1 /*- 2 * Copyright (c) 1991, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * This code is derived from software contributed to Berkeley by 6 * Ronnie Kon at Mindcraft Inc., Kevin Lew and Elmer Yglesias. 7 * 8 * %sccs.include.redist.c% 9 */ 10 11 #if defined(LIBC_SCCS) && !defined(lint) 12 static char sccsid[] = "@(#)heapsort.c 8.1 (Berkeley) 06/04/93"; 13 #endif /* LIBC_SCCS and not lint */ 14 15 #include <sys/types.h> 16 #include <errno.h> 17 #include <stdlib.h> 18 #include <stddef.h> 19 20 /* 21 * Swap two areas of size number of bytes. Although qsort(3) permits random 22 * blocks of memory to be sorted, sorting pointers is almost certainly the 23 * common case (and, were it not, could easily be made so). Regardless, it 24 * isn't worth optimizing; the SWAP's get sped up by the cache, and pointer 25 * arithmetic gets lost in the time required for comparison function calls. 26 */ 27 #define SWAP(a, b, count, size, tmp) { \ 28 count = size; \ 29 do { \ 30 tmp = *a; \ 31 *a++ = *b; \ 32 *b++ = tmp; \ 33 } while (--count); \ 34 } 35 36 /* Copy one block of size size to another. */ 37 #define COPY(a, b, count, size, tmp1, tmp2) { \ 38 count = size; \ 39 tmp1 = a; \ 40 tmp2 = b; \ 41 do { \ 42 *tmp1++ = *tmp2++; \ 43 } while (--count); \ 44 } 45 46 /* 47 * Build the list into a heap, where a heap is defined such that for 48 * the records K1 ... KN, Kj/2 >= Kj for 1 <= j/2 <= j <= N. 49 * 50 * There two cases. If j == nmemb, select largest of Ki and Kj. If 51 * j < nmemb, select largest of Ki, Kj and Kj+1. 52 */ 53 #define CREATE(initval, nmemb, par_i, child_i, par, child, size, count, tmp) { \ 54 for (par_i = initval; (child_i = par_i * 2) <= nmemb; \ 55 par_i = child_i) { \ 56 child = base + child_i * size; \ 57 if (child_i < nmemb && compar(child, child + size) < 0) { \ 58 child += size; \ 59 ++child_i; \ 60 } \ 61 par = base + par_i * size; \ 62 if (compar(child, par) <= 0) \ 63 break; \ 64 SWAP(par, child, count, size, tmp); \ 65 } \ 66 } 67 68 /* 69 * Select the top of the heap and 'heapify'. Since by far the most expensive 70 * action is the call to the compar function, a considerable optimization 71 * in the average case can be achieved due to the fact that k, the displaced 72 * elememt, is ususally quite small, so it would be preferable to first 73 * heapify, always maintaining the invariant that the larger child is copied 74 * over its parent's record. 75 * 76 * Then, starting from the *bottom* of the heap, finding k's correct place, 77 * again maintianing the invariant. As a result of the invariant no element 78 * is 'lost' when k is assigned its correct place in the heap. 79 * 80 * The time savings from this optimization are on the order of 15-20% for the 81 * average case. See Knuth, Vol. 3, page 158, problem 18. 82 * 83 * XXX Don't break the #define SELECT line, below. Reiser cpp gets upset. 84 */ 85 #define SELECT(par_i, child_i, nmemb, par, child, size, k, count, tmp1, tmp2) { \ 86 for (par_i = 1; (child_i = par_i * 2) <= nmemb; par_i = child_i) { \ 87 child = base + child_i * size; \ 88 if (child_i < nmemb && compar(child, child + size) < 0) { \ 89 child += size; \ 90 ++child_i; \ 91 } \ 92 par = base + par_i * size; \ 93 COPY(par, child, count, size, tmp1, tmp2); \ 94 } \ 95 for (;;) { \ 96 child_i = par_i; \ 97 par_i = child_i / 2; \ 98 child = base + child_i * size; \ 99 par = base + par_i * size; \ 100 if (child_i == 1 || compar(k, par) < 0) { \ 101 COPY(child, k, count, size, tmp1, tmp2); \ 102 break; \ 103 } \ 104 COPY(child, par, count, size, tmp1, tmp2); \ 105 } \ 106 } 107 108 /* 109 * Heapsort -- Knuth, Vol. 3, page 145. Runs in O (N lg N), both average 110 * and worst. While heapsort is faster than the worst case of quicksort, 111 * the BSD quicksort does median selection so that the chance of finding 112 * a data set that will trigger the worst case is nonexistent. Heapsort's 113 * only advantage over quicksort is that it requires little additional memory. 114 */ 115 int 116 heapsort(vbase, nmemb, size, compar) 117 void *vbase; 118 size_t nmemb, size; 119 int (*compar) __P((const void *, const void *)); 120 { 121 register int cnt, i, j, l; 122 register char tmp, *tmp1, *tmp2; 123 char *base, *k, *p, *t; 124 125 if (nmemb <= 1) 126 return (0); 127 128 if (!size) { 129 errno = EINVAL; 130 return (-1); 131 } 132 133 if ((k = malloc(size)) == NULL) 134 return (-1); 135 136 /* 137 * Items are numbered from 1 to nmemb, so offset from size bytes 138 * below the starting address. 139 */ 140 base = (char *)vbase - size; 141 142 for (l = nmemb / 2 + 1; --l;) 143 CREATE(l, nmemb, i, j, t, p, size, cnt, tmp); 144 145 /* 146 * For each element of the heap, save the largest element into its 147 * final slot, save the displaced element (k), then recreate the 148 * heap. 149 */ 150 while (nmemb > 1) { 151 COPY(k, base + nmemb * size, cnt, size, tmp1, tmp2); 152 COPY(base + nmemb * size, base + size, cnt, size, tmp1, tmp2); 153 --nmemb; 154 SELECT(i, j, nmemb, t, p, size, k, cnt, tmp1, tmp2); 155 } 156 free(k); 157 return (0); 158 } 159