1 /* Stable-sorting of an array using mergesort.
2 Copyright (C) 2009-2023 Free Software Foundation, Inc.
3 Written by Bruno Haible <bruno@clisp.org>, 2009.
4
5 This file is free software: you can redistribute it and/or modify
6 it under the terms of the GNU Lesser General Public License as
7 published by the Free Software Foundation; either version 2.1 of the
8 License, or (at your option) any later version.
9
10 This file is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public License
16 along with this program. If not, see <https://www.gnu.org/licenses/>. */
17
18 /* This file implements stable sorting of an array, using the mergesort
19 algorithm.
20 Worst-case running time for an array of length N is O(N log N).
21 Unlike the mpsort module, the algorithm here attempts to minimize not
22 only the number of comparisons, but also the number of copying operations.
23
24 Before including this file, you need to define
25 ELEMENT The type of every array element.
26 COMPARE A two-argument macro that takes two 'const ELEMENT *'
27 pointers and returns a negative, zero, or positive 'int'
28 value if the element pointed to by the first argument is,
29 respectively, less, equal, or greater than the element
30 pointed to by the second argument.
31 STATIC The storage class of the functions being defined.
32 STATIC_FROMTO (Optional.) Overrides STATIC for the 'merge_sort_fromto'
33 function.
34 Before including this file, you also need to include:
35 #include <stddef.h>
36 */
37
38 /* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into
39 dst[0..n1+n2-1]. In case of ambiguity, put the elements of src1
40 before the elements of src2.
41 n1 and n2 must be > 0.
42 The arrays src1 and src2 must not overlap the dst array, except that
43 src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1]. */
44 static void
45 merge (const ELEMENT *src1, size_t n1,
46 const ELEMENT *src2, size_t n2,
47 ELEMENT *dst)
48 {
49 for (;;) /* while (n1 > 0 && n2 > 0) */
50 {
51 if (COMPARE (src1, src2) <= 0)
52 {
53 *dst++ = *src1++;
54 n1--;
55 if (n1 == 0)
56 break;
57 }
58 else
59 {
60 *dst++ = *src2++;
61 n2--;
62 if (n2 == 0)
63 break;
64 }
65 }
66 /* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0. */
67 if (n1 > 0)
68 {
69 if (dst != src1)
70 do
71 {
72 *dst++ = *src1++;
73 n1--;
74 }
75 while (n1 > 0);
76 }
77 else /* n2 > 0 */
78 {
79 if (dst != src2)
80 do
81 {
82 *dst++ = *src2++;
83 n2--;
84 }
85 while (n2 > 0);
86 }
87 }
88
89 /* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary
90 (scratch) storage.
91 The arrays src, dst, tmp must not overlap. */
92 #ifdef STATIC_FROMTO
93 STATIC_FROMTO
94 #else
95 STATIC
96 #endif
97 void
98 merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp)
99 {
100 switch (n)
101 {
102 case 0:
103 return;
104 case 1:
105 /* Nothing to do. */
106 dst[0] = src[0];
107 return;
108 case 2:
109 /* Trivial case. */
110 if (COMPARE (&src[0], &src[1]) <= 0)
111 {
112 /* src[0] <= src[1] */
113 dst[0] = src[0];
114 dst[1] = src[1];
115 }
116 else
117 {
118 dst[0] = src[1];
119 dst[1] = src[0];
120 }
121 break;
122 case 3:
123 /* Simple case. */
124 if (COMPARE (&src[0], &src[1]) <= 0)
125 {
126 if (COMPARE (&src[1], &src[2]) <= 0)
127 {
128 /* src[0] <= src[1] <= src[2] */
129 dst[0] = src[0];
130 dst[1] = src[1];
131 dst[2] = src[2];
132 }
133 else if (COMPARE (&src[0], &src[2]) <= 0)
134 {
135 /* src[0] <= src[2] < src[1] */
136 dst[0] = src[0];
137 dst[1] = src[2];
138 dst[2] = src[1];
139 }
140 else
141 {
142 /* src[2] < src[0] <= src[1] */
143 dst[0] = src[2];
144 dst[1] = src[0];
145 dst[2] = src[1];
146 }
147 }
148 else
149 {
150 if (COMPARE (&src[0], &src[2]) <= 0)
151 {
152 /* src[1] < src[0] <= src[2] */
153 dst[0] = src[1];
154 dst[1] = src[0];
155 dst[2] = src[2];
156 }
157 else if (COMPARE (&src[1], &src[2]) <= 0)
158 {
159 /* src[1] <= src[2] < src[0] */
160 dst[0] = src[1];
161 dst[1] = src[2];
162 dst[2] = src[0];
163 }
164 else
165 {
166 /* src[2] < src[1] < src[0] */
167 dst[0] = src[2];
168 dst[1] = src[1];
169 dst[2] = src[0];
170 }
171 }
172 break;
173 default:
174 {
175 size_t n1 = n / 2;
176 size_t n2 = (n + 1) / 2;
177 /* Note: n1 + n2 = n, n1 <= n2. */
178 /* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1]. */
179 merge_sort_fromto (src + n1, dst + n1, n2, tmp);
180 /* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1]. */
181 merge_sort_fromto (src, tmp, n1, dst);
182 /* Merge the two half results. */
183 merge (tmp, n1, dst + n1, n2, dst);
184 }
185 break;
186 }
187 }
188
189 /* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage.
190 The arrays src, tmp must not overlap. */
191 STATIC void
192 merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp)
193 {
194 switch (n)
195 {
196 case 0:
197 case 1:
198 /* Nothing to do. */
199 return;
200 case 2:
201 /* Trivial case. */
202 if (COMPARE (&src[0], &src[1]) <= 0)
203 {
204 /* src[0] <= src[1] */
205 }
206 else
207 {
208 ELEMENT t = src[0];
209 src[0] = src[1];
210 src[1] = t;
211 }
212 break;
213 case 3:
214 /* Simple case. */
215 if (COMPARE (&src[0], &src[1]) <= 0)
216 {
217 if (COMPARE (&src[1], &src[2]) <= 0)
218 {
219 /* src[0] <= src[1] <= src[2] */
220 }
221 else if (COMPARE (&src[0], &src[2]) <= 0)
222 {
223 /* src[0] <= src[2] < src[1] */
224 ELEMENT t = src[1];
225 src[1] = src[2];
226 src[2] = t;
227 }
228 else
229 {
230 /* src[2] < src[0] <= src[1] */
231 ELEMENT t = src[0];
232 src[0] = src[2];
233 src[2] = src[1];
234 src[1] = t;
235 }
236 }
237 else
238 {
239 if (COMPARE (&src[0], &src[2]) <= 0)
240 {
241 /* src[1] < src[0] <= src[2] */
242 ELEMENT t = src[0];
243 src[0] = src[1];
244 src[1] = t;
245 }
246 else if (COMPARE (&src[1], &src[2]) <= 0)
247 {
248 /* src[1] <= src[2] < src[0] */
249 ELEMENT t = src[0];
250 src[0] = src[1];
251 src[1] = src[2];
252 src[2] = t;
253 }
254 else
255 {
256 /* src[2] < src[1] < src[0] */
257 ELEMENT t = src[0];
258 src[0] = src[2];
259 src[2] = t;
260 }
261 }
262 break;
263 default:
264 {
265 size_t n1 = n / 2;
266 size_t n2 = (n + 1) / 2;
267 /* Note: n1 + n2 = n, n1 <= n2. */
268 /* Sort src[n1..n-1], scratching tmp[0..n2-1]. */
269 merge_sort_inplace (src + n1, n2, tmp);
270 /* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1]. */
271 merge_sort_fromto (src, tmp, n1, tmp + n1);
272 /* Merge the two half results. */
273 merge (tmp, n1, src + n1, n2, src);
274 }
275 break;
276 }
277 }
278
279 #undef ELEMENT
280 #undef COMPARE
281 #undef STATIC