| 1 | /* |
| 2 | * tree234.c: reasonably generic counted 2-3-4 tree routines. |
| 3 | * |
| 4 | * This file is copyright 1999-2001 Simon Tatham. |
| 5 | * |
| 6 | * Permission is hereby granted, free of charge, to any person |
| 7 | * obtaining a copy of this software and associated documentation |
| 8 | * files (the "Software"), to deal in the Software without |
| 9 | * restriction, including without limitation the rights to use, |
| 10 | * copy, modify, merge, publish, distribute, sublicense, and/or |
| 11 | * sell copies of the Software, and to permit persons to whom the |
| 12 | * Software is furnished to do so, subject to the following |
| 13 | * conditions: |
| 14 | * |
| 15 | * The above copyright notice and this permission notice shall be |
| 16 | * included in all copies or substantial portions of the Software. |
| 17 | * |
| 18 | * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, |
| 19 | * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES |
| 20 | * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND |
| 21 | * NONINFRINGEMENT. IN NO EVENT SHALL SIMON TATHAM BE LIABLE FOR |
| 22 | * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF |
| 23 | * CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN |
| 24 | * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| 25 | * SOFTWARE. |
| 26 | */ |
| 27 | |
| 28 | #include <stdio.h> |
| 29 | #include <stdlib.h> |
| 30 | #include <assert.h> |
| 31 | |
| 32 | #include "tree234.h" |
| 33 | |
| 34 | #define smalloc malloc |
| 35 | #define sfree free |
| 36 | |
| 37 | #define mknew(typ) ( (typ *) smalloc (sizeof (typ)) ) |
| 38 | |
| 39 | #ifdef TEST |
| 40 | #define LOG(x) (printf x) |
| 41 | #else |
| 42 | #define LOG(x) |
| 43 | #endif |
| 44 | |
| 45 | typedef struct node234_Tag node234; |
| 46 | |
| 47 | struct tree234_Tag { |
| 48 | node234 *root; |
| 49 | cmpfn234 cmp; |
| 50 | }; |
| 51 | |
| 52 | struct node234_Tag { |
| 53 | node234 *parent; |
| 54 | node234 *kids[4]; |
| 55 | int counts[4]; |
| 56 | void *elems[3]; |
| 57 | }; |
| 58 | |
| 59 | /* |
| 60 | * Create a 2-3-4 tree. |
| 61 | */ |
| 62 | tree234 *newtree234(cmpfn234 cmp) { |
| 63 | tree234 *ret = mknew(tree234); |
| 64 | LOG(("created tree %p\n", ret)); |
| 65 | ret->root = NULL; |
| 66 | ret->cmp = cmp; |
| 67 | return ret; |
| 68 | } |
| 69 | |
| 70 | /* |
| 71 | * Free a 2-3-4 tree (not including freeing the elements). |
| 72 | */ |
| 73 | static void freenode234(node234 *n) { |
| 74 | if (!n) |
| 75 | return; |
| 76 | freenode234(n->kids[0]); |
| 77 | freenode234(n->kids[1]); |
| 78 | freenode234(n->kids[2]); |
| 79 | freenode234(n->kids[3]); |
| 80 | sfree(n); |
| 81 | } |
| 82 | void freetree234(tree234 *t) { |
| 83 | freenode234(t->root); |
| 84 | sfree(t); |
| 85 | } |
| 86 | |
| 87 | /* |
| 88 | * Internal function to count a node. |
| 89 | */ |
| 90 | static int countnode234(node234 *n) { |
| 91 | int count = 0; |
| 92 | int i; |
| 93 | if (!n) |
| 94 | return 0; |
| 95 | for (i = 0; i < 4; i++) |
| 96 | count += n->counts[i]; |
| 97 | for (i = 0; i < 3; i++) |
| 98 | if (n->elems[i]) |
| 99 | count++; |
| 100 | return count; |
| 101 | } |
| 102 | |
| 103 | /* |
| 104 | * Count the elements in a tree. |
| 105 | */ |
| 106 | int count234(tree234 *t) { |
| 107 | if (t->root) |
| 108 | return countnode234(t->root); |
| 109 | else |
| 110 | return 0; |
| 111 | } |
| 112 | |
| 113 | /* |
| 114 | * Propagate a node overflow up a tree until it stops. Returns 0 or |
| 115 | * 1, depending on whether the root had to be split or not. |
| 116 | */ |
| 117 | static int add234_insert(node234 *left, void *e, node234 *right, |
| 118 | node234 **root, node234 *n, int ki) { |
| 119 | int lcount, rcount; |
| 120 | /* |
| 121 | * We need to insert the new left/element/right set in n at |
| 122 | * child position ki. |
| 123 | */ |
| 124 | lcount = countnode234(left); |
| 125 | rcount = countnode234(right); |
| 126 | while (n) { |
| 127 | LOG((" at %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 128 | n, |
| 129 | n->kids[0], n->counts[0], n->elems[0], |
| 130 | n->kids[1], n->counts[1], n->elems[1], |
| 131 | n->kids[2], n->counts[2], n->elems[2], |
| 132 | n->kids[3], n->counts[3])); |
| 133 | LOG((" need to insert %p/%d \"%s\" %p/%d at position %d\n", |
| 134 | left, lcount, e, right, rcount, ki)); |
| 135 | if (n->elems[1] == NULL) { |
| 136 | /* |
| 137 | * Insert in a 2-node; simple. |
| 138 | */ |
| 139 | if (ki == 0) { |
| 140 | LOG((" inserting on left of 2-node\n")); |
| 141 | n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1]; |
| 142 | n->elems[1] = n->elems[0]; |
| 143 | n->kids[1] = right; n->counts[1] = rcount; |
| 144 | n->elems[0] = e; |
| 145 | n->kids[0] = left; n->counts[0] = lcount; |
| 146 | } else { /* ki == 1 */ |
| 147 | LOG((" inserting on right of 2-node\n")); |
| 148 | n->kids[2] = right; n->counts[2] = rcount; |
| 149 | n->elems[1] = e; |
| 150 | n->kids[1] = left; n->counts[1] = lcount; |
| 151 | } |
| 152 | if (n->kids[0]) n->kids[0]->parent = n; |
| 153 | if (n->kids[1]) n->kids[1]->parent = n; |
| 154 | if (n->kids[2]) n->kids[2]->parent = n; |
| 155 | LOG((" done\n")); |
| 156 | break; |
| 157 | } else if (n->elems[2] == NULL) { |
| 158 | /* |
| 159 | * Insert in a 3-node; simple. |
| 160 | */ |
| 161 | if (ki == 0) { |
| 162 | LOG((" inserting on left of 3-node\n")); |
| 163 | n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2]; |
| 164 | n->elems[2] = n->elems[1]; |
| 165 | n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1]; |
| 166 | n->elems[1] = n->elems[0]; |
| 167 | n->kids[1] = right; n->counts[1] = rcount; |
| 168 | n->elems[0] = e; |
| 169 | n->kids[0] = left; n->counts[0] = lcount; |
| 170 | } else if (ki == 1) { |
| 171 | LOG((" inserting in middle of 3-node\n")); |
| 172 | n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2]; |
| 173 | n->elems[2] = n->elems[1]; |
| 174 | n->kids[2] = right; n->counts[2] = rcount; |
| 175 | n->elems[1] = e; |
| 176 | n->kids[1] = left; n->counts[1] = lcount; |
| 177 | } else { /* ki == 2 */ |
| 178 | LOG((" inserting on right of 3-node\n")); |
| 179 | n->kids[3] = right; n->counts[3] = rcount; |
| 180 | n->elems[2] = e; |
| 181 | n->kids[2] = left; n->counts[2] = lcount; |
| 182 | } |
| 183 | if (n->kids[0]) n->kids[0]->parent = n; |
| 184 | if (n->kids[1]) n->kids[1]->parent = n; |
| 185 | if (n->kids[2]) n->kids[2]->parent = n; |
| 186 | if (n->kids[3]) n->kids[3]->parent = n; |
| 187 | LOG((" done\n")); |
| 188 | break; |
| 189 | } else { |
| 190 | node234 *m = mknew(node234); |
| 191 | m->parent = n->parent; |
| 192 | LOG((" splitting a 4-node; created new node %p\n", m)); |
| 193 | /* |
| 194 | * Insert in a 4-node; split into a 2-node and a |
| 195 | * 3-node, and move focus up a level. |
| 196 | * |
| 197 | * I don't think it matters which way round we put the |
| 198 | * 2 and the 3. For simplicity, we'll put the 3 first |
| 199 | * always. |
| 200 | */ |
| 201 | if (ki == 0) { |
| 202 | m->kids[0] = left; m->counts[0] = lcount; |
| 203 | m->elems[0] = e; |
| 204 | m->kids[1] = right; m->counts[1] = rcount; |
| 205 | m->elems[1] = n->elems[0]; |
| 206 | m->kids[2] = n->kids[1]; m->counts[2] = n->counts[1]; |
| 207 | e = n->elems[1]; |
| 208 | n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2]; |
| 209 | n->elems[0] = n->elems[2]; |
| 210 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
| 211 | } else if (ki == 1) { |
| 212 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
| 213 | m->elems[0] = n->elems[0]; |
| 214 | m->kids[1] = left; m->counts[1] = lcount; |
| 215 | m->elems[1] = e; |
| 216 | m->kids[2] = right; m->counts[2] = rcount; |
| 217 | e = n->elems[1]; |
| 218 | n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2]; |
| 219 | n->elems[0] = n->elems[2]; |
| 220 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
| 221 | } else if (ki == 2) { |
| 222 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
| 223 | m->elems[0] = n->elems[0]; |
| 224 | m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1]; |
| 225 | m->elems[1] = n->elems[1]; |
| 226 | m->kids[2] = left; m->counts[2] = lcount; |
| 227 | /* e = e; */ |
| 228 | n->kids[0] = right; n->counts[0] = rcount; |
| 229 | n->elems[0] = n->elems[2]; |
| 230 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
| 231 | } else { /* ki == 3 */ |
| 232 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
| 233 | m->elems[0] = n->elems[0]; |
| 234 | m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1]; |
| 235 | m->elems[1] = n->elems[1]; |
| 236 | m->kids[2] = n->kids[2]; m->counts[2] = n->counts[2]; |
| 237 | n->kids[0] = left; n->counts[0] = lcount; |
| 238 | n->elems[0] = e; |
| 239 | n->kids[1] = right; n->counts[1] = rcount; |
| 240 | e = n->elems[2]; |
| 241 | } |
| 242 | m->kids[3] = n->kids[3] = n->kids[2] = NULL; |
| 243 | m->counts[3] = n->counts[3] = n->counts[2] = 0; |
| 244 | m->elems[2] = n->elems[2] = n->elems[1] = NULL; |
| 245 | if (m->kids[0]) m->kids[0]->parent = m; |
| 246 | if (m->kids[1]) m->kids[1]->parent = m; |
| 247 | if (m->kids[2]) m->kids[2]->parent = m; |
| 248 | if (n->kids[0]) n->kids[0]->parent = n; |
| 249 | if (n->kids[1]) n->kids[1]->parent = n; |
| 250 | LOG((" left (%p): %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", m, |
| 251 | m->kids[0], m->counts[0], m->elems[0], |
| 252 | m->kids[1], m->counts[1], m->elems[1], |
| 253 | m->kids[2], m->counts[2])); |
| 254 | LOG((" right (%p): %p/%d \"%s\" %p/%d\n", n, |
| 255 | n->kids[0], n->counts[0], n->elems[0], |
| 256 | n->kids[1], n->counts[1])); |
| 257 | left = m; lcount = countnode234(left); |
| 258 | right = n; rcount = countnode234(right); |
| 259 | } |
| 260 | if (n->parent) |
| 261 | ki = (n->parent->kids[0] == n ? 0 : |
| 262 | n->parent->kids[1] == n ? 1 : |
| 263 | n->parent->kids[2] == n ? 2 : 3); |
| 264 | n = n->parent; |
| 265 | } |
| 266 | |
| 267 | /* |
| 268 | * If we've come out of here by `break', n will still be |
| 269 | * non-NULL and all we need to do is go back up the tree |
| 270 | * updating counts. If we've come here because n is NULL, we |
| 271 | * need to create a new root for the tree because the old one |
| 272 | * has just split into two. */ |
| 273 | if (n) { |
| 274 | while (n->parent) { |
| 275 | int count = countnode234(n); |
| 276 | int childnum; |
| 277 | childnum = (n->parent->kids[0] == n ? 0 : |
| 278 | n->parent->kids[1] == n ? 1 : |
| 279 | n->parent->kids[2] == n ? 2 : 3); |
| 280 | n->parent->counts[childnum] = count; |
| 281 | n = n->parent; |
| 282 | } |
| 283 | return 0; /* root unchanged */ |
| 284 | } else { |
| 285 | LOG((" root is overloaded, split into two\n")); |
| 286 | (*root) = mknew(node234); |
| 287 | (*root)->kids[0] = left; (*root)->counts[0] = lcount; |
| 288 | (*root)->elems[0] = e; |
| 289 | (*root)->kids[1] = right; (*root)->counts[1] = rcount; |
| 290 | (*root)->elems[1] = NULL; |
| 291 | (*root)->kids[2] = NULL; (*root)->counts[2] = 0; |
| 292 | (*root)->elems[2] = NULL; |
| 293 | (*root)->kids[3] = NULL; (*root)->counts[3] = 0; |
| 294 | (*root)->parent = NULL; |
| 295 | if ((*root)->kids[0]) (*root)->kids[0]->parent = (*root); |
| 296 | if ((*root)->kids[1]) (*root)->kids[1]->parent = (*root); |
| 297 | LOG((" new root is %p/%d \"%s\" %p/%d\n", |
| 298 | (*root)->kids[0], (*root)->counts[0], |
| 299 | (*root)->elems[0], |
| 300 | (*root)->kids[1], (*root)->counts[1])); |
| 301 | return 1; /* root moved */ |
| 302 | } |
| 303 | } |
| 304 | |
| 305 | /* |
| 306 | * Add an element e to a 2-3-4 tree t. Returns e on success, or if |
| 307 | * an existing element compares equal, returns that. |
| 308 | */ |
| 309 | static void *add234_internal(tree234 *t, void *e, int index) { |
| 310 | node234 *n; |
| 311 | int ki; |
| 312 | void *orig_e = e; |
| 313 | int c; |
| 314 | |
| 315 | LOG(("adding element \"%s\" to tree %p\n", e, t)); |
| 316 | if (t->root == NULL) { |
| 317 | t->root = mknew(node234); |
| 318 | t->root->elems[1] = t->root->elems[2] = NULL; |
| 319 | t->root->kids[0] = t->root->kids[1] = NULL; |
| 320 | t->root->kids[2] = t->root->kids[3] = NULL; |
| 321 | t->root->counts[0] = t->root->counts[1] = 0; |
| 322 | t->root->counts[2] = t->root->counts[3] = 0; |
| 323 | t->root->parent = NULL; |
| 324 | t->root->elems[0] = e; |
| 325 | LOG((" created root %p\n", t->root)); |
| 326 | return orig_e; |
| 327 | } |
| 328 | |
| 329 | n = t->root; |
| 330 | while (n) { |
| 331 | LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 332 | n, |
| 333 | n->kids[0], n->counts[0], n->elems[0], |
| 334 | n->kids[1], n->counts[1], n->elems[1], |
| 335 | n->kids[2], n->counts[2], n->elems[2], |
| 336 | n->kids[3], n->counts[3])); |
| 337 | if (index >= 0) { |
| 338 | if (!n->kids[0]) { |
| 339 | /* |
| 340 | * Leaf node. We want to insert at kid position |
| 341 | * equal to the index: |
| 342 | * |
| 343 | * 0 A 1 B 2 C 3 |
| 344 | */ |
| 345 | ki = index; |
| 346 | } else { |
| 347 | /* |
| 348 | * Internal node. We always descend through it (add |
| 349 | * always starts at the bottom, never in the |
| 350 | * middle). |
| 351 | */ |
| 352 | if (index <= n->counts[0]) { |
| 353 | ki = 0; |
| 354 | } else if (index -= n->counts[0] + 1, index <= n->counts[1]) { |
| 355 | ki = 1; |
| 356 | } else if (index -= n->counts[1] + 1, index <= n->counts[2]) { |
| 357 | ki = 2; |
| 358 | } else if (index -= n->counts[2] + 1, index <= n->counts[3]) { |
| 359 | ki = 3; |
| 360 | } else |
| 361 | return NULL; /* error: index out of range */ |
| 362 | } |
| 363 | } else { |
| 364 | if ((c = t->cmp(e, n->elems[0])) < 0) |
| 365 | ki = 0; |
| 366 | else if (c == 0) |
| 367 | return n->elems[0]; /* already exists */ |
| 368 | else if (n->elems[1] == NULL || (c = t->cmp(e, n->elems[1])) < 0) |
| 369 | ki = 1; |
| 370 | else if (c == 0) |
| 371 | return n->elems[1]; /* already exists */ |
| 372 | else if (n->elems[2] == NULL || (c = t->cmp(e, n->elems[2])) < 0) |
| 373 | ki = 2; |
| 374 | else if (c == 0) |
| 375 | return n->elems[2]; /* already exists */ |
| 376 | else |
| 377 | ki = 3; |
| 378 | } |
| 379 | LOG((" moving to child %d (%p)\n", ki, n->kids[ki])); |
| 380 | if (!n->kids[ki]) |
| 381 | break; |
| 382 | n = n->kids[ki]; |
| 383 | } |
| 384 | |
| 385 | add234_insert(NULL, e, NULL, &t->root, n, ki); |
| 386 | |
| 387 | return orig_e; |
| 388 | } |
| 389 | |
| 390 | void *add234(tree234 *t, void *e) { |
| 391 | if (!t->cmp) /* tree is unsorted */ |
| 392 | return NULL; |
| 393 | |
| 394 | return add234_internal(t, e, -1); |
| 395 | } |
| 396 | void *addpos234(tree234 *t, void *e, int index) { |
| 397 | if (index < 0 || /* index out of range */ |
| 398 | t->cmp) /* tree is sorted */ |
| 399 | return NULL; /* return failure */ |
| 400 | |
| 401 | return add234_internal(t, e, index); /* this checks the upper bound */ |
| 402 | } |
| 403 | |
| 404 | /* |
| 405 | * Look up the element at a given numeric index in a 2-3-4 tree. |
| 406 | * Returns NULL if the index is out of range. |
| 407 | */ |
| 408 | void *index234(tree234 *t, int index) { |
| 409 | node234 *n; |
| 410 | |
| 411 | if (!t->root) |
| 412 | return NULL; /* tree is empty */ |
| 413 | |
| 414 | if (index < 0 || index >= countnode234(t->root)) |
| 415 | return NULL; /* out of range */ |
| 416 | |
| 417 | n = t->root; |
| 418 | |
| 419 | while (n) { |
| 420 | if (index < n->counts[0]) |
| 421 | n = n->kids[0]; |
| 422 | else if (index -= n->counts[0] + 1, index < 0) |
| 423 | return n->elems[0]; |
| 424 | else if (index < n->counts[1]) |
| 425 | n = n->kids[1]; |
| 426 | else if (index -= n->counts[1] + 1, index < 0) |
| 427 | return n->elems[1]; |
| 428 | else if (index < n->counts[2]) |
| 429 | n = n->kids[2]; |
| 430 | else if (index -= n->counts[2] + 1, index < 0) |
| 431 | return n->elems[2]; |
| 432 | else |
| 433 | n = n->kids[3]; |
| 434 | } |
| 435 | |
| 436 | /* We shouldn't ever get here. I wonder how we did. */ |
| 437 | return NULL; |
| 438 | } |
| 439 | |
| 440 | /* |
| 441 | * Find an element e in a sorted 2-3-4 tree t. Returns NULL if not |
| 442 | * found. e is always passed as the first argument to cmp, so cmp |
| 443 | * can be an asymmetric function if desired. cmp can also be passed |
| 444 | * as NULL, in which case the compare function from the tree proper |
| 445 | * will be used. |
| 446 | */ |
| 447 | void *findrelpos234(tree234 *t, void *e, cmpfn234 cmp, |
| 448 | int relation, int *index) { |
| 449 | node234 *n; |
| 450 | void *ret; |
| 451 | int c; |
| 452 | int idx, ecount, kcount, cmpret; |
| 453 | |
| 454 | if (t->root == NULL) |
| 455 | return NULL; |
| 456 | |
| 457 | if (cmp == NULL) |
| 458 | cmp = t->cmp; |
| 459 | |
| 460 | n = t->root; |
| 461 | /* |
| 462 | * Attempt to find the element itself. |
| 463 | */ |
| 464 | idx = 0; |
| 465 | ecount = -1; |
| 466 | /* |
| 467 | * Prepare a fake `cmp' result if e is NULL. |
| 468 | */ |
| 469 | cmpret = 0; |
| 470 | if (e == NULL) { |
| 471 | assert(relation == REL234_LT || relation == REL234_GT); |
| 472 | if (relation == REL234_LT) |
| 473 | cmpret = +1; /* e is a max: always greater */ |
| 474 | else if (relation == REL234_GT) |
| 475 | cmpret = -1; /* e is a min: always smaller */ |
| 476 | } |
| 477 | while (1) { |
| 478 | for (kcount = 0; kcount < 4; kcount++) { |
| 479 | if (kcount >= 3 || n->elems[kcount] == NULL || |
| 480 | (c = cmpret ? cmpret : cmp(e, n->elems[kcount])) < 0) { |
| 481 | break; |
| 482 | } |
| 483 | if (n->kids[kcount]) idx += n->counts[kcount]; |
| 484 | if (c == 0) { |
| 485 | ecount = kcount; |
| 486 | break; |
| 487 | } |
| 488 | idx++; |
| 489 | } |
| 490 | if (ecount >= 0) |
| 491 | break; |
| 492 | if (n->kids[kcount]) |
| 493 | n = n->kids[kcount]; |
| 494 | else |
| 495 | break; |
| 496 | } |
| 497 | |
| 498 | if (ecount >= 0) { |
| 499 | /* |
| 500 | * We have found the element we're looking for. It's |
| 501 | * n->elems[ecount], at tree index idx. If our search |
| 502 | * relation is EQ, LE or GE we can now go home. |
| 503 | */ |
| 504 | if (relation != REL234_LT && relation != REL234_GT) { |
| 505 | if (index) *index = idx; |
| 506 | return n->elems[ecount]; |
| 507 | } |
| 508 | |
| 509 | /* |
| 510 | * Otherwise, we'll do an indexed lookup for the previous |
| 511 | * or next element. (It would be perfectly possible to |
| 512 | * implement these search types in a non-counted tree by |
| 513 | * going back up from where we are, but far more fiddly.) |
| 514 | */ |
| 515 | if (relation == REL234_LT) |
| 516 | idx--; |
| 517 | else |
| 518 | idx++; |
| 519 | } else { |
| 520 | /* |
| 521 | * We've found our way to the bottom of the tree and we |
| 522 | * know where we would insert this node if we wanted to: |
| 523 | * we'd put it in in place of the (empty) subtree |
| 524 | * n->kids[kcount], and it would have index idx |
| 525 | * |
| 526 | * But the actual element isn't there. So if our search |
| 527 | * relation is EQ, we're doomed. |
| 528 | */ |
| 529 | if (relation == REL234_EQ) |
| 530 | return NULL; |
| 531 | |
| 532 | /* |
| 533 | * Otherwise, we must do an index lookup for index idx-1 |
| 534 | * (if we're going left - LE or LT) or index idx (if we're |
| 535 | * going right - GE or GT). |
| 536 | */ |
| 537 | if (relation == REL234_LT || relation == REL234_LE) { |
| 538 | idx--; |
| 539 | } |
| 540 | } |
| 541 | |
| 542 | /* |
| 543 | * We know the index of the element we want; just call index234 |
| 544 | * to do the rest. This will return NULL if the index is out of |
| 545 | * bounds, which is exactly what we want. |
| 546 | */ |
| 547 | ret = index234(t, idx); |
| 548 | if (ret && index) *index = idx; |
| 549 | return ret; |
| 550 | } |
| 551 | void *find234(tree234 *t, void *e, cmpfn234 cmp) { |
| 552 | return findrelpos234(t, e, cmp, REL234_EQ, NULL); |
| 553 | } |
| 554 | void *findrel234(tree234 *t, void *e, cmpfn234 cmp, int relation) { |
| 555 | return findrelpos234(t, e, cmp, relation, NULL); |
| 556 | } |
| 557 | void *findpos234(tree234 *t, void *e, cmpfn234 cmp, int *index) { |
| 558 | return findrelpos234(t, e, cmp, REL234_EQ, index); |
| 559 | } |
| 560 | |
| 561 | /* |
| 562 | * Tree transformation used in delete and split: move a subtree |
| 563 | * right, from child ki of a node to the next child. Update k and |
| 564 | * index so that they still point to the same place in the |
| 565 | * transformed tree. Assumes the destination child is not full, and |
| 566 | * that the source child does have a subtree to spare. Can cope if |
| 567 | * the destination child is undersized. |
| 568 | * |
| 569 | * . C . . B . |
| 570 | * / \ -> / \ |
| 571 | * [more] a A b B c d D e [more] a A b c C d D e |
| 572 | * |
| 573 | * . C . . B . |
| 574 | * / \ -> / \ |
| 575 | * [more] a A b B c d [more] a A b c C d |
| 576 | */ |
| 577 | static void trans234_subtree_right(node234 *n, int ki, int *k, int *index) { |
| 578 | node234 *src, *dest; |
| 579 | int i, srclen, adjust; |
| 580 | |
| 581 | src = n->kids[ki]; |
| 582 | dest = n->kids[ki+1]; |
| 583 | |
| 584 | LOG((" trans234_subtree_right(%p, %d):\n", n, ki)); |
| 585 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 586 | n, |
| 587 | n->kids[0], n->counts[0], n->elems[0], |
| 588 | n->kids[1], n->counts[1], n->elems[1], |
| 589 | n->kids[2], n->counts[2], n->elems[2], |
| 590 | n->kids[3], n->counts[3])); |
| 591 | LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 592 | src, |
| 593 | src->kids[0], src->counts[0], src->elems[0], |
| 594 | src->kids[1], src->counts[1], src->elems[1], |
| 595 | src->kids[2], src->counts[2], src->elems[2], |
| 596 | src->kids[3], src->counts[3])); |
| 597 | LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 598 | dest, |
| 599 | dest->kids[0], dest->counts[0], dest->elems[0], |
| 600 | dest->kids[1], dest->counts[1], dest->elems[1], |
| 601 | dest->kids[2], dest->counts[2], dest->elems[2], |
| 602 | dest->kids[3], dest->counts[3])); |
| 603 | /* |
| 604 | * Move over the rest of the destination node to make space. |
| 605 | */ |
| 606 | dest->kids[3] = dest->kids[2]; dest->counts[3] = dest->counts[2]; |
| 607 | dest->elems[2] = dest->elems[1]; |
| 608 | dest->kids[2] = dest->kids[1]; dest->counts[2] = dest->counts[1]; |
| 609 | dest->elems[1] = dest->elems[0]; |
| 610 | dest->kids[1] = dest->kids[0]; dest->counts[1] = dest->counts[0]; |
| 611 | |
| 612 | /* which element to move over */ |
| 613 | i = (src->elems[2] ? 2 : src->elems[1] ? 1 : 0); |
| 614 | |
| 615 | dest->elems[0] = n->elems[ki]; |
| 616 | n->elems[ki] = src->elems[i]; |
| 617 | src->elems[i] = NULL; |
| 618 | |
| 619 | dest->kids[0] = src->kids[i+1]; dest->counts[0] = src->counts[i+1]; |
| 620 | src->kids[i+1] = NULL; src->counts[i+1] = 0; |
| 621 | |
| 622 | if (dest->kids[0]) dest->kids[0]->parent = dest; |
| 623 | |
| 624 | adjust = dest->counts[0] + 1; |
| 625 | |
| 626 | n->counts[ki] -= adjust; |
| 627 | n->counts[ki+1] += adjust; |
| 628 | |
| 629 | srclen = n->counts[ki]; |
| 630 | |
| 631 | if (k) { |
| 632 | LOG((" before: k,index = %d,%d\n", (*k), (*index))); |
| 633 | if ((*k) == ki && (*index) > srclen) { |
| 634 | (*index) -= srclen + 1; |
| 635 | (*k)++; |
| 636 | } else if ((*k) == ki+1) { |
| 637 | (*index) += adjust; |
| 638 | } |
| 639 | LOG((" after: k,index = %d,%d\n", (*k), (*index))); |
| 640 | } |
| 641 | |
| 642 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 643 | n, |
| 644 | n->kids[0], n->counts[0], n->elems[0], |
| 645 | n->kids[1], n->counts[1], n->elems[1], |
| 646 | n->kids[2], n->counts[2], n->elems[2], |
| 647 | n->kids[3], n->counts[3])); |
| 648 | LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 649 | src, |
| 650 | src->kids[0], src->counts[0], src->elems[0], |
| 651 | src->kids[1], src->counts[1], src->elems[1], |
| 652 | src->kids[2], src->counts[2], src->elems[2], |
| 653 | src->kids[3], src->counts[3])); |
| 654 | LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 655 | dest, |
| 656 | dest->kids[0], dest->counts[0], dest->elems[0], |
| 657 | dest->kids[1], dest->counts[1], dest->elems[1], |
| 658 | dest->kids[2], dest->counts[2], dest->elems[2], |
| 659 | dest->kids[3], dest->counts[3])); |
| 660 | } |
| 661 | |
| 662 | /* |
| 663 | * Tree transformation used in delete and split: move a subtree |
| 664 | * left, from child ki of a node to the previous child. Update k |
| 665 | * and index so that they still point to the same place in the |
| 666 | * transformed tree. Assumes the destination child is not full, and |
| 667 | * that the source child does have a subtree to spare. Can cope if |
| 668 | * the destination child is undersized. |
| 669 | * |
| 670 | * . B . . C . |
| 671 | * / \ -> / \ |
| 672 | * a A b c C d D e [more] a A b B c d D e [more] |
| 673 | * |
| 674 | * . A . . B . |
| 675 | * / \ -> / \ |
| 676 | * a b B c C d [more] a A b c C d [more] |
| 677 | */ |
| 678 | static void trans234_subtree_left(node234 *n, int ki, int *k, int *index) { |
| 679 | node234 *src, *dest; |
| 680 | int i, adjust; |
| 681 | |
| 682 | src = n->kids[ki]; |
| 683 | dest = n->kids[ki-1]; |
| 684 | |
| 685 | LOG((" trans234_subtree_left(%p, %d):\n", n, ki)); |
| 686 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 687 | n, |
| 688 | n->kids[0], n->counts[0], n->elems[0], |
| 689 | n->kids[1], n->counts[1], n->elems[1], |
| 690 | n->kids[2], n->counts[2], n->elems[2], |
| 691 | n->kids[3], n->counts[3])); |
| 692 | LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 693 | dest, |
| 694 | dest->kids[0], dest->counts[0], dest->elems[0], |
| 695 | dest->kids[1], dest->counts[1], dest->elems[1], |
| 696 | dest->kids[2], dest->counts[2], dest->elems[2], |
| 697 | dest->kids[3], dest->counts[3])); |
| 698 | LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 699 | src, |
| 700 | src->kids[0], src->counts[0], src->elems[0], |
| 701 | src->kids[1], src->counts[1], src->elems[1], |
| 702 | src->kids[2], src->counts[2], src->elems[2], |
| 703 | src->kids[3], src->counts[3])); |
| 704 | |
| 705 | /* where in dest to put it */ |
| 706 | i = (dest->elems[1] ? 2 : dest->elems[0] ? 1 : 0); |
| 707 | dest->elems[i] = n->elems[ki-1]; |
| 708 | n->elems[ki-1] = src->elems[0]; |
| 709 | |
| 710 | dest->kids[i+1] = src->kids[0]; dest->counts[i+1] = src->counts[0]; |
| 711 | |
| 712 | if (dest->kids[i+1]) dest->kids[i+1]->parent = dest; |
| 713 | |
| 714 | /* |
| 715 | * Move over the rest of the source node. |
| 716 | */ |
| 717 | src->kids[0] = src->kids[1]; src->counts[0] = src->counts[1]; |
| 718 | src->elems[0] = src->elems[1]; |
| 719 | src->kids[1] = src->kids[2]; src->counts[1] = src->counts[2]; |
| 720 | src->elems[1] = src->elems[2]; |
| 721 | src->kids[2] = src->kids[3]; src->counts[2] = src->counts[3]; |
| 722 | src->elems[2] = NULL; |
| 723 | src->kids[3] = NULL; src->counts[3] = 0; |
| 724 | |
| 725 | adjust = dest->counts[i+1] + 1; |
| 726 | |
| 727 | n->counts[ki] -= adjust; |
| 728 | n->counts[ki-1] += adjust; |
| 729 | |
| 730 | if (k) { |
| 731 | LOG((" before: k,index = %d,%d\n", (*k), (*index))); |
| 732 | if ((*k) == ki) { |
| 733 | (*index) -= adjust; |
| 734 | if ((*index) < 0) { |
| 735 | (*index) += n->counts[ki-1] + 1; |
| 736 | (*k)--; |
| 737 | } |
| 738 | } |
| 739 | LOG((" after: k,index = %d,%d\n", (*k), (*index))); |
| 740 | } |
| 741 | |
| 742 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 743 | n, |
| 744 | n->kids[0], n->counts[0], n->elems[0], |
| 745 | n->kids[1], n->counts[1], n->elems[1], |
| 746 | n->kids[2], n->counts[2], n->elems[2], |
| 747 | n->kids[3], n->counts[3])); |
| 748 | LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 749 | dest, |
| 750 | dest->kids[0], dest->counts[0], dest->elems[0], |
| 751 | dest->kids[1], dest->counts[1], dest->elems[1], |
| 752 | dest->kids[2], dest->counts[2], dest->elems[2], |
| 753 | dest->kids[3], dest->counts[3])); |
| 754 | LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 755 | src, |
| 756 | src->kids[0], src->counts[0], src->elems[0], |
| 757 | src->kids[1], src->counts[1], src->elems[1], |
| 758 | src->kids[2], src->counts[2], src->elems[2], |
| 759 | src->kids[3], src->counts[3])); |
| 760 | } |
| 761 | |
| 762 | /* |
| 763 | * Tree transformation used in delete and split: merge child nodes |
| 764 | * ki and ki+1 of a node. Update k and index so that they still |
| 765 | * point to the same place in the transformed tree. Assumes both |
| 766 | * children _are_ sufficiently small. |
| 767 | * |
| 768 | * . B . . |
| 769 | * / \ -> | |
| 770 | * a A b c C d a A b B c C d |
| 771 | * |
| 772 | * This routine can also cope with either child being undersized: |
| 773 | * |
| 774 | * . A . . |
| 775 | * / \ -> | |
| 776 | * a b B c a A b B c |
| 777 | * |
| 778 | * . A . . |
| 779 | * / \ -> | |
| 780 | * a b B c C d a A b B c C d |
| 781 | */ |
| 782 | static void trans234_subtree_merge(node234 *n, int ki, int *k, int *index) { |
| 783 | node234 *left, *right; |
| 784 | int i, leftlen, rightlen, lsize, rsize; |
| 785 | |
| 786 | left = n->kids[ki]; leftlen = n->counts[ki]; |
| 787 | right = n->kids[ki+1]; rightlen = n->counts[ki+1]; |
| 788 | |
| 789 | LOG((" trans234_subtree_merge(%p, %d):\n", n, ki)); |
| 790 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 791 | n, |
| 792 | n->kids[0], n->counts[0], n->elems[0], |
| 793 | n->kids[1], n->counts[1], n->elems[1], |
| 794 | n->kids[2], n->counts[2], n->elems[2], |
| 795 | n->kids[3], n->counts[3])); |
| 796 | LOG((" left %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 797 | left, |
| 798 | left->kids[0], left->counts[0], left->elems[0], |
| 799 | left->kids[1], left->counts[1], left->elems[1], |
| 800 | left->kids[2], left->counts[2], left->elems[2], |
| 801 | left->kids[3], left->counts[3])); |
| 802 | LOG((" right %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 803 | right, |
| 804 | right->kids[0], right->counts[0], right->elems[0], |
| 805 | right->kids[1], right->counts[1], right->elems[1], |
| 806 | right->kids[2], right->counts[2], right->elems[2], |
| 807 | right->kids[3], right->counts[3])); |
| 808 | |
| 809 | assert(!left->elems[2] && !right->elems[2]); /* neither is large! */ |
| 810 | lsize = (left->elems[1] ? 2 : left->elems[0] ? 1 : 0); |
| 811 | rsize = (right->elems[1] ? 2 : right->elems[0] ? 1 : 0); |
| 812 | |
| 813 | left->elems[lsize] = n->elems[ki]; |
| 814 | |
| 815 | for (i = 0; i < rsize+1; i++) { |
| 816 | left->kids[lsize+1+i] = right->kids[i]; |
| 817 | left->counts[lsize+1+i] = right->counts[i]; |
| 818 | if (left->kids[lsize+1+i]) |
| 819 | left->kids[lsize+1+i]->parent = left; |
| 820 | if (i < rsize) |
| 821 | left->elems[lsize+1+i] = right->elems[i]; |
| 822 | } |
| 823 | |
| 824 | n->counts[ki] += rightlen + 1; |
| 825 | |
| 826 | sfree(right); |
| 827 | |
| 828 | /* |
| 829 | * Move the rest of n up by one. |
| 830 | */ |
| 831 | for (i = ki+1; i < 3; i++) { |
| 832 | n->kids[i] = n->kids[i+1]; |
| 833 | n->counts[i] = n->counts[i+1]; |
| 834 | } |
| 835 | for (i = ki; i < 2; i++) { |
| 836 | n->elems[i] = n->elems[i+1]; |
| 837 | } |
| 838 | n->kids[3] = NULL; |
| 839 | n->counts[3] = 0; |
| 840 | n->elems[2] = NULL; |
| 841 | |
| 842 | if (k) { |
| 843 | LOG((" before: k,index = %d,%d\n", (*k), (*index))); |
| 844 | if ((*k) == ki+1) { |
| 845 | (*k)--; |
| 846 | (*index) += leftlen + 1; |
| 847 | } else if ((*k) > ki+1) { |
| 848 | (*k)--; |
| 849 | } |
| 850 | LOG((" after: k,index = %d,%d\n", (*k), (*index))); |
| 851 | } |
| 852 | |
| 853 | LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 854 | n, |
| 855 | n->kids[0], n->counts[0], n->elems[0], |
| 856 | n->kids[1], n->counts[1], n->elems[1], |
| 857 | n->kids[2], n->counts[2], n->elems[2], |
| 858 | n->kids[3], n->counts[3])); |
| 859 | LOG((" merged %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 860 | left, |
| 861 | left->kids[0], left->counts[0], left->elems[0], |
| 862 | left->kids[1], left->counts[1], left->elems[1], |
| 863 | left->kids[2], left->counts[2], left->elems[2], |
| 864 | left->kids[3], left->counts[3])); |
| 865 | |
| 866 | } |
| 867 | |
| 868 | /* |
| 869 | * Delete an element e in a 2-3-4 tree. Does not free the element, |
| 870 | * merely removes all links to it from the tree nodes. |
| 871 | */ |
| 872 | static void *delpos234_internal(tree234 *t, int index) { |
| 873 | node234 *n; |
| 874 | void *retval; |
| 875 | int ki, i; |
| 876 | |
| 877 | retval = NULL; |
| 878 | |
| 879 | n = t->root; /* by assumption this is non-NULL */ |
| 880 | LOG(("deleting item %d from tree %p\n", index, t)); |
| 881 | while (1) { |
| 882 | node234 *sub; |
| 883 | |
| 884 | LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d index=%d\n", |
| 885 | n, |
| 886 | n->kids[0], n->counts[0], n->elems[0], |
| 887 | n->kids[1], n->counts[1], n->elems[1], |
| 888 | n->kids[2], n->counts[2], n->elems[2], |
| 889 | n->kids[3], n->counts[3], |
| 890 | index)); |
| 891 | if (index <= n->counts[0]) { |
| 892 | ki = 0; |
| 893 | } else if (index -= n->counts[0]+1, index <= n->counts[1]) { |
| 894 | ki = 1; |
| 895 | } else if (index -= n->counts[1]+1, index <= n->counts[2]) { |
| 896 | ki = 2; |
| 897 | } else if (index -= n->counts[2]+1, index <= n->counts[3]) { |
| 898 | ki = 3; |
| 899 | } else { |
| 900 | assert(0); /* can't happen */ |
| 901 | } |
| 902 | |
| 903 | if (!n->kids[0]) |
| 904 | break; /* n is a leaf node; we're here! */ |
| 905 | |
| 906 | /* |
| 907 | * Check to see if we've found our target element. If so, |
| 908 | * we must choose a new target (we'll use the old target's |
| 909 | * successor, which will be in a leaf), move it into the |
| 910 | * place of the old one, continue down to the leaf and |
| 911 | * delete the old copy of the new target. |
| 912 | */ |
| 913 | if (index == n->counts[ki]) { |
| 914 | node234 *m; |
| 915 | LOG((" found element in internal node, index %d\n", ki)); |
| 916 | assert(n->elems[ki]); /* must be a kid _before_ an element */ |
| 917 | ki++; index = 0; |
| 918 | for (m = n->kids[ki]; m->kids[0]; m = m->kids[0]) |
| 919 | continue; |
| 920 | LOG((" replacing with element \"%s\" from leaf node %p\n", |
| 921 | m->elems[0], m)); |
| 922 | retval = n->elems[ki-1]; |
| 923 | n->elems[ki-1] = m->elems[0]; |
| 924 | } |
| 925 | |
| 926 | /* |
| 927 | * Recurse down to subtree ki. If it has only one element, |
| 928 | * we have to do some transformation to start with. |
| 929 | */ |
| 930 | LOG((" moving to subtree %d\n", ki)); |
| 931 | sub = n->kids[ki]; |
| 932 | if (!sub->elems[1]) { |
| 933 | LOG((" subtree has only one element!\n")); |
| 934 | if (ki > 0 && n->kids[ki-1]->elems[1]) { |
| 935 | /* |
| 936 | * Child ki has only one element, but child |
| 937 | * ki-1 has two or more. So we need to move a |
| 938 | * subtree from ki-1 to ki. |
| 939 | */ |
| 940 | trans234_subtree_right(n, ki-1, &ki, &index); |
| 941 | } else if (ki < 3 && n->kids[ki+1] && |
| 942 | n->kids[ki+1]->elems[1]) { |
| 943 | /* |
| 944 | * Child ki has only one element, but ki+1 has |
| 945 | * two or more. Move a subtree from ki+1 to ki. |
| 946 | */ |
| 947 | trans234_subtree_left(n, ki+1, &ki, &index); |
| 948 | } else { |
| 949 | /* |
| 950 | * ki is small with only small neighbours. Pick a |
| 951 | * neighbour and merge with it. |
| 952 | */ |
| 953 | trans234_subtree_merge(n, ki>0 ? ki-1 : ki, &ki, &index); |
| 954 | sub = n->kids[ki]; |
| 955 | |
| 956 | if (!n->elems[0]) { |
| 957 | /* |
| 958 | * The root is empty and needs to be |
| 959 | * removed. |
| 960 | */ |
| 961 | LOG((" shifting root!\n")); |
| 962 | t->root = sub; |
| 963 | sub->parent = NULL; |
| 964 | sfree(n); |
| 965 | n = NULL; |
| 966 | } |
| 967 | } |
| 968 | } |
| 969 | |
| 970 | if (n) |
| 971 | n->counts[ki]--; |
| 972 | n = sub; |
| 973 | } |
| 974 | |
| 975 | /* |
| 976 | * Now n is a leaf node, and ki marks the element number we |
| 977 | * want to delete. We've already arranged for the leaf to be |
| 978 | * bigger than minimum size, so let's just go to it. |
| 979 | */ |
| 980 | assert(!n->kids[0]); |
| 981 | if (!retval) |
| 982 | retval = n->elems[ki]; |
| 983 | |
| 984 | for (i = ki; i < 2 && n->elems[i+1]; i++) |
| 985 | n->elems[i] = n->elems[i+1]; |
| 986 | n->elems[i] = NULL; |
| 987 | |
| 988 | /* |
| 989 | * It's just possible that we have reduced the leaf to zero |
| 990 | * size. This can only happen if it was the root - so destroy |
| 991 | * it and make the tree empty. |
| 992 | */ |
| 993 | if (!n->elems[0]) { |
| 994 | LOG((" removed last element in tree, destroying empty root\n")); |
| 995 | assert(n == t->root); |
| 996 | sfree(n); |
| 997 | t->root = NULL; |
| 998 | } |
| 999 | |
| 1000 | return retval; /* finished! */ |
| 1001 | } |
| 1002 | void *delpos234(tree234 *t, int index) { |
| 1003 | if (index < 0 || index >= countnode234(t->root)) |
| 1004 | return NULL; |
| 1005 | return delpos234_internal(t, index); |
| 1006 | } |
| 1007 | void *del234(tree234 *t, void *e) { |
| 1008 | int index; |
| 1009 | if (!findrelpos234(t, e, NULL, REL234_EQ, &index)) |
| 1010 | return NULL; /* it wasn't in there anyway */ |
| 1011 | return delpos234_internal(t, index); /* it's there; delete it. */ |
| 1012 | } |
| 1013 | |
| 1014 | /* |
| 1015 | * Join two subtrees together with a separator element between |
| 1016 | * them, given their relative height. |
| 1017 | * |
| 1018 | * (Height<0 means the left tree is shorter, >0 means the right |
| 1019 | * tree is shorter, =0 means (duh) they're equal.) |
| 1020 | * |
| 1021 | * It is assumed that any checks needed on the ordering criterion |
| 1022 | * have _already_ been done. |
| 1023 | * |
| 1024 | * The value returned in `height' is 0 or 1 depending on whether the |
| 1025 | * resulting tree is the same height as the original larger one, or |
| 1026 | * one higher. |
| 1027 | */ |
| 1028 | static node234 *join234_internal(node234 *left, void *sep, |
| 1029 | node234 *right, int *height) { |
| 1030 | node234 *root, *node; |
| 1031 | int relht = *height; |
| 1032 | int ki; |
| 1033 | |
| 1034 | LOG((" join: joining %p \"%s\" %p, relative height is %d\n", |
| 1035 | left, sep, right, relht)); |
| 1036 | if (relht == 0) { |
| 1037 | /* |
| 1038 | * The trees are the same height. Create a new one-element |
| 1039 | * root containing the separator and pointers to the two |
| 1040 | * nodes. |
| 1041 | */ |
| 1042 | node234 *newroot; |
| 1043 | newroot = mknew(node234); |
| 1044 | newroot->kids[0] = left; newroot->counts[0] = countnode234(left); |
| 1045 | newroot->elems[0] = sep; |
| 1046 | newroot->kids[1] = right; newroot->counts[1] = countnode234(right); |
| 1047 | newroot->elems[1] = NULL; |
| 1048 | newroot->kids[2] = NULL; newroot->counts[2] = 0; |
| 1049 | newroot->elems[2] = NULL; |
| 1050 | newroot->kids[3] = NULL; newroot->counts[3] = 0; |
| 1051 | newroot->parent = NULL; |
| 1052 | if (left) left->parent = newroot; |
| 1053 | if (right) right->parent = newroot; |
| 1054 | *height = 1; |
| 1055 | LOG((" join: same height, brand new root\n")); |
| 1056 | return newroot; |
| 1057 | } |
| 1058 | |
| 1059 | /* |
| 1060 | * This now works like the addition algorithm on the larger |
| 1061 | * tree. We're replacing a single kid pointer with two kid |
| 1062 | * pointers separated by an element; if that causes the node to |
| 1063 | * overload, we split it in two, move a separator element up to |
| 1064 | * the next node, and repeat. |
| 1065 | */ |
| 1066 | if (relht < 0) { |
| 1067 | /* |
| 1068 | * Left tree is shorter. Search down the right tree to find |
| 1069 | * the pointer we're inserting at. |
| 1070 | */ |
| 1071 | node = root = right; |
| 1072 | while (++relht < 0) { |
| 1073 | node = node->kids[0]; |
| 1074 | } |
| 1075 | ki = 0; |
| 1076 | right = node->kids[ki]; |
| 1077 | } else { |
| 1078 | /* |
| 1079 | * Right tree is shorter; search down the left to find the |
| 1080 | * pointer we're inserting at. |
| 1081 | */ |
| 1082 | node = root = left; |
| 1083 | while (--relht > 0) { |
| 1084 | if (node->elems[2]) |
| 1085 | node = node->kids[3]; |
| 1086 | else if (node->elems[1]) |
| 1087 | node = node->kids[2]; |
| 1088 | else |
| 1089 | node = node->kids[1]; |
| 1090 | } |
| 1091 | if (node->elems[2]) |
| 1092 | ki = 3; |
| 1093 | else if (node->elems[1]) |
| 1094 | ki = 2; |
| 1095 | else |
| 1096 | ki = 1; |
| 1097 | left = node->kids[ki]; |
| 1098 | } |
| 1099 | |
| 1100 | /* |
| 1101 | * Now proceed as for addition. |
| 1102 | */ |
| 1103 | *height = add234_insert(left, sep, right, &root, node, ki); |
| 1104 | |
| 1105 | return root; |
| 1106 | } |
| 1107 | static int height234(tree234 *t) { |
| 1108 | int level = 0; |
| 1109 | node234 *n = t->root; |
| 1110 | while (n) { |
| 1111 | level++; |
| 1112 | n = n->kids[0]; |
| 1113 | } |
| 1114 | return level; |
| 1115 | } |
| 1116 | tree234 *join234(tree234 *t1, tree234 *t2) { |
| 1117 | int size2 = countnode234(t2->root); |
| 1118 | if (size2 > 0) { |
| 1119 | void *element; |
| 1120 | int relht; |
| 1121 | |
| 1122 | if (t1->cmp) { |
| 1123 | element = index234(t2, 0); |
| 1124 | element = findrelpos234(t1, element, NULL, REL234_GE, NULL); |
| 1125 | if (element) |
| 1126 | return NULL; |
| 1127 | } |
| 1128 | |
| 1129 | element = delpos234(t2, 0); |
| 1130 | relht = height234(t1) - height234(t2); |
| 1131 | t1->root = join234_internal(t1->root, element, t2->root, &relht); |
| 1132 | t2->root = NULL; |
| 1133 | } |
| 1134 | return t1; |
| 1135 | } |
| 1136 | tree234 *join234r(tree234 *t1, tree234 *t2) { |
| 1137 | int size1 = countnode234(t1->root); |
| 1138 | if (size1 > 0) { |
| 1139 | void *element; |
| 1140 | int relht; |
| 1141 | |
| 1142 | if (t2->cmp) { |
| 1143 | element = index234(t1, size1-1); |
| 1144 | element = findrelpos234(t2, element, NULL, REL234_LE, NULL); |
| 1145 | if (element) |
| 1146 | return NULL; |
| 1147 | } |
| 1148 | |
| 1149 | element = delpos234(t1, size1-1); |
| 1150 | relht = height234(t1) - height234(t2); |
| 1151 | t2->root = join234_internal(t1->root, element, t2->root, &relht); |
| 1152 | t1->root = NULL; |
| 1153 | } |
| 1154 | return t2; |
| 1155 | } |
| 1156 | |
| 1157 | /* |
| 1158 | * Split out the first <index> elements in a tree and return a |
| 1159 | * pointer to the root node. Leave the root node of the remainder |
| 1160 | * in t. |
| 1161 | */ |
| 1162 | static node234 *split234_internal(tree234 *t, int index) { |
| 1163 | node234 *halves[2], *n, *sib, *sub; |
| 1164 | node234 *lparent, *rparent; |
| 1165 | int ki, pki, i, half, lcount, rcount; |
| 1166 | |
| 1167 | n = t->root; |
| 1168 | LOG(("splitting tree %p at point %d\n", t, index)); |
| 1169 | |
| 1170 | /* |
| 1171 | * Easy special cases. After this we have also dealt completely |
| 1172 | * with the empty-tree case and we can assume the root exists. |
| 1173 | */ |
| 1174 | if (index == 0) /* return nothing */ |
| 1175 | return NULL; |
| 1176 | if (index == countnode234(t->root)) { /* return the whole tree */ |
| 1177 | node234 *ret = t->root; |
| 1178 | t->root = NULL; |
| 1179 | return ret; |
| 1180 | } |
| 1181 | |
| 1182 | /* |
| 1183 | * Search down the tree to find the split point. |
| 1184 | */ |
| 1185 | lparent = rparent = NULL; |
| 1186 | while (n) { |
| 1187 | LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d index=%d\n", |
| 1188 | n, |
| 1189 | n->kids[0], n->counts[0], n->elems[0], |
| 1190 | n->kids[1], n->counts[1], n->elems[1], |
| 1191 | n->kids[2], n->counts[2], n->elems[2], |
| 1192 | n->kids[3], n->counts[3], |
| 1193 | index)); |
| 1194 | lcount = index; |
| 1195 | rcount = countnode234(n) - lcount; |
| 1196 | if (index <= n->counts[0]) { |
| 1197 | ki = 0; |
| 1198 | } else if (index -= n->counts[0]+1, index <= n->counts[1]) { |
| 1199 | ki = 1; |
| 1200 | } else if (index -= n->counts[1]+1, index <= n->counts[2]) { |
| 1201 | ki = 2; |
| 1202 | } else { |
| 1203 | index -= n->counts[2]+1; |
| 1204 | ki = 3; |
| 1205 | } |
| 1206 | |
| 1207 | LOG((" splitting at subtree %d\n", ki)); |
| 1208 | sub = n->kids[ki]; |
| 1209 | |
| 1210 | LOG((" splitting at child index %d\n", ki)); |
| 1211 | |
| 1212 | /* |
| 1213 | * Split the node, put halves[0] on the right of the left |
| 1214 | * one and halves[1] on the left of the right one, put the |
| 1215 | * new node pointers in halves[0] and halves[1], and go up |
| 1216 | * a level. |
| 1217 | */ |
| 1218 | sib = mknew(node234); |
| 1219 | for (i = 0; i < 3; i++) { |
| 1220 | if (i+ki < 3 && n->elems[i+ki]) { |
| 1221 | sib->elems[i] = n->elems[i+ki]; |
| 1222 | sib->kids[i+1] = n->kids[i+ki+1]; |
| 1223 | if (sib->kids[i+1]) sib->kids[i+1]->parent = sib; |
| 1224 | sib->counts[i+1] = n->counts[i+ki+1]; |
| 1225 | n->elems[i+ki] = NULL; |
| 1226 | n->kids[i+ki+1] = NULL; |
| 1227 | n->counts[i+ki+1] = 0; |
| 1228 | } else { |
| 1229 | sib->elems[i] = NULL; |
| 1230 | sib->kids[i+1] = NULL; |
| 1231 | sib->counts[i+1] = 0; |
| 1232 | } |
| 1233 | } |
| 1234 | if (lparent) { |
| 1235 | lparent->kids[pki] = n; |
| 1236 | lparent->counts[pki] = lcount; |
| 1237 | n->parent = lparent; |
| 1238 | rparent->kids[0] = sib; |
| 1239 | rparent->counts[0] = rcount; |
| 1240 | sib->parent = rparent; |
| 1241 | } else { |
| 1242 | halves[0] = n; |
| 1243 | n->parent = NULL; |
| 1244 | halves[1] = sib; |
| 1245 | sib->parent = NULL; |
| 1246 | } |
| 1247 | lparent = n; |
| 1248 | rparent = sib; |
| 1249 | pki = ki; |
| 1250 | LOG((" left node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 1251 | n, |
| 1252 | n->kids[0], n->counts[0], n->elems[0], |
| 1253 | n->kids[1], n->counts[1], n->elems[1], |
| 1254 | n->kids[2], n->counts[2], n->elems[2], |
| 1255 | n->kids[3], n->counts[3])); |
| 1256 | LOG((" right node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 1257 | sib, |
| 1258 | sib->kids[0], sib->counts[0], sib->elems[0], |
| 1259 | sib->kids[1], sib->counts[1], sib->elems[1], |
| 1260 | sib->kids[2], sib->counts[2], sib->elems[2], |
| 1261 | sib->kids[3], sib->counts[3])); |
| 1262 | |
| 1263 | n = sub; |
| 1264 | } |
| 1265 | |
| 1266 | /* |
| 1267 | * We've come off the bottom here, so we've successfully split |
| 1268 | * the tree into two equally high subtrees. The only problem is |
| 1269 | * that some of the nodes down the fault line will be smaller |
| 1270 | * than the minimum permitted size. (Since this is a 2-3-4 |
| 1271 | * tree, that means they'll be zero-element one-child nodes.) |
| 1272 | */ |
| 1273 | LOG((" fell off bottom, lroot is %p, rroot is %p\n", |
| 1274 | halves[0], halves[1])); |
| 1275 | lparent->counts[pki] = rparent->counts[0] = 0; |
| 1276 | lparent->kids[pki] = rparent->kids[0] = NULL; |
| 1277 | |
| 1278 | /* |
| 1279 | * So now we go back down the tree from each of the two roots, |
| 1280 | * fixing up undersize nodes. |
| 1281 | */ |
| 1282 | for (half = 0; half < 2; half++) { |
| 1283 | /* |
| 1284 | * Remove the root if it's undersize (it will contain only |
| 1285 | * one child pointer, so just throw it away and replace it |
| 1286 | * with its child). This might happen several times. |
| 1287 | */ |
| 1288 | while (halves[half] && !halves[half]->elems[0]) { |
| 1289 | LOG((" root %p is undersize, throwing away\n", halves[half])); |
| 1290 | halves[half] = halves[half]->kids[0]; |
| 1291 | sfree(halves[half]->parent); |
| 1292 | halves[half]->parent = NULL; |
| 1293 | LOG((" new root is %p\n", halves[half])); |
| 1294 | } |
| 1295 | |
| 1296 | n = halves[half]; |
| 1297 | while (n) { |
| 1298 | void (*toward)(node234 *n, int ki, int *k, int *index); |
| 1299 | int ni, merge; |
| 1300 | |
| 1301 | /* |
| 1302 | * Now we have a potentially undersize node on the |
| 1303 | * right (if half==0) or left (if half==1). Sort it |
| 1304 | * out, by merging with a neighbour or by transferring |
| 1305 | * subtrees over. At this time we must also ensure that |
| 1306 | * nodes are bigger than minimum, in case we need an |
| 1307 | * element to merge two nodes below. |
| 1308 | */ |
| 1309 | LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", |
| 1310 | n, |
| 1311 | n->kids[0], n->counts[0], n->elems[0], |
| 1312 | n->kids[1], n->counts[1], n->elems[1], |
| 1313 | n->kids[2], n->counts[2], n->elems[2], |
| 1314 | n->kids[3], n->counts[3])); |
| 1315 | if (half == 1) { |
| 1316 | ki = 0; /* the kid we're interested in */ |
| 1317 | ni = 1; /* the neighbour */ |
| 1318 | merge = 0; /* for merge: leftmost of the two */ |
| 1319 | toward = trans234_subtree_left; |
| 1320 | } else { |
| 1321 | ki = (n->kids[3] ? 3 : n->kids[2] ? 2 : 1); |
| 1322 | ni = ki-1; |
| 1323 | merge = ni; |
| 1324 | toward = trans234_subtree_right; |
| 1325 | } |
| 1326 | |
| 1327 | sub = n->kids[ki]; |
| 1328 | if (sub && !sub->elems[1]) { |
| 1329 | /* |
| 1330 | * This node is undersized or minimum-size. If we |
| 1331 | * can merge it with its neighbour, we do so; |
| 1332 | * otherwise we must be able to transfer subtrees |
| 1333 | * over to it until it is greater than minimum |
| 1334 | * size. |
| 1335 | */ |
| 1336 | int undersized = (!sub->elems[0]); |
| 1337 | LOG((" child %d is %ssize\n", ki, |
| 1338 | undersized ? "under" : "minimum-")); |
| 1339 | LOG((" neighbour is %s\n", |
| 1340 | n->kids[ni]->elems[2] ? "large" : |
| 1341 | n->kids[ni]->elems[1] ? "medium" : "small")); |
| 1342 | if (!n->kids[ni]->elems[1] || |
| 1343 | (undersized && !n->kids[ni]->elems[2])) { |
| 1344 | /* |
| 1345 | * Neighbour is small, or possibly neighbour is |
| 1346 | * medium and we are undersize. |
| 1347 | */ |
| 1348 | trans234_subtree_merge(n, merge, NULL, NULL); |
| 1349 | sub = n->kids[merge]; |
| 1350 | if (!n->elems[0]) { |
| 1351 | /* |
| 1352 | * n is empty, and hence must have been the |
| 1353 | * root and needs to be removed. |
| 1354 | */ |
| 1355 | assert(!n->parent); |
| 1356 | LOG((" shifting root!\n")); |
| 1357 | halves[half] = sub; |
| 1358 | halves[half]->parent = NULL; |
| 1359 | sfree(n); |
| 1360 | } |
| 1361 | } else { |
| 1362 | /* Neighbour is big enough to move trees over. */ |
| 1363 | toward(n, ni, NULL, NULL); |
| 1364 | if (undersized) |
| 1365 | toward(n, ni, NULL, NULL); |
| 1366 | } |
| 1367 | } |
| 1368 | n = sub; |
| 1369 | } |
| 1370 | } |
| 1371 | |
| 1372 | t->root = halves[1]; |
| 1373 | return halves[0]; |
| 1374 | } |
| 1375 | tree234 *splitpos234(tree234 *t, int index, int before) { |
| 1376 | tree234 *ret; |
| 1377 | node234 *n; |
| 1378 | int count; |
| 1379 | |
| 1380 | count = countnode234(t->root); |
| 1381 | if (index < 0 || index > count) |
| 1382 | return NULL; /* error */ |
| 1383 | ret = newtree234(t->cmp); |
| 1384 | n = split234_internal(t, index); |
| 1385 | if (before) { |
| 1386 | /* We want to return the ones before the index. */ |
| 1387 | ret->root = n; |
| 1388 | } else { |
| 1389 | /* |
| 1390 | * We want to keep the ones before the index and return the |
| 1391 | * ones after. |
| 1392 | */ |
| 1393 | ret->root = t->root; |
| 1394 | t->root = n; |
| 1395 | } |
| 1396 | return ret; |
| 1397 | } |
| 1398 | tree234 *split234(tree234 *t, void *e, cmpfn234 cmp, int rel) { |
| 1399 | int before; |
| 1400 | int index; |
| 1401 | |
| 1402 | assert(rel != REL234_EQ); |
| 1403 | |
| 1404 | if (rel == REL234_GT || rel == REL234_GE) { |
| 1405 | before = 1; |
| 1406 | rel = (rel == REL234_GT ? REL234_LE : REL234_LT); |
| 1407 | } else { |
| 1408 | before = 0; |
| 1409 | } |
| 1410 | if (!findrelpos234(t, e, cmp, rel, &index)) |
| 1411 | index = 0; |
| 1412 | |
| 1413 | return splitpos234(t, index+1, before); |
| 1414 | } |
| 1415 | |
| 1416 | static node234 *copynode234(node234 *n, copyfn234 copyfn, void *copyfnstate) { |
| 1417 | int i; |
| 1418 | node234 *n2 = mknew(node234); |
| 1419 | |
| 1420 | for (i = 0; i < 3; i++) { |
| 1421 | if (n->elems[i] && copyfn) |
| 1422 | n2->elems[i] = copyfn(copyfnstate, n->elems[i]); |
| 1423 | else |
| 1424 | n2->elems[i] = n->elems[i]; |
| 1425 | } |
| 1426 | |
| 1427 | for (i = 0; i < 4; i++) { |
| 1428 | if (n->kids[i]) { |
| 1429 | n2->kids[i] = copynode234(n->kids[i], copyfn, copyfnstate); |
| 1430 | n2->kids[i]->parent = n2; |
| 1431 | } else { |
| 1432 | n2->kids[i] = NULL; |
| 1433 | } |
| 1434 | n2->counts[i] = n->counts[i]; |
| 1435 | } |
| 1436 | |
| 1437 | return n2; |
| 1438 | } |
| 1439 | tree234 *copytree234(tree234 *t, copyfn234 copyfn, void *copyfnstate) { |
| 1440 | tree234 *t2; |
| 1441 | |
| 1442 | t2 = newtree234(t->cmp); |
| 1443 | t2->root = copynode234(t->root, copyfn, copyfnstate); |
| 1444 | t2->root->parent = NULL; |
| 1445 | |
| 1446 | return t2; |
| 1447 | } |
| 1448 | |
| 1449 | #ifdef TEST |
| 1450 | |
| 1451 | /* |
| 1452 | * Test code for the 2-3-4 tree. This code maintains an alternative |
| 1453 | * representation of the data in the tree, in an array (using the |
| 1454 | * obvious and slow insert and delete functions). After each tree |
| 1455 | * operation, the verify() function is called, which ensures all |
| 1456 | * the tree properties are preserved: |
| 1457 | * - node->child->parent always equals node |
| 1458 | * - tree->root->parent always equals NULL |
| 1459 | * - number of kids == 0 or number of elements + 1; |
| 1460 | * - tree has the same depth everywhere |
| 1461 | * - every node has at least one element |
| 1462 | * - subtree element counts are accurate |
| 1463 | * - any NULL kid pointer is accompanied by a zero count |
| 1464 | * - in a sorted tree: ordering property between elements of a |
| 1465 | * node and elements of its children is preserved |
| 1466 | * and also ensures the list represented by the tree is the same |
| 1467 | * list it should be. (This last check also doubly verifies the |
| 1468 | * ordering properties, because the `same list it should be' is by |
| 1469 | * definition correctly ordered. It also ensures all nodes are |
| 1470 | * distinct, because the enum functions would get caught in a loop |
| 1471 | * if not.) |
| 1472 | */ |
| 1473 | |
| 1474 | #include <stdarg.h> |
| 1475 | |
| 1476 | #define srealloc realloc |
| 1477 | |
| 1478 | /* |
| 1479 | * Error reporting function. |
| 1480 | */ |
| 1481 | void error(char *fmt, ...) { |
| 1482 | va_list ap; |
| 1483 | printf("ERROR: "); |
| 1484 | va_start(ap, fmt); |
| 1485 | vfprintf(stdout, fmt, ap); |
| 1486 | va_end(ap); |
| 1487 | printf("\n"); |
| 1488 | } |
| 1489 | |
| 1490 | /* The array representation of the data. */ |
| 1491 | void **array; |
| 1492 | int arraylen, arraysize; |
| 1493 | cmpfn234 cmp; |
| 1494 | |
| 1495 | /* The tree representation of the same data. */ |
| 1496 | tree234 *tree; |
| 1497 | |
| 1498 | /* |
| 1499 | * Routines to provide a diagnostic printout of a tree. Currently |
| 1500 | * relies on every element in the tree being a one-character string |
| 1501 | * :-) |
| 1502 | */ |
| 1503 | typedef struct { |
| 1504 | char **levels; |
| 1505 | } dispctx; |
| 1506 | |
| 1507 | int dispnode(node234 *n, int level, dispctx *ctx) { |
| 1508 | if (level == 0) { |
| 1509 | int xpos = strlen(ctx->levels[0]); |
| 1510 | int len; |
| 1511 | |
| 1512 | if (n->elems[2]) |
| 1513 | len = sprintf(ctx->levels[0]+xpos, " %s%s%s", |
| 1514 | n->elems[0], n->elems[1], n->elems[2]); |
| 1515 | else if (n->elems[1]) |
| 1516 | len = sprintf(ctx->levels[0]+xpos, " %s%s", |
| 1517 | n->elems[0], n->elems[1]); |
| 1518 | else |
| 1519 | len = sprintf(ctx->levels[0]+xpos, " %s", |
| 1520 | n->elems[0]); |
| 1521 | return xpos + 1 + (len-1) / 2; |
| 1522 | } else { |
| 1523 | int xpos[4], nkids; |
| 1524 | int nodelen, mypos, myleft, x, i; |
| 1525 | |
| 1526 | xpos[0] = dispnode(n->kids[0], level-3, ctx); |
| 1527 | xpos[1] = dispnode(n->kids[1], level-3, ctx); |
| 1528 | nkids = 2; |
| 1529 | if (n->kids[2]) { |
| 1530 | xpos[2] = dispnode(n->kids[2], level-3, ctx); |
| 1531 | nkids = 3; |
| 1532 | } |
| 1533 | if (n->kids[3]) { |
| 1534 | xpos[3] = dispnode(n->kids[3], level-3, ctx); |
| 1535 | nkids = 4; |
| 1536 | } |
| 1537 | |
| 1538 | if (nkids == 4) |
| 1539 | mypos = (xpos[1] + xpos[2]) / 2; |
| 1540 | else if (nkids == 3) |
| 1541 | mypos = xpos[1]; |
| 1542 | else |
| 1543 | mypos = (xpos[0] + xpos[1]) / 2; |
| 1544 | nodelen = nkids * 2 - 1; |
| 1545 | myleft = mypos - ((nodelen-1)/2); |
| 1546 | assert(myleft >= xpos[0]); |
| 1547 | assert(myleft + nodelen-1 <= xpos[nkids-1]); |
| 1548 | |
| 1549 | x = strlen(ctx->levels[level]); |
| 1550 | while (x <= xpos[0] && x < myleft) |
| 1551 | ctx->levels[level][x++] = ' '; |
| 1552 | while (x < myleft) |
| 1553 | ctx->levels[level][x++] = '_'; |
| 1554 | if (nkids==4) |
| 1555 | x += sprintf(ctx->levels[level]+x, ".%s.%s.%s.", |
| 1556 | n->elems[0], n->elems[1], n->elems[2]); |
| 1557 | else if (nkids==3) |
| 1558 | x += sprintf(ctx->levels[level]+x, ".%s.%s.", |
| 1559 | n->elems[0], n->elems[1]); |
| 1560 | else |
| 1561 | x += sprintf(ctx->levels[level]+x, ".%s.", |
| 1562 | n->elems[0]); |
| 1563 | while (x < xpos[nkids-1]) |
| 1564 | ctx->levels[level][x++] = '_'; |
| 1565 | ctx->levels[level][x] = '\0'; |
| 1566 | |
| 1567 | x = strlen(ctx->levels[level-1]); |
| 1568 | for (i = 0; i < nkids; i++) { |
| 1569 | int rpos, pos; |
| 1570 | rpos = xpos[i]; |
| 1571 | if (i > 0 && i < nkids-1) |
| 1572 | pos = myleft + 2*i; |
| 1573 | else |
| 1574 | pos = rpos; |
| 1575 | if (rpos < pos) |
| 1576 | rpos++; |
| 1577 | while (x < pos && x < rpos) |
| 1578 | ctx->levels[level-1][x++] = ' '; |
| 1579 | if (x == pos) |
| 1580 | ctx->levels[level-1][x++] = '|'; |
| 1581 | while (x < pos || x < rpos) |
| 1582 | ctx->levels[level-1][x++] = '_'; |
| 1583 | if (x == pos) |
| 1584 | ctx->levels[level-1][x++] = '|'; |
| 1585 | } |
| 1586 | ctx->levels[level-1][x] = '\0'; |
| 1587 | |
| 1588 | x = strlen(ctx->levels[level-2]); |
| 1589 | for (i = 0; i < nkids; i++) { |
| 1590 | int rpos = xpos[i]; |
| 1591 | |
| 1592 | while (x < rpos) |
| 1593 | ctx->levels[level-2][x++] = ' '; |
| 1594 | ctx->levels[level-2][x++] = '|'; |
| 1595 | } |
| 1596 | ctx->levels[level-2][x] = '\0'; |
| 1597 | |
| 1598 | return mypos; |
| 1599 | } |
| 1600 | } |
| 1601 | |
| 1602 | void disptree(tree234 *t) { |
| 1603 | dispctx ctx; |
| 1604 | char *leveldata; |
| 1605 | int width = count234(t); |
| 1606 | int ht = height234(t) * 3 - 2; |
| 1607 | int i; |
| 1608 | |
| 1609 | if (!t->root) { |
| 1610 | printf("[empty tree]\n"); |
| 1611 | } |
| 1612 | |
| 1613 | leveldata = smalloc(ht * (width+2)); |
| 1614 | ctx.levels = smalloc(ht * sizeof(char *)); |
| 1615 | for (i = 0; i < ht; i++) { |
| 1616 | ctx.levels[i] = leveldata + i * (width+2); |
| 1617 | ctx.levels[i][0] = '\0'; |
| 1618 | } |
| 1619 | |
| 1620 | (void) dispnode(t->root, ht-1, &ctx); |
| 1621 | |
| 1622 | for (i = ht; i-- ;) |
| 1623 | printf("%s\n", ctx.levels[i]); |
| 1624 | |
| 1625 | sfree(ctx.levels); |
| 1626 | sfree(leveldata); |
| 1627 | } |
| 1628 | |
| 1629 | typedef struct { |
| 1630 | int treedepth; |
| 1631 | int elemcount; |
| 1632 | } chkctx; |
| 1633 | |
| 1634 | int chknode(chkctx *ctx, int level, node234 *node, |
| 1635 | void *lowbound, void *highbound) { |
| 1636 | int nkids, nelems; |
| 1637 | int i; |
| 1638 | int count; |
| 1639 | |
| 1640 | /* Count the non-NULL kids. */ |
| 1641 | for (nkids = 0; nkids < 4 && node->kids[nkids]; nkids++); |
| 1642 | /* Ensure no kids beyond the first NULL are non-NULL. */ |
| 1643 | for (i = nkids; i < 4; i++) |
| 1644 | if (node->kids[i]) { |
| 1645 | error("node %p: nkids=%d but kids[%d] non-NULL", |
| 1646 | node, nkids, i); |
| 1647 | } else if (node->counts[i]) { |
| 1648 | error("node %p: kids[%d] NULL but count[%d]=%d nonzero", |
| 1649 | node, i, i, node->counts[i]); |
| 1650 | } |
| 1651 | |
| 1652 | /* Count the non-NULL elements. */ |
| 1653 | for (nelems = 0; nelems < 3 && node->elems[nelems]; nelems++); |
| 1654 | /* Ensure no elements beyond the first NULL are non-NULL. */ |
| 1655 | for (i = nelems; i < 3; i++) |
| 1656 | if (node->elems[i]) { |
| 1657 | error("node %p: nelems=%d but elems[%d] non-NULL", |
| 1658 | node, nelems, i); |
| 1659 | } |
| 1660 | |
| 1661 | if (nkids == 0) { |
| 1662 | /* |
| 1663 | * If nkids==0, this is a leaf node; verify that the tree |
| 1664 | * depth is the same everywhere. |
| 1665 | */ |
| 1666 | if (ctx->treedepth < 0) |
| 1667 | ctx->treedepth = level; /* we didn't know the depth yet */ |
| 1668 | else if (ctx->treedepth != level) |
| 1669 | error("node %p: leaf at depth %d, previously seen depth %d", |
| 1670 | node, level, ctx->treedepth); |
| 1671 | } else { |
| 1672 | /* |
| 1673 | * If nkids != 0, then it should be nelems+1, unless nelems |
| 1674 | * is 0 in which case nkids should also be 0 (and so we |
| 1675 | * shouldn't be in this condition at all). |
| 1676 | */ |
| 1677 | int shouldkids = (nelems ? nelems+1 : 0); |
| 1678 | if (nkids != shouldkids) { |
| 1679 | error("node %p: %d elems should mean %d kids but has %d", |
| 1680 | node, nelems, shouldkids, nkids); |
| 1681 | } |
| 1682 | } |
| 1683 | |
| 1684 | /* |
| 1685 | * nelems should be at least 1. |
| 1686 | */ |
| 1687 | if (nelems == 0) { |
| 1688 | error("node %p: no elems", node, nkids); |
| 1689 | } |
| 1690 | |
| 1691 | /* |
| 1692 | * Add nelems to the running element count of the whole tree. |
| 1693 | */ |
| 1694 | ctx->elemcount += nelems; |
| 1695 | |
| 1696 | /* |
| 1697 | * Check ordering property: all elements should be strictly > |
| 1698 | * lowbound, strictly < highbound, and strictly < each other in |
| 1699 | * sequence. (lowbound and highbound are NULL at edges of tree |
| 1700 | * - both NULL at root node - and NULL is considered to be < |
| 1701 | * everything and > everything. IYSWIM.) |
| 1702 | */ |
| 1703 | if (cmp) { |
| 1704 | for (i = -1; i < nelems; i++) { |
| 1705 | void *lower = (i == -1 ? lowbound : node->elems[i]); |
| 1706 | void *higher = (i+1 == nelems ? highbound : node->elems[i+1]); |
| 1707 | if (lower && higher && cmp(lower, higher) >= 0) { |
| 1708 | error("node %p: kid comparison [%d=%s,%d=%s] failed", |
| 1709 | node, i, lower, i+1, higher); |
| 1710 | } |
| 1711 | } |
| 1712 | } |
| 1713 | |
| 1714 | /* |
| 1715 | * Check parent pointers: all non-NULL kids should have a |
| 1716 | * parent pointer coming back to this node. |
| 1717 | */ |
| 1718 | for (i = 0; i < nkids; i++) |
| 1719 | if (node->kids[i]->parent != node) { |
| 1720 | error("node %p kid %d: parent ptr is %p not %p", |
| 1721 | node, i, node->kids[i]->parent, node); |
| 1722 | } |
| 1723 | |
| 1724 | |
| 1725 | /* |
| 1726 | * Now (finally!) recurse into subtrees. |
| 1727 | */ |
| 1728 | count = nelems; |
| 1729 | |
| 1730 | for (i = 0; i < nkids; i++) { |
| 1731 | void *lower = (i == 0 ? lowbound : node->elems[i-1]); |
| 1732 | void *higher = (i >= nelems ? highbound : node->elems[i]); |
| 1733 | int subcount = chknode(ctx, level+1, node->kids[i], lower, higher); |
| 1734 | if (node->counts[i] != subcount) { |
| 1735 | error("node %p kid %d: count says %d, subtree really has %d", |
| 1736 | node, i, node->counts[i], subcount); |
| 1737 | } |
| 1738 | count += subcount; |
| 1739 | } |
| 1740 | |
| 1741 | return count; |
| 1742 | } |
| 1743 | |
| 1744 | void verifytree(tree234 *tree, void **array, int arraylen) { |
| 1745 | chkctx ctx; |
| 1746 | int i; |
| 1747 | void *p; |
| 1748 | |
| 1749 | ctx.treedepth = -1; /* depth unknown yet */ |
| 1750 | ctx.elemcount = 0; /* no elements seen yet */ |
| 1751 | /* |
| 1752 | * Verify validity of tree properties. |
| 1753 | */ |
| 1754 | if (tree->root) { |
| 1755 | if (tree->root->parent != NULL) |
| 1756 | error("root->parent is %p should be null", tree->root->parent); |
| 1757 | chknode(&ctx, 0, tree->root, NULL, NULL); |
| 1758 | } |
| 1759 | printf("tree depth: %d\n", ctx.treedepth); |
| 1760 | /* |
| 1761 | * Enumerate the tree and ensure it matches up to the array. |
| 1762 | */ |
| 1763 | for (i = 0; NULL != (p = index234(tree, i)); i++) { |
| 1764 | if (i >= arraylen) |
| 1765 | error("tree contains more than %d elements", arraylen); |
| 1766 | if (array[i] != p) |
| 1767 | error("enum at position %d: array says %s, tree says %s", |
| 1768 | i, array[i], p); |
| 1769 | } |
| 1770 | if (ctx.elemcount != i) { |
| 1771 | error("tree really contains %d elements, enum gave %d", |
| 1772 | ctx.elemcount, i); |
| 1773 | } |
| 1774 | if (i < arraylen) { |
| 1775 | error("enum gave only %d elements, array has %d", i, arraylen); |
| 1776 | } |
| 1777 | i = count234(tree); |
| 1778 | if (ctx.elemcount != i) { |
| 1779 | error("tree really contains %d elements, count234 gave %d", |
| 1780 | ctx.elemcount, i); |
| 1781 | } |
| 1782 | } |
| 1783 | void verify(void) { verifytree(tree, array, arraylen); } |
| 1784 | |
| 1785 | void internal_addtest(void *elem, int index, void *realret) { |
| 1786 | int i, j; |
| 1787 | void *retval; |
| 1788 | |
| 1789 | if (arraysize < arraylen+1) { |
| 1790 | arraysize = arraylen+1+256; |
| 1791 | array = (array == NULL ? smalloc(arraysize*sizeof(*array)) : |
| 1792 | srealloc(array, arraysize*sizeof(*array))); |
| 1793 | } |
| 1794 | |
| 1795 | i = index; |
| 1796 | /* now i points to the first element >= elem */ |
| 1797 | retval = elem; /* expect elem returned (success) */ |
| 1798 | for (j = arraylen; j > i; j--) |
| 1799 | array[j] = array[j-1]; |
| 1800 | array[i] = elem; /* add elem to array */ |
| 1801 | arraylen++; |
| 1802 | |
| 1803 | if (realret != retval) { |
| 1804 | error("add: retval was %p expected %p", realret, retval); |
| 1805 | } |
| 1806 | |
| 1807 | verify(); |
| 1808 | } |
| 1809 | |
| 1810 | void addtest(void *elem) { |
| 1811 | int i; |
| 1812 | void *realret; |
| 1813 | |
| 1814 | realret = add234(tree, elem); |
| 1815 | |
| 1816 | i = 0; |
| 1817 | while (i < arraylen && cmp(elem, array[i]) > 0) |
| 1818 | i++; |
| 1819 | if (i < arraylen && !cmp(elem, array[i])) { |
| 1820 | void *retval = array[i]; /* expect that returned not elem */ |
| 1821 | if (realret != retval) { |
| 1822 | error("add: retval was %p expected %p", realret, retval); |
| 1823 | } |
| 1824 | } else |
| 1825 | internal_addtest(elem, i, realret); |
| 1826 | } |
| 1827 | |
| 1828 | void addpostest(void *elem, int i) { |
| 1829 | void *realret; |
| 1830 | |
| 1831 | realret = addpos234(tree, elem, i); |
| 1832 | |
| 1833 | internal_addtest(elem, i, realret); |
| 1834 | } |
| 1835 | |
| 1836 | void delpostest(int i) { |
| 1837 | int index = i; |
| 1838 | void *elem = array[i], *ret; |
| 1839 | |
| 1840 | /* i points to the right element */ |
| 1841 | while (i < arraylen-1) { |
| 1842 | array[i] = array[i+1]; |
| 1843 | i++; |
| 1844 | } |
| 1845 | arraylen--; /* delete elem from array */ |
| 1846 | |
| 1847 | if (tree->cmp) |
| 1848 | ret = del234(tree, elem); |
| 1849 | else |
| 1850 | ret = delpos234(tree, index); |
| 1851 | |
| 1852 | if (ret != elem) { |
| 1853 | error("del returned %p, expected %p", ret, elem); |
| 1854 | } |
| 1855 | |
| 1856 | verify(); |
| 1857 | } |
| 1858 | |
| 1859 | void deltest(void *elem) { |
| 1860 | int i; |
| 1861 | |
| 1862 | i = 0; |
| 1863 | while (i < arraylen && cmp(elem, array[i]) > 0) |
| 1864 | i++; |
| 1865 | if (i >= arraylen || cmp(elem, array[i]) != 0) |
| 1866 | return; /* don't do it! */ |
| 1867 | delpostest(i); |
| 1868 | } |
| 1869 | |
| 1870 | /* A sample data set and test utility. Designed for pseudo-randomness, |
| 1871 | * and yet repeatability. */ |
| 1872 | |
| 1873 | /* |
| 1874 | * This random number generator uses the `portable implementation' |
| 1875 | * given in ANSI C99 draft N869. It assumes `unsigned' is 32 bits; |
| 1876 | * change it if not. |
| 1877 | */ |
| 1878 | int randomnumber(unsigned *seed) { |
| 1879 | *seed *= 1103515245; |
| 1880 | *seed += 12345; |
| 1881 | return ((*seed) / 65536) % 32768; |
| 1882 | } |
| 1883 | |
| 1884 | int mycmp(void *av, void *bv) { |
| 1885 | char const *a = (char const *)av; |
| 1886 | char const *b = (char const *)bv; |
| 1887 | return strcmp(a, b); |
| 1888 | } |
| 1889 | |
| 1890 | #define lenof(x) ( sizeof((x)) / sizeof(*(x)) ) |
| 1891 | |
| 1892 | char *strings[] = { |
| 1893 | "0", "2", "3", "I", "K", "d", "H", "J", "Q", "N", "n", "q", "j", "i", |
| 1894 | "7", "G", "F", "D", "b", "x", "g", "B", "e", "v", "V", "T", "f", "E", |
| 1895 | "S", "8", "A", "k", "X", "p", "C", "R", "a", "o", "r", "O", "Z", "u", |
| 1896 | "6", "1", "w", "L", "P", "M", "c", "U", "h", "9", "t", "5", "W", "Y", |
| 1897 | "m", "s", "l", "4", |
| 1898 | #if 0 |
| 1899 | "a", "ab", "absque", "coram", "de", |
| 1900 | "palam", "clam", "cum", "ex", "e", |
| 1901 | "sine", "tenus", "pro", "prae", |
| 1902 | "banana", "carrot", "cabbage", "broccoli", "onion", "zebra", |
| 1903 | "penguin", "blancmange", "pangolin", "whale", "hedgehog", |
| 1904 | "giraffe", "peanut", "bungee", "foo", "bar", "baz", "quux", |
| 1905 | "murfl", "spoo", "breen", "flarn", "octothorpe", |
| 1906 | "snail", "tiger", "elephant", "octopus", "warthog", "armadillo", |
| 1907 | "aardvark", "wyvern", "dragon", "elf", "dwarf", "orc", "goblin", |
| 1908 | "pixie", "basilisk", "warg", "ape", "lizard", "newt", "shopkeeper", |
| 1909 | "wand", "ring", "amulet" |
| 1910 | #endif |
| 1911 | }; |
| 1912 | |
| 1913 | #define NSTR lenof(strings) |
| 1914 | |
| 1915 | void findtest(void) { |
| 1916 | static const int rels[] = { |
| 1917 | REL234_EQ, REL234_GE, REL234_LE, REL234_LT, REL234_GT |
| 1918 | }; |
| 1919 | static const char *const relnames[] = { |
| 1920 | "EQ", "GE", "LE", "LT", "GT" |
| 1921 | }; |
| 1922 | int i, j, rel, index; |
| 1923 | char *p, *ret, *realret, *realret2; |
| 1924 | int lo, hi, mid, c; |
| 1925 | |
| 1926 | for (i = 0; i < (int)NSTR; i++) { |
| 1927 | p = strings[i]; |
| 1928 | for (j = 0; j < (int)(sizeof(rels)/sizeof(*rels)); j++) { |
| 1929 | rel = rels[j]; |
| 1930 | |
| 1931 | lo = 0; hi = arraylen-1; |
| 1932 | while (lo <= hi) { |
| 1933 | mid = (lo + hi) / 2; |
| 1934 | c = strcmp(p, array[mid]); |
| 1935 | if (c < 0) |
| 1936 | hi = mid-1; |
| 1937 | else if (c > 0) |
| 1938 | lo = mid+1; |
| 1939 | else |
| 1940 | break; |
| 1941 | } |
| 1942 | |
| 1943 | if (c == 0) { |
| 1944 | if (rel == REL234_LT) |
| 1945 | ret = (mid > 0 ? array[--mid] : NULL); |
| 1946 | else if (rel == REL234_GT) |
| 1947 | ret = (mid < arraylen-1 ? array[++mid] : NULL); |
| 1948 | else |
| 1949 | ret = array[mid]; |
| 1950 | } else { |
| 1951 | assert(lo == hi+1); |
| 1952 | if (rel == REL234_LT || rel == REL234_LE) { |
| 1953 | mid = hi; |
| 1954 | ret = (hi >= 0 ? array[hi] : NULL); |
| 1955 | } else if (rel == REL234_GT || rel == REL234_GE) { |
| 1956 | mid = lo; |
| 1957 | ret = (lo < arraylen ? array[lo] : NULL); |
| 1958 | } else |
| 1959 | ret = NULL; |
| 1960 | } |
| 1961 | |
| 1962 | realret = findrelpos234(tree, p, NULL, rel, &index); |
| 1963 | if (realret != ret) { |
| 1964 | error("find(\"%s\",%s) gave %s should be %s", |
| 1965 | p, relnames[j], realret, ret); |
| 1966 | } |
| 1967 | if (realret && index != mid) { |
| 1968 | error("find(\"%s\",%s) gave %d should be %d", |
| 1969 | p, relnames[j], index, mid); |
| 1970 | } |
| 1971 | if (realret && rel == REL234_EQ) { |
| 1972 | realret2 = index234(tree, index); |
| 1973 | if (realret2 != realret) { |
| 1974 | error("find(\"%s\",%s) gave %s(%d) but %d -> %s", |
| 1975 | p, relnames[j], realret, index, index, realret2); |
| 1976 | } |
| 1977 | } |
| 1978 | #if 0 |
| 1979 | printf("find(\"%s\",%s) gave %s(%d)\n", p, relnames[j], |
| 1980 | realret, index); |
| 1981 | #endif |
| 1982 | } |
| 1983 | } |
| 1984 | |
| 1985 | realret = findrelpos234(tree, NULL, NULL, REL234_GT, &index); |
| 1986 | if (arraylen && (realret != array[0] || index != 0)) { |
| 1987 | error("find(NULL,GT) gave %s(%d) should be %s(0)", |
| 1988 | realret, index, array[0]); |
| 1989 | } else if (!arraylen && (realret != NULL)) { |
| 1990 | error("find(NULL,GT) gave %s(%d) should be NULL", |
| 1991 | realret, index); |
| 1992 | } |
| 1993 | |
| 1994 | realret = findrelpos234(tree, NULL, NULL, REL234_LT, &index); |
| 1995 | if (arraylen && (realret != array[arraylen-1] || index != arraylen-1)) { |
| 1996 | error("find(NULL,LT) gave %s(%d) should be %s(0)", |
| 1997 | realret, index, array[arraylen-1]); |
| 1998 | } else if (!arraylen && (realret != NULL)) { |
| 1999 | error("find(NULL,LT) gave %s(%d) should be NULL", |
| 2000 | realret, index); |
| 2001 | } |
| 2002 | } |
| 2003 | |
| 2004 | void splittest(tree234 *tree, void **array, int arraylen) { |
| 2005 | int i; |
| 2006 | tree234 *tree3, *tree4; |
| 2007 | for (i = 0; i <= arraylen; i++) { |
| 2008 | tree3 = copytree234(tree, NULL, NULL); |
| 2009 | tree4 = splitpos234(tree3, i, 0); |
| 2010 | verifytree(tree3, array, i); |
| 2011 | verifytree(tree4, array+i, arraylen-i); |
| 2012 | join234(tree3, tree4); |
| 2013 | freetree234(tree4); /* left empty by join */ |
| 2014 | verifytree(tree3, array, arraylen); |
| 2015 | freetree234(tree3); |
| 2016 | } |
| 2017 | } |
| 2018 | |
| 2019 | int main(void) { |
| 2020 | int in[NSTR]; |
| 2021 | int i, j, k; |
| 2022 | int tworoot, tmplen; |
| 2023 | unsigned seed = 0; |
| 2024 | tree234 *tree2, *tree3, *tree4; |
| 2025 | int c; |
| 2026 | |
| 2027 | setvbuf(stdout, NULL, _IOLBF, 0); |
| 2028 | |
| 2029 | for (i = 0; i < (int)NSTR; i++) in[i] = 0; |
| 2030 | array = NULL; |
| 2031 | arraylen = arraysize = 0; |
| 2032 | tree = newtree234(mycmp); |
| 2033 | cmp = mycmp; |
| 2034 | |
| 2035 | verify(); |
| 2036 | for (i = 0; i < 10000; i++) { |
| 2037 | j = randomnumber(&seed); |
| 2038 | j %= NSTR; |
| 2039 | printf("trial: %d\n", i); |
| 2040 | if (in[j]) { |
| 2041 | printf("deleting %s (%d)\n", strings[j], j); |
| 2042 | deltest(strings[j]); |
| 2043 | in[j] = 0; |
| 2044 | } else { |
| 2045 | printf("adding %s (%d)\n", strings[j], j); |
| 2046 | addtest(strings[j]); |
| 2047 | in[j] = 1; |
| 2048 | } |
| 2049 | disptree(tree); |
| 2050 | findtest(); |
| 2051 | } |
| 2052 | |
| 2053 | while (arraylen > 0) { |
| 2054 | j = randomnumber(&seed); |
| 2055 | j %= arraylen; |
| 2056 | deltest(array[j]); |
| 2057 | } |
| 2058 | |
| 2059 | freetree234(tree); |
| 2060 | |
| 2061 | /* |
| 2062 | * Now try an unsorted tree. We don't really need to test |
| 2063 | * delpos234 because we know del234 is based on it, so it's |
| 2064 | * already been tested in the above sorted-tree code; but for |
| 2065 | * completeness we'll use it to tear down our unsorted tree |
| 2066 | * once we've built it. |
| 2067 | */ |
| 2068 | tree = newtree234(NULL); |
| 2069 | cmp = NULL; |
| 2070 | verify(); |
| 2071 | for (i = 0; i < 1000; i++) { |
| 2072 | printf("trial: %d\n", i); |
| 2073 | j = randomnumber(&seed); |
| 2074 | j %= NSTR; |
| 2075 | k = randomnumber(&seed); |
| 2076 | k %= count234(tree)+1; |
| 2077 | printf("adding string %s at index %d\n", strings[j], k); |
| 2078 | addpostest(strings[j], k); |
| 2079 | } |
| 2080 | |
| 2081 | /* |
| 2082 | * While we have this tree in its full form, we'll take a copy |
| 2083 | * of it to use in split and join testing. |
| 2084 | */ |
| 2085 | tree2 = copytree234(tree, NULL, NULL); |
| 2086 | verifytree(tree2, array, arraylen);/* check the copy is accurate */ |
| 2087 | /* |
| 2088 | * Split tests. Split the tree at every possible point and |
| 2089 | * check the resulting subtrees. |
| 2090 | */ |
| 2091 | tworoot = (!tree2->root->elems[1]);/* see if it has a 2-root */ |
| 2092 | splittest(tree2, array, arraylen); |
| 2093 | /* |
| 2094 | * Now do the split test again, but on a tree that has a 2-root |
| 2095 | * (if the previous one didn't) or doesn't (if the previous one |
| 2096 | * did). |
| 2097 | */ |
| 2098 | tmplen = arraylen; |
| 2099 | while ((!tree2->root->elems[1]) == tworoot) { |
| 2100 | delpos234(tree2, --tmplen); |
| 2101 | } |
| 2102 | printf("now trying splits on second tree\n"); |
| 2103 | splittest(tree2, array, tmplen); |
| 2104 | freetree234(tree2); |
| 2105 | |
| 2106 | /* |
| 2107 | * Back to the main testing of uncounted trees. |
| 2108 | */ |
| 2109 | while (count234(tree) > 0) { |
| 2110 | printf("cleanup: tree size %d\n", count234(tree)); |
| 2111 | j = randomnumber(&seed); |
| 2112 | j %= count234(tree); |
| 2113 | printf("deleting string %s from index %d\n", (char *)array[j], j); |
| 2114 | delpostest(j); |
| 2115 | } |
| 2116 | freetree234(tree); |
| 2117 | |
| 2118 | /* |
| 2119 | * Finally, do some testing on split/join on _sorted_ trees. At |
| 2120 | * the same time, we'll be testing split on very small trees. |
| 2121 | */ |
| 2122 | tree = newtree234(mycmp); |
| 2123 | cmp = mycmp; |
| 2124 | arraylen = 0; |
| 2125 | for (i = 0; i < 16; i++) { |
| 2126 | addtest(strings[i]); |
| 2127 | tree2 = copytree234(tree, NULL, NULL); |
| 2128 | splittest(tree2, array, arraylen); |
| 2129 | freetree234(tree2); |
| 2130 | } |
| 2131 | freetree234(tree); |
| 2132 | |
| 2133 | /* |
| 2134 | * Test silly cases of join: join(emptytree, emptytree), and |
| 2135 | * also ensure join correctly spots when sorted trees fail the |
| 2136 | * ordering constraint. |
| 2137 | */ |
| 2138 | tree = newtree234(mycmp); |
| 2139 | tree2 = newtree234(mycmp); |
| 2140 | tree3 = newtree234(mycmp); |
| 2141 | tree4 = newtree234(mycmp); |
| 2142 | assert(mycmp(strings[0], strings[1]) < 0); /* just in case :-) */ |
| 2143 | add234(tree2, strings[1]); |
| 2144 | add234(tree4, strings[0]); |
| 2145 | array[0] = strings[0]; |
| 2146 | array[1] = strings[1]; |
| 2147 | verifytree(tree, array, 0); |
| 2148 | verifytree(tree2, array+1, 1); |
| 2149 | verifytree(tree3, array, 0); |
| 2150 | verifytree(tree4, array, 1); |
| 2151 | |
| 2152 | /* |
| 2153 | * So: |
| 2154 | * - join(tree,tree3) should leave both tree and tree3 unchanged. |
| 2155 | * - joinr(tree,tree2) should leave both tree and tree2 unchanged. |
| 2156 | * - join(tree4,tree3) should leave both tree3 and tree4 unchanged. |
| 2157 | * - join(tree, tree2) should move the element from tree2 to tree. |
| 2158 | * - joinr(tree4, tree3) should move the element from tree4 to tree3. |
| 2159 | * - join(tree,tree3) should return NULL and leave both unchanged. |
| 2160 | * - join(tree3,tree) should work and create a bigger tree in tree3. |
| 2161 | */ |
| 2162 | assert(tree == join234(tree, tree3)); |
| 2163 | verifytree(tree, array, 0); |
| 2164 | verifytree(tree3, array, 0); |
| 2165 | assert(tree2 == join234r(tree, tree2)); |
| 2166 | verifytree(tree, array, 0); |
| 2167 | verifytree(tree2, array+1, 1); |
| 2168 | assert(tree4 == join234(tree4, tree3)); |
| 2169 | verifytree(tree3, array, 0); |
| 2170 | verifytree(tree4, array, 1); |
| 2171 | assert(tree == join234(tree, tree2)); |
| 2172 | verifytree(tree, array+1, 1); |
| 2173 | verifytree(tree2, array, 0); |
| 2174 | assert(tree3 == join234r(tree4, tree3)); |
| 2175 | verifytree(tree3, array, 1); |
| 2176 | verifytree(tree4, array, 0); |
| 2177 | assert(NULL == join234(tree, tree3)); |
| 2178 | verifytree(tree, array+1, 1); |
| 2179 | verifytree(tree3, array, 1); |
| 2180 | assert(tree3 == join234(tree3, tree)); |
| 2181 | verifytree(tree3, array, 2); |
| 2182 | verifytree(tree, array, 0); |
| 2183 | |
| 2184 | return 0; |
| 2185 | } |
| 2186 | |
| 2187 | #endif |
| 2188 | |
| 2189 | #if 0 /* sorted list of strings might be useful */ |
| 2190 | { |
| 2191 | "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", |
| 2192 | } |
| 2193 | #endif |