protected BSTVertex delete(BSTVertex T, int v) {
if (T == null) return T; // cannot find the item to be deleted
if (T.key == v) { // this is the node to be deleted
if (T.left == null && T.right == null) // this is a leaf
T = null; // simply erase this node
else if (T.left == null && T.right != null) { // only one child at right
BSTVertex temp = T;
T.right.parent = T.parent;
T = T.right; // bypass T
temp = null;
} else if (T.left != null && T.right == null) { // only one child at left
BSTVertex temp = T;
T.left.parent = T.parent;
T = T.left; // bypass T
temp = null;
} else { // has two children, find successor
int successorV = successor(v);
T.key = successorV; // replace this key with the successor's key
T.right = delete(T.right, successorV); // delete the old successorV
}
} else if (T.key < v) // search to the right
T.right = delete(T.right, v);
else // search to the left
T.left = delete(T.left, v);
return T; // return the updated BST
}
@Override
protected BSTVertex delete(BSTVertex T, Name v) {
if (T == null) return T; // cannot find the item to be deleted
if (T.key.babyName.equals(v.babyName)) { // this is the node to be deleted
if (T.left == null && T.right == null) { // this is a leaf
T = null; // simply erase this node
} else if (T.left == null && T.right != null) { // only one child at right
T.right.parent = T.parent;
T = T.right; // bypass T
} else if (T.left != null && T.right == null) { // only one child at left
T.left.parent = T.parent;
T = T.left; // bypass T
} else { // has two children, find successor
Name successorV = successor(v);
T.key = successorV; // replace this key with the successor's key
T.right = delete(T.right, successorV); // delete the old successorV
}
} else if (T.key.babyName.compareTo(v.babyName) < 0) { // search to the right
T.right = delete(T.right, v);
} else { // search to the left
T.left = delete(T.left, v);
}
updateHeight(T);
updateSize(T);
// Balance the tree after deletion
T = balance(T);
return T; // return the updated BST
}
protected BSTVertex insert(BSTVertex T, int v) {
if (T == null) return new BSTVertex(v); // insertion point is found
if (T.key < v) { // search to the right
T.right = insert(T.right, v);
T.right.parent = T;
} else { // search to the left
T.left = insert(T.left, v);
T.left.parent = T;
}
return T; // return the updated BST
}
protected BSTVertex insert(BSTVertex T, Name v) {
if (T == null) return new BSTVertex(v); // insertion point is found
if (T.key.babyName.compareTo(v.babyName) < 0) { // search to the right
T.right = insert(T.right, v);
T.right.parent = T;
} else { // search to the left
T.left = insert(T.left, v);
T.left.parent = T;
}
T.height = 1 + Math.max(getHeight(T.left), getHeight(T.right));
return T; // return the updated BST
}
public BSTVertex balance(BSTVertex T) {
// Check the balance factor
if (getBalanceFactor(T) == 2 && getBalanceFactor(T.left) == 1) {
T = rotateRight(T);
} else if (getBalanceFactor(T) == 2 && getBalanceFactor(T.left) == -1) {
T.left = rotateLeft(T.left);
T = rotateRight(T);
} else if (getBalanceFactor(T) == -2 && getBalanceFactor(T.right) == 1) {
T.right = rotateRight(T.right);
T = rotateLeft(T);
} else if (getBalanceFactor(T) == -2 && getBalanceFactor(T.right) == -1) {
T = rotateLeft(T);
} else {; // No need to do anything
}
return T;
}
@Override
protected BSTVertex insert(BSTVertex T, Name v) {
if (T == null) return new BSTVertex(v); // insertion point is found
if (T.key.babyName.compareTo(v.babyName) < 0) { // search to the right
T.right = insert(T.right, v);
T.right.parent = T;
} else { // search to the left
T.left = insert(T.left, v);
T.left.parent = T;
}
updateHeight(T);
T.size++;
// Balance the tree after insertion
T = balance(T);
return T; // return the updated BST
}
private BSTVertex rotateLeft(BSTVertex T) {
BSTVertex w = T.right;
// Connect the right node of T (which is w) to the parent of T
w.parent = T.parent;
// Put w above T
T.parent = w;
// Left node of w is shifted to right of T to replace w
T.right = w.left;
// Need to set the parent of w.left unless w.left does not exist
if (w.left != null) {
w.left.parent = T;
}
// Set T, which is under w, to w.left
w.left = T;
if (w.parent != null) {
if (w.parent.left == T) {
w.parent.left = w;
} else {
w.parent.right = w;
}
}
updateHeight(T);
updateHeight(w);
// Only T and w has new sizes
w.size = T.size;
T.size = getSize(T.left) + getSize(T.right) + 1;
return w;
}
private BSTVertex rotateRight(BSTVertex T) {
BSTVertex w = T.left;
w.parent = T.parent;
T.parent = w;
T.left = w.right;
if (w.right != null) {
w.right.parent = T;
}
w.right = T;
if (w.parent != null) {
if (w.parent.left == T) {
w.parent.left = w;
} else {
w.parent.right = w;
}
}
updateHeight(T);
updateHeight(w);
w.size = T.size;
T.size = getSize(T.left) + getSize(T.right) + 1;
return w;
}
protected void updateSize(BSTVertex T) {
if (T != null) {
T.size = 1 + getSize(T.left) + getSize(T.right);
}
}
protected void updateHeight(BSTVertex T) {
if (T != null) {
T.height = 1 + Math.max(getHeight(T.left), getHeight(T.right));
}
}