/*
* Operations INSERT and DELETE, when run on a tree with n keys,
* take O(logN) time.Because they modify the tree, the result
* may violate the red-black properties.To restore these properties,
* we must change the colors of some of the nodes in the tree
* and also change the pointer structure.
*/
static void interval_insert_color(struct interval_node *node,
struct interval_node **root)
{
struct interval_node *parent, *gparent;
while ((parent = node->in_parent) && node_is_red(parent)) {
gparent = parent->in_parent;
/* Parent is RED, so gparent must not be NULL */
if (node_is_left_child(parent)) {
struct interval_node *uncle;
uncle = gparent->in_right;
if (uncle && node_is_red(uncle)) {
uncle->in_color = INTERVAL_BLACK;
parent->in_color = INTERVAL_BLACK;
gparent->in_color = INTERVAL_RED;
node = gparent;
continue;
}
if (parent->in_right == node) {
__rotate_left(parent, root);
interval_swap(node, parent);
}
parent->in_color = INTERVAL_BLACK;
gparent->in_color = INTERVAL_RED;
__rotate_right(gparent, root);
} else {
struct interval_node *uncle;
uncle = gparent->in_left;
if (uncle && node_is_red(uncle)) {
uncle->in_color = INTERVAL_BLACK;
parent->in_color = INTERVAL_BLACK;
gparent->in_color = INTERVAL_RED;
node = gparent;
continue;
}
if (node_is_left_child(node)) {
__rotate_right(parent, root);
interval_swap(node, parent);
}
parent->in_color = INTERVAL_BLACK;
gparent->in_color = INTERVAL_RED;
__rotate_left(gparent, root);
}
}
(*root)->in_color = INTERVAL_BLACK;
}
/* The left rotation "pivots" around the link from node to node->right, and
* - node will be linked to node->right's left child, and
* - node->right's left child will be linked to node's right child.
*/
static void __rotate_left(struct interval_node *node,
struct interval_node **root)
{
struct interval_node *right = node->in_right;
struct interval_node *parent = node->in_parent;
node->in_right = right->in_left;
if (node->in_right)
right->in_left->in_parent = node;
right->in_left = node;
right->in_parent = parent;
if (parent) {
if (node_is_left_child(node))
parent->in_left = right;
else
parent->in_right = right;
} else {
*root = right;
}
node->in_parent = right;
/* update max_high for node and right */
__rotate_change_maxhigh(node, right);
}
static struct interval_node *interval_prev(struct interval_node *node)
{
if (!node)
return NULL;
if (node->in_left)
return interval_last(node->in_left);
while (node->in_parent && node_is_left_child(node))
node = node->in_parent;
return node->in_parent;
}
static struct interval_node *interval_prev(struct interval_node *node)
{
ENTRY;
if (!node)
RETURN(NULL);
if (node->in_left)
RETURN(interval_last(node->in_left));
while (node->in_parent && node_is_left_child(node))
node = node->in_parent;
RETURN(node->in_parent);
}
void interval_erase(struct interval_node *node,
struct interval_node **root)
{
struct interval_node *child, *parent;
int color;
LASSERT(interval_is_intree(node));
node->in_intree = 0;
if (!node->in_left) {
child = node->in_right;
} else if (!node->in_right) {
child = node->in_left;
} else { /* Both left and right child are not NULL */
struct interval_node *old = node;
node = interval_next(node);
child = node->in_right;
parent = node->in_parent;
color = node->in_color;
if (child)
child->in_parent = parent;
if (parent == old)
parent->in_right = child;
else
parent->in_left = child;
node->in_color = old->in_color;
node->in_right = old->in_right;
node->in_left = old->in_left;
node->in_parent = old->in_parent;
if (old->in_parent) {
if (node_is_left_child(old))
old->in_parent->in_left = node;
else
old->in_parent->in_right = node;
} else {
*root = node;
}
old->in_left->in_parent = node;
if (old->in_right)
old->in_right->in_parent = node;
update_maxhigh(child ? : parent, node->in_max_high);
update_maxhigh(node, old->in_max_high);
if (parent == old)
parent = node;
goto color;
}
parent = node->in_parent;
color = node->in_color;
if (child)
child->in_parent = parent;
if (parent) {
if (node_is_left_child(node))
parent->in_left = child;
else
parent->in_right = child;
} else {
*root = child;
}
update_maxhigh(child ? : parent, node->in_max_high);
color:
if (color == INTERVAL_BLACK)
interval_erase_color(child, parent, root);
}
