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
|
/* A Fibonacci heap datatype.
Copyright 1998, 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
Contributed by Daniel Berlin (dan@cgsoftware.com).
This file is part of GCC.
GCC 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.
GCC 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 GCC; see the file COPYING. If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/* Fibonacci heaps are somewhat complex, but, there's an article in
DDJ that explains them pretty well:
http://www.ddj.com/articles/1997/9701/9701o/9701o.htm?topic=algoritms
Introduction to algorithms by Corman and Rivest also goes over them.
The original paper that introduced them is "Fibonacci heaps and their
uses in improved network optimization algorithms" by Tarjan and
Fredman (JACM 34(3), July 1987).
Amortized and real worst case time for operations:
ExtractMin: O(lg n) amortized. O(n) worst case.
DecreaseKey: O(1) amortized. O(lg n) worst case.
Insert: O(2) amortized. O(1) actual.
Union: O(1) amortized. O(1) actual. */
#ifndef _FIBHEAP_H_
#define _FIBHEAP_H_
#include "ansidecl.h"
typedef long fibheapkey_t;
typedef struct fibheap
{
size_t nodes;
struct fibnode *min;
struct fibnode *root;
} *fibheap_t;
typedef struct fibnode
{
struct fibnode *parent;
struct fibnode *child;
struct fibnode *left;
struct fibnode *right;
fibheapkey_t key;
void *data;
#ifdef __GNUC__
__extension__ unsigned long int degree : 31;
__extension__ unsigned long int mark : 1;
#else
unsigned int degree : 31;
unsigned int mark : 1;
#endif
} *fibnode_t;
extern fibheap_t fibheap_new PARAMS ((void));
extern fibnode_t fibheap_insert PARAMS ((fibheap_t, fibheapkey_t, void *));
extern int fibheap_empty PARAMS ((fibheap_t));
extern fibheapkey_t fibheap_min_key PARAMS ((fibheap_t));
extern fibheapkey_t fibheap_replace_key PARAMS ((fibheap_t, fibnode_t,
fibheapkey_t));
extern void *fibheap_replace_key_data PARAMS ((fibheap_t, fibnode_t,
fibheapkey_t, void *));
extern void *fibheap_extract_min PARAMS ((fibheap_t));
extern void *fibheap_min PARAMS ((fibheap_t));
extern void *fibheap_replace_data PARAMS ((fibheap_t, fibnode_t, void *));
extern void *fibheap_delete_node PARAMS ((fibheap_t, fibnode_t));
extern void fibheap_delete PARAMS ((fibheap_t));
extern fibheap_t fibheap_union PARAMS ((fibheap_t, fibheap_t));
#endif /* _FIBHEAP_H_ */
|
