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1 Red-black Trees (rbtree) in Linux
2 January 18, 2007
3 Rob Landley <rob@landley.net>
4 =============================
5
6 What are red-black trees, and what are they for?
7 ------------------------------------------------
8
9 Red-black trees are a type of self-balancing binary search tree, used for
10 storing sortable key/value data pairs. This differs from radix trees (which
11 are used to efficiently store sparse arrays and thus use long integer indexes
12 to insert/access/delete nodes) and hash tables (which are not kept sorted to
13 be easily traversed in order, and must be tuned for a specific size and
14 hash function where rbtrees scale gracefully storing arbitrary keys).
15
16 Red-black trees are similar to AVL trees, but provide faster real-time bounded
17 worst case performance for insertion and deletion (at most two rotations and
18 three rotations, respectively, to balance the tree), with slightly slower
19 (but still O(log n)) lookup time.
20
21 To quote Linux Weekly News:
22
23 There are a number of red-black trees in use in the kernel.
24 The anticipatory, deadline, and CFQ I/O schedulers all employ
25 rbtrees to track requests; the packet CD/DVD driver does the same.
26 The high-resolution timer code uses an rbtree to organize outstanding
27 timer requests. The ext3 filesystem tracks directory entries in a
28 red-black tree. Virtual memory areas (VMAs) are tracked with red-black
29 trees, as are epoll file descriptors, cryptographic keys, and network
30 packets in the "hierarchical token bucket" scheduler.
31
32 This document covers use of the Linux rbtree implementation. For more
33 information on the nature and implementation of Red Black Trees, see:
34
35 Linux Weekly News article on red-black trees
36 http://lwn.net/Articles/184495/
37
38 Wikipedia entry on red-black trees
39 http://en.wikipedia.org/wiki/Red-black_tree
40
41 Linux implementation of red-black trees
42 ---------------------------------------
43
44 Linux's rbtree implementation lives in the file "lib/rbtree.c". To use it,
45 "#include <linux/rbtree.h>".
46
47 The Linux rbtree implementation is optimized for speed, and thus has one
48 less layer of indirection (and better cache locality) than more traditional
49 tree implementations. Instead of using pointers to separate rb_node and data
50 structures, each instance of struct rb_node is embedded in the data structure
51 it organizes. And instead of using a comparison callback function pointer,
52 users are expected to write their own tree search and insert functions
53 which call the provided rbtree functions. Locking is also left up to the
54 user of the rbtree code.
55
56 Creating a new rbtree
57 ---------------------
58
59 Data nodes in an rbtree tree are structures containing a struct rb_node member:
60
61 struct mytype {
62 struct rb_node node;
63 char *keystring;
64 };
65
66 When dealing with a pointer to the embedded struct rb_node, the containing data
67 structure may be accessed with the standard container_of() macro. In addition,
68 individual members may be accessed directly via rb_entry(node, type, member).
69
70 At the root of each rbtree is an rb_root structure, which is initialized to be
71 empty via:
72
73 struct rb_root mytree = RB_ROOT;
74
75 Searching for a value in an rbtree
76 ----------------------------------
77
78 Writing a search function for your tree is fairly straightforward: start at the
79 root, compare each value, and follow the left or right branch as necessary.
80
81 Example:
82
83 struct mytype *my_search(struct rb_root *root, char *string)
84 {
85 struct rb_node *node = root->rb_node;
86
87 while (node) {
88 struct mytype *data = container_of(node, struct mytype, node);
89 int result;
90
91 result = strcmp(string, data->keystring);
92
93 if (result < 0)
94 node = node->rb_left;
95 else if (result > 0)
96 node = node->rb_right;
97 else
98 return data;
99 }
100 return NULL;
101 }
102
103 Inserting data into an rbtree
104 -----------------------------
105
106 Inserting data in the tree involves first searching for the place to insert the
107 new node, then inserting the node and rebalancing ("recoloring") the tree.
108
109 The search for insertion differs from the previous search by finding the
110 location of the pointer on which to graft the new node. The new node also
111 needs a link to its parent node for rebalancing purposes.
112
113 Example:
114
115 int my_insert(struct rb_root *root, struct mytype *data)
116 {
117 struct rb_node **new = &(root->rb_node), *parent = NULL;
118
119 /* Figure out where to put new node */
120 while (*new) {
121 struct mytype *this = container_of(*new, struct mytype, node);
122 int result = strcmp(data->keystring, this->keystring);
123
124 parent = *new;
125 if (result < 0)
126 new = &((*new)->rb_left);
127 else if (result > 0)
128 new = &((*new)->rb_right);
129 else
130 return FALSE;
131 }
132
133 /* Add new node and rebalance tree. */
134 rb_link_node(data->node, parent, new);
135 rb_insert_color(data->node, root);
136
137 return TRUE;
138 }
139
140 Removing or replacing existing data in an rbtree
141 ------------------------------------------------
142
143 To remove an existing node from a tree, call:
144
145 void rb_erase(struct rb_node *victim, struct rb_root *tree);
146
147 Example:
148
149 struct mytype *data = mysearch(mytree, "walrus");
150
151 if (data) {
152 rb_erase(data->node, mytree);
153 myfree(data);
154 }
155
156 To replace an existing node in a tree with a new one with the same key, call:
157
158 void rb_replace_node(struct rb_node *old, struct rb_node *new,
159 struct rb_root *tree);
160
161 Replacing a node this way does not re-sort the tree: If the new node doesn't
162 have the same key as the old node, the rbtree will probably become corrupted.
163
164 Iterating through the elements stored in an rbtree (in sort order)
165 ------------------------------------------------------------------
166
167 Four functions are provided for iterating through an rbtree's contents in
168 sorted order. These work on arbitrary trees, and should not need to be
169 modified or wrapped (except for locking purposes):
170
171 struct rb_node *rb_first(struct rb_root *tree);
172 struct rb_node *rb_last(struct rb_root *tree);
173 struct rb_node *rb_next(struct rb_node *node);
174 struct rb_node *rb_prev(struct rb_node *node);
175
176 To start iterating, call rb_first() or rb_last() with a pointer to the root
177 of the tree, which will return a pointer to the node structure contained in
178 the first or last element in the tree. To continue, fetch the next or previous
179 node by calling rb_next() or rb_prev() on the current node. This will return
180 NULL when there are no more nodes left.
181
182 The iterator functions return a pointer to the embedded struct rb_node, from
183 which the containing data structure may be accessed with the container_of()
184 macro, and individual members may be accessed directly via
185 rb_entry(node, type, member).
186
187 Example:
188
189 struct rb_node *node;
190 for (node = rb_first(&mytree); node; node = rb_next(node))
191 printk("key=%s\n", rb_entry(node, int, keystring));
192