heapsort.c revision 1573
11573Srgrimes/*- 21573Srgrimes * Copyright (c) 1991, 1993 31573Srgrimes * The Regents of the University of California. All rights reserved. 41573Srgrimes * 51573Srgrimes * This code is derived from software contributed to Berkeley by 61573Srgrimes * Ronnie Kon at Mindcraft Inc., Kevin Lew and Elmer Yglesias. 71573Srgrimes * 81573Srgrimes * Redistribution and use in source and binary forms, with or without 91573Srgrimes * modification, are permitted provided that the following conditions 101573Srgrimes * are met: 111573Srgrimes * 1. Redistributions of source code must retain the above copyright 121573Srgrimes * notice, this list of conditions and the following disclaimer. 131573Srgrimes * 2. Redistributions in binary form must reproduce the above copyright 141573Srgrimes * notice, this list of conditions and the following disclaimer in the 151573Srgrimes * documentation and/or other materials provided with the distribution. 161573Srgrimes * 3. All advertising materials mentioning features or use of this software 171573Srgrimes * must display the following acknowledgement: 181573Srgrimes * This product includes software developed by the University of 191573Srgrimes * California, Berkeley and its contributors. 201573Srgrimes * 4. Neither the name of the University nor the names of its contributors 211573Srgrimes * may be used to endorse or promote products derived from this software 221573Srgrimes * without specific prior written permission. 231573Srgrimes * 241573Srgrimes * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 251573Srgrimes * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 261573Srgrimes * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 271573Srgrimes * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 281573Srgrimes * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 291573Srgrimes * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 301573Srgrimes * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 311573Srgrimes * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 321573Srgrimes * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 331573Srgrimes * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 341573Srgrimes * SUCH DAMAGE. 351573Srgrimes */ 361573Srgrimes 371573Srgrimes#if defined(LIBC_SCCS) && !defined(lint) 381573Srgrimesstatic char sccsid[] = "@(#)heapsort.c 8.1 (Berkeley) 6/4/93"; 391573Srgrimes#endif /* LIBC_SCCS and not lint */ 401573Srgrimes 411573Srgrimes#include <sys/types.h> 421573Srgrimes#include <errno.h> 431573Srgrimes#include <stdlib.h> 441573Srgrimes#include <stddef.h> 451573Srgrimes 461573Srgrimes/* 471573Srgrimes * Swap two areas of size number of bytes. Although qsort(3) permits random 481573Srgrimes * blocks of memory to be sorted, sorting pointers is almost certainly the 491573Srgrimes * common case (and, were it not, could easily be made so). Regardless, it 501573Srgrimes * isn't worth optimizing; the SWAP's get sped up by the cache, and pointer 511573Srgrimes * arithmetic gets lost in the time required for comparison function calls. 521573Srgrimes */ 531573Srgrimes#define SWAP(a, b, count, size, tmp) { \ 541573Srgrimes count = size; \ 551573Srgrimes do { \ 561573Srgrimes tmp = *a; \ 571573Srgrimes *a++ = *b; \ 581573Srgrimes *b++ = tmp; \ 591573Srgrimes } while (--count); \ 601573Srgrimes} 611573Srgrimes 621573Srgrimes/* Copy one block of size size to another. */ 631573Srgrimes#define COPY(a, b, count, size, tmp1, tmp2) { \ 641573Srgrimes count = size; \ 651573Srgrimes tmp1 = a; \ 661573Srgrimes tmp2 = b; \ 671573Srgrimes do { \ 681573Srgrimes *tmp1++ = *tmp2++; \ 691573Srgrimes } while (--count); \ 701573Srgrimes} 711573Srgrimes 721573Srgrimes/* 731573Srgrimes * Build the list into a heap, where a heap is defined such that for 741573Srgrimes * the records K1 ... KN, Kj/2 >= Kj for 1 <= j/2 <= j <= N. 751573Srgrimes * 761573Srgrimes * There two cases. If j == nmemb, select largest of Ki and Kj. If 771573Srgrimes * j < nmemb, select largest of Ki, Kj and Kj+1. 781573Srgrimes */ 791573Srgrimes#define CREATE(initval, nmemb, par_i, child_i, par, child, size, count, tmp) { \ 801573Srgrimes for (par_i = initval; (child_i = par_i * 2) <= nmemb; \ 811573Srgrimes par_i = child_i) { \ 821573Srgrimes child = base + child_i * size; \ 831573Srgrimes if (child_i < nmemb && compar(child, child + size) < 0) { \ 841573Srgrimes child += size; \ 851573Srgrimes ++child_i; \ 861573Srgrimes } \ 871573Srgrimes par = base + par_i * size; \ 881573Srgrimes if (compar(child, par) <= 0) \ 891573Srgrimes break; \ 901573Srgrimes SWAP(par, child, count, size, tmp); \ 911573Srgrimes } \ 921573Srgrimes} 931573Srgrimes 941573Srgrimes/* 951573Srgrimes * Select the top of the heap and 'heapify'. Since by far the most expensive 961573Srgrimes * action is the call to the compar function, a considerable optimization 971573Srgrimes * in the average case can be achieved due to the fact that k, the displaced 981573Srgrimes * elememt, is ususally quite small, so it would be preferable to first 991573Srgrimes * heapify, always maintaining the invariant that the larger child is copied 1001573Srgrimes * over its parent's record. 1011573Srgrimes * 1021573Srgrimes * Then, starting from the *bottom* of the heap, finding k's correct place, 1031573Srgrimes * again maintianing the invariant. As a result of the invariant no element 1041573Srgrimes * is 'lost' when k is assigned its correct place in the heap. 1051573Srgrimes * 1061573Srgrimes * The time savings from this optimization are on the order of 15-20% for the 1071573Srgrimes * average case. See Knuth, Vol. 3, page 158, problem 18. 1081573Srgrimes * 1091573Srgrimes * XXX Don't break the #define SELECT line, below. Reiser cpp gets upset. 1101573Srgrimes */ 1111573Srgrimes#define SELECT(par_i, child_i, nmemb, par, child, size, k, count, tmp1, tmp2) { \ 1121573Srgrimes for (par_i = 1; (child_i = par_i * 2) <= nmemb; par_i = child_i) { \ 1131573Srgrimes child = base + child_i * size; \ 1141573Srgrimes if (child_i < nmemb && compar(child, child + size) < 0) { \ 1151573Srgrimes child += size; \ 1161573Srgrimes ++child_i; \ 1171573Srgrimes } \ 1181573Srgrimes par = base + par_i * size; \ 1191573Srgrimes COPY(par, child, count, size, tmp1, tmp2); \ 1201573Srgrimes } \ 1211573Srgrimes for (;;) { \ 1221573Srgrimes child_i = par_i; \ 1231573Srgrimes par_i = child_i / 2; \ 1241573Srgrimes child = base + child_i * size; \ 1251573Srgrimes par = base + par_i * size; \ 1261573Srgrimes if (child_i == 1 || compar(k, par) < 0) { \ 1271573Srgrimes COPY(child, k, count, size, tmp1, tmp2); \ 1281573Srgrimes break; \ 1291573Srgrimes } \ 1301573Srgrimes COPY(child, par, count, size, tmp1, tmp2); \ 1311573Srgrimes } \ 1321573Srgrimes} 1331573Srgrimes 1341573Srgrimes/* 1351573Srgrimes * Heapsort -- Knuth, Vol. 3, page 145. Runs in O (N lg N), both average 1361573Srgrimes * and worst. While heapsort is faster than the worst case of quicksort, 1371573Srgrimes * the BSD quicksort does median selection so that the chance of finding 1381573Srgrimes * a data set that will trigger the worst case is nonexistent. Heapsort's 1391573Srgrimes * only advantage over quicksort is that it requires little additional memory. 1401573Srgrimes */ 1411573Srgrimesint 1421573Srgrimesheapsort(vbase, nmemb, size, compar) 1431573Srgrimes void *vbase; 1441573Srgrimes size_t nmemb, size; 1451573Srgrimes int (*compar) __P((const void *, const void *)); 1461573Srgrimes{ 1471573Srgrimes register int cnt, i, j, l; 1481573Srgrimes register char tmp, *tmp1, *tmp2; 1491573Srgrimes char *base, *k, *p, *t; 1501573Srgrimes 1511573Srgrimes if (nmemb <= 1) 1521573Srgrimes return (0); 1531573Srgrimes 1541573Srgrimes if (!size) { 1551573Srgrimes errno = EINVAL; 1561573Srgrimes return (-1); 1571573Srgrimes } 1581573Srgrimes 1591573Srgrimes if ((k = malloc(size)) == NULL) 1601573Srgrimes return (-1); 1611573Srgrimes 1621573Srgrimes /* 1631573Srgrimes * Items are numbered from 1 to nmemb, so offset from size bytes 1641573Srgrimes * below the starting address. 1651573Srgrimes */ 1661573Srgrimes base = (char *)vbase - size; 1671573Srgrimes 1681573Srgrimes for (l = nmemb / 2 + 1; --l;) 1691573Srgrimes CREATE(l, nmemb, i, j, t, p, size, cnt, tmp); 1701573Srgrimes 1711573Srgrimes /* 1721573Srgrimes * For each element of the heap, save the largest element into its 1731573Srgrimes * final slot, save the displaced element (k), then recreate the 1741573Srgrimes * heap. 1751573Srgrimes */ 1761573Srgrimes while (nmemb > 1) { 1771573Srgrimes COPY(k, base + nmemb * size, cnt, size, tmp1, tmp2); 1781573Srgrimes COPY(base + nmemb * size, base + size, cnt, size, tmp1, tmp2); 1791573Srgrimes --nmemb; 1801573Srgrimes SELECT(i, j, nmemb, t, p, size, k, cnt, tmp1, tmp2); 1811573Srgrimes } 1821573Srgrimes free(k); 1831573Srgrimes return (0); 1841573Srgrimes} 185