4 * Intrusive, nonrecursive AVL tree data structure (self-balancing binary search
10 * This file is placed into the public domain. You can do whatever you want
19 #include <inttypes.h> /* for uintptr_t */
22 # define AVL_INLINE inline __attribute__((always_inline))
24 # define AVL_INLINE inline
27 /* Node in an AVL tree. Embed this in some other data structure. */
28 struct avl_tree_node {
30 /* Pointer to left child or NULL */
31 struct avl_tree_node *left;
33 /* Pointer to right child or NULL */
34 struct avl_tree_node *right;
36 /* Pointer to parent combined with the balance factor. This saves 4 or
37 * 8 bytes of memory depending on the CPU architecture.
39 * Low 2 bits: One greater than the balance factor of this subtree,
40 * which is equal to height(right) - height(left). The mapping is:
47 * The rest of the bits are the pointer to the parent node. It must be
48 * 4-byte aligned, and it will be NULL if this is the root note and
49 * therefore has no parent. */
50 uintptr_t parent_balance;
53 /* Cast an AVL tree node to the containing data structure. */
54 #define avl_tree_entry(entry, type, member) \
55 ((type*) ((char *)(entry) - offsetof(type, member)))
57 /* Extracts the parent pointer from the specified AVL tree node.
58 * Returns the parent pointer, or NULL if @node is the root node. */
59 static AVL_INLINE struct avl_tree_node *
60 avl_get_parent(const struct avl_tree_node *node)
62 return (struct avl_tree_node *)(node->parent_balance & ~3);
65 /* Mark the node as unlinked from any tree. */
66 static AVL_INLINE void
67 avl_tree_node_set_unlinked(struct avl_tree_node *node)
69 node->parent_balance = (uintptr_t)node;
72 /* Returns true iff the specified node has been marked with
73 * avl_tree_node_set_unlinked() and has not subsequently been inserted into a
75 static AVL_INLINE bool
76 avl_tree_node_is_unlinked(const struct avl_tree_node *node)
78 return node->parent_balance == (uintptr_t)node;
81 /* Internal use only */
83 avl_tree_rebalance_after_insert(struct avl_tree_node **root_ptr,
84 struct avl_tree_node *inserted);
87 * Look up an item in an AVL tree.
90 * Pointer to the root of the AVL tree. (This can be NULL --- that just
91 * means the tree is empty.)
94 * First argument to pass to the comparison callback --- generally a
95 * pointer to an object equal to the one being searched for.
98 * Comparison callback. Must return < 0, 0, or > 0 if the first argument
99 * is less than, equal to, or greater than the second argument,
100 * respectively. The first argument will be @cmp_ctx and the second
101 * argument will be a pointer to the AVL tree node of an item in the tree.
103 * Returns a pointer to the AVL tree node embedded in the resulting item, or
104 * NULL if the item was not found.
106 static AVL_INLINE struct avl_tree_node *
107 avl_tree_lookup(const struct avl_tree_node *root,
109 int (*cmp)(const void *, const struct avl_tree_node *))
111 const struct avl_tree_node *cur = root;
114 int res = (*cmp)(cmp_ctx, cur);
122 return (struct avl_tree_node*)cur;
125 /* Same as avl_tree_lookup(), just uses a more specific type for the comparison
126 * function. Specifically, the item being searched for is expected to be in the
127 * same format as those already in the tree, with an embedded 'struct
129 static AVL_INLINE struct avl_tree_node *
130 avl_tree_lookup_node(const struct avl_tree_node *root,
131 const struct avl_tree_node *node,
132 int (*cmp)(const struct avl_tree_node *,
133 const struct avl_tree_node *))
135 return avl_tree_lookup(root,
137 (int (*) (const void *,
138 const struct avl_tree_node *))cmp);
142 * Insert an item into an AVL tree.
145 * Pointer to the pointer to the root of the AVL tree. (Indirection is
146 * needed because the root node may change.) Initialize *root_ptr to NULL
150 * Pointer to the `struct avl_tree_node' embedded in the item to insert.
151 * No members in it need be pre-initialized, although members in the
152 * containing structure should be pre-initialized so that @cmp can use them
156 * Comparison callback. Must return < 0, 0, or > 0 if the first argument
157 * is less than, equal to, or greater than the second argument,
158 * respectively. The first argument will be @item and the second
159 * argument will be a pointer to an AVL tree node embedded in some
160 * previously-inserted item that @item is being compared with.
162 * Returns NULL if the item was successfully inserted, otherwise the node of a
163 * previously-inserted item which compared equal to @item and prevented the new
164 * insertion of @item.
166 static AVL_INLINE struct avl_tree_node *
167 avl_tree_insert(struct avl_tree_node **root_ptr,
168 struct avl_tree_node *item,
169 int (*cmp)(const struct avl_tree_node *,
170 const struct avl_tree_node *))
172 struct avl_tree_node **cur_ptr = root_ptr, *cur = NULL;
177 res = (*cmp)(item, cur);
179 cur_ptr = &cur->left;
181 cur_ptr = &cur->right;
186 item->parent_balance = (uintptr_t)cur | 1;
187 avl_tree_rebalance_after_insert(root_ptr, item);
192 avl_tree_remove(struct avl_tree_node **root_ptr, struct avl_tree_node *node);
194 /* Nonrecursive AVL tree traversal functions */
196 extern struct avl_tree_node *
197 avl_tree_first_in_order(const struct avl_tree_node *root);
199 extern struct avl_tree_node *
200 avl_tree_next_in_order(const struct avl_tree_node *prev);
202 extern struct avl_tree_node *
203 avl_tree_first_in_postorder(const struct avl_tree_node *root);
205 extern struct avl_tree_node *
206 avl_tree_next_in_postorder(const struct avl_tree_node *prev,
207 const struct avl_tree_node *prev_parent);
209 #endif /* _AVL_TREE_H_ */