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
25 # warning "AVL tree functions may not be inlined as intended"
28 /* Node in an AVL tree. Embed this in some other data structure. */
29 struct avl_tree_node {
31 /* Pointer to left child or NULL */
32 struct avl_tree_node *left;
34 /* Pointer to right child or NULL */
35 struct avl_tree_node *right;
37 /* Pointer to parent combined with the balance factor. This saves 4 or
38 * 8 bytes of memory depending on the CPU architecture.
40 * Low 2 bits: One greater than the balance factor of this subtree,
41 * which is equal to height(right) - height(left). The mapping is:
48 * The rest of the bits are the pointer to the parent node. It must be
49 * 4-byte aligned, and it will be NULL if this is the root node and
50 * therefore has no parent. */
51 uintptr_t parent_balance;
54 /* Cast an AVL tree node to the containing data structure. */
55 #define avl_tree_entry(entry, type, member) \
56 ((type*) ((char *)(entry) - offsetof(type, member)))
58 /* Returns a pointer to the parent of the specified AVL tree node, or NULL if it
59 * is already the root of the tree. */
60 static AVL_INLINE struct avl_tree_node *
61 avl_get_parent(const struct avl_tree_node *node)
63 return (struct avl_tree_node *)(node->parent_balance & ~3);
66 /* Marks the specified AVL tree node as unlinked from any tree. */
67 static AVL_INLINE void
68 avl_tree_node_set_unlinked(struct avl_tree_node *node)
70 node->parent_balance = (uintptr_t)node;
73 /* Returns true iff the specified AVL tree node has been marked with
74 * avl_tree_node_set_unlinked() and has not subsequently been inserted into a
76 static AVL_INLINE bool
77 avl_tree_node_is_unlinked(const struct avl_tree_node *node)
79 return node->parent_balance == (uintptr_t)node;
82 /* (Internal use only) */
84 avl_tree_rebalance_after_insert(struct avl_tree_node **root_ptr,
85 struct avl_tree_node *inserted);
88 * Looks up an item in the specified AVL tree.
91 * Pointer to the root of the AVL tree. (This can be NULL --- that just
92 * means the tree is empty.)
95 * First argument to pass to the comparison callback. This generally
96 * should be a pointer to an object equal to the one being searched for.
99 * Comparison callback. Must return < 0, 0, or > 0 if the first argument
100 * is less than, equal to, or greater than the second argument,
101 * respectively. The first argument will be @cmp_ctx and the second
102 * argument will be a pointer to the AVL tree node of an item in the tree.
104 * Returns a pointer to the AVL tree node of the resulting item, or NULL if the
105 * item was not found.
109 * struct int_wrapper {
111 * struct avl_tree_node index_node;
114 * static int _avl_cmp_int_to_node(const void *intptr,
115 * const struct avl_tree_node *nodeptr)
117 * int n1 = *(const int *)intptr;
118 * int n2 = avl_tree_entry(nodeptr, struct int_wrapper, index_node)->data;
127 * bool contains_int(struct avl_tree_node *root, int n)
129 * struct avl_tree_node *result;
131 * result = avl_tree_lookup(root, &n, _avl_cmp_int_to_node);
132 * return result ? true : false;
135 static AVL_INLINE struct avl_tree_node *
136 avl_tree_lookup(const struct avl_tree_node *root,
138 int (*cmp)(const void *, const struct avl_tree_node *))
140 const struct avl_tree_node *cur = root;
143 int res = (*cmp)(cmp_ctx, cur);
151 return (struct avl_tree_node*)cur;
154 /* Same as avl_tree_lookup(), but uses a more specific type for the comparison
155 * function. Specifically, with this function the item being searched for is
156 * expected to be in the same format as those already in the tree, with an
157 * embedded 'struct avl_tree_node'. */
158 static AVL_INLINE struct avl_tree_node *
159 avl_tree_lookup_node(const struct avl_tree_node *root,
160 const struct avl_tree_node *node,
161 int (*cmp)(const struct avl_tree_node *,
162 const struct avl_tree_node *))
164 return avl_tree_lookup(root,
166 (int (*) (const void *,
167 const struct avl_tree_node *))cmp);
171 * Inserts an item into the specified AVL tree.
174 * Location of the AVL tree's root pointer. Indirection is needed because
175 * the root node may change as a result of rotations caused by the
176 * insertion. Initialize *root_ptr to NULL for an empty tree.
179 * Pointer to the `struct avl_tree_node' embedded in the item to insert.
180 * No members in it need be pre-initialized, although members in the
181 * containing structure should be pre-initialized so that @cmp can use them
185 * Comparison callback. Must return < 0, 0, or > 0 if the first argument
186 * is less than, equal to, or greater than the second argument,
187 * respectively. The first argument will be @item and the second
188 * argument will be a pointer to an AVL tree node embedded in some
189 * previously-inserted item to which @item is being compared.
191 * If no item in the tree is comparatively equal (via @cmp) to @item, inserts
192 * @item and returns NULL. Otherwise does nothing and returns a pointer to the
193 * AVL tree node embedded in the previously-inserted item which compared equal
198 * struct int_wrapper {
200 * struct avl_tree_node index_node;
203 * #define GET_DATA(i) avl_tree_entry((i), struct int_wrapper, index_node)->data
205 * static int _avl_cmp_ints(const struct avl_tree_node *node1,
206 * const struct avl_tree_node *node2)
208 * int n1 = GET_DATA(node1);
209 * int n2 = GET_DATA(node2);
218 * bool insert_int(struct avl_tree_node **root_ptr, int data)
220 * struct int_wrapper *i = malloc(sizeof(struct int_wrapper));
222 * if (avl_tree_insert(root_ptr, &i->index_node, _avl_cmp_ints)) {
230 static AVL_INLINE struct avl_tree_node *
231 avl_tree_insert(struct avl_tree_node **root_ptr,
232 struct avl_tree_node *item,
233 int (*cmp)(const struct avl_tree_node *,
234 const struct avl_tree_node *))
236 struct avl_tree_node **cur_ptr = root_ptr, *cur = NULL;
241 res = (*cmp)(item, cur);
243 cur_ptr = &cur->left;
245 cur_ptr = &cur->right;
250 item->parent_balance = (uintptr_t)cur | 1;
251 avl_tree_rebalance_after_insert(root_ptr, item);
255 /* Removes an item from the specified AVL tree.
256 * See implementation for details. */
258 avl_tree_remove(struct avl_tree_node **root_ptr, struct avl_tree_node *node);
260 /* Nonrecursive AVL tree traversal functions */
262 extern struct avl_tree_node *
263 avl_tree_first_in_order(const struct avl_tree_node *root);
265 extern struct avl_tree_node *
266 avl_tree_next_in_order(const struct avl_tree_node *prev);
268 extern struct avl_tree_node *
269 avl_tree_first_in_postorder(const struct avl_tree_node *root);
271 extern struct avl_tree_node *
272 avl_tree_next_in_postorder(const struct avl_tree_node *prev,
273 const struct avl_tree_node *prev_parent);
276 * Iterate through the nodes in an AVL tree in sorted order.
277 * You may not modify the tree during the iteration.
280 * Variable that will receive a pointer to each struct inserted into the
283 * Root of the AVL tree.
285 * Type of *child_struct.
287 * Member of @struct_name type that is the AVL tree node.
291 * struct int_wrapper {
293 * struct avl_tree_node index_node;
296 * void print_ints(struct avl_tree_node *root)
298 * struct int_wrapper *i;
300 * avl_tree_for_each_in_order(i, root, struct int_wrapper, index_node)
301 * printf("%d\n", i->data);
304 #define avl_tree_for_each_in_order(child_struct, root, \
305 struct_name, struct_member) \
306 for (struct avl_tree_node *_cur = \
307 avl_tree_first_in_order(root); \
308 _cur && ((child_struct) = \
309 avl_tree_entry(_cur, struct_name, \
310 struct_member), 1); \
311 _cur = avl_tree_next_in_order(_cur))
314 * Like avl_tree_for_each_in_order(), but iterates through the nodes in
315 * postorder, so the current node may be deleted or freed.
317 #define avl_tree_for_each_in_postorder(child_struct, root, \
318 struct_name, struct_member) \
319 for (struct avl_tree_node *_cur = \
320 avl_tree_first_in_postorder(root), *_parent; \
321 _cur && ((child_struct) = \
322 avl_tree_entry(_cur, struct_name, \
324 && (_parent = avl_get_parent(_cur), 1); \
325 _cur = avl_tree_next_in_postorder(_cur, _parent))
327 #endif /* _AVL_TREE_H_ */