@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
}