void make_balance_after_insert(ptr_rbnode node) {
//case 1 : root node
if (node->parent == NULL) {
node->color = BLACK;
return;
}
//case 2 : parent is black
if (node->parent->color == BLACK) {
return; //nothing to do
}
//now it is guaranteed that node has grandparent
//case 3 : p and u = red, g = black
ptr_rbnode g = get_grandparent(node), u = get_uncle(node), p = node->parent;
assert(g);
if (p->color == RED && u->color == RED && g->color == BLACK) {
p->color = BLACK; u->color = BLACK; g->color = RED;
make_balance_after_insert(g);
/* this recursive operation will take O(log N) in worst case and O(1) in average case
because the time complexity distribution would have a form of geometric distribution. */
return;
}
//case 4,5 : p = red, u = black, g = black; -> guaranteed
//if node, p and g is not on a line, rotate
//case 4 would be changed into case 5
assert(p->color == RED && u->color == BLACK && g->color == BLACK);
if (g->left == p && p->right == node) {
rotate_left(p);
node = node->left;
//for case 5
g = get_grandparent(node), u = get_uncle(node), p = node->parent;
}
else if (g->right == p && p->left == node) {
rotate_right(p);
// for case 5
g = get_grandparent(node), u = get_uncle(node), p = node->parent;
node = node->right;
}
g = get_grandparent(node), u = get_uncle(node), p = node->parent;
//case 5
assert((p->left == node && g->left == p)
|| (p->right == node && g->right == p));
p->color = BLACK;
g->color = RED;
if (p->left == node) {
rotate_right(g);
}
else {
rotate_left(g);
}
}
/* W. 2+3) Parent of node must be black, otherwise recolor and flush */
static void insert_check_2 (DLRBT_Tree *tree, DLRBT_Node *node)
{
/* if the parent is not black, we need to change that... */
if (node && node->parent && node->parent->tree_col) {
DLRBT_Node *unc= get_uncle(node);
/* if uncle and parent are both red, need to change them to black and make
* the parent black in order to satisfy the criteria of each node having the
* same number of black nodes to its leaves
*/
if (unc && unc->tree_col) {
DLRBT_Node *gp= get_grandparent(node);
/* make the n-1 generation nodes black */
node->parent->tree_col= unc->tree_col= DLRBT_BLACK;
/* - make the grandparent red, so that we maintain alternating red/black property
* (it must exist, so no need to check for NULL here),
* - as the grandparent may now cause inconsistencies with the rest of the tree,
* we must flush up the tree and perform checks/rebalancing/repainting, using the
* grandparent as the node of interest
*/
gp->tree_col= DLRBT_RED;
insert_check_1(tree, gp);
}
else {
/* we've got an unbalanced branch going down the grandparent to the parent,
* so need to perform some rotations to re-balance the tree
*/
insert_check_3(tree, node);
}
}
}
/* W. 4+5) Perform rotation on sub-tree containing the 'new' node, then do any */
static void insert_check_3(DLRBT_Tree *tree, DLRBT_Node *node)
{
DLRBT_Node *gp = get_grandparent(node);
/* check that grandparent and node->parent exist
* (jut in case... really shouldn't happen on a good tree) */
if (node && node->parent && gp) {
/* a left rotation will switch the roles of node and its parent, assuming that
* the parent is the left child of the grandparent... otherwise, rotation direction
* should be swapped
*/
if ((node == node->parent->right) && (node->parent == gp->left)) {
rotate_left(tree, node);
node = node->left;
}
else if ((node == node->parent->left) && (node->parent == gp->right)) {
rotate_right(tree, node);
node = node->right;
}
/* fix old parent's color-tagging, and perform rotation on the old parent in the
* opposite direction if needed for the current situation
* NOTE: in the code above, node pointer is changed to point to the old parent
*/
if (node) {
/* get 'new' grandparent (i.e. grandparent for old-parent (node)) */
gp = get_grandparent(node);
/* modify the coloring of the grandparent and parent
* so that they still satisfy the constraints */
node->parent->tree_col = DLRBT_BLACK;
gp->tree_col = DLRBT_RED;
/* if there are several nodes that all form a left chain, do a right rotation to correct
* this (or a rotation in the opposite direction if they all form a right chain) */
if ((node == node->parent->left) && (node->parent == gp->left)) {
rotate_right(tree, gp);
}
else { // if ((node == node->parent->right) && (node->parent == gp->right))
rotate_left(tree, gp);
}
}
}
}
int main() {
srand(time(NULL));
node* tree = create_bst(40);
for(uint i = 0; i < 10; ++i) {
int elem = rand() % 100 + 1;
insert(&tree, elem);
}
insert(&tree, 1337);
display_tree(tree);
node* test = search(tree, 1337);
printf("Grandparent of 1337 is: %d", get_grandparent(tree, test)->data);
return 0;
}
/* get the 'uncle' - the sibling of the parent - of the given node */
static DLRBT_Node *get_uncle (DLRBT_Node *node)
{
DLRBT_Node *gpn= get_grandparent(node);
/* return the child of the grandparent which isn't the node's parent */
if (gpn) {
if (gpn->left == node->parent)
return gpn->right;
else
return gpn->left;
}
/* not found */
return NULL;
}
ptr_rbnode get_uncle(ptr_rbnode node) {
ptr_rbnode g = get_grandparent(node);
if (g) {
if (g->left == node->parent) {
return g->right;
}
else if (g->right == node->parent) {
return g->left;
}
else {
assert(0 && "Tree Collapsed");
}
}
else
return NULL;
}
