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
|
/*
* Copyright (c) 2010-2017 Richard Braun.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*
* Upstream site with license notes :
* http://git.sceen.net/rbraun/librbraun.git/
*/
#ifndef AVLTREE_I_H
#define AVLTREE_I_H
#include <assert.h>
#include <stddef.h>
#include <stdint.h>
#include "macros.h"
/*
* AVL node structure.
*
* To reduce the number of branches and the instruction cache footprint,
* the left and right child pointers are stored in an array, and the symmetry
* of most tree operations is exploited by using left/right variables when
* referring to children.
*
* In addition, this implementation assumes that all nodes are at least 4-byte
* aligned, so that the two least significant bits of the parent member can
* be used to store the balance of the node. This is true for all modern 32
* and 64 bits architectures, as long as the nodes aren't embedded in
* structures with special alignment constraints such as member packing.
*
* To avoid issues with signed operations when handling a negative balance,
* the raw values stored in the parent member are always positive, and are
* actually one more than the value they represent. It is then easy to obtain
* a balance of -1 from a raw value of 0.
*/
struct avltree_node {
uintptr_t parent;
struct avltree_node *children[2];
};
/*
* AVL tree structure.
*/
struct avltree {
struct avltree_node *root;
};
/*
* Masks applied on the parent member of a node to obtain either the
* balance or the parent address.
*/
#define AVLTREE_BALANCE_MASK ((uintptr_t)0x3)
#define AVLTREE_PARENT_MASK (~AVLTREE_BALANCE_MASK)
/*
* Special raw balance values.
*/
#define AVLTREE_BALANCE_ZERO ((uintptr_t)1)
#define AVLTREE_BALANCE_INVALID AVLTREE_BALANCE_MASK
/*
* Masks applied on slots to obtain either the child index or the parent
* address.
*/
#define AVLTREE_SLOT_INDEX_MASK ((uintptr_t)0x1)
#define AVLTREE_SLOT_PARENT_MASK (~AVLTREE_SLOT_INDEX_MASK)
/*
* Return true if the given index is a valid child index.
*/
static inline int
avltree_check_index(int index)
{
return index == (index & 1);
}
/*
* Convert the result of a comparison (or a balance) into an index in the
* children array (0 or 1).
*
* This function is mostly used when looking up a node.
*/
static inline int
avltree_d2i(int diff)
{
return !(diff <= 0);
}
/*
* Return true if the given pointer is suitably aligned.
*/
static inline int
avltree_node_check_alignment(const struct avltree_node *node)
{
return ((uintptr_t)node & AVLTREE_BALANCE_MASK) == 0;
}
/*
* Return the parent of a node.
*/
static inline struct avltree_node *
avltree_node_parent(const struct avltree_node *node)
{
return (struct avltree_node *)(node->parent & AVLTREE_PARENT_MASK);
}
/*
* Translate an insertion point into a slot.
*/
static inline avltree_slot_t
avltree_slot(struct avltree_node *parent, int index)
{
assert(avltree_node_check_alignment(parent));
assert(avltree_check_index(index));
return (avltree_slot_t)parent | index;
}
/*
* Extract the parent address from a slot.
*/
static inline struct avltree_node *
avltree_slot_parent(avltree_slot_t slot)
{
return (struct avltree_node *)(slot & AVLTREE_SLOT_PARENT_MASK);
}
/*
* Extract the index from a slot.
*/
static inline int
avltree_slot_index(avltree_slot_t slot)
{
return slot & AVLTREE_SLOT_INDEX_MASK;
}
/*
* Insert a node in a tree, rebalancing it if necessary.
*
* The index parameter is the index in the children array of the parent where
* the new node is to be inserted. It is ignored if the parent is NULL.
*
* This function is intended to be used by the avltree_insert() macro only.
*/
void avltree_insert_rebalance(struct avltree *tree, struct avltree_node *parent,
int index, struct avltree_node *node);
/*
* Return the previous or next node relative to a location in a tree.
*
* The parent and index parameters define the location, which can be empty.
* The direction parameter is either AVLTREE_LEFT (to obtain the previous
* node) or AVLTREE_RIGHT (to obtain the next one).
*/
struct avltree_node * avltree_nearest(struct avltree_node *parent, int index,
int direction);
/*
* Return the first or last node of a tree.
*
* The direction parameter is either AVLTREE_LEFT (to obtain the first node)
* or AVLTREE_RIGHT (to obtain the last one).
*/
struct avltree_node * avltree_firstlast(const struct avltree *tree,
int direction);
/*
* Return the node next to, or previous to the given node.
*
* The direction parameter is either AVLTREE_LEFT (to obtain the previous node)
* or AVLTREE_RIGHT (to obtain the next one).
*/
struct avltree_node * avltree_walk(struct avltree_node *node, int direction);
/*
* Return the left-most deepest node of a tree, which is the starting point of
* the postorder traversal performed by avltree_for_each_remove().
*/
struct avltree_node * avltree_postwalk_deepest(const struct avltree *tree);
/*
* Unlink a node from its tree and return the next (right) node in postorder.
*/
struct avltree_node * avltree_postwalk_unlink(struct avltree_node *node);
#endif /* AVLTREE_I_H */
|
