1/* Stable-sorting of an array using mergesort. 2 Copyright (C) 2009, 2010 Free Software Foundation, Inc. 3 Written by Bruno Haible <bruno@clisp.org>, 2009. 4 5 This program is free software: you can redistribute it and/or modify it 6 under the terms of the GNU Lesser General Public License as published 7 by the Free Software Foundation; either version 3 of the License, or 8 (at your option) any later version. 9 10 This program 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 GNU 13 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 <http://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 Before including this file, you also need to include: 33 #include <stddef.h> 34 */ 35 36/* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into 37 dst[0..n1+n2-1]. In case of ambiguity, put the elements of src1 38 before the elements of src2. 39 n1 and n2 must be > 0. 40 The arrays src1 and src2 must not overlap the dst array, except that 41 src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1]. */ 42static void 43merge (const ELEMENT *src1, size_t n1, 44 const ELEMENT *src2, size_t n2, 45 ELEMENT *dst) 46{ 47 for (;;) /* while (n1 > 0 && n2 > 0) */ 48 { 49 if (COMPARE (src1, src2) <= 0) 50 { 51 *dst++ = *src1++; 52 n1--; 53 if (n1 == 0) 54 break; 55 } 56 else 57 { 58 *dst++ = *src2++; 59 n2--; 60 if (n2 == 0) 61 break; 62 } 63 } 64 /* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0. */ 65 if (n1 > 0) 66 { 67 if (dst != src1) 68 do 69 { 70 *dst++ = *src1++; 71 n1--; 72 } 73 while (n1 > 0); 74 } 75 else /* n2 > 0 */ 76 { 77 if (dst != src2) 78 do 79 { 80 *dst++ = *src2++; 81 n2--; 82 } 83 while (n2 > 0); 84 } 85} 86 87/* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary 88 (scratch) storage. 89 The arrays src, dst, tmp must not overlap. */ 90STATIC void 91merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp) 92{ 93 switch (n) 94 { 95 case 0: 96 return; 97 case 1: 98 /* Nothing to do. */ 99 dst[0] = src[0]; 100 return; 101 case 2: 102 /* Trivial case. */ 103 if (COMPARE (&src[0], &src[1]) <= 0) 104 { 105 /* src[0] <= src[1] */ 106 dst[0] = src[0]; 107 dst[1] = src[1]; 108 } 109 else 110 { 111 dst[0] = src[1]; 112 dst[1] = src[0]; 113 } 114 break; 115 case 3: 116 /* Simple case. */ 117 if (COMPARE (&src[0], &src[1]) <= 0) 118 { 119 if (COMPARE (&src[1], &src[2]) <= 0) 120 { 121 /* src[0] <= src[1] <= src[2] */ 122 dst[0] = src[0]; 123 dst[1] = src[1]; 124 dst[2] = src[2]; 125 } 126 else if (COMPARE (&src[0], &src[2]) <= 0) 127 { 128 /* src[0] <= src[2] < src[1] */ 129 dst[0] = src[0]; 130 dst[1] = src[2]; 131 dst[2] = src[1]; 132 } 133 else 134 { 135 /* src[2] < src[0] <= src[1] */ 136 dst[0] = src[2]; 137 dst[1] = src[0]; 138 dst[2] = src[1]; 139 } 140 } 141 else 142 { 143 if (COMPARE (&src[0], &src[2]) <= 0) 144 { 145 /* src[1] < src[0] <= src[2] */ 146 dst[0] = src[1]; 147 dst[1] = src[0]; 148 dst[2] = src[2]; 149 } 150 else if (COMPARE (&src[1], &src[2]) <= 0) 151 { 152 /* src[1] <= src[2] < src[0] */ 153 dst[0] = src[1]; 154 dst[1] = src[2]; 155 dst[2] = src[0]; 156 } 157 else 158 { 159 /* src[2] < src[1] < src[0] */ 160 dst[0] = src[2]; 161 dst[1] = src[1]; 162 dst[2] = src[0]; 163 } 164 } 165 break; 166 default: 167 { 168 size_t n1 = n / 2; 169 size_t n2 = (n + 1) / 2; 170 /* Note: n1 + n2 = n, n1 <= n2. */ 171 /* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1]. */ 172 merge_sort_fromto (src + n1, dst + n1, n2, tmp); 173 /* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1]. */ 174 merge_sort_fromto (src, tmp, n1, dst); 175 /* Merge the two half results. */ 176 merge (tmp, n1, dst + n1, n2, dst); 177 } 178 break; 179 } 180} 181 182/* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage. 183 The arrays src, tmp must not overlap. */ 184STATIC void 185merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp) 186{ 187 switch (n) 188 { 189 case 0: 190 case 1: 191 /* Nothing to do. */ 192 return; 193 case 2: 194 /* Trivial case. */ 195 if (COMPARE (&src[0], &src[1]) <= 0) 196 { 197 /* src[0] <= src[1] */ 198 } 199 else 200 { 201 ELEMENT t = src[0]; 202 src[0] = src[1]; 203 src[1] = t; 204 } 205 break; 206 case 3: 207 /* Simple case. */ 208 if (COMPARE (&src[0], &src[1]) <= 0) 209 { 210 if (COMPARE (&src[1], &src[2]) <= 0) 211 { 212 /* src[0] <= src[1] <= src[2] */ 213 } 214 else if (COMPARE (&src[0], &src[2]) <= 0) 215 { 216 /* src[0] <= src[2] < src[1] */ 217 ELEMENT t = src[1]; 218 src[1] = src[2]; 219 src[2] = t; 220 } 221 else 222 { 223 /* src[2] < src[0] <= src[1] */ 224 ELEMENT t = src[0]; 225 src[0] = src[2]; 226 src[2] = src[1]; 227 src[1] = t; 228 } 229 } 230 else 231 { 232 if (COMPARE (&src[0], &src[2]) <= 0) 233 { 234 /* src[1] < src[0] <= src[2] */ 235 ELEMENT t = src[0]; 236 src[0] = src[1]; 237 src[1] = t; 238 } 239 else if (COMPARE (&src[1], &src[2]) <= 0) 240 { 241 /* src[1] <= src[2] < src[0] */ 242 ELEMENT t = src[0]; 243 src[0] = src[1]; 244 src[1] = src[2]; 245 src[2] = t; 246 } 247 else 248 { 249 /* src[2] < src[1] < src[0] */ 250 ELEMENT t = src[0]; 251 src[0] = src[2]; 252 src[2] = t; 253 } 254 } 255 break; 256 default: 257 { 258 size_t n1 = n / 2; 259 size_t n2 = (n + 1) / 2; 260 /* Note: n1 + n2 = n, n1 <= n2. */ 261 /* Sort src[n1..n-1], scratching tmp[0..n2-1]. */ 262 merge_sort_inplace (src + n1, n2, tmp); 263 /* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1]. */ 264 merge_sort_fromto (src, tmp, n1, tmp + n1); 265 /* Merge the two half results. */ 266 merge (tmp, n1, src + n1, n2, src); 267 } 268 break; 269 } 270} 271 272#undef ELEMENT 273#undef COMPARE 274#undef STATIC 275