heapsort.c

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/*-
 * Copyright (c) 1991, 1993
 *  The Regents of the University of California.  All rights reserved.
 *
 * This code is derived from software contributed to Berkeley by
 * Ronnie Kon at Mindcraft Inc., Kevin Lew and Elmer Yglesias.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 4. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#include <stddef.h>
#include <stdlib.h>

/*
 * Swap two areas of size number of bytes.  Although qsort(3) permits random
 * blocks of memory to be sorted, sorting pointers is almost certainly the
 * common case (and, were it not, could easily be made so).  Regardless, it
 * isn't worth optimizing; the SWAP's get sped up by the cache, and pointer
 * arithmetic gets lost in the time required for comparison function calls.
 */
#define SWAP(a, b, count, size, tmp) \
    {                                \
        count = size;                \
        do                           \
        {                            \
            tmp = *a;                \
            *a++ = *b;               \
            *b++ = tmp;              \
        } while(--count);            \
    }

/* Copy one block of size size to another. */
#define COPY(a, b, count, size, tmp1, tmp2) \
    {                                       \
        count = size;                       \
        tmp1 = a;                           \
        tmp2 = b;                           \
        do                                  \
        {                                   \
            *tmp1++ = *tmp2++;              \
        } while(--count);                   \
    }

/*
 * Build the list into a heap, where a heap is defined such that for
 * the records K1 ... KN, Kj/2 >= Kj for 1 <= j/2 <= j <= N.
 *
 * There two cases.  If j == nmemb, select largest of Ki and Kj.  If
 * j < nmemb, select largest of Ki, Kj and Kj+1.
 */
#define CREATE(initval, nmemb, par_i, child_i, par, child, size, count, tmp)  \
    {                                                                         \
        for(par_i = initval; (child_i = par_i * 2) <= nmemb; par_i = child_i) \
        {                                                                     \
            child = base + child_i * size;                                    \
            if(child_i < nmemb && compar(child, child + size) < 0)            \
            {                                                                 \
                child += size;                                                \
                ++child_i;                                                    \
            }                                                                 \
            par = base + par_i * size;                                        \
            if(compar(child, par) <= 0)                                       \
                break;                                                        \
            SWAP(par, child, count, size, tmp);                               \
        }                                                                     \
    }

/*
 * Select the top of the heap and 'heapify'.  Since by far the most expensive
 * action is the call to the compar function, a considerable optimization
 * in the average case can be achieved due to the fact that k, the displaced
 * elememt, is ususally quite small, so it would be preferable to first
 * heapify, always maintaining the invariant that the larger child is copied
 * over its parent's record.
 *
 * Then, starting from the *bottom* of the heap, finding k's correct place,
 * again maintianing the invariant.  As a result of the invariant no element
 * is 'lost' when k is assigned its correct place in the heap.
 *
 * The time savings from this optimization are on the order of 15-20% for the
 * average case. See Knuth, Vol. 3, page 158, problem 18.
 *
 * XXX Don't break the #define SELECT line, below.  Reiser cpp gets upset.
 */
#define SELECT(par_i, child_i, nmemb, par, child, size, k, count, tmp1, tmp2) \
    {                                                                         \
        for(par_i = 1; (child_i = par_i * 2) <= nmemb; par_i = child_i)       \
        {                                                                     \
            child = base + child_i * size;                                    \
            if(child_i < nmemb && compar(child, child + size) < 0)            \
            {                                                                 \
                child += size;                                                \
                ++child_i;                                                    \
            }                                                                 \
            par = base + par_i * size;                                        \
            COPY(par, child, count, size, tmp1, tmp2);                        \
        }                                                                     \
        for(;;)                                                               \
        {                                                                     \
            child_i = par_i;                                                  \
            par_i = child_i / 2;                                              \
            child = base + child_i * size;                                    \
            par = base + par_i * size;                                        \
            if(child_i == 1 || compar(k, par) < 0)                            \
            {                                                                 \
                COPY(child, k, count, size, tmp1, tmp2);                      \
                break;                                                        \
            }                                                                 \
            COPY(child, par, count, size, tmp1, tmp2);                        \
        }                                                                     \
    }

/*
 * Heapsort -- Knuth, Vol. 3, page 145.  Runs in O (N lg N), both average
 * and worst.  While heapsort is faster than the worst case of quicksort,
 * the BSD quicksort does median selection so that the chance of finding
 * a data set that will trigger the worst case is nonexistent.  Heapsort's
 * only advantage over quicksort is that it requires little additional memory.
 */
int heapsort(vbase, nmemb, size, compar) void* vbase;
size_t nmemb, size;
int (*compar)(const void*, const void*);
{
    size_t cnt, i, j, l;
    char tmp, *tmp1, *tmp2;
    char *base, *k, *p, *t;

    if(nmemb <= 1)
    {
        {
            return (0);
        }
    }

    if(!size)
    {
        // errno = EINVAL;
        return (-1);
    }

    if((k = malloc(size)) == NULL)
    {
        {
            return (-1);
        }
    }

    /*
     * Items are numbered from 1 to nmemb, so offset from size bytes
     * below the starting address.
     */
    base = (char*)vbase - size;

    for(l = nmemb / 2 + 1; --l;)
        CREATE(l, nmemb, i, j, t, p, size, cnt, tmp);

    /*
     * For each element of the heap, save the largest element into its
     * final slot, save the displaced element (k), then recreate the
     * heap.
     */
    while(nmemb > 1)
    {
        COPY(k, base + nmemb * size, cnt, size, tmp1, tmp2);
        COPY(base + nmemb * size, base + size, cnt, size, tmp1, tmp2);
        --nmemb;
        SELECT(i, j, nmemb, t, p, size, k, cnt, tmp1, tmp2);
    }
    free(k);
    return (0);
}