Consider the following extension to the tree-locking protocol, which allows both shared and exclusive locks:

• A transaction can be either a read-only transaction, in which case it can request only shared locks, or an update transaction, in which case it can request only exclusive locks.

• Each transactionmust follow the rules of the tree protocol. Read-only transactions may lock any data item first, whereas update transactions must lock the root first. Show that the protocol ensures serializability and deadlock freedom.