Based on kernel version 2.6.25. Page generated on 2008-04-18 21:22 EST.
1 Red-black Trees (rbtree) in Linux 2 January 18, 2007 3 Rob Landley <rob[AT]landley[DOT]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));
