void rbtree_remove_fixup(rb_tree * tree, rb_node * node)
{
rb_node *curr_node = node;
rb_node *sibling;
while (curr_node != tree->root && curr_node->color == black) {
/* Get a pointer to the current node's sibling (notice
* that the node's parent must exist, since the node
* is not the root).
*/
if (curr_node == curr_node->parent->left) {
/* If the current node is a left child, its
* sibling is the right child of the parent.
*/
sibling = curr_node->parent->right;
/* Check the sibling's color. Notice that NULL
* nodes are treated as if they are colored
* black.
*/
if (sibling && sibling->color == red) {
/* In case the sibling is red, color
* it black and rotate. Then color
* the parent red (the grandparent is
* now black)
*/
sibling->color = black;
curr_node->parent->color = red;
rbtree_rotate_left(tree, curr_node->parent);
sibling = curr_node->parent->right;
}
if (sibling &&
(!(sibling->left) || sibling->left->color == black)
&& (!(sibling->right)
|| sibling->right->color == black)) {
/* If the sibling has two black
* children, color it red
*/
sibling->color = red;
if (curr_node->parent->color == red) {
/* If the parent is red, we
* can safely color it black
* and terminate the fix
* process.
*/
curr_node->parent->color = black;
/* In order to stop the while loop */
curr_node = tree->root;
} else {
/* The black depth of the
* entire sub-tree rooted at
* the parent is now too small
* - fix it up recursively.
*/
curr_node = curr_node->parent;
}
} else {
if (!sibling) {
/* Take special care of the
* case of a NULL sibling
*/
if (curr_node->parent->color == red) {
curr_node->parent->color =
black;
/* In order to stop
* the while loop */
curr_node = tree->root;
} else {
curr_node = curr_node->parent;
}
} else {
/* In this case, at least one
* of the sibling's children
* is red. It is therfore
* obvious that the sibling
* itself is black.
*/
if (sibling->right
&& sibling->right->color == red) {
/* If the right child
* of the sibling is
* red, color it black
* and rotate around
* the current parent.
*/
sibling->right->color = black;
rbtree_rotate_left(tree,
curr_node->
parent);
} else {
/* If the left child
* of the sibling is
* red, rotate around
* the sibling, then
* rotate around the
* new sibling of our
* current node.
*/
rbtree_rotate_right(tree,
sibling);
sibling =
curr_node->parent->right;
rbtree_rotate_left(tree,
sibling);
}
/* It is now safe to color the
* parent black and to
* terminate the fix process.
*/
if (curr_node->parent->parent)
curr_node->parent->parent->
color =
curr_node->parent->color;
curr_node->parent->color = black;
/* In order to stop the while loop */
curr_node = tree->root;
}
}
} else {
/* If the current node is a right child, its
* sibling is the left child of the parent.
*/
sibling = curr_node->parent->left;
/* Check the sibling's color. Notice that NULL
* nodes are treated as if they are colored
* black.
*/
if (sibling && sibling->color == red) {
/* In case the sibling is red, color
* it black and rotate. Then color
* the parent red (the grandparent is
* now black).
*/
sibling->color = black;
curr_node->parent->color = red;
rbtree_rotate_right(tree, curr_node->parent);
sibling = curr_node->parent->left;
}
if (sibling &&
(!(sibling->left) || sibling->left->color == black)
&& (!(sibling->right)
|| sibling->right->color == black)) {
/* If the sibling has two black children, color it red */
sibling->color = red;
if (curr_node->parent->color == red) {
/* If the parent is red, we
* can safely color it black
* and terminate the fix-up
* process.
*/
curr_node->parent->color = black;
/* In order to stop the while
* loop
*/
curr_node = tree->root;
} else {
/* The black depth of the
* entire sub-tree rooted at
* the parent is now too small
* - fix it up recursively.
*/
curr_node = curr_node->parent;
}
} else {
if (!sibling) {
/* Take special care of the
* case of a NULL sibling */
if (curr_node->parent->color == red) {
curr_node->parent->color =
black;
/* In order to stop
* the while loop */
curr_node = tree->root;
} else {
curr_node = curr_node->parent;
}
} else {
/* In this case, at least one
* of the sibling's children is
* red. It is therfore obvious
* that the sibling itself is
* black.
*/
if (sibling->left
&& sibling->left->color == red) {
/* If the left child
* of the sibling is
* red, color it black
* and rotate around
* the current parent
*/
sibling->left->color = black;
rbtree_rotate_right(tree,
curr_node->
parent);
} else {
/* If the right child
* of the sibling is
* red, rotate around
* the sibling, then
* rotate around the
* new sibling of our
* current node
*/
rbtree_rotate_left(tree,
sibling);
sibling =
curr_node->parent->left;
rbtree_rotate_right(tree,
sibling);
}
/* It is now safe to color the
* parent black and to
* terminate the fix process.
*/
if (curr_node->parent->parent)
curr_node->parent->parent->
color =
curr_node->parent->color;
curr_node->parent->color = black;
/* In order to stop the while loop */
curr_node = tree->root;
}
}
}
}
/* The root can always be colored black */
curr_node->color = black;
}
void rbtree_insert_fixup(rb_tree * tree, rb_node * node)
{
/* Fix the red-black propreties. We may have inserted a red
* leaf as the child of a red parent - so we have to fix the
* coloring of the parent recursively.
*/
rb_node *curr_node = node;
rb_node *grandparent;
rb_node *uncle;
assert(node && node->color == red);
while (curr_node != tree->root && curr_node->parent->color == red) {
/* Get a pointer to the current node's grandparent
* (the root is always black, so the red parent must
* have a parent).
*/
grandparent = curr_node->parent->parent;
if (curr_node->parent == grandparent->left) {
/* If the red parent is a left child, the
* uncle is the right child of the grandparent.
*/
uncle = grandparent->right;
if (uncle && uncle->color == red) {
/* If both parent and uncle are red,
* color them black and color the
* grandparent red. In case of a NULL
* uncle, treat it as a black node
*/
curr_node->parent->color = black;
uncle->color = black;
grandparent->color = red;
/* Move to the grandparent */
curr_node = grandparent;
} else {
/* Make sure the current node is a
* right child. If not, left-rotate the
* parent's sub-tree so the parent
* becomes the right child of the
* current node (see _rotate_left).
*/
if (curr_node == curr_node->parent->right) {
curr_node = curr_node->parent;
rbtree_rotate_left(tree, curr_node);
}
/* Color the parent black and the
* grandparent red
*/
curr_node->parent->color = black;
grandparent->color = red;
/* Right-rotate the grandparent's
* sub-tree
*/
rbtree_rotate_right(tree, grandparent);
}
} else {
/* If the red parent is a right child, the
* uncle is the left child of the grandparent.
*/
uncle = grandparent->left;
if (uncle && uncle->color == red) {
/* If both parent and uncle are red,
* color them black and color the
* grandparent red. In case of a NULL
* uncle, treat it as a black node
*/
curr_node->parent->color = black;
uncle->color = black;
grandparent->color = red;
/* Move to the grandparent */
curr_node = grandparent;
} else {
/* Make sure the current node is a
* left child. If not, right-rotate
* the parent's sub-tree so the parent
* becomes the left child of the
* current node.
*/
if (curr_node == curr_node->parent->left) {
curr_node = curr_node->parent;
rbtree_rotate_right(tree, curr_node);
}
/* Color the parent black and the
* grandparent red
*/
curr_node->parent->color = black;
grandparent->color = red;
/* Left-rotate the grandparent's
* sub-tree
*/
rbtree_rotate_left(tree, grandparent);
}
}
}
/* Make sure that the root is black */
tree->root->color = black;
}
/*!
* Fix-up the red-black tree properties after a removal operation
*
* \param tree The tree
*
* \param node The child of the node that has just been removed from the tree
*/
void rbtree_remove_fixup(rbtree_t * tree, rbnode_t * node)
{
rbnode_t * curr_node = node;
rbnode_t * sibling;
while (curr_node != tree->root && curr_node->color == RB_BLACK)
{
/* Get a pointer to the current node's sibling (notice that the node's
* parent must exist, since the node is not the root).
*/
if (curr_node == curr_node->parent->left)
{
/* If the current node is a left child, its sibling is the right
* child of the parent.
*/
sibling = curr_node->parent->right;
/* Check the sibling's color. Notice that NULL nodes are treated
* as if they are colored black.
*/
if (sibling && sibling->color == RB_RED)
{
/* In case the sibling is red, color it black and rotate.
* Then color the parent red (and the grandparent is now black).
*/
sibling->color = RB_BLACK;
curr_node->parent->color = RB_RED;
rbtree_rotate_left(tree, curr_node->parent);
sibling = curr_node->parent->right;
}
if (sibling &&
(!(sibling->left) || sibling->left->color == RB_BLACK) &&
(!(sibling->right) || sibling->right->color == RB_BLACK))
{
/* If the sibling has two black children, color it red */
sibling->color = RB_RED;
if (curr_node->parent->color == RB_RED)
{
/*
* If the parent is red, we can safely color it black
* and terminate the fix-up process.
*/
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
else
{
/*
* The black depth of the entire sub-tree rooted at the parent is
* now too small - fix it up recursively.
*/
curr_node = curr_node->parent;
}
}
else
{
if (!sibling)
{
/* Take special care of the case of a NULL sibling */
if (curr_node->parent->color == RB_RED)
{
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
else
{
curr_node = curr_node->parent;
}
}
else
{
/* In this case, at least one of the sibling's children is red.
* It is therfore obvious that the sibling itself is black.
*/
if (sibling->right && sibling->right->color == RB_RED)
{
/*
* If the right child of the sibling is red, color it
* black and rotate around the current parent.
*/
sibling->right->color = RB_BLACK;
rbtree_rotate_left(tree, curr_node->parent);
}
else
{
/* If the left child of the sibling is red, rotate
* around the sibling, then rotate around the new
* sibling of our current node.
*/
rbtree_rotate_right(tree, sibling);
sibling = curr_node->parent->right;
rbtree_rotate_left(tree, sibling);
}
/*
* It is now safe to color the parent black and
* to terminate the fix-up process.
*/
if (curr_node->parent->parent)
curr_node->parent->parent->color =
curr_node->parent->color;
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
}
}
else
{
/*
* If the current node is a right child, its sibling is the left
* child of the parent.
*/
sibling = curr_node->parent->left;
/*
* Check the sibling's color. Notice that NULL nodes are treated
* as if they are colored black.
*/
if (sibling && sibling->color == RB_RED)
{
/*
* In case the sibling is red, color it black and rotate.
* Then color the parent red (and the grandparent is now black).
*/
sibling->color = RB_BLACK;
curr_node->parent->color = RB_RED;
rbtree_rotate_right(tree, curr_node->parent);
sibling = curr_node->parent->left;
}
if (sibling &&
(!(sibling->left) || sibling->left->color == RB_BLACK) &&
(!(sibling->right) || sibling->right->color == RB_BLACK))
{
/* If the sibling has two black children, color it red */
sibling->color = RB_RED;
if (curr_node->parent->color == RB_RED)
{
/*
* If the parent is red, we can safely color it black
* and terminate the fix-up process.
*/
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
else
{
/*
* The black depth of the entire sub-tree rooted at
* the parent is now too small - fix it up recursively.
*/
curr_node = curr_node->parent;
}
}
else
{
if (!sibling)
{
/* Take special care of the case of a NULL sibling */
if (curr_node->parent->color == RB_RED)
{
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
else
{
curr_node = curr_node->parent;
}
}
else
{
/* In this case, at least one of the sibling's children is red.
* It is therfore obvious that the sibling itself is black.
*/
if (sibling->left && sibling->left->color == RB_RED)
{
/* If the left child of the sibling is red, color it
* black and rotate around the current parent
*/
sibling->left->color = RB_BLACK;
rbtree_rotate_right(tree, curr_node->parent);
}
else
{
/*
* If the right child of the sibling is red, rotate
* around the sibling, then rotate around the new
* sibling of our current node.
*/
rbtree_rotate_left(tree, sibling);
sibling = curr_node->parent->left;
rbtree_rotate_right(tree, sibling);
}
/*
* It is now safe to color the parent black and to
* terminate the fix-up process.
*/
if (curr_node->parent->parent)
curr_node->parent->parent->color =
curr_node->parent->color;
curr_node->parent->color = RB_BLACK;
/* In order to stop the while loop */
curr_node = tree->root;
}
}
}
}
/* The root can always be colored black */
curr_node->color = RB_BLACK;
}
static void
rbtree_insert_fixup(rbtree_t *rbtree, rbnode_t *node)
{
rbnode_t *uncle;
/* While not at the root and need fixing... */
while (node != rbtree->root && node->parent->color == RED) {
/* If our parent is left child of our grandparent... */
if (node->parent == node->parent->parent->left) {
uncle = node->parent->parent->right;
/* If our uncle is red... */
if (uncle->color == RED) {
/* Paint the parent and the uncle black... */
node->parent->color = BLACK;
uncle->color = BLACK;
/* And the grandparent red... */
node->parent->parent->color = RED;
/* And continue fixing the grandparent */
node = node->parent->parent;
} else { /* Our uncle is black... */
/* Are we the right child? */
if (node == node->parent->right) {
node = node->parent;
rbtree_rotate_left(rbtree, node);
}
/* Now we're the left child, repaint and rotate... */
node->parent->color = BLACK;
node->parent->parent->color = RED;
rbtree_rotate_right(rbtree, node->parent->parent);
}
} else {
uncle = node->parent->parent->left;
/* If our uncle is red... */
if (uncle->color == RED) {
/* Paint the parent and the uncle black... */
node->parent->color = BLACK;
uncle->color = BLACK;
/* And the grandparent red... */
node->parent->parent->color = RED;
/* And continue fixing the grandparent */
node = node->parent->parent;
} else { /* Our uncle is black... */
/* Are we the right child? */
if (node == node->parent->left) {
node = node->parent;
rbtree_rotate_right(rbtree, node);
}
/* Now we're the right child, repaint and rotate... */
node->parent->color = BLACK;
node->parent->parent->color = RED;
rbtree_rotate_left(rbtree, node->parent->parent);
}
}
}
rbtree->root->color = BLACK;
}
/*!
* Fix-up the red-black tree properties after an insertion operation
* so it maintains the red-black properties.
*
* \param tree The tree
*
* \param node The node that has just been inserted to the tree
*
* \pre The color of node must be red
*/
void rbtree_insert_fixup
(
rbtree_t * tree,
rbnode_t * node
)
{
/*
* Fix the red-black propreties: we may have inserted a red
* leaf as the child of a red parent - so we have to fix the
* coloring of the parent recursively.
*/
rbnode_t * curr_node = node;
rbnode_t * grandparent;
rbnode_t *uncle;
ASSERT(node && node->color == RB_RED);
while (curr_node != tree->root &&
curr_node->parent->color == RB_RED)
{
/*
* Get a pointer to the current node's grandparent
* (notice the root is always black, so the red
* parent must have a parent).
*/
grandparent = curr_node->parent->parent;
if (curr_node->parent == grandparent->left)
{
/* If the red parent is a left child, the uncle is the right child of
* the grandparent.
*/
uncle = grandparent->right;
if (uncle && uncle->color == RB_RED)
{
/* If both parent and uncle are red, color them black and color the
* grandparent red.
* In case of a NULL uncle, we treat it as a black node.
*/
curr_node->parent->color = RB_BLACK;
uncle->color = RB_BLACK;
grandparent->color = RB_RED;
/* Move to the grandparent */
curr_node = grandparent;
}
else
{
/* Make sure the current node is a right child. If not, left-rotate
* the parent's sub-tree so the parent becomes the right child of the
* current node (see _rotate_left).
*/
if (curr_node == curr_node->parent->right)
{
curr_node = curr_node->parent;
rbtree_rotate_left(tree, curr_node);
}
/* Color the parent black and the grandparent red */
curr_node->parent->color = RB_BLACK;
grandparent->color = RB_RED;
/* Right-rotate the grandparent's sub-tree */
rbtree_rotate_right(tree, grandparent);
}
}
else
{
/* If the red parent is a right child, the uncle is the left child of
* the grandparent.
*/
uncle = grandparent->left;
if (uncle && uncle->color == RB_RED)
{
/* If both parent and uncle are red, color them black and color the
* grandparent red.
* In case of a NULL uncle, we treat it as a black node.
*/
curr_node->parent->color = RB_BLACK;
uncle->color = RB_BLACK;
grandparent->color = RB_RED;
/* Move to the grandparent */
curr_node = grandparent;
}
else
{
/* Make sure the current node is a left child. If not, right-rotate
* the parent's sub-tree so the parent becomes the left child of the
* current node.
*/
if (curr_node == curr_node->parent->left)
{
curr_node = curr_node->parent;
rbtree_rotate_right(tree, curr_node);
}
/* Color the parent black and the grandparent red */
curr_node->parent->color = RB_BLACK;
grandparent->color = RB_RED;
/* Left-rotate the grandparent's sub-tree */
rbtree_rotate_left(tree, grandparent);
}
}
}
/* Make sure that the root is black */
tree->root->color = RB_BLACK;
}