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
heapsort(vbase,nmemb,size,compar)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