febd9a0f |
1 | /* |
d2371c81 |
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. |
febd9a0f |
26 | */ |
27 | |
28 | #include <stdio.h> |
29 | #include <stdlib.h> |
d2371c81 |
30 | #include <assert.h> |
dcbde236 |
31 | |
febd9a0f |
32 | #include "tree234.h" |
33 | |
d2371c81 |
34 | #define smalloc malloc |
35 | #define sfree free |
36 | |
dcbde236 |
37 | #define mknew(typ) ( (typ *) smalloc (sizeof (typ)) ) |
febd9a0f |
38 | |
39 | #ifdef TEST |
40 | #define LOG(x) (printf x) |
41 | #else |
42 | #define LOG(x) |
43 | #endif |
44 | |
d2371c81 |
45 | typedef struct node234_Tag node234; |
46 | |
febd9a0f |
47 | struct tree234_Tag { |
48 | node234 *root; |
49 | cmpfn234 cmp; |
50 | }; |
51 | |
52 | struct node234_Tag { |
53 | node234 *parent; |
54 | node234 *kids[4]; |
d2371c81 |
55 | int counts[4]; |
febd9a0f |
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 | /* |
d2371c81 |
88 | * Internal function to count a node. |
89 | */ |
90 | static int countnode234(node234 *n) { |
91 | int count = 0; |
92 | int i; |
c404e5b3 |
93 | if (!n) |
94 | return 0; |
d2371c81 |
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 | /* |
febd9a0f |
114 | * Add an element e to a 2-3-4 tree t. Returns e on success, or if |
115 | * an existing element compares equal, returns that. |
116 | */ |
d2371c81 |
117 | static void *add234_internal(tree234 *t, void *e, int index) { |
febd9a0f |
118 | node234 *n, **np, *left, *right; |
119 | void *orig_e = e; |
d2371c81 |
120 | int c, lcount, rcount; |
febd9a0f |
121 | |
122 | LOG(("adding node %p to tree %p\n", e, t)); |
123 | if (t->root == NULL) { |
124 | t->root = mknew(node234); |
125 | t->root->elems[1] = t->root->elems[2] = NULL; |
126 | t->root->kids[0] = t->root->kids[1] = NULL; |
127 | t->root->kids[2] = t->root->kids[3] = NULL; |
d2371c81 |
128 | t->root->counts[0] = t->root->counts[1] = 0; |
129 | t->root->counts[2] = t->root->counts[3] = 0; |
febd9a0f |
130 | t->root->parent = NULL; |
131 | t->root->elems[0] = e; |
132 | LOG((" created root %p\n", t->root)); |
133 | return orig_e; |
134 | } |
135 | |
136 | np = &t->root; |
137 | while (*np) { |
d2371c81 |
138 | int childnum; |
febd9a0f |
139 | n = *np; |
d2371c81 |
140 | LOG((" node %p: %p/%d [%p] %p/%d [%p] %p/%d [%p] %p/%d\n", |
141 | n, |
142 | n->kids[0], n->counts[0], n->elems[0], |
143 | n->kids[1], n->counts[1], n->elems[1], |
144 | n->kids[2], n->counts[2], n->elems[2], |
145 | n->kids[3], n->counts[3])); |
146 | if (index >= 0) { |
147 | if (!n->kids[0]) { |
148 | /* |
149 | * Leaf node. We want to insert at kid position |
150 | * equal to the index: |
151 | * |
152 | * 0 A 1 B 2 C 3 |
153 | */ |
154 | childnum = index; |
155 | } else { |
156 | /* |
157 | * Internal node. We always descend through it (add |
158 | * always starts at the bottom, never in the |
159 | * middle). |
160 | */ |
161 | do { /* this is a do ... while (0) to allow `break' */ |
162 | if (index <= n->counts[0]) { |
163 | childnum = 0; |
164 | break; |
165 | } |
166 | index -= n->counts[0] + 1; |
167 | if (index <= n->counts[1]) { |
168 | childnum = 1; |
169 | break; |
170 | } |
171 | index -= n->counts[1] + 1; |
172 | if (index <= n->counts[2]) { |
173 | childnum = 2; |
174 | break; |
175 | } |
176 | index -= n->counts[2] + 1; |
177 | if (index <= n->counts[3]) { |
178 | childnum = 3; |
179 | break; |
180 | } |
181 | return NULL; /* error: index out of range */ |
182 | } while (0); |
183 | } |
184 | } else { |
185 | if ((c = t->cmp(e, n->elems[0])) < 0) |
186 | childnum = 0; |
187 | else if (c == 0) |
188 | return n->elems[0]; /* already exists */ |
189 | else if (n->elems[1] == NULL || (c = t->cmp(e, n->elems[1])) < 0) |
190 | childnum = 1; |
191 | else if (c == 0) |
192 | return n->elems[1]; /* already exists */ |
193 | else if (n->elems[2] == NULL || (c = t->cmp(e, n->elems[2])) < 0) |
194 | childnum = 2; |
195 | else if (c == 0) |
196 | return n->elems[2]; /* already exists */ |
197 | else |
198 | childnum = 3; |
199 | } |
200 | np = &n->kids[childnum]; |
201 | LOG((" moving to child %d (%p)\n", childnum, *np)); |
febd9a0f |
202 | } |
203 | |
204 | /* |
205 | * We need to insert the new element in n at position np. |
206 | */ |
d2371c81 |
207 | left = NULL; lcount = 0; |
208 | right = NULL; rcount = 0; |
febd9a0f |
209 | while (n) { |
d2371c81 |
210 | LOG((" at %p: %p/%d [%p] %p/%d [%p] %p/%d [%p] %p/%d\n", |
211 | n, |
212 | n->kids[0], n->counts[0], n->elems[0], |
213 | n->kids[1], n->counts[1], n->elems[1], |
214 | n->kids[2], n->counts[2], n->elems[2], |
215 | n->kids[3], n->counts[3])); |
216 | LOG((" need to insert %p/%d [%p] %p/%d at position %d\n", |
217 | left, lcount, e, right, rcount, np - n->kids)); |
febd9a0f |
218 | if (n->elems[1] == NULL) { |
219 | /* |
220 | * Insert in a 2-node; simple. |
221 | */ |
222 | if (np == &n->kids[0]) { |
223 | LOG((" inserting on left of 2-node\n")); |
d2371c81 |
224 | n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1]; |
febd9a0f |
225 | n->elems[1] = n->elems[0]; |
d2371c81 |
226 | n->kids[1] = right; n->counts[1] = rcount; |
febd9a0f |
227 | n->elems[0] = e; |
d2371c81 |
228 | n->kids[0] = left; n->counts[0] = lcount; |
febd9a0f |
229 | } else { /* np == &n->kids[1] */ |
230 | LOG((" inserting on right of 2-node\n")); |
d2371c81 |
231 | n->kids[2] = right; n->counts[2] = rcount; |
febd9a0f |
232 | n->elems[1] = e; |
d2371c81 |
233 | n->kids[1] = left; n->counts[1] = lcount; |
febd9a0f |
234 | } |
235 | if (n->kids[0]) n->kids[0]->parent = n; |
236 | if (n->kids[1]) n->kids[1]->parent = n; |
237 | if (n->kids[2]) n->kids[2]->parent = n; |
238 | LOG((" done\n")); |
239 | break; |
240 | } else if (n->elems[2] == NULL) { |
241 | /* |
242 | * Insert in a 3-node; simple. |
243 | */ |
244 | if (np == &n->kids[0]) { |
245 | LOG((" inserting on left of 3-node\n")); |
d2371c81 |
246 | n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2]; |
febd9a0f |
247 | n->elems[2] = n->elems[1]; |
d2371c81 |
248 | n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1]; |
febd9a0f |
249 | n->elems[1] = n->elems[0]; |
d2371c81 |
250 | n->kids[1] = right; n->counts[1] = rcount; |
febd9a0f |
251 | n->elems[0] = e; |
d2371c81 |
252 | n->kids[0] = left; n->counts[0] = lcount; |
febd9a0f |
253 | } else if (np == &n->kids[1]) { |
254 | LOG((" inserting in middle of 3-node\n")); |
d2371c81 |
255 | n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2]; |
febd9a0f |
256 | n->elems[2] = n->elems[1]; |
d2371c81 |
257 | n->kids[2] = right; n->counts[2] = rcount; |
febd9a0f |
258 | n->elems[1] = e; |
d2371c81 |
259 | n->kids[1] = left; n->counts[1] = lcount; |
febd9a0f |
260 | } else { /* np == &n->kids[2] */ |
261 | LOG((" inserting on right of 3-node\n")); |
d2371c81 |
262 | n->kids[3] = right; n->counts[3] = rcount; |
febd9a0f |
263 | n->elems[2] = e; |
d2371c81 |
264 | n->kids[2] = left; n->counts[2] = lcount; |
febd9a0f |
265 | } |
266 | if (n->kids[0]) n->kids[0]->parent = n; |
267 | if (n->kids[1]) n->kids[1]->parent = n; |
268 | if (n->kids[2]) n->kids[2]->parent = n; |
269 | if (n->kids[3]) n->kids[3]->parent = n; |
270 | LOG((" done\n")); |
271 | break; |
272 | } else { |
273 | node234 *m = mknew(node234); |
274 | m->parent = n->parent; |
275 | LOG((" splitting a 4-node; created new node %p\n", m)); |
276 | /* |
277 | * Insert in a 4-node; split into a 2-node and a |
278 | * 3-node, and move focus up a level. |
279 | * |
280 | * I don't think it matters which way round we put the |
281 | * 2 and the 3. For simplicity, we'll put the 3 first |
282 | * always. |
283 | */ |
284 | if (np == &n->kids[0]) { |
d2371c81 |
285 | m->kids[0] = left; m->counts[0] = lcount; |
febd9a0f |
286 | m->elems[0] = e; |
d2371c81 |
287 | m->kids[1] = right; m->counts[1] = rcount; |
febd9a0f |
288 | m->elems[1] = n->elems[0]; |
d2371c81 |
289 | m->kids[2] = n->kids[1]; m->counts[2] = n->counts[1]; |
febd9a0f |
290 | e = n->elems[1]; |
d2371c81 |
291 | n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2]; |
febd9a0f |
292 | n->elems[0] = n->elems[2]; |
d2371c81 |
293 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
febd9a0f |
294 | } else if (np == &n->kids[1]) { |
d2371c81 |
295 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
febd9a0f |
296 | m->elems[0] = n->elems[0]; |
d2371c81 |
297 | m->kids[1] = left; m->counts[1] = lcount; |
febd9a0f |
298 | m->elems[1] = e; |
d2371c81 |
299 | m->kids[2] = right; m->counts[2] = rcount; |
febd9a0f |
300 | e = n->elems[1]; |
d2371c81 |
301 | n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2]; |
febd9a0f |
302 | n->elems[0] = n->elems[2]; |
d2371c81 |
303 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
febd9a0f |
304 | } else if (np == &n->kids[2]) { |
d2371c81 |
305 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
febd9a0f |
306 | m->elems[0] = n->elems[0]; |
d2371c81 |
307 | m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1]; |
febd9a0f |
308 | m->elems[1] = n->elems[1]; |
d2371c81 |
309 | m->kids[2] = left; m->counts[2] = lcount; |
febd9a0f |
310 | /* e = e; */ |
d2371c81 |
311 | n->kids[0] = right; n->counts[0] = rcount; |
febd9a0f |
312 | n->elems[0] = n->elems[2]; |
d2371c81 |
313 | n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3]; |
febd9a0f |
314 | } else { /* np == &n->kids[3] */ |
d2371c81 |
315 | m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0]; |
febd9a0f |
316 | m->elems[0] = n->elems[0]; |
d2371c81 |
317 | m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1]; |
febd9a0f |
318 | m->elems[1] = n->elems[1]; |
d2371c81 |
319 | m->kids[2] = n->kids[2]; m->counts[2] = n->counts[2]; |
320 | n->kids[0] = left; n->counts[0] = lcount; |
febd9a0f |
321 | n->elems[0] = e; |
d2371c81 |
322 | n->kids[1] = right; n->counts[1] = rcount; |
febd9a0f |
323 | e = n->elems[2]; |
324 | } |
325 | m->kids[3] = n->kids[3] = n->kids[2] = NULL; |
d2371c81 |
326 | m->counts[3] = n->counts[3] = n->counts[2] = 0; |
febd9a0f |
327 | m->elems[2] = n->elems[2] = n->elems[1] = NULL; |
328 | if (m->kids[0]) m->kids[0]->parent = m; |
329 | if (m->kids[1]) m->kids[1]->parent = m; |
330 | if (m->kids[2]) m->kids[2]->parent = m; |
331 | if (n->kids[0]) n->kids[0]->parent = n; |
332 | if (n->kids[1]) n->kids[1]->parent = n; |
d2371c81 |
333 | LOG((" left (%p): %p/%d [%p] %p/%d [%p] %p/%d\n", m, |
334 | m->kids[0], m->counts[0], m->elems[0], |
335 | m->kids[1], m->counts[1], m->elems[1], |
336 | m->kids[2], m->counts[2])); |
337 | LOG((" right (%p): %p/%d [%p] %p/%d\n", n, |
338 | n->kids[0], n->counts[0], n->elems[0], |
339 | n->kids[1], n->counts[1])); |
340 | left = m; lcount = countnode234(left); |
341 | right = n; rcount = countnode234(right); |
febd9a0f |
342 | } |
343 | if (n->parent) |
344 | np = (n->parent->kids[0] == n ? &n->parent->kids[0] : |
345 | n->parent->kids[1] == n ? &n->parent->kids[1] : |
346 | n->parent->kids[2] == n ? &n->parent->kids[2] : |
347 | &n->parent->kids[3]); |
348 | n = n->parent; |
349 | } |
350 | |
351 | /* |
352 | * If we've come out of here by `break', n will still be |
d2371c81 |
353 | * non-NULL and all we need to do is go back up the tree |
354 | * updating counts. If we've come here because n is NULL, we |
355 | * need to create a new root for the tree because the old one |
356 | * has just split into two. */ |
357 | if (n) { |
358 | while (n->parent) { |
359 | int count = countnode234(n); |
360 | int childnum; |
361 | childnum = (n->parent->kids[0] == n ? 0 : |
362 | n->parent->kids[1] == n ? 1 : |
363 | n->parent->kids[2] == n ? 2 : 3); |
364 | n->parent->counts[childnum] = count; |
365 | n = n->parent; |
366 | } |
367 | } else { |
febd9a0f |
368 | LOG((" root is overloaded, split into two\n")); |
369 | t->root = mknew(node234); |
d2371c81 |
370 | t->root->kids[0] = left; t->root->counts[0] = lcount; |
febd9a0f |
371 | t->root->elems[0] = e; |
d2371c81 |
372 | t->root->kids[1] = right; t->root->counts[1] = rcount; |
febd9a0f |
373 | t->root->elems[1] = NULL; |
d2371c81 |
374 | t->root->kids[2] = NULL; t->root->counts[2] = 0; |
febd9a0f |
375 | t->root->elems[2] = NULL; |
d2371c81 |
376 | t->root->kids[3] = NULL; t->root->counts[3] = 0; |
febd9a0f |
377 | t->root->parent = NULL; |
378 | if (t->root->kids[0]) t->root->kids[0]->parent = t->root; |
379 | if (t->root->kids[1]) t->root->kids[1]->parent = t->root; |
d2371c81 |
380 | LOG((" new root is %p/%d [%p] %p/%d\n", |
381 | t->root->kids[0], t->root->counts[0], |
382 | t->root->elems[0], |
383 | t->root->kids[1], t->root->counts[1])); |
febd9a0f |
384 | } |
385 | |
386 | return orig_e; |
387 | } |
388 | |
d2371c81 |
389 | void *add234(tree234 *t, void *e) { |
390 | if (!t->cmp) /* tree is unsorted */ |
391 | return NULL; |
392 | |
393 | return add234_internal(t, e, -1); |
394 | } |
395 | void *addpos234(tree234 *t, void *e, int index) { |
396 | if (index < 0 || /* index out of range */ |
397 | t->cmp) /* tree is sorted */ |
398 | return NULL; /* return failure */ |
399 | |
400 | return add234_internal(t, e, index); /* this checks the upper bound */ |
401 | } |
402 | |
febd9a0f |
403 | /* |
d2371c81 |
404 | * Look up the element at a given numeric index in a 2-3-4 tree. |
405 | * Returns NULL if the index is out of range. |
febd9a0f |
406 | */ |
d2371c81 |
407 | void *index234(tree234 *t, int index) { |
febd9a0f |
408 | node234 *n; |
febd9a0f |
409 | |
d2371c81 |
410 | if (!t->root) |
411 | return NULL; /* tree is empty */ |
febd9a0f |
412 | |
d2371c81 |
413 | if (index < 0 || index >= countnode234(t->root)) |
414 | return NULL; /* out of range */ |
febd9a0f |
415 | |
416 | n = t->root; |
d2371c81 |
417 | |
febd9a0f |
418 | while (n) { |
d2371c81 |
419 | if (index < n->counts[0]) |
febd9a0f |
420 | n = n->kids[0]; |
d2371c81 |
421 | else if (index -= n->counts[0] + 1, index < 0) |
febd9a0f |
422 | return n->elems[0]; |
d2371c81 |
423 | else if (index < n->counts[1]) |
febd9a0f |
424 | n = n->kids[1]; |
d2371c81 |
425 | else if (index -= n->counts[1] + 1, index < 0) |
febd9a0f |
426 | return n->elems[1]; |
d2371c81 |
427 | else if (index < n->counts[2]) |
febd9a0f |
428 | n = n->kids[2]; |
d2371c81 |
429 | else if (index -= n->counts[2] + 1, index < 0) |
febd9a0f |
430 | return n->elems[2]; |
431 | else |
432 | n = n->kids[3]; |
433 | } |
434 | |
d2371c81 |
435 | /* We shouldn't ever get here. I wonder how we did. */ |
436 | return NULL; |
437 | } |
438 | |
439 | /* |
440 | * Find an element e in a sorted 2-3-4 tree t. Returns NULL if not |
441 | * found. e is always passed as the first argument to cmp, so cmp |
442 | * can be an asymmetric function if desired. cmp can also be passed |
443 | * as NULL, in which case the compare function from the tree proper |
444 | * will be used. |
445 | */ |
446 | void *findrelpos234(tree234 *t, void *e, cmpfn234 cmp, |
447 | int relation, int *index) { |
448 | node234 *n; |
449 | void *ret; |
450 | int c; |
451 | int idx, ecount, kcount, cmpret; |
452 | |
453 | if (t->root == NULL) |
454 | return NULL; |
455 | |
456 | if (cmp == NULL) |
457 | cmp = t->cmp; |
458 | |
459 | n = t->root; |
febd9a0f |
460 | /* |
d2371c81 |
461 | * Attempt to find the element itself. |
febd9a0f |
462 | */ |
d2371c81 |
463 | idx = 0; |
464 | ecount = -1; |
465 | /* |
466 | * Prepare a fake `cmp' result if e is NULL. |
467 | */ |
468 | cmpret = 0; |
469 | if (e == NULL) { |
470 | assert(relation == REL234_LT || relation == REL234_GT); |
471 | if (relation == REL234_LT) |
472 | cmpret = +1; /* e is a max: always greater */ |
473 | else if (relation == REL234_GT) |
474 | cmpret = -1; /* e is a min: always smaller */ |
475 | } |
476 | while (1) { |
477 | for (kcount = 0; kcount < 4; kcount++) { |
478 | if (kcount >= 3 || n->elems[kcount] == NULL || |
479 | (c = cmpret ? cmpret : cmp(e, n->elems[kcount])) < 0) { |
480 | break; |
481 | } |
482 | if (n->kids[kcount]) idx += n->counts[kcount]; |
483 | if (c == 0) { |
484 | ecount = kcount; |
485 | break; |
486 | } |
487 | idx++; |
488 | } |
489 | if (ecount >= 0) |
490 | break; |
491 | if (n->kids[kcount]) |
492 | n = n->kids[kcount]; |
493 | else |
494 | break; |
495 | } |
496 | |
497 | if (ecount >= 0) { |
498 | /* |
499 | * We have found the element we're looking for. It's |
500 | * n->elems[ecount], at tree index idx. If our search |
501 | * relation is EQ, LE or GE we can now go home. |
502 | */ |
503 | if (relation != REL234_LT && relation != REL234_GT) { |
504 | if (index) *index = idx; |
505 | return n->elems[ecount]; |
506 | } |
507 | |
508 | /* |
509 | * Otherwise, we'll do an indexed lookup for the previous |
510 | * or next element. (It would be perfectly possible to |
511 | * implement these search types in a non-counted tree by |
512 | * going back up from where we are, but far more fiddly.) |
513 | */ |
514 | if (relation == REL234_LT) |
515 | idx--; |
516 | else |
517 | idx++; |
518 | } else { |
519 | /* |
520 | * We've found our way to the bottom of the tree and we |
521 | * know where we would insert this node if we wanted to: |
522 | * we'd put it in in place of the (empty) subtree |
523 | * n->kids[kcount], and it would have index idx |
524 | * |
525 | * But the actual element isn't there. So if our search |
526 | * relation is EQ, we're doomed. |
527 | */ |
528 | if (relation == REL234_EQ) |
529 | return NULL; |
530 | |
531 | /* |
532 | * Otherwise, we must do an index lookup for index idx-1 |
533 | * (if we're going left - LE or LT) or index idx (if we're |
534 | * going right - GE or GT). |
535 | */ |
536 | if (relation == REL234_LT || relation == REL234_LE) { |
537 | idx--; |
538 | } |
539 | } |
540 | |
541 | /* |
542 | * We know the index of the element we want; just call index234 |
543 | * to do the rest. This will return NULL if the index is out of |
544 | * bounds, which is exactly what we want. |
545 | */ |
546 | ret = index234(t, idx); |
547 | if (ret && index) *index = idx; |
548 | return ret; |
549 | } |
550 | void *find234(tree234 *t, void *e, cmpfn234 cmp) { |
551 | return findrelpos234(t, e, cmp, REL234_EQ, NULL); |
552 | } |
553 | void *findrel234(tree234 *t, void *e, cmpfn234 cmp, int relation) { |
554 | return findrelpos234(t, e, cmp, relation, NULL); |
555 | } |
556 | void *findpos234(tree234 *t, void *e, cmpfn234 cmp, int *index) { |
557 | return findrelpos234(t, e, cmp, REL234_EQ, index); |
febd9a0f |
558 | } |
559 | |
560 | /* |
561 | * Delete an element e in a 2-3-4 tree. Does not free the element, |
562 | * merely removes all links to it from the tree nodes. |
563 | */ |
d2371c81 |
564 | static void *delpos234_internal(tree234 *t, int index) { |
febd9a0f |
565 | node234 *n; |
d2371c81 |
566 | void *retval; |
febd9a0f |
567 | int ei = -1; |
568 | |
d2371c81 |
569 | retval = 0; |
570 | |
febd9a0f |
571 | n = t->root; |
d2371c81 |
572 | LOG(("deleting item %d from tree %p\n", index, t)); |
febd9a0f |
573 | while (1) { |
574 | while (n) { |
febd9a0f |
575 | int ki; |
576 | node234 *sub; |
577 | |
d2371c81 |
578 | LOG((" node %p: %p/%d [%p] %p/%d [%p] %p/%d [%p] %p/%d index=%d\n", |
579 | n, |
580 | n->kids[0], n->counts[0], n->elems[0], |
581 | n->kids[1], n->counts[1], n->elems[1], |
582 | n->kids[2], n->counts[2], n->elems[2], |
583 | n->kids[3], n->counts[3], |
584 | index)); |
585 | if (index < n->counts[0]) { |
febd9a0f |
586 | ki = 0; |
d2371c81 |
587 | } else if (index -= n->counts[0]+1, index < 0) { |
febd9a0f |
588 | ei = 0; break; |
d2371c81 |
589 | } else if (index < n->counts[1]) { |
febd9a0f |
590 | ki = 1; |
d2371c81 |
591 | } else if (index -= n->counts[1]+1, index < 0) { |
febd9a0f |
592 | ei = 1; break; |
d2371c81 |
593 | } else if (index < n->counts[2]) { |
febd9a0f |
594 | ki = 2; |
d2371c81 |
595 | } else if (index -= n->counts[2]+1, index < 0) { |
febd9a0f |
596 | ei = 2; break; |
597 | } else { |
598 | ki = 3; |
599 | } |
600 | /* |
601 | * Recurse down to subtree ki. If it has only one element, |
602 | * we have to do some transformation to start with. |
603 | */ |
604 | LOG((" moving to subtree %d\n", ki)); |
605 | sub = n->kids[ki]; |
606 | if (!sub->elems[1]) { |
607 | LOG((" subtree has only one element!\n", ki)); |
608 | if (ki > 0 && n->kids[ki-1]->elems[1]) { |
609 | /* |
610 | * Case 3a, left-handed variant. Child ki has |
611 | * only one element, but child ki-1 has two or |
612 | * more. So we need to move a subtree from ki-1 |
613 | * to ki. |
614 | * |
615 | * . C . . B . |
616 | * / \ -> / \ |
617 | * [more] a A b B c d D e [more] a A b c C d D e |
618 | */ |
619 | node234 *sib = n->kids[ki-1]; |
620 | int lastelem = (sib->elems[2] ? 2 : |
621 | sib->elems[1] ? 1 : 0); |
622 | sub->kids[2] = sub->kids[1]; |
d2371c81 |
623 | sub->counts[2] = sub->counts[1]; |
febd9a0f |
624 | sub->elems[1] = sub->elems[0]; |
625 | sub->kids[1] = sub->kids[0]; |
d2371c81 |
626 | sub->counts[1] = sub->counts[0]; |
febd9a0f |
627 | sub->elems[0] = n->elems[ki-1]; |
628 | sub->kids[0] = sib->kids[lastelem+1]; |
d2371c81 |
629 | sub->counts[0] = sib->counts[lastelem+1]; |
100122a9 |
630 | if (sub->kids[0]) sub->kids[0]->parent = sub; |
febd9a0f |
631 | n->elems[ki-1] = sib->elems[lastelem]; |
632 | sib->kids[lastelem+1] = NULL; |
d2371c81 |
633 | sib->counts[lastelem+1] = 0; |
febd9a0f |
634 | sib->elems[lastelem] = NULL; |
d2371c81 |
635 | n->counts[ki] = countnode234(sub); |
febd9a0f |
636 | LOG((" case 3a left\n")); |
d2371c81 |
637 | LOG((" index and left subtree count before adjustment: %d, %d\n", |
638 | index, n->counts[ki-1])); |
639 | index += n->counts[ki-1]; |
640 | n->counts[ki-1] = countnode234(sib); |
641 | index -= n->counts[ki-1]; |
642 | LOG((" index and left subtree count after adjustment: %d, %d\n", |
643 | index, n->counts[ki-1])); |
febd9a0f |
644 | } else if (ki < 3 && n->kids[ki+1] && |
645 | n->kids[ki+1]->elems[1]) { |
646 | /* |
647 | * Case 3a, right-handed variant. ki has only |
648 | * one element but ki+1 has two or more. Move a |
649 | * subtree from ki+1 to ki. |
650 | * |
651 | * . B . . C . |
652 | * / \ -> / \ |
653 | * a A b c C d D e [more] a A b B c d D e [more] |
654 | */ |
655 | node234 *sib = n->kids[ki+1]; |
656 | int j; |
657 | sub->elems[1] = n->elems[ki]; |
658 | sub->kids[2] = sib->kids[0]; |
d2371c81 |
659 | sub->counts[2] = sib->counts[0]; |
100122a9 |
660 | if (sub->kids[2]) sub->kids[2]->parent = sub; |
febd9a0f |
661 | n->elems[ki] = sib->elems[0]; |
662 | sib->kids[0] = sib->kids[1]; |
d2371c81 |
663 | sib->counts[0] = sib->counts[1]; |
febd9a0f |
664 | for (j = 0; j < 2 && sib->elems[j+1]; j++) { |
665 | sib->kids[j+1] = sib->kids[j+2]; |
d2371c81 |
666 | sib->counts[j+1] = sib->counts[j+2]; |
febd9a0f |
667 | sib->elems[j] = sib->elems[j+1]; |
668 | } |
669 | sib->kids[j+1] = NULL; |
d2371c81 |
670 | sib->counts[j+1] = 0; |
febd9a0f |
671 | sib->elems[j] = NULL; |
d2371c81 |
672 | n->counts[ki] = countnode234(sub); |
673 | n->counts[ki+1] = countnode234(sib); |
febd9a0f |
674 | LOG((" case 3a right\n")); |
675 | } else { |
676 | /* |
677 | * Case 3b. ki has only one element, and has no |
678 | * neighbour with more than one. So pick a |
679 | * neighbour and merge it with ki, taking an |
680 | * element down from n to go in the middle. |
681 | * |
682 | * . B . . |
683 | * / \ -> | |
684 | * a A b c C d a A b B c C d |
685 | * |
686 | * (Since at all points we have avoided |
687 | * descending to a node with only one element, |
688 | * we can be sure that n is not reduced to |
689 | * nothingness by this move, _unless_ it was |
690 | * the very first node, ie the root of the |
691 | * tree. In that case we remove the now-empty |
692 | * root and replace it with its single large |
693 | * child as shown.) |
694 | */ |
695 | node234 *sib; |
696 | int j; |
697 | |
d2371c81 |
698 | if (ki > 0) { |
febd9a0f |
699 | ki--; |
d2371c81 |
700 | index += n->counts[ki] + 1; |
701 | } |
febd9a0f |
702 | sib = n->kids[ki]; |
703 | sub = n->kids[ki+1]; |
704 | |
705 | sub->kids[3] = sub->kids[1]; |
d2371c81 |
706 | sub->counts[3] = sub->counts[1]; |
febd9a0f |
707 | sub->elems[2] = sub->elems[0]; |
708 | sub->kids[2] = sub->kids[0]; |
d2371c81 |
709 | sub->counts[2] = sub->counts[0]; |
febd9a0f |
710 | sub->elems[1] = n->elems[ki]; |
711 | sub->kids[1] = sib->kids[1]; |
d2371c81 |
712 | sub->counts[1] = sib->counts[1]; |
100122a9 |
713 | if (sub->kids[1]) sub->kids[1]->parent = sub; |
febd9a0f |
714 | sub->elems[0] = sib->elems[0]; |
715 | sub->kids[0] = sib->kids[0]; |
d2371c81 |
716 | sub->counts[0] = sib->counts[0]; |
100122a9 |
717 | if (sub->kids[0]) sub->kids[0]->parent = sub; |
febd9a0f |
718 | |
d2371c81 |
719 | n->counts[ki+1] = countnode234(sub); |
720 | |
febd9a0f |
721 | sfree(sib); |
722 | |
723 | /* |
724 | * That's built the big node in sub. Now we |
725 | * need to remove the reference to sib in n. |
726 | */ |
727 | for (j = ki; j < 3 && n->kids[j+1]; j++) { |
728 | n->kids[j] = n->kids[j+1]; |
d2371c81 |
729 | n->counts[j] = n->counts[j+1]; |
febd9a0f |
730 | n->elems[j] = j<2 ? n->elems[j+1] : NULL; |
731 | } |
732 | n->kids[j] = NULL; |
d2371c81 |
733 | n->counts[j] = 0; |
febd9a0f |
734 | if (j < 3) n->elems[j] = NULL; |
2d56b16f |
735 | LOG((" case 3b ki=%d\n", ki)); |
febd9a0f |
736 | |
737 | if (!n->elems[0]) { |
738 | /* |
739 | * The root is empty and needs to be |
740 | * removed. |
741 | */ |
742 | LOG((" shifting root!\n")); |
743 | t->root = sub; |
744 | sub->parent = NULL; |
745 | sfree(n); |
746 | } |
747 | } |
748 | } |
749 | n = sub; |
750 | } |
d2371c81 |
751 | if (!retval) |
752 | retval = n->elems[ei]; |
753 | |
febd9a0f |
754 | if (ei==-1) |
d2371c81 |
755 | return NULL; /* although this shouldn't happen */ |
febd9a0f |
756 | |
757 | /* |
758 | * Treat special case: this is the one remaining item in |
759 | * the tree. n is the tree root (no parent), has one |
760 | * element (no elems[1]), and has no kids (no kids[0]). |
761 | */ |
762 | if (!n->parent && !n->elems[1] && !n->kids[0]) { |
763 | LOG((" removed last element in tree\n")); |
764 | sfree(n); |
765 | t->root = NULL; |
d2371c81 |
766 | return retval; |
febd9a0f |
767 | } |
768 | |
769 | /* |
770 | * Now we have the element we want, as n->elems[ei], and we |
771 | * have also arranged for that element not to be the only |
772 | * one in its node. So... |
773 | */ |
774 | |
775 | if (!n->kids[0] && n->elems[1]) { |
776 | /* |
777 | * Case 1. n is a leaf node with more than one element, |
778 | * so it's _really easy_. Just delete the thing and |
779 | * we're done. |
780 | */ |
781 | int i; |
782 | LOG((" case 1\n")); |
a4a19e73 |
783 | for (i = ei; i < 2 && n->elems[i+1]; i++) |
febd9a0f |
784 | n->elems[i] = n->elems[i+1]; |
785 | n->elems[i] = NULL; |
d2371c81 |
786 | /* |
787 | * Having done that to the leaf node, we now go back up |
788 | * the tree fixing the counts. |
789 | */ |
790 | while (n->parent) { |
791 | int childnum; |
792 | childnum = (n->parent->kids[0] == n ? 0 : |
793 | n->parent->kids[1] == n ? 1 : |
794 | n->parent->kids[2] == n ? 2 : 3); |
795 | n->parent->counts[childnum]--; |
796 | n = n->parent; |
797 | } |
798 | return retval; /* finished! */ |
febd9a0f |
799 | } else if (n->kids[ei]->elems[1]) { |
800 | /* |
801 | * Case 2a. n is an internal node, and the root of the |
802 | * subtree to the left of e has more than one element. |
803 | * So find the predecessor p to e (ie the largest node |
804 | * in that subtree), place it where e currently is, and |
805 | * then start the deletion process over again on the |
806 | * subtree with p as target. |
807 | */ |
808 | node234 *m = n->kids[ei]; |
809 | void *target; |
810 | LOG((" case 2a\n")); |
811 | while (m->kids[0]) { |
812 | m = (m->kids[3] ? m->kids[3] : |
813 | m->kids[2] ? m->kids[2] : |
814 | m->kids[1] ? m->kids[1] : m->kids[0]); |
815 | } |
816 | target = (m->elems[2] ? m->elems[2] : |
817 | m->elems[1] ? m->elems[1] : m->elems[0]); |
818 | n->elems[ei] = target; |
d2371c81 |
819 | index = n->counts[ei]-1; |
febd9a0f |
820 | n = n->kids[ei]; |
febd9a0f |
821 | } else if (n->kids[ei+1]->elems[1]) { |
822 | /* |
823 | * Case 2b, symmetric to 2a but s/left/right/ and |
824 | * s/predecessor/successor/. (And s/largest/smallest/). |
825 | */ |
826 | node234 *m = n->kids[ei+1]; |
827 | void *target; |
828 | LOG((" case 2b\n")); |
829 | while (m->kids[0]) { |
830 | m = m->kids[0]; |
831 | } |
832 | target = m->elems[0]; |
833 | n->elems[ei] = target; |
834 | n = n->kids[ei+1]; |
d2371c81 |
835 | index = 0; |
febd9a0f |
836 | } else { |
837 | /* |
838 | * Case 2c. n is an internal node, and the subtrees to |
839 | * the left and right of e both have only one element. |
840 | * So combine the two subnodes into a single big node |
841 | * with their own elements on the left and right and e |
842 | * in the middle, then restart the deletion process on |
843 | * that subtree, with e still as target. |
844 | */ |
845 | node234 *a = n->kids[ei], *b = n->kids[ei+1]; |
846 | int j; |
847 | |
848 | LOG((" case 2c\n")); |
849 | a->elems[1] = n->elems[ei]; |
850 | a->kids[2] = b->kids[0]; |
d2371c81 |
851 | a->counts[2] = b->counts[0]; |
100122a9 |
852 | if (a->kids[2]) a->kids[2]->parent = a; |
febd9a0f |
853 | a->elems[2] = b->elems[0]; |
854 | a->kids[3] = b->kids[1]; |
d2371c81 |
855 | a->counts[3] = b->counts[1]; |
100122a9 |
856 | if (a->kids[3]) a->kids[3]->parent = a; |
febd9a0f |
857 | sfree(b); |
d2371c81 |
858 | n->counts[ei] = countnode234(a); |
febd9a0f |
859 | /* |
860 | * That's built the big node in a, and destroyed b. Now |
861 | * remove the reference to b (and e) in n. |
862 | */ |
863 | for (j = ei; j < 2 && n->elems[j+1]; j++) { |
864 | n->elems[j] = n->elems[j+1]; |
865 | n->kids[j+1] = n->kids[j+2]; |
d2371c81 |
866 | n->counts[j+1] = n->counts[j+2]; |
febd9a0f |
867 | } |
868 | n->elems[j] = NULL; |
869 | n->kids[j+1] = NULL; |
d2371c81 |
870 | n->counts[j+1] = 0; |
e9e9556d |
871 | /* |
872 | * It's possible, in this case, that we've just removed |
873 | * the only element in the root of the tree. If so, |
874 | * shift the root. |
875 | */ |
876 | if (n->elems[0] == NULL) { |
877 | LOG((" shifting root!\n")); |
878 | t->root = a; |
879 | a->parent = NULL; |
880 | sfree(n); |
881 | } |
febd9a0f |
882 | /* |
883 | * Now go round the deletion process again, with n |
884 | * pointing at the new big node and e still the same. |
885 | */ |
886 | n = a; |
d2371c81 |
887 | index = a->counts[0] + a->counts[1] + 1; |
febd9a0f |
888 | } |
889 | } |
890 | } |
d2371c81 |
891 | void *delpos234(tree234 *t, int index) { |
892 | if (index < 0 || index >= countnode234(t->root)) |
febd9a0f |
893 | return NULL; |
d2371c81 |
894 | return delpos234_internal(t, index); |
febd9a0f |
895 | } |
d2371c81 |
896 | void *del234(tree234 *t, void *e) { |
897 | int index; |
898 | if (!findrelpos234(t, e, NULL, REL234_EQ, &index)) |
899 | return NULL; /* it wasn't in there anyway */ |
900 | return delpos234_internal(t, index); /* it's there; delete it. */ |
febd9a0f |
901 | } |
902 | |
903 | #ifdef TEST |
904 | |
2d56b16f |
905 | /* |
906 | * Test code for the 2-3-4 tree. This code maintains an alternative |
907 | * representation of the data in the tree, in an array (using the |
908 | * obvious and slow insert and delete functions). After each tree |
7aa7c43a |
909 | * operation, the verify() function is called, which ensures all |
d2371c81 |
910 | * the tree properties are preserved: |
911 | * - node->child->parent always equals node |
912 | * - tree->root->parent always equals NULL |
913 | * - number of kids == 0 or number of elements + 1; |
914 | * - tree has the same depth everywhere |
915 | * - every node has at least one element |
916 | * - subtree element counts are accurate |
917 | * - any NULL kid pointer is accompanied by a zero count |
918 | * - in a sorted tree: ordering property between elements of a |
919 | * node and elements of its children is preserved |
920 | * and also ensures the list represented by the tree is the same |
921 | * list it should be. (This last check also doubly verifies the |
922 | * ordering properties, because the `same list it should be' is by |
923 | * definition correctly ordered. It also ensures all nodes are |
924 | * distinct, because the enum functions would get caught in a loop |
925 | * if not.) |
2d56b16f |
926 | */ |
927 | |
928 | #include <stdarg.h> |
929 | |
d2371c81 |
930 | #define srealloc realloc |
931 | |
2d56b16f |
932 | /* |
933 | * Error reporting function. |
934 | */ |
935 | void error(char *fmt, ...) { |
936 | va_list ap; |
937 | printf("ERROR: "); |
938 | va_start(ap, fmt); |
939 | vfprintf(stdout, fmt, ap); |
940 | va_end(ap); |
941 | printf("\n"); |
942 | } |
943 | |
944 | /* The array representation of the data. */ |
945 | void **array; |
946 | int arraylen, arraysize; |
947 | cmpfn234 cmp; |
948 | |
949 | /* The tree representation of the same data. */ |
950 | tree234 *tree; |
951 | |
952 | typedef struct { |
953 | int treedepth; |
954 | int elemcount; |
955 | } chkctx; |
956 | |
d2371c81 |
957 | int chknode(chkctx *ctx, int level, node234 *node, |
2d56b16f |
958 | void *lowbound, void *highbound) { |
959 | int nkids, nelems; |
960 | int i; |
d2371c81 |
961 | int count; |
2d56b16f |
962 | |
963 | /* Count the non-NULL kids. */ |
964 | for (nkids = 0; nkids < 4 && node->kids[nkids]; nkids++); |
965 | /* Ensure no kids beyond the first NULL are non-NULL. */ |
966 | for (i = nkids; i < 4; i++) |
967 | if (node->kids[i]) { |
968 | error("node %p: nkids=%d but kids[%d] non-NULL", |
969 | node, nkids, i); |
d2371c81 |
970 | } else if (node->counts[i]) { |
971 | error("node %p: kids[%d] NULL but count[%d]=%d nonzero", |
972 | node, i, i, node->counts[i]); |
973 | } |
2d56b16f |
974 | |
975 | /* Count the non-NULL elements. */ |
976 | for (nelems = 0; nelems < 3 && node->elems[nelems]; nelems++); |
977 | /* Ensure no elements beyond the first NULL are non-NULL. */ |
978 | for (i = nelems; i < 3; i++) |
979 | if (node->elems[i]) { |
980 | error("node %p: nelems=%d but elems[%d] non-NULL", |
981 | node, nelems, i); |
982 | } |
983 | |
984 | if (nkids == 0) { |
985 | /* |
986 | * If nkids==0, this is a leaf node; verify that the tree |
987 | * depth is the same everywhere. |
988 | */ |
989 | if (ctx->treedepth < 0) |
990 | ctx->treedepth = level; /* we didn't know the depth yet */ |
991 | else if (ctx->treedepth != level) |
992 | error("node %p: leaf at depth %d, previously seen depth %d", |
993 | node, level, ctx->treedepth); |
994 | } else { |
995 | /* |
996 | * If nkids != 0, then it should be nelems+1, unless nelems |
997 | * is 0 in which case nkids should also be 0 (and so we |
998 | * shouldn't be in this condition at all). |
999 | */ |
1000 | int shouldkids = (nelems ? nelems+1 : 0); |
1001 | if (nkids != shouldkids) { |
1002 | error("node %p: %d elems should mean %d kids but has %d", |
1003 | node, nelems, shouldkids, nkids); |
1004 | } |
1005 | } |
1006 | |
1007 | /* |
1008 | * nelems should be at least 1. |
1009 | */ |
1010 | if (nelems == 0) { |
1011 | error("node %p: no elems", node, nkids); |
1012 | } |
1013 | |
1014 | /* |
d2371c81 |
1015 | * Add nelems to the running element count of the whole tree. |
2d56b16f |
1016 | */ |
1017 | ctx->elemcount += nelems; |
1018 | |
1019 | /* |
1020 | * Check ordering property: all elements should be strictly > |
1021 | * lowbound, strictly < highbound, and strictly < each other in |
1022 | * sequence. (lowbound and highbound are NULL at edges of tree |
1023 | * - both NULL at root node - and NULL is considered to be < |
1024 | * everything and > everything. IYSWIM.) |
1025 | */ |
d2371c81 |
1026 | if (cmp) { |
1027 | for (i = -1; i < nelems; i++) { |
1028 | void *lower = (i == -1 ? lowbound : node->elems[i]); |
1029 | void *higher = (i+1 == nelems ? highbound : node->elems[i+1]); |
1030 | if (lower && higher && cmp(lower, higher) >= 0) { |
1031 | error("node %p: kid comparison [%d=%s,%d=%s] failed", |
1032 | node, i, lower, i+1, higher); |
1033 | } |
1034 | } |
2d56b16f |
1035 | } |
1036 | |
1037 | /* |
1038 | * Check parent pointers: all non-NULL kids should have a |
1039 | * parent pointer coming back to this node. |
1040 | */ |
1041 | for (i = 0; i < nkids; i++) |
1042 | if (node->kids[i]->parent != node) { |
1043 | error("node %p kid %d: parent ptr is %p not %p", |
1044 | node, i, node->kids[i]->parent, node); |
1045 | } |
1046 | |
1047 | |
1048 | /* |
1049 | * Now (finally!) recurse into subtrees. |
1050 | */ |
d2371c81 |
1051 | count = nelems; |
1052 | |
2d56b16f |
1053 | for (i = 0; i < nkids; i++) { |
1054 | void *lower = (i == 0 ? lowbound : node->elems[i-1]); |
1055 | void *higher = (i >= nelems ? highbound : node->elems[i]); |
d2371c81 |
1056 | int subcount = chknode(ctx, level+1, node->kids[i], lower, higher); |
1057 | if (node->counts[i] != subcount) { |
1058 | error("node %p kid %d: count says %d, subtree really has %d", |
1059 | node, i, node->counts[i], subcount); |
1060 | } |
1061 | count += subcount; |
2d56b16f |
1062 | } |
d2371c81 |
1063 | |
1064 | return count; |
2d56b16f |
1065 | } |
1066 | |
1067 | void verify(void) { |
1068 | chkctx ctx; |
2d56b16f |
1069 | int i; |
1070 | void *p; |
1071 | |
1072 | ctx.treedepth = -1; /* depth unknown yet */ |
1073 | ctx.elemcount = 0; /* no elements seen yet */ |
1074 | /* |
1075 | * Verify validity of tree properties. |
1076 | */ |
d2371c81 |
1077 | if (tree->root) { |
1078 | if (tree->root->parent != NULL) |
1079 | error("root->parent is %p should be null", tree->root->parent); |
2d56b16f |
1080 | chknode(&ctx, 0, tree->root, NULL, NULL); |
d2371c81 |
1081 | } |
2d56b16f |
1082 | printf("tree depth: %d\n", ctx.treedepth); |
1083 | /* |
1084 | * Enumerate the tree and ensure it matches up to the array. |
1085 | */ |
d2371c81 |
1086 | for (i = 0; NULL != (p = index234(tree, i)); i++) { |
2d56b16f |
1087 | if (i >= arraylen) |
1088 | error("tree contains more than %d elements", arraylen); |
1089 | if (array[i] != p) |
1090 | error("enum at position %d: array says %s, tree says %s", |
1091 | i, array[i], p); |
1092 | } |
d2371c81 |
1093 | if (ctx.elemcount != i) { |
2d56b16f |
1094 | error("tree really contains %d elements, enum gave %d", |
d2371c81 |
1095 | ctx.elemcount, i); |
2d56b16f |
1096 | } |
1097 | if (i < arraylen) { |
1098 | error("enum gave only %d elements, array has %d", i, arraylen); |
1099 | } |
d2371c81 |
1100 | i = count234(tree); |
1101 | if (ctx.elemcount != i) { |
1102 | error("tree really contains %d elements, count234 gave %d", |
1103 | ctx.elemcount, i); |
1104 | } |
2d56b16f |
1105 | } |
1106 | |
d2371c81 |
1107 | void internal_addtest(void *elem, int index, void *realret) { |
2d56b16f |
1108 | int i, j; |
d2371c81 |
1109 | void *retval; |
2d56b16f |
1110 | |
1111 | if (arraysize < arraylen+1) { |
1112 | arraysize = arraylen+1+256; |
dcbde236 |
1113 | array = (array == NULL ? smalloc(arraysize*sizeof(*array)) : |
1114 | srealloc(array, arraysize*sizeof(*array))); |
2d56b16f |
1115 | } |
1116 | |
d2371c81 |
1117 | i = index; |
2d56b16f |
1118 | /* now i points to the first element >= elem */ |
d2371c81 |
1119 | retval = elem; /* expect elem returned (success) */ |
1120 | for (j = arraylen; j > i; j--) |
1121 | array[j] = array[j-1]; |
1122 | array[i] = elem; /* add elem to array */ |
1123 | arraylen++; |
2d56b16f |
1124 | |
2d56b16f |
1125 | if (realret != retval) { |
1126 | error("add: retval was %p expected %p", realret, retval); |
1127 | } |
1128 | |
1129 | verify(); |
1130 | } |
1131 | |
d2371c81 |
1132 | void addtest(void *elem) { |
2d56b16f |
1133 | int i; |
d2371c81 |
1134 | void *realret; |
1135 | |
1136 | realret = add234(tree, elem); |
2d56b16f |
1137 | |
1138 | i = 0; |
1139 | while (i < arraylen && cmp(elem, array[i]) > 0) |
1140 | i++; |
d2371c81 |
1141 | if (i < arraylen && !cmp(elem, array[i])) { |
1142 | void *retval = array[i]; /* expect that returned not elem */ |
1143 | if (realret != retval) { |
1144 | error("add: retval was %p expected %p", realret, retval); |
1145 | } |
1146 | } else |
1147 | internal_addtest(elem, i, realret); |
1148 | } |
1149 | |
1150 | void addpostest(void *elem, int i) { |
1151 | void *realret; |
1152 | |
1153 | realret = addpos234(tree, elem, i); |
1154 | |
1155 | internal_addtest(elem, i, realret); |
1156 | } |
1157 | |
1158 | void delpostest(int i) { |
1159 | int index = i; |
1160 | void *elem = array[i], *ret; |
1161 | |
1162 | /* i points to the right element */ |
1163 | while (i < arraylen-1) { |
1164 | array[i] = array[i+1]; |
1165 | i++; |
2d56b16f |
1166 | } |
d2371c81 |
1167 | arraylen--; /* delete elem from array */ |
1168 | |
1169 | if (tree->cmp) |
1170 | ret = del234(tree, elem); |
1171 | else |
1172 | ret = delpos234(tree, index); |
2d56b16f |
1173 | |
d2371c81 |
1174 | if (ret != elem) { |
1175 | error("del returned %p, expected %p", ret, elem); |
1176 | } |
2d56b16f |
1177 | |
1178 | verify(); |
febd9a0f |
1179 | } |
2d56b16f |
1180 | |
d2371c81 |
1181 | void deltest(void *elem) { |
1182 | int i; |
1183 | |
1184 | i = 0; |
1185 | while (i < arraylen && cmp(elem, array[i]) > 0) |
1186 | i++; |
1187 | if (i >= arraylen || cmp(elem, array[i]) != 0) |
1188 | return; /* don't do it! */ |
1189 | delpostest(i); |
1190 | } |
1191 | |
2d56b16f |
1192 | /* A sample data set and test utility. Designed for pseudo-randomness, |
1193 | * and yet repeatability. */ |
1194 | |
1195 | /* |
1196 | * This random number generator uses the `portable implementation' |
1197 | * given in ANSI C99 draft N869. It assumes `unsigned' is 32 bits; |
1198 | * change it if not. |
1199 | */ |
1200 | int randomnumber(unsigned *seed) { |
1201 | *seed *= 1103515245; |
1202 | *seed += 12345; |
1203 | return ((*seed) / 65536) % 32768; |
febd9a0f |
1204 | } |
1205 | |
2d56b16f |
1206 | int mycmp(void *av, void *bv) { |
1207 | char const *a = (char const *)av; |
1208 | char const *b = (char const *)bv; |
febd9a0f |
1209 | return strcmp(a, b); |
1210 | } |
1211 | |
2d56b16f |
1212 | #define lenof(x) ( sizeof((x)) / sizeof(*(x)) ) |
1213 | |
1214 | char *strings[] = { |
1215 | "a", "ab", "absque", "coram", "de", |
1216 | "palam", "clam", "cum", "ex", "e", |
1217 | "sine", "tenus", "pro", "prae", |
1218 | "banana", "carrot", "cabbage", "broccoli", "onion", "zebra", |
1219 | "penguin", "blancmange", "pangolin", "whale", "hedgehog", |
1220 | "giraffe", "peanut", "bungee", "foo", "bar", "baz", "quux", |
1221 | "murfl", "spoo", "breen", "flarn", "octothorpe", |
1222 | "snail", "tiger", "elephant", "octopus", "warthog", "armadillo", |
1223 | "aardvark", "wyvern", "dragon", "elf", "dwarf", "orc", "goblin", |
1224 | "pixie", "basilisk", "warg", "ape", "lizard", "newt", "shopkeeper", |
1225 | "wand", "ring", "amulet" |
1226 | }; |
1227 | |
1228 | #define NSTR lenof(strings) |
1229 | |
d2371c81 |
1230 | int findtest(void) { |
1231 | const static int rels[] = { |
1232 | REL234_EQ, REL234_GE, REL234_LE, REL234_LT, REL234_GT |
1233 | }; |
1234 | const static char *const relnames[] = { |
1235 | "EQ", "GE", "LE", "LT", "GT" |
1236 | }; |
1237 | int i, j, rel, index; |
1238 | char *p, *ret, *realret, *realret2; |
1239 | int lo, hi, mid, c; |
1240 | |
1241 | for (i = 0; i < NSTR; i++) { |
1242 | p = strings[i]; |
1243 | for (j = 0; j < sizeof(rels)/sizeof(*rels); j++) { |
1244 | rel = rels[j]; |
1245 | |
1246 | lo = 0; hi = arraylen-1; |
1247 | while (lo <= hi) { |
1248 | mid = (lo + hi) / 2; |
1249 | c = strcmp(p, array[mid]); |
1250 | if (c < 0) |
1251 | hi = mid-1; |
1252 | else if (c > 0) |
1253 | lo = mid+1; |
1254 | else |
1255 | break; |
1256 | } |
1257 | |
1258 | if (c == 0) { |
1259 | if (rel == REL234_LT) |
1260 | ret = (mid > 0 ? array[--mid] : NULL); |
1261 | else if (rel == REL234_GT) |
1262 | ret = (mid < arraylen-1 ? array[++mid] : NULL); |
1263 | else |
1264 | ret = array[mid]; |
1265 | } else { |
1266 | assert(lo == hi+1); |
1267 | if (rel == REL234_LT || rel == REL234_LE) { |
1268 | mid = hi; |
1269 | ret = (hi >= 0 ? array[hi] : NULL); |
1270 | } else if (rel == REL234_GT || rel == REL234_GE) { |
1271 | mid = lo; |
1272 | ret = (lo < arraylen ? array[lo] : NULL); |
1273 | } else |
1274 | ret = NULL; |
1275 | } |
1276 | |
1277 | realret = findrelpos234(tree, p, NULL, rel, &index); |
1278 | if (realret != ret) { |
1279 | error("find(\"%s\",%s) gave %s should be %s", |
1280 | p, relnames[j], realret, ret); |
1281 | } |
1282 | if (realret && index != mid) { |
1283 | error("find(\"%s\",%s) gave %d should be %d", |
1284 | p, relnames[j], index, mid); |
1285 | } |
1286 | if (realret && rel == REL234_EQ) { |
1287 | realret2 = index234(tree, index); |
1288 | if (realret2 != realret) { |
1289 | error("find(\"%s\",%s) gave %s(%d) but %d -> %s", |
1290 | p, relnames[j], realret, index, index, realret2); |
1291 | } |
1292 | } |
1293 | #if 0 |
1294 | printf("find(\"%s\",%s) gave %s(%d)\n", p, relnames[j], |
1295 | realret, index); |
1296 | #endif |
1297 | } |
1298 | } |
1299 | |
1300 | realret = findrelpos234(tree, NULL, NULL, REL234_GT, &index); |
1301 | if (arraylen && (realret != array[0] || index != 0)) { |
1302 | error("find(NULL,GT) gave %s(%d) should be %s(0)", |
1303 | realret, index, array[0]); |
1304 | } else if (!arraylen && (realret != NULL)) { |
1305 | error("find(NULL,GT) gave %s(%d) should be NULL", |
1306 | realret, index); |
1307 | } |
1308 | |
1309 | realret = findrelpos234(tree, NULL, NULL, REL234_LT, &index); |
1310 | if (arraylen && (realret != array[arraylen-1] || index != arraylen-1)) { |
1311 | error("find(NULL,LT) gave %s(%d) should be %s(0)", |
1312 | realret, index, array[arraylen-1]); |
1313 | } else if (!arraylen && (realret != NULL)) { |
1314 | error("find(NULL,LT) gave %s(%d) should be NULL", |
1315 | realret, index); |
1316 | } |
1317 | } |
1318 | |
febd9a0f |
1319 | int main(void) { |
2d56b16f |
1320 | int in[NSTR]; |
d2371c81 |
1321 | int i, j, k; |
2d56b16f |
1322 | unsigned seed = 0; |
1323 | |
1324 | for (i = 0; i < NSTR; i++) in[i] = 0; |
1325 | array = NULL; |
1326 | arraylen = arraysize = 0; |
1327 | tree = newtree234(mycmp); |
1328 | cmp = mycmp; |
1329 | |
1330 | verify(); |
1331 | for (i = 0; i < 10000; i++) { |
1332 | j = randomnumber(&seed); |
1333 | j %= NSTR; |
1334 | printf("trial: %d\n", i); |
1335 | if (in[j]) { |
1336 | printf("deleting %s (%d)\n", strings[j], j); |
1337 | deltest(strings[j]); |
1338 | in[j] = 0; |
1339 | } else { |
1340 | printf("adding %s (%d)\n", strings[j], j); |
1341 | addtest(strings[j]); |
1342 | in[j] = 1; |
1343 | } |
d2371c81 |
1344 | findtest(); |
2d56b16f |
1345 | } |
1346 | |
1347 | while (arraylen > 0) { |
1348 | j = randomnumber(&seed); |
1349 | j %= arraylen; |
1350 | deltest(array[j]); |
1351 | } |
1352 | |
d2371c81 |
1353 | freetree234(tree); |
1354 | |
1355 | /* |
1356 | * Now try an unsorted tree. We don't really need to test |
1357 | * delpos234 because we know del234 is based on it, so it's |
1358 | * already been tested in the above sorted-tree code; but for |
1359 | * completeness we'll use it to tear down our unsorted tree |
1360 | * once we've built it. |
1361 | */ |
1362 | tree = newtree234(NULL); |
1363 | cmp = NULL; |
1364 | verify(); |
1365 | for (i = 0; i < 1000; i++) { |
1366 | printf("trial: %d\n", i); |
1367 | j = randomnumber(&seed); |
1368 | j %= NSTR; |
1369 | k = randomnumber(&seed); |
1370 | k %= count234(tree)+1; |
1371 | printf("adding string %s at index %d\n", strings[j], k); |
1372 | addpostest(strings[j], k); |
1373 | } |
1374 | while (count234(tree) > 0) { |
1375 | printf("cleanup: tree size %d\n", count234(tree)); |
1376 | j = randomnumber(&seed); |
1377 | j %= count234(tree); |
1378 | printf("deleting string %s from index %d\n", array[j], j); |
1379 | delpostest(j); |
1380 | } |
1381 | |
2d56b16f |
1382 | return 0; |
febd9a0f |
1383 | } |
2d56b16f |
1384 | |
febd9a0f |
1385 | #endif |