/*
* Repair the tree after a node has been deleted by rotating and repainting
* colors to restore the 4 properties inherent in red-black trees.
*/
static void
rbrepair(struct rbtree *tree, struct rbnode *node)
{
struct rbnode *sibling;
while (node->color == black && node != rbroot(tree)) {
if (node == node->parent->left) {
sibling = node->parent->right;
if (sibling->color == red) {
sibling->color = black;
node->parent->color = red;
rotate_left(tree, node->parent);
sibling = node->parent->right;
}
if (sibling->right->color == black && sibling->left->color == black) {
sibling->color = red;
node = node->parent;
} else {
if (sibling->right->color == black) {
sibling->left->color = black;
sibling->color = red;
rotate_right(tree, sibling);
sibling = node->parent->right;
}
sibling->color = node->parent->color;
node->parent->color = black;
sibling->right->color = black;
rotate_left(tree, node->parent);
node = rbroot(tree); /* exit loop */
}
} else { /* if (node == node->parent->right) */
sibling = node->parent->left;
if (sibling->color == red) {
sibling->color = black;
node->parent->color = red;
rotate_right(tree, node->parent);
sibling = node->parent->left;
}
if (sibling->right->color == black && sibling->left->color == black) {
sibling->color = red;
node = node->parent;
} else {
if (sibling->left->color == black) {
sibling->right->color = black;
sibling->color = red;
rotate_left(tree, sibling);
sibling = node->parent->left;
}
sibling->color = node->parent->color;
node->parent->color = black;
sibling->left->color = black;
rotate_right(tree, node->parent);
node = rbroot(tree); /* exit loop */
}
}
}
node->color = black;
}
/*
* Returns the successor of node, or nil if there is none.
*/
static struct rbnode *
rbsuccessor(struct rbtree *tree, struct rbnode *node)
{
struct rbnode *succ;
if ((succ = node->right) != rbnil(tree)) {
while (succ->left != rbnil(tree))
succ = succ->left;
} else {
/* No right child, move up until we find it or hit the root */
for (succ = node->parent; node == succ->right; succ = succ->parent)
node = succ;
if (succ == rbroot(tree))
succ = rbnil(tree);
}
return succ;
}
/*
* Returns the successor of node, or nil if there is none.
*/
static struct rbnode *
rbsuccessor(struct rbtree *tree, struct rbnode *node)
{
struct rbnode *succ;
debug_decl(rbsuccessor, SUDO_DEBUG_RBTREE)
if ((succ = node->right) != rbnil(tree)) {
while (succ->left != rbnil(tree))
succ = succ->left;
} else {
/* No right child, move up until we find it or hit the root */
for (succ = node->parent; node == succ->right; succ = succ->parent)
node = succ;
if (succ == rbroot(tree))
succ = rbnil(tree);
}
debug_return_ptr(succ);
}
/*
* Delete node 'z' from the tree and return its data pointer.
*/
void *rbdelete(struct rbtree *tree, struct rbnode *z)
{
struct rbnode *x, *y;
void *data = z->data;
if (z->left == rbnil(tree) || z->right == rbnil(tree))
y = z;
else
y = rbsuccessor(tree, z);
x = (y->left == rbnil(tree)) ? y->right : y->left;
if ((x->parent = y->parent) == rbroot(tree)) {
rbfirst(tree) = x;
} else {
if (y == y->parent->left)
y->parent->left = x;
else
y->parent->right = x;
}
if (y->color == black)
rbrepair(tree, x);
if (y != z) {
y->left = z->left;
y->right = z->right;
y->parent = z->parent;
y->color = z->color;
z->left->parent = z->right->parent = y;
if (z == z->parent->left)
z->parent->left = y;
else
z->parent->right = y;
}
free(z);
return data;
}
/*
* Insert data pointer into a redblack tree.
* Returns a NULL pointer on success. If a node matching "data"
* already exists, a pointer to the existant node is returned.
*/
struct rbnode *
rbinsert(struct rbtree *tree, void *data)
{
struct rbnode *node = rbfirst(tree);
struct rbnode *parent = rbroot(tree);
int res;
/* Find correct insertion point. */
while (node != rbnil(tree)) {
parent = node;
if ((res = tree->compar(data, node->data)) == 0)
return node;
node = res < 0 ? node->left : node->right;
}
node = (struct rbnode *) emalloc(sizeof(*node));
node->data = data;
node->left = node->right = rbnil(tree);
node->parent = parent;
if (parent == rbroot(tree) || tree->compar(data, parent->data) < 0)
parent->left = node;
else
parent->right = node;
node->color = red;
/*
* If the parent node is black we are all set, if it is red we have
* the following possible cases to deal with. We iterate through
* the rest of the tree to make sure none of the required properties
* is violated.
*
* 1) The uncle is red. We repaint both the parent and uncle black
* and repaint the grandparent node red.
*
* 2) The uncle is black and the new node is the right child of its
* parent, and the parent in turn is the left child of its parent.
* We do a left rotation to switch the roles of the parent and
* child, relying on further iterations to fixup the old parent.
*
* 3) The uncle is black and the new node is the left child of its
* parent, and the parent in turn is the left child of its parent.
* We switch the colors of the parent and grandparent and perform
* a right rotation around the grandparent. This makes the former
* parent the parent of the new node and the former grandparent.
*
* Note that because we use a sentinel for the root node we never
* need to worry about replacing the root.
*/
while (node->parent->color == red) {
struct rbnode *uncle;
if (node->parent == node->parent->parent->left) {
uncle = node->parent->parent->right;
if (uncle->color == red) {
node->parent->color = black;
uncle->color = black;
node->parent->parent->color = red;
node = node->parent->parent;
} else /* if (uncle->color == black) */ {
if (node == node->parent->right) {
node = node->parent;
rotate_left(tree, node);
}
node->parent->color = black;
node->parent->parent->color = red;
rotate_right(tree, node->parent->parent);
}
} else { /* if (node->parent == node->parent->parent->right) */
uncle = node->parent->parent->left;
if (uncle->color == red) {
node->parent->color = black;
uncle->color = black;
node->parent->parent->color = red;
node = node->parent->parent;
} else /* if (uncle->color == black) */ {
if (node == node->parent->left) {
node = node->parent;
rotate_right(tree, node);
}
node->parent->color = black;
node->parent->parent->color = red;
rotate_left(tree, node->parent->parent);
}
}
}
rbfirst(tree)->color = black; /* first node is always black */
return NULL;
}
