Documentation/rbtree.txt

   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