| 1 | /* A Fibonacci heap datatype. |
| 2 | Copyright 1998, 1999, 2000, 2001 Free Software Foundation, Inc. |
| 3 | Contributed by Daniel Berlin (dan@cgsoftware.com). |
| 4 | |
| 5 | This file is part of GNU CC. |
| 6 | |
| 7 | GNU CC is free software; you can redistribute it and/or modify it |
| 8 | under the terms of the GNU General Public License as published by |
| 9 | the Free Software Foundation; either version 2, or (at your option) |
| 10 | any later version. |
| 11 | |
| 12 | GNU CC is distributed in the hope that it will be useful, but |
| 13 | WITHOUT ANY WARRANTY; without even the implied warranty of |
| 14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 15 | General Public License for more details. |
| 16 | |
| 17 | You should have received a copy of the GNU General Public License |
| 18 | along with GNU CC; see the file COPYING. If not, write to |
| 19 | the Free Software Foundation, 51 Franklin Street - Fifth Floor, |
| 20 | Boston, MA 02110-1301, USA. */ |
| 21 | |
| 22 | #ifdef HAVE_CONFIG_H |
| 23 | #include "config.h" |
| 24 | #endif |
| 25 | #ifdef HAVE_LIMITS_H |
| 26 | #include <limits.h> |
| 27 | #endif |
| 28 | #ifdef HAVE_STDLIB_H |
| 29 | #include <stdlib.h> |
| 30 | #endif |
| 31 | #ifdef HAVE_STRING_H |
| 32 | #include <string.h> |
| 33 | #endif |
| 34 | #include "libiberty.h" |
| 35 | #include "fibheap.h" |
| 36 | |
| 37 | |
| 38 | #define FIBHEAPKEY_MIN LONG_MIN |
| 39 | |
| 40 | static void fibheap_ins_root (fibheap_t, fibnode_t); |
| 41 | static void fibheap_rem_root (fibheap_t, fibnode_t); |
| 42 | static void fibheap_consolidate (fibheap_t); |
| 43 | static void fibheap_link (fibheap_t, fibnode_t, fibnode_t); |
| 44 | static void fibheap_cut (fibheap_t, fibnode_t, fibnode_t); |
| 45 | static void fibheap_cascading_cut (fibheap_t, fibnode_t); |
| 46 | static fibnode_t fibheap_extr_min_node (fibheap_t); |
| 47 | static int fibheap_compare (fibheap_t, fibnode_t, fibnode_t); |
| 48 | static int fibheap_comp_data (fibheap_t, fibheapkey_t, void *, fibnode_t); |
| 49 | static fibnode_t fibnode_new (void); |
| 50 | static void fibnode_insert_after (fibnode_t, fibnode_t); |
| 51 | #define fibnode_insert_before(a, b) fibnode_insert_after (a->left, b) |
| 52 | static fibnode_t fibnode_remove (fibnode_t); |
| 53 | |
| 54 | \f |
| 55 | /* Create a new fibonacci heap. */ |
| 56 | fibheap_t |
| 57 | fibheap_new (void) |
| 58 | { |
| 59 | return (fibheap_t) xcalloc (1, sizeof (struct fibheap)); |
| 60 | } |
| 61 | |
| 62 | /* Create a new fibonacci heap node. */ |
| 63 | static fibnode_t |
| 64 | fibnode_new (void) |
| 65 | { |
| 66 | fibnode_t node; |
| 67 | |
| 68 | node = (fibnode_t) xcalloc (1, sizeof *node); |
| 69 | node->left = node; |
| 70 | node->right = node; |
| 71 | |
| 72 | return node; |
| 73 | } |
| 74 | |
| 75 | static inline int |
| 76 | fibheap_compare (fibheap_t heap ATTRIBUTE_UNUSED, fibnode_t a, fibnode_t b) |
| 77 | { |
| 78 | if (a->key < b->key) |
| 79 | return -1; |
| 80 | if (a->key > b->key) |
| 81 | return 1; |
| 82 | return 0; |
| 83 | } |
| 84 | |
| 85 | static inline int |
| 86 | fibheap_comp_data (fibheap_t heap, fibheapkey_t key, void *data, fibnode_t b) |
| 87 | { |
| 88 | struct fibnode a; |
| 89 | |
| 90 | a.key = key; |
| 91 | a.data = data; |
| 92 | |
| 93 | return fibheap_compare (heap, &a, b); |
| 94 | } |
| 95 | |
| 96 | /* Insert DATA, with priority KEY, into HEAP. */ |
| 97 | fibnode_t |
| 98 | fibheap_insert (fibheap_t heap, fibheapkey_t key, void *data) |
| 99 | { |
| 100 | fibnode_t node; |
| 101 | |
| 102 | /* Create the new node. */ |
| 103 | node = fibnode_new (); |
| 104 | |
| 105 | /* Set the node's data. */ |
| 106 | node->data = data; |
| 107 | node->key = key; |
| 108 | |
| 109 | /* Insert it into the root list. */ |
| 110 | fibheap_ins_root (heap, node); |
| 111 | |
| 112 | /* If their was no minimum, or this key is less than the min, |
| 113 | it's the new min. */ |
| 114 | if (heap->min == NULL || node->key < heap->min->key) |
| 115 | heap->min = node; |
| 116 | |
| 117 | heap->nodes++; |
| 118 | |
| 119 | return node; |
| 120 | } |
| 121 | |
| 122 | /* Return the data of the minimum node (if we know it). */ |
| 123 | void * |
| 124 | fibheap_min (fibheap_t heap) |
| 125 | { |
| 126 | /* If there is no min, we can't easily return it. */ |
| 127 | if (heap->min == NULL) |
| 128 | return NULL; |
| 129 | return heap->min->data; |
| 130 | } |
| 131 | |
| 132 | /* Return the key of the minimum node (if we know it). */ |
| 133 | fibheapkey_t |
| 134 | fibheap_min_key (fibheap_t heap) |
| 135 | { |
| 136 | /* If there is no min, we can't easily return it. */ |
| 137 | if (heap->min == NULL) |
| 138 | return 0; |
| 139 | return heap->min->key; |
| 140 | } |
| 141 | |
| 142 | /* Union HEAPA and HEAPB into a new heap. */ |
| 143 | fibheap_t |
| 144 | fibheap_union (fibheap_t heapa, fibheap_t heapb) |
| 145 | { |
| 146 | fibnode_t a_root, b_root, temp; |
| 147 | |
| 148 | /* If one of the heaps is empty, the union is just the other heap. */ |
| 149 | if ((a_root = heapa->root) == NULL) |
| 150 | { |
| 151 | free (heapa); |
| 152 | return heapb; |
| 153 | } |
| 154 | if ((b_root = heapb->root) == NULL) |
| 155 | { |
| 156 | free (heapb); |
| 157 | return heapa; |
| 158 | } |
| 159 | |
| 160 | /* Merge them to the next nodes on the opposite chain. */ |
| 161 | a_root->left->right = b_root; |
| 162 | b_root->left->right = a_root; |
| 163 | temp = a_root->left; |
| 164 | a_root->left = b_root->left; |
| 165 | b_root->left = temp; |
| 166 | heapa->nodes += heapb->nodes; |
| 167 | |
| 168 | /* And set the new minimum, if it's changed. */ |
| 169 | if (fibheap_compare (heapa, heapb->min, heapa->min) < 0) |
| 170 | heapa->min = heapb->min; |
| 171 | |
| 172 | free (heapb); |
| 173 | return heapa; |
| 174 | } |
| 175 | |
| 176 | /* Extract the data of the minimum node from HEAP. */ |
| 177 | void * |
| 178 | fibheap_extract_min (fibheap_t heap) |
| 179 | { |
| 180 | fibnode_t z; |
| 181 | void *ret = NULL; |
| 182 | |
| 183 | /* If we don't have a min set, it means we have no nodes. */ |
| 184 | if (heap->min != NULL) |
| 185 | { |
| 186 | /* Otherwise, extract the min node, free the node, and return the |
| 187 | node's data. */ |
| 188 | z = fibheap_extr_min_node (heap); |
| 189 | ret = z->data; |
| 190 | free (z); |
| 191 | } |
| 192 | |
| 193 | return ret; |
| 194 | } |
| 195 | |
| 196 | /* Replace both the KEY and the DATA associated with NODE. */ |
| 197 | void * |
| 198 | fibheap_replace_key_data (fibheap_t heap, fibnode_t node, |
| 199 | fibheapkey_t key, void *data) |
| 200 | { |
| 201 | void *odata; |
| 202 | fibheapkey_t okey; |
| 203 | fibnode_t y; |
| 204 | |
| 205 | /* If we wanted to, we could actually do a real increase by redeleting and |
| 206 | inserting. However, this would require O (log n) time. So just bail out |
| 207 | for now. */ |
| 208 | if (fibheap_comp_data (heap, key, data, node) > 0) |
| 209 | return NULL; |
| 210 | |
| 211 | odata = node->data; |
| 212 | okey = node->key; |
| 213 | node->data = data; |
| 214 | node->key = key; |
| 215 | y = node->parent; |
| 216 | |
| 217 | /* Short-circuit if the key is the same, as we then don't have to |
| 218 | do anything. Except if we're trying to force the new node to |
| 219 | be the new minimum for delete. */ |
| 220 | if (okey == key && okey != FIBHEAPKEY_MIN) |
| 221 | return odata; |
| 222 | |
| 223 | /* These two compares are specifically <= 0 to make sure that in the case |
| 224 | of equality, a node we replaced the data on, becomes the new min. This |
| 225 | is needed so that delete's call to extractmin gets the right node. */ |
| 226 | if (y != NULL && fibheap_compare (heap, node, y) <= 0) |
| 227 | { |
| 228 | fibheap_cut (heap, node, y); |
| 229 | fibheap_cascading_cut (heap, y); |
| 230 | } |
| 231 | |
| 232 | if (fibheap_compare (heap, node, heap->min) <= 0) |
| 233 | heap->min = node; |
| 234 | |
| 235 | return odata; |
| 236 | } |
| 237 | |
| 238 | /* Replace the DATA associated with NODE. */ |
| 239 | void * |
| 240 | fibheap_replace_data (fibheap_t heap, fibnode_t node, void *data) |
| 241 | { |
| 242 | return fibheap_replace_key_data (heap, node, node->key, data); |
| 243 | } |
| 244 | |
| 245 | /* Replace the KEY associated with NODE. */ |
| 246 | fibheapkey_t |
| 247 | fibheap_replace_key (fibheap_t heap, fibnode_t node, fibheapkey_t key) |
| 248 | { |
| 249 | int okey = node->key; |
| 250 | fibheap_replace_key_data (heap, node, key, node->data); |
| 251 | return okey; |
| 252 | } |
| 253 | |
| 254 | /* Delete NODE from HEAP. */ |
| 255 | void * |
| 256 | fibheap_delete_node (fibheap_t heap, fibnode_t node) |
| 257 | { |
| 258 | void *ret = node->data; |
| 259 | |
| 260 | /* To perform delete, we just make it the min key, and extract. */ |
| 261 | fibheap_replace_key (heap, node, FIBHEAPKEY_MIN); |
| 262 | if (node != heap->min) |
| 263 | { |
| 264 | fprintf (stderr, "Can't force minimum on fibheap.\n"); |
| 265 | abort (); |
| 266 | } |
| 267 | fibheap_extract_min (heap); |
| 268 | |
| 269 | return ret; |
| 270 | } |
| 271 | |
| 272 | /* Delete HEAP. */ |
| 273 | void |
| 274 | fibheap_delete (fibheap_t heap) |
| 275 | { |
| 276 | while (heap->min != NULL) |
| 277 | free (fibheap_extr_min_node (heap)); |
| 278 | |
| 279 | free (heap); |
| 280 | } |
| 281 | |
| 282 | /* Determine if HEAP is empty. */ |
| 283 | int |
| 284 | fibheap_empty (fibheap_t heap) |
| 285 | { |
| 286 | return heap->nodes == 0; |
| 287 | } |
| 288 | |
| 289 | /* Extract the minimum node of the heap. */ |
| 290 | static fibnode_t |
| 291 | fibheap_extr_min_node (fibheap_t heap) |
| 292 | { |
| 293 | fibnode_t ret = heap->min; |
| 294 | fibnode_t x, y, orig; |
| 295 | |
| 296 | /* Attach the child list of the minimum node to the root list of the heap. |
| 297 | If there is no child list, we don't do squat. */ |
| 298 | for (x = ret->child, orig = NULL; x != orig && x != NULL; x = y) |
| 299 | { |
| 300 | if (orig == NULL) |
| 301 | orig = x; |
| 302 | y = x->right; |
| 303 | x->parent = NULL; |
| 304 | fibheap_ins_root (heap, x); |
| 305 | } |
| 306 | |
| 307 | /* Remove the old root. */ |
| 308 | fibheap_rem_root (heap, ret); |
| 309 | heap->nodes--; |
| 310 | |
| 311 | /* If we are left with no nodes, then the min is NULL. */ |
| 312 | if (heap->nodes == 0) |
| 313 | heap->min = NULL; |
| 314 | else |
| 315 | { |
| 316 | /* Otherwise, consolidate to find new minimum, as well as do the reorg |
| 317 | work that needs to be done. */ |
| 318 | heap->min = ret->right; |
| 319 | fibheap_consolidate (heap); |
| 320 | } |
| 321 | |
| 322 | return ret; |
| 323 | } |
| 324 | |
| 325 | /* Insert NODE into the root list of HEAP. */ |
| 326 | static void |
| 327 | fibheap_ins_root (fibheap_t heap, fibnode_t node) |
| 328 | { |
| 329 | /* If the heap is currently empty, the new node becomes the singleton |
| 330 | circular root list. */ |
| 331 | if (heap->root == NULL) |
| 332 | { |
| 333 | heap->root = node; |
| 334 | node->left = node; |
| 335 | node->right = node; |
| 336 | return; |
| 337 | } |
| 338 | |
| 339 | /* Otherwise, insert it in the circular root list between the root |
| 340 | and it's right node. */ |
| 341 | fibnode_insert_after (heap->root, node); |
| 342 | } |
| 343 | |
| 344 | /* Remove NODE from the rootlist of HEAP. */ |
| 345 | static void |
| 346 | fibheap_rem_root (fibheap_t heap, fibnode_t node) |
| 347 | { |
| 348 | if (node->left == node) |
| 349 | heap->root = NULL; |
| 350 | else |
| 351 | heap->root = fibnode_remove (node); |
| 352 | } |
| 353 | |
| 354 | /* Consolidate the heap. */ |
| 355 | static void |
| 356 | fibheap_consolidate (fibheap_t heap) |
| 357 | { |
| 358 | fibnode_t a[1 + 8 * sizeof (long)]; |
| 359 | fibnode_t w; |
| 360 | fibnode_t y; |
| 361 | fibnode_t x; |
| 362 | int i; |
| 363 | int d; |
| 364 | int D; |
| 365 | |
| 366 | D = 1 + 8 * sizeof (long); |
| 367 | |
| 368 | memset (a, 0, sizeof (fibnode_t) * D); |
| 369 | |
| 370 | while ((w = heap->root) != NULL) |
| 371 | { |
| 372 | x = w; |
| 373 | fibheap_rem_root (heap, w); |
| 374 | d = x->degree; |
| 375 | while (a[d] != NULL) |
| 376 | { |
| 377 | y = a[d]; |
| 378 | if (fibheap_compare (heap, x, y) > 0) |
| 379 | { |
| 380 | fibnode_t temp; |
| 381 | temp = x; |
| 382 | x = y; |
| 383 | y = temp; |
| 384 | } |
| 385 | fibheap_link (heap, y, x); |
| 386 | a[d] = NULL; |
| 387 | d++; |
| 388 | } |
| 389 | a[d] = x; |
| 390 | } |
| 391 | heap->min = NULL; |
| 392 | for (i = 0; i < D; i++) |
| 393 | if (a[i] != NULL) |
| 394 | { |
| 395 | fibheap_ins_root (heap, a[i]); |
| 396 | if (heap->min == NULL || fibheap_compare (heap, a[i], heap->min) < 0) |
| 397 | heap->min = a[i]; |
| 398 | } |
| 399 | } |
| 400 | |
| 401 | /* Make NODE a child of PARENT. */ |
| 402 | static void |
| 403 | fibheap_link (fibheap_t heap ATTRIBUTE_UNUSED, |
| 404 | fibnode_t node, fibnode_t parent) |
| 405 | { |
| 406 | if (parent->child == NULL) |
| 407 | parent->child = node; |
| 408 | else |
| 409 | fibnode_insert_before (parent->child, node); |
| 410 | node->parent = parent; |
| 411 | parent->degree++; |
| 412 | node->mark = 0; |
| 413 | } |
| 414 | |
| 415 | /* Remove NODE from PARENT's child list. */ |
| 416 | static void |
| 417 | fibheap_cut (fibheap_t heap, fibnode_t node, fibnode_t parent) |
| 418 | { |
| 419 | fibnode_remove (node); |
| 420 | parent->degree--; |
| 421 | fibheap_ins_root (heap, node); |
| 422 | node->parent = NULL; |
| 423 | node->mark = 0; |
| 424 | } |
| 425 | |
| 426 | static void |
| 427 | fibheap_cascading_cut (fibheap_t heap, fibnode_t y) |
| 428 | { |
| 429 | fibnode_t z; |
| 430 | |
| 431 | while ((z = y->parent) != NULL) |
| 432 | { |
| 433 | if (y->mark == 0) |
| 434 | { |
| 435 | y->mark = 1; |
| 436 | return; |
| 437 | } |
| 438 | else |
| 439 | { |
| 440 | fibheap_cut (heap, y, z); |
| 441 | y = z; |
| 442 | } |
| 443 | } |
| 444 | } |
| 445 | |
| 446 | static void |
| 447 | fibnode_insert_after (fibnode_t a, fibnode_t b) |
| 448 | { |
| 449 | if (a == a->right) |
| 450 | { |
| 451 | a->right = b; |
| 452 | a->left = b; |
| 453 | b->right = a; |
| 454 | b->left = a; |
| 455 | } |
| 456 | else |
| 457 | { |
| 458 | b->right = a->right; |
| 459 | a->right->left = b; |
| 460 | a->right = b; |
| 461 | b->left = a; |
| 462 | } |
| 463 | } |
| 464 | |
| 465 | static fibnode_t |
| 466 | fibnode_remove (fibnode_t node) |
| 467 | { |
| 468 | fibnode_t ret; |
| 469 | |
| 470 | if (node == node->left) |
| 471 | ret = NULL; |
| 472 | else |
| 473 | ret = node->left; |
| 474 | |
| 475 | if (node->parent != NULL && node->parent->child == node) |
| 476 | node->parent->child = ret; |
| 477 | |
| 478 | node->right->left = node->left; |
| 479 | node->left->right = node->right; |
| 480 | |
| 481 | node->parent = NULL; |
| 482 | node->left = node; |
| 483 | node->right = node; |
| 484 | |
| 485 | return ret; |
| 486 | } |