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ru.algorithms
- RU.ALGORITHMS ----------------------------------------------------------------
From : Yuriy Kaminskiy 2:5020/517.21 12 Dec 2001 06:08:38
To : Maxim Lanovoy
Subject : Re: Дайте алгоритм быстрой сортировки
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Hello, Maxim!
>>>>> On 10:54 11/12/2001, Maxim Lanovoy <2:463/1124.6> writes:
IG> чтобы сортировал любые элементы, как стандартный qsort. Только,
IG> желательно, не рекурсивный.
ML> Сортировка Хоаре по определению рекурсивная.
Фу. Hикто не мешает реализовать рекурсию вручную с помощью
стека. Hакладные расходы этом заметно меньше.
Ко всему прочему, 1) быстрая сортировка неэффективна на коротких (4..12 элт.
отрезках (следует использовать сортировку простыми вставками) 2) выбор в
качестве медианы первого или последнего элемента - очевидная дурость,
потому как в этом случае уже отсортированный массив становиться *худшим*
случаем (т.е. O(n^2) операций; ОЧЕHЬ плохо!); более предпочтительно
использовать медиану-из-трех 3) твоя реализация qsort нереентерабельна
(плохо!) 4) если компилятор не оптимизирует tail-recursion, то
максимальный расход стека в твоей реализации будет O(n) вместо O(log
n) [ОЧЕHЬ плохо!]
Для сравнения, см. реализацию qsort из glibc. Или еще более
продвинутую реализацию из perl-5.6.0.
--
Yuriy Kaminskiy.
--=-=-=
Content-Type: application/octet-stream
Content-Disposition: attachment; filename=qsort.c
Content-Description: glibc-2.0.7/stdlib/qsort.c
/* Copyright (C) 1991, 1992, 1996, 1997 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 Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include <stdlib.h>
#include <string.h>
extern void _quicksort __P ((void *const pbase, size_t total_elems,
size_t size, __compar_fn_t cmp));
/* 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.
This particular magic number was chosen to work best on a Sun 4/260. */
#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. */
#define STACK_SIZE (8 * sizeof(unsigned long int))
#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 pointer that store the
next array partition to sort. To save time, this maximum amount
of space required to store an array of MAX_INT is allocated on the
stack. Assuming a 32-bit integer, this needs only 32 *
sizeof(stack_node) == 136 bits. Pretty cheap, actually.
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 (n)
stack size is needed (actually O(1) in this case)! */
void
_quicksort (pbase, total_elems, size, cmp)
void *const pbase;
size_t total_elems;
size_t size;
int (*cmp) __P ((const void *, const void *));
{
register char *base_ptr = (char *) pbase;
/* Allocating SIZE bytes for a pivot buffer facilitates a better
algorithm below since we can do comparisons directly on the pivot. */
char *pivot_buffer = (char *) __alloca (size);
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)];
/* Largest size needed for 32-bit int!!! */
stack_node stack[STACK_SIZE];
stack_node *top = stack + 1;
while (STACK_NOT_EMPTY)
{
char *left_ptr;
char *right_ptr;
char *pivot = pivot_buffer;
/* 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. */
char *mid = lo + size * ((hi - lo) / size >> 1);
if ((*cmp) ((void *) mid, (void *) lo) < 0)
SWAP (mid, lo, size);
if ((*cmp) ((void *) hi, (void *) mid) < 0)
SWAP (mid, hi, size);
else
goto jump_over;
if ((*cmp) ((void *) mid, (void *) lo) < 0)
SWAP (mid, lo, size);
jump_over:;
memcpy (pivot, mid, size);
pivot = pivot_buffer;
left_ptr = lo + size;
right_ptr = hi - size;
/* Here's the famous ``collapse the walls'' section of quicksort.
Gotta like those tight inner loops! They are the main reason
that this algorithm runs much faster than others. */
do
{
while ((*cmp) ((void *) left_ptr, (void *) pivot) < 0)
left_ptr += size;
while ((*cmp) ((void *) pivot, (void *) right_ptr) < 0)
right_ptr -= size;
if (left_ptr < right_ptr)
{
SWAP (left_ptr, right_ptr, size);
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) < 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) < 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;
}
}
}
}
}
--=-=-=--
--- Gnus/5.0808 (Gnus v5.8.8) XEmacs/21.1 (Cuyahoga Valley)
* Origin: none (2:5020/517.21@fidonet)
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