part of its data as a function of its immediate children's
data. Furthermore, augmented data defined in this way can be
efficiently maintained as the tree changes over time.
-
+
For example, suppose we define the "size" of a node as the sum
of the "size" of its immediate children, plus 1. In such an
annotated BST with height H, we can find the node that would
larger tree is rearranged, e.g. via a series of rotations,
then the implementation will not call the reaugmentation
function outside of the subtree, because the overall
- augmentation data for the subtree is assumed not to changed.
+ augmentation data for the subtree is assumed not to change.
This optimization is valid for the forms of augmentation
described in CLR and Knuth (see below), and it is possible
that it is valid for every efficient binary search tree
struct abt_node node; // Embedded binary tree element.
int data; // Primary value.
int count; // Number of nodes in subtree,
- // including this node.
+ // including this node.
};
// Returns the `struct element' that NODE is embedded within.
// strcmp-type return value.
static int
compare_elements (const struct abt_node *a_, const struct abt_node *b_,
- const void *aux)
+ const void *aux)
{
const struct element *a = node_to_element (a_);
const struct element *b = node_to_element (b_);
reaugment_elements (struct abt_node *node_,
const struct abt_node *left,
const struct abt_node *right,
- const void *aux)
+ const void *aux)
{
struct element *node = node_to_element (node_);
node->count = 1;
// Finds and returns the element in ABT that is in the given
// 0-based POSITION in in-order.
static struct element *
- find_by_position (struct abt *abt, int position)
+ find_by_position (struct abt *abt, int position)
{
struct abt_node *p;
- for (p = abt->root; p != NULL; )
+ for (p = abt->root; p != NULL; )
{
int p_pos = p->down[0] ? node_to_element (p->down[0])->count : 0;
if (position == p_pos)
return node_to_element (p);
else if (position < p_pos)
- p = p->down[0];
+ p = p->down[0];
else
{
p = p->down[1];
((STRUCT *) ((char *) (NODE) - offsetof (STRUCT, MEMBER)))
/* Node in an augmented binary tree. */
-struct abt_node
+struct abt_node
{
struct abt_node *up; /* Parent (NULL for root). */
struct abt_node *down[2]; /* Left child, right child. */
const void *aux);
/* An augmented binary tree. */
-struct abt
+struct abt
{
struct abt_node *root; /* Tree's root, NULL if empty. */
abt_compare_func *compare; /* To compare nodes. */
const void *aux);
struct abt_node *abt_insert (struct abt *, struct abt_node *);
+void abt_insert_after (struct abt *,
+ const struct abt_node *, struct abt_node *);
+void abt_insert_before (struct abt *,
+ const struct abt_node *, struct abt_node *);
void abt_delete (struct abt *, struct abt_node *);
struct abt_node *abt_first (const struct abt *);