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);
}
}
}
