
char *lo = base_ptr;
char *hi = &lo[size * (total_elems - 1)];
stack_node stack[STACK_SIZE];
stack_node *top = stack;
PUSH (NULL, NULL);
while (STACK_NOT_EMPTY)
{
char *left_ptr;
char *right_ptr;
/* Select median value from among LO, MID, and HI. Rearrange
LO and HI so the three values are sorted. This lowers the
probability of picking a pathological pivot value and
skips a comparison for both the LEFT_PTR and RIGHT_PTR in
the while loops. */
char *mid = lo + size * ((hi - lo) / size >> 1);
if ((*cmp) ((void *) mid, (void *) lo, size) < 0)
SWAP (mid, lo, size);
if ((*cmp) ((void *) hi, (void *) mid, size) < 0)
SWAP (mid, hi, size);
else
goto jump_over;
if ((*cmp) ((void *) mid, (void *) lo, size) < 0)
SWAP (mid, lo, size);
jump_over:
;
left_ptr = lo + size;
right_ptr = hi - size;
/* collapse the walls section of quicksort.
They are the main reason
that this algorithm runs much faster than others. */
do
{
while ((*cmp) ((void *) left_ptr, (void *) mid, size) < 0)
left_ptr += size;
while ((*cmp) ((void *) mid, (void *) right_ptr, size) < 0)
right_ptr -= size;
if (left_ptr < right_ptr)
{
SWAP (left_ptr, right_ptr, size);
if (mid == left_ptr)
mid = right_ptr;
else if (mid == right_ptr)
mid = left_ptr;
left_ptr += size;
right_ptr -= size;
}
else if (left_ptr == right_ptr)
{
left_ptr += size;
right_ptr -= size;
break;
}
}
while (left_ptr <= right_ptr);
/* Set up pointers for next iteration. First determine whether
left and right partitions are below the threshold size. If so,
ignore one or both. Otherwise, push the larger partition's
bounds on the stack and continue sorting the smaller one. */
if ((size_t) (right_ptr - lo) <= max_thresh)
{
if ((size_t) (hi - left_ptr) <= max_thresh)
/* Ignore both small partitions. */
POP (lo, hi);
else
/* Ignore small left partition. */
lo = left_ptr;
}
else if ((size_t) (hi - left_ptr) <= max_thresh)
/* Ignore small right partition. */
hi = right_ptr;
else if ((right_ptr - lo) > (hi - left_ptr))
{
/* Push larger left partition indices. */
PUSH (lo, right_ptr);
lo = left_ptr;
}
else
{
/* Push larger right partition indices. */
PUSH (left_ptr, hi);
hi = right_ptr;
}
}
}
/* Once the BASE_PTR array is partially sorted by quicksort the rest
is completely sorted using insertion sort, since this is efficient
for partitions below MAX_THRESH size. BASE_PTR points to the beginning
of the array to sort, and END_PTR points at the very last element in
the array (*not* one beyond it!). */
#define min(x, y) ((x) < (y) ? (x) : (y))
{
char *const end_ptr = &base_ptr[size * (total_elems - 1)];
char *tmp_ptr = base_ptr;
char *thresh = min(end_ptr, base_ptr + max_thresh);
register char *run_ptr;
/* Find smallest element in first threshold and place it at the
array's beginning. This is the smallest array element,
and the operation speeds up insertion sort's inner loop. */
for (run_ptr = tmp_ptr + size; run_ptr <= thresh; run_ptr += size)
if ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, size) < 0)
tmp_ptr = run_ptr;
if (tmp_ptr != base_ptr)
SWAP (tmp_ptr, base_ptr, size);
/* Insertion sort, running from left-hand-side up to right-hand-side. */
run_ptr = base_ptr + size;
while ((run_ptr += size) <= end_ptr)
{
tmp_ptr = run_ptr - size;
while ((*cmp) ((void *) run_ptr, (void *) tmp_ptr, size) < 0)
tmp_ptr -= size;
tmp_ptr += size;
if (tmp_ptr != run_ptr)
{
char *trav;
trav = run_ptr + size;
while (--trav >= run_ptr)
{
char c = *trav;
char *hi, *lo;
for (hi = lo = trav; (lo -= size) >= tmp_ptr; hi = lo)
*hi = *lo;
*hi = c;
}
}
}
}
}
int compare (const void *arg1, const void *arg2,int size)
{
return(memcmp(arg1, arg2,size));
}
#ifndef __MVS__
char testArray[10][50] = {
};
int main ()
{
int i;
_quicksort((char *) &testArray, 10, 50, compare);
return 0;
}
#endif
References
- Software—Practice and Experience, Vol. 23(11), 1249–1265 (November 1993) Engineering a Sort Function, Jon L. Bentley M. Douglas McIlroy