Consider the tree shown below. Describe the steps involved in executing each of the

following operations according to the tree$-$index concurrency control algorithm discussed in Section $17\mathrm{.}5\mathrm{.}2,$ in

terms of the order in which nodes are locked, unlocked, read, and written. Be specific about the kind of lock

obtained and answer each part independently of the others, always starting with the tree shown.

$($a$)$ Search for data entry $40$