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 contained in the item
102 * inserted into the AVL tree.
104 * Returns a pointer to the AVL tree node embedded in the resulting item, or
105 * NULL if the item was not found.
107 static AVL_INLINE struct avl_tree_node *
108 avl_tree_lookup(const struct avl_tree_node *root,
110 int (*cmp)(const void *, const struct avl_tree_node *))
112 const struct avl_tree_node *cur = root;
115 int res = (*cmp)(cmp_ctx, cur);
123 return (struct avl_tree_node*)cur;
126 /* Same as avl_tree_lookup(), just uses a more specific type for the comparison
127 * function. Specifically, the item being searched for is expected to be in the
128 * same format as those already in the tree, with an embedded 'struct
130 static AVL_INLINE struct avl_tree_node *
131 avl_tree_lookup_node(const struct avl_tree_node *root,
132 const struct avl_tree_node *node,
133 int (*cmp)(const struct avl_tree_node *,
134 const struct avl_tree_node *))
136 return avl_tree_lookup(root,
138 (int (*) (const void *,
139 const struct avl_tree_node *))cmp);
143 * Insert an item into an AVL tree.
146 * Pointer to the pointer to the root of the AVL tree. (Indirection is
147 * needed because the root node may change.) Initialize *root_ptr to NULL
151 * Pointer to the `struct avl_tree_node' embedded in the item to insert.
152 * No members in it need be pre-initialized, although members in the
153 * containing structure should be pre-initialized so that @cmp can use them
157 * Comparison callback. Must return < 0, 0, or > 0 if the first argument
158 * is less than, equal to, or greater than the second argument,
159 * respectively. The first argument will be @item and the second
160 * argument will be a pointer to an AVL tree node embedded in some
161 * previously-inserted item that @item is being compared with.
163 * Returns NULL if the item was successfully inserted, otherwise the node of a
164 * previously-inserted item which compared equal to @item and prevented the new
165 * insertion of @item.
167 static AVL_INLINE struct avl_tree_node *
168 avl_tree_insert(struct avl_tree_node **root_ptr,
169 struct avl_tree_node *item,
170 int (*cmp)(const struct avl_tree_node *,
171 const struct avl_tree_node *))
173 struct avl_tree_node **cur_ptr = root_ptr, *cur = NULL;
178 res = (*cmp)(item, cur);
180 cur_ptr = &cur->left;
182 cur_ptr = &cur->right;
187 item->parent_balance = (uintptr_t)cur | 1;
188 avl_tree_rebalance_after_insert(root_ptr, item);
193 avl_tree_remove(struct avl_tree_node **root_ptr, struct avl_tree_node *node);
195 /* Nonrecursive AVL tree traversal functions */
197 extern struct avl_tree_node *
198 avl_tree_first_in_order(const struct avl_tree_node *root);
200 extern struct avl_tree_node *
201 avl_tree_next_in_order(const struct avl_tree_node *prev);
203 extern struct avl_tree_node *
204 avl_tree_first_in_postorder(const struct avl_tree_node *root);
206 extern struct avl_tree_node *
207 avl_tree_next_in_postorder(const struct avl_tree_node *prev,
208 const struct avl_tree_node *prev_parent);
210 #endif /* _AVL_TREE_H_ */