1. stdlib/bsearch.c
以下代码实现了有序数组的二分搜索。
1 /* $NetBSD: bsearch.c,v 1.14.6.1 2012/04/17 00:05:25 yamt Exp $ */
2
3 /*
4 * Copyright (c) 1990, 1993
5 * The Regents of the University of California. All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of the University nor the names of its contributors
16 * may be used to endorse or promote products derived from this software
17 * without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS‘‘ AND
20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29 * SUCH DAMAGE.
30 */
31
32 #include <sys/cdefs.h>
33 #if defined(LIBC_SCCS) && !defined(lint)
34 #if 0
35 static char sccsid[] = "@(#)bsearch.c 8.1 (Berkeley) 6/4/93";
36 #else
37 __RCSID("$NetBSD: bsearch.c,v 1.14.6.1 2012/04/17 00:05:25 yamt Exp $");
38 #endif
39 #endif /* LIBC_SCCS and not lint */
40
41 #include <assert.h>
42 #include <errno.h>
43 #include <stdlib.h>
44
45 /*
46 * Perform a binary search.
47 *
48 * The code below is a bit sneaky. After a comparison fails, we
49 * divide the work in half by moving either left or right. If lim
50 * is odd, moving left simply involves halving lim: e.g., when lim
51 * is 5 we look at item 2, so we change lim to 2 so that we will
52 * look at items 0 & 1. If lim is even, the same applies. If lim
53 * is odd, moving right again involes halving lim, this time moving
54 * the base up one item past p: e.g., when lim is 5 we change base
55 * to item 3 and make lim 2 so that we will look at items 3 and 4.
56 * If lim is even, however, we have to shrink it by one before
57 * halving: e.g., when lim is 4, we still looked at item 2, so we
58 * have to make lim 3, then halve, obtaining 1, so that we will only
59 * look at item 3.
60 */
61 void *
62 bsearch(const void *key, const void *base0, size_t nmemb, size_t size,
63 int (*compar)(const void *, const void *))
64 {
65 const char *base = base0;
66 size_t lim;
67 int cmp;
68 const void *p;
69
70 _DIAGASSERT(key != NULL);
71 _DIAGASSERT(base0 != NULL || nmemb == 0);
72 _DIAGASSERT(compar != NULL);
73
74 for (lim = nmemb; lim != 0; lim >>= 1) {
75 p = base + (lim >> 1) * size;
76 cmp = (*compar)(key, p);
77 if (cmp == 0)
78 return __UNCONST(p);
79 if (cmp > 0) { /* key > p: move right */
80 base = (const char *)p + size;
81 lim--;
82 } /* else move left */
83 }
84 return (NULL);
85 }
以上代码的正确性由其循环变式和不变式共同保证。设欲搜索的结果为 $R$（如果存在的话），每次迭代保证 $R\in[base,base+lim)$，迭代后 $lim$ 至少减半。
在第一轮迭代开始之前，以上命题显然成立。假设某次迭代前有 $R\in[base,base+lim)$，我们首先计算 $p=base+\lfloor lim/2\rfloor$ 的值并与 *key 进行比较：
(i) 如果二者相等则 $p$ 所在指针即为搜索结果，直接返回；
(ii) 如果 (*compar)(key,p)<0，则说明 $R\in[base,p)=[base,base+\lfloor lim/2 \rfloor)$，故直接赋值 $lim := \lfloor lim/2\rfloor$；
(iii) 如果 (*compar)(key,p)>0，则说明 $R\in[p+1,base+lim)=[base+\lfloor lim/2\rfloor+1,base+lim)$，需要赋值 $base := p+1$ 和 $$\begin{align*}lim&:= lim-\lfloor lim/2\rfloor-1 = \lceil lim/2\rceil-1\\ &= \lfloor(lim+1)/2\rfloor-1 = \lfloor(lim-1)/2\rfloor\end{align*}$$
第一种情况退出循环不必考虑，其余两种都有 $lim_{new}\leq \lfloor lim_{old}/2\rfloor$，保证循环能够终止。
2. stdlib/qsort.c
以下代码实现了快速排序，我已根据自己理解做了部分注释。
1 /* $NetBSD: qsort.c,v 1.21.4.1 2012/10/30 18:58:59 yamt Exp $ */
2
3 /*-
4 * Copyright (c) 1992, 1993
5 * The Regents of the University of California. All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of the University nor the names of its contributors
16 * may be used to endorse or promote products derived from this software
17 * without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS‘‘ AND
20 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
21 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
22 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
23 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
24 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
25 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
26 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
27 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
28 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
29 * SUCH DAMAGE.
30 */
31
32 #include <sys/cdefs.h>
33 #if defined(LIBC_SCCS) && !defined(lint)
34 #if 0
35 static char sccsid[] = "@(#)qsort.c 8.1 (Berkeley) 6/4/93";
36 #else
37 __RCSID("$NetBSD: qsort.c,v 1.21.4.1 2012/10/30 18:58:59 yamt Exp $");
38 #endif
39 #endif /* LIBC_SCCS and not lint */
40
41 #include <sys/types.h>
42
43 #include <assert.h>
44 #include <errno.h>
45 #include <stdlib.h>
46
47 static inline char *med3(char *, char *, char *,
48 int (*)(const void *, const void *));
49 static inline void swapfunc(char *, char *, size_t, int);
50
51 #define min(a, b) (a) < (b) ? a : b
52
53 /*
54 * Qsort routine from Bentley & McIlroy‘s "Engineering a Sort Function".
55 */
56 #define swapcode(TYPE, parmi, parmj, n) { 57 size_t i = (n) / sizeof (TYPE); 58 TYPE *pi = (TYPE *)(void *)(parmi); 59 TYPE *pj = (TYPE *)(void *)(parmj); 60 do { 61 TYPE t = *pi; 62 *pi++ = *pj; 63 *pj++ = t; 64 } while (--i > 0); 65 }
66
67 #define SWAPINIT(a, es) swaptype = ((char *)a - (char *)0) % sizeof(long) || 68 es % sizeof(long) ? 2 : es == sizeof(long)? 0 : 1;
69
70 static inline void
71 swapfunc(char *a, char *b, size_t n, int swaptype)
72 {
73
74 if (swaptype <= 1)
75 swapcode(long, a, b, n)
76 else
77 swapcode(char, a, b, n)
78 }
79
80 #define swap(a, b) 81 if (swaptype == 0) { 82 long t = *(long *)(void *)(a); 83 *(long *)(void *)(a) = *(long *)(void *)(b); 84 *(long *)(void *)(b) = t; 85 } else 86 swapfunc(a, b, es, swaptype)
87
88 #define vecswap(a, b, n) if ((n) > 0) swapfunc((a), (b), (size_t)(n), swaptype)
89
90 static inline char *
91 med3(char *a, char *b, char *c,
92 int (*cmp)(const void *, const void *))
93 {
94
95 return cmp(a, b) < 0 ?
96 (cmp(b, c) < 0 ? b : (cmp(a, c) < 0 ? c : a ))
97 :(cmp(b, c) > 0 ? b : (cmp(a, c) < 0 ? a : c ));
98 }
99
100 void
101 qsort(void *a, size_t n, size_t es,
102 int (*cmp)(const void *, const void *))
103 {
104 char *pa, *pb, *pc, *pd, *pl, *pm, *pn;
105 size_t d, r;
106 int swaptype, cmp_result;
107
108 _DIAGASSERT(a != NULL || n == 0 || es == 0);
109 _DIAGASSERT(cmp != NULL);
110
111 loop: SWAPINIT(a, es);
112 if (n < 7) {
113 /* For small input, Insertion Sort is more efficient, */
114 for (pm = (char *) a + es; pm < (char *) a + n * es; pm += es)
115 for (pl = pm; pl > (char *) a && cmp(pl - es, pl) > 0;
116 pl -= es)
117 swap(pl, pl - es);
118 return;
119 } /* otherwise Quicksort is adopted */
120
121 /* Choose a good pivot and put it at the head of the array;
122 * larger the input is, more complicated mechanism is exploited. */
123 pm = (char *) a + (n / 2) * es;
124 if (n > 7) {
125 pl = (char *) a;
126 pn = (char *) a + (n - 1) * es;
127 if (n > 40) {
128 d = (n / 8) * es;
129 pl = med3(pl, pl + d, pl + 2 * d, cmp);
130 pm = med3(pm - d, pm, pm + d, cmp);
131 pn = med3(pn - 2 * d, pn - d, pn, cmp);
132 }
133 pm = med3(pl, pm, pn, cmp);
134 }
135 swap(a, pm);
136
137 /* Loop for Partition: */
138 pa = pb = (char *) a + es;
139 pc = pd = (char *) a + (n - 1) * es;
140 for (;;) {
141 /* [a,pa) are equal to the pivot;
142 * [pa,pb) are smaller than the pivot;
143 * [pb,pc] are unknown elements;
144 * (pc,pd] are larger than the pivot;
145 * (pd,pn) are equal to the pivot*/
146 while (pb <= pc && (cmp_result = cmp(pb, a)) <= 0) {
147 /* search from left to right for the 1st element
148 * larger than the pivot */
149 if (cmp_result == 0) {
150 swap(pa, pb);
151 pa += es;
152 }
153 pb += es;
154 }
155 while (pb <= pc && (cmp_result = cmp(pc, a)) >= 0) {
156 /* search from right to left for the 1st element
157 * smaller than the pivot */
158 if (cmp_result == 0) {
159 swap(pc, pd);
160 pd -= es;
161 }
162 pc -= es;
163 }
164 if (pb > pc)
165 break;
166 swap(pb, pc);
167 pb += es;
168 pc -= es;
169 }
170 pn = (char *) a + n * es;
171 r = min(pa - (char *) a, pb - pa);
172 vecswap(a, pb - r, r);
173 r = min((size_t)(pd - pc), pn - pd - es);
174 vecswap(pb, pn - r, r);
175 /* [a,a+pb-pa) is smaller than the pivot
176 * [a+pb-pa,pn-pd+pc) is equal to the pivot
177 * [pn-pd+pc,pn) is larger than the pivot */
178
179 /* Divide and Conquer: */
180 if ((r = pb - pa) > es)
181 /* recursion for left part [a, a+pb-a) */
182 qsort(a, r / es, es, cmp);
183 if ((r = pd - pc) > es) {
184 /* Iterate rather than recurse to save stack space */
185 a = pn - r;
186 n = r / es;
187 goto loop;
188 } /* qsort(pn - r, r / es, es, cmp); */
189 }
References:
1. NetBSD stdlib源码：http://cvsweb.netbsd.org/bsdweb.cgi/src/lib/libc/stdlib/
时间： 2024-08-02 14:30:21