1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
|
/* A Fibonacci heap datatype.
Copyright 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
Contributed by Daniel Berlin (dan@cgsoftware.com).
This file is part of GNU CC.
GNU CC is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
GNU CC is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with GNU CC; see the file COPYING. If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#ifdef HAVE_LIMITS_H
#include <limits.h>
#endif
#ifdef HAVE_STDLIB_H
#include <stdlib.h>
#endif
#ifdef HAVE_STRING_H
#include <string.h>
#endif
#include "libiberty.h"
#include "fibheap.h"
#define FIBHEAPKEY_MIN LONG_MIN
static void fibheap_ins_root PARAMS ((fibheap_t, fibnode_t));
static void fibheap_rem_root PARAMS ((fibheap_t, fibnode_t));
static void fibheap_consolidate PARAMS ((fibheap_t));
static void fibheap_link PARAMS ((fibheap_t, fibnode_t, fibnode_t));
static void fibheap_cut PARAMS ((fibheap_t, fibnode_t, fibnode_t));
static void fibheap_cascading_cut PARAMS ((fibheap_t, fibnode_t));
static fibnode_t fibheap_extr_min_node PARAMS ((fibheap_t));
static int fibheap_compare PARAMS ((fibheap_t, fibnode_t, fibnode_t));
static int fibheap_comp_data PARAMS ((fibheap_t, fibheapkey_t, void *,
fibnode_t));
static fibnode_t fibnode_new PARAMS ((void));
static void fibnode_insert_after PARAMS ((fibnode_t, fibnode_t));
#define fibnode_insert_before(a, b) fibnode_insert_after (a->left, b)
static fibnode_t fibnode_remove PARAMS ((fibnode_t));
/* Create a new fibonacci heap. */
fibheap_t
fibheap_new ()
{
return (fibheap_t) xcalloc (1, sizeof (struct fibheap));
}
/* Create a new fibonacci heap node. */
static fibnode_t
fibnode_new ()
{
fibnode_t node;
node = xcalloc (1, sizeof *node);
node->left = node;
node->right = node;
return node;
}
static inline int
fibheap_compare (heap, a, b)
fibheap_t heap ATTRIBUTE_UNUSED;
fibnode_t a;
fibnode_t b;
{
if (a->key < b->key)
return -1;
if (a->key > b->key)
return 1;
return 0;
}
static inline int
fibheap_comp_data (heap, key, data, b)
fibheap_t heap;
fibheapkey_t key;
void *data;
fibnode_t b;
{
struct fibnode a;
a.key = key;
a.data = data;
return fibheap_compare (heap, &a, b);
}
/* Insert DATA, with priority KEY, into HEAP. */
fibnode_t
fibheap_insert (heap, key, data)
fibheap_t heap;
fibheapkey_t key;
void *data;
{
fibnode_t node;
/* Create the new node. */
node = fibnode_new ();
/* Set the node's data. */
node->data = data;
node->key = key;
/* Insert it into the root list. */
fibheap_ins_root (heap, node);
/* If their was no minimum, or this key is less than the min,
it's the new min. */
if (heap->min == NULL || node->key < heap->min->key)
heap->min = node;
heap->nodes++;
return node;
}
/* Return the data of the minimum node (if we know it). */
void *
fibheap_min (heap)
fibheap_t heap;
{
/* If there is no min, we can't easily return it. */
if (heap->min == NULL)
return NULL;
return heap->min->data;
}
/* Return the key of the minimum node (if we know it). */
fibheapkey_t
fibheap_min_key (heap)
fibheap_t heap;
{
/* If there is no min, we can't easily return it. */
if (heap->min == NULL)
return 0;
return heap->min->key;
}
/* Union HEAPA and HEAPB into a new heap. */
fibheap_t
fibheap_union (heapa, heapb)
fibheap_t heapa;
fibheap_t heapb;
{
fibnode_t a_root, b_root, temp;
/* If one of the heaps is empty, the union is just the other heap. */
if ((a_root = heapa->root) == NULL)
{
free (heapa);
return heapb;
}
if ((b_root = heapb->root) == NULL)
{
free (heapb);
return heapa;
}
/* Merge them to the next nodes on the opposite chain. */
a_root->left->right = b_root;
b_root->left->right = a_root;
temp = a_root->left;
a_root->left = b_root->left;
b_root->left = temp;
heapa->nodes += heapb->nodes;
/* And set the new minimum, if it's changed. */
if (fibheap_compare (heapa, heapb->min, heapa->min) < 0)
heapa->min = heapb->min;
free (heapb);
return heapa;
}
/* Extract the data of the minimum node from HEAP. */
void *
fibheap_extract_min (heap)
fibheap_t heap;
{
fibnode_t z;
void *ret = NULL;
/* If we don't have a min set, it means we have no nodes. */
if (heap->min != NULL)
{
/* Otherwise, extract the min node, free the node, and return the
node's data. */
z = fibheap_extr_min_node (heap);
ret = z->data;
free (z);
}
return ret;
}
/* Replace both the KEY and the DATA associated with NODE. */
void *
fibheap_replace_key_data (heap, node, key, data)
fibheap_t heap;
fibnode_t node;
fibheapkey_t key;
void *data;
{
void *odata;
int okey;
fibnode_t y;
/* If we wanted to, we could actually do a real increase by redeleting and
inserting. However, this would require O (log n) time. So just bail out
for now. */
if (fibheap_comp_data (heap, key, data, node) > 0)
return NULL;
odata = node->data;
okey = node->key;
node->data = data;
node->key = key;
y = node->parent;
if (okey == key)
return odata;
/* These two compares are specifically <= 0 to make sure that in the case
of equality, a node we replaced the data on, becomes the new min. This
is needed so that delete's call to extractmin gets the right node. */
if (y != NULL && fibheap_compare (heap, node, y) <= 0)
{
fibheap_cut (heap, node, y);
fibheap_cascading_cut (heap, y);
}
if (fibheap_compare (heap, node, heap->min) <= 0)
heap->min = node;
return odata;
}
/* Replace the DATA associated with NODE. */
void *
fibheap_replace_data (heap, node, data)
fibheap_t heap;
fibnode_t node;
void *data;
{
return fibheap_replace_key_data (heap, node, node->key, data);
}
/* Replace the KEY associated with NODE. */
fibheapkey_t
fibheap_replace_key (heap, node, key)
fibheap_t heap;
fibnode_t node;
fibheapkey_t key;
{
int okey = node->key;
fibheap_replace_key_data (heap, node, key, node->data);
return okey;
}
/* Delete NODE from HEAP. */
void *
fibheap_delete_node (heap, node)
fibheap_t heap;
fibnode_t node;
{
void *ret = node->data;
/* To perform delete, we just make it the min key, and extract. */
fibheap_replace_key (heap, node, FIBHEAPKEY_MIN);
fibheap_extract_min (heap);
return ret;
}
/* Delete HEAP. */
void
fibheap_delete (heap)
fibheap_t heap;
{
while (heap->min != NULL)
free (fibheap_extr_min_node (heap));
free (heap);
}
/* Determine if HEAP is empty. */
int
fibheap_empty (heap)
fibheap_t heap;
{
return heap->nodes == 0;
}
/* Extract the minimum node of the heap. */
static fibnode_t
fibheap_extr_min_node (heap)
fibheap_t heap;
{
fibnode_t ret = heap->min;
fibnode_t x, y, orig;
/* Attach the child list of the minimum node to the root list of the heap.
If there is no child list, we don't do squat. */
for (x = ret->child, orig = NULL; x != orig && x != NULL; x = y)
{
if (orig == NULL)
orig = x;
y = x->right;
x->parent = NULL;
fibheap_ins_root (heap, x);
}
/* Remove the old root. */
fibheap_rem_root (heap, ret);
heap->nodes--;
/* If we are left with no nodes, then the min is NULL. */
if (heap->nodes == 0)
heap->min = NULL;
else
{
/* Otherwise, consolidate to find new minimum, as well as do the reorg
work that needs to be done. */
heap->min = ret->right;
fibheap_consolidate (heap);
}
return ret;
}
/* Insert NODE into the root list of HEAP. */
static void
fibheap_ins_root (heap, node)
fibheap_t heap;
fibnode_t node;
{
/* If the heap is currently empty, the new node becomes the singleton
circular root list. */
if (heap->root == NULL)
{
heap->root = node;
node->left = node;
node->right = node;
return;
}
/* Otherwise, insert it in the circular root list between the root
and it's right node. */
fibnode_insert_after (heap->root, node);
}
/* Remove NODE from the rootlist of HEAP. */
static void
fibheap_rem_root (heap, node)
fibheap_t heap;
fibnode_t node;
{
if (node->left == node)
heap->root = NULL;
else
heap->root = fibnode_remove (node);
}
/* Consolidate the heap. */
static void
fibheap_consolidate (heap)
fibheap_t heap;
{
fibnode_t a[1 + 8 * sizeof (long)];
fibnode_t w;
fibnode_t y;
fibnode_t x;
int i;
int d;
int D;
D = 1 + 8 * sizeof (long);
memset (a, 0, sizeof (fibnode_t) * D);
while ((w = heap->root) != NULL)
{
x = w;
fibheap_rem_root (heap, w);
d = x->degree;
while (a[d] != NULL)
{
y = a[d];
if (fibheap_compare (heap, x, y) > 0)
{
fibnode_t temp;
temp = x;
x = y;
y = temp;
}
fibheap_link (heap, y, x);
a[d] = NULL;
d++;
}
a[d] = x;
}
heap->min = NULL;
for (i = 0; i < D; i++)
if (a[i] != NULL)
{
fibheap_ins_root (heap, a[i]);
if (heap->min == NULL || fibheap_compare (heap, a[i], heap->min) < 0)
heap->min = a[i];
}
}
/* Make NODE a child of PARENT. */
static void
fibheap_link (heap, node, parent)
fibheap_t heap ATTRIBUTE_UNUSED;
fibnode_t node;
fibnode_t parent;
{
if (parent->child == NULL)
parent->child = node;
else
fibnode_insert_before (parent->child, node);
node->parent = parent;
parent->degree++;
node->mark = 0;
}
/* Remove NODE from PARENT's child list. */
static void
fibheap_cut (heap, node, parent)
fibheap_t heap;
fibnode_t node;
fibnode_t parent;
{
fibnode_remove (node);
parent->degree--;
fibheap_ins_root (heap, node);
node->parent = NULL;
node->mark = 0;
}
static void
fibheap_cascading_cut (heap, y)
fibheap_t heap;
fibnode_t y;
{
fibnode_t z;
while ((z = y->parent) != NULL)
{
if (y->mark == 0)
{
y->mark = 1;
return;
}
else
{
fibheap_cut (heap, y, z);
y = z;
}
}
}
static void
fibnode_insert_after (a, b)
fibnode_t a;
fibnode_t b;
{
if (a == a->right)
{
a->right = b;
a->left = b;
b->right = a;
b->left = a;
}
else
{
b->right = a->right;
a->right->left = b;
a->right = b;
b->left = a;
}
}
static fibnode_t
fibnode_remove (node)
fibnode_t node;
{
fibnode_t ret;
if (node == node->left)
ret = NULL;
else
ret = node->left;
if (node->parent != NULL && node->parent->child == node)
node->parent->child = ret;
node->right->left = node->left;
node->left->right = node->right;
node->parent = NULL;
node->left = node;
node->right = node;
return ret;
}
|