Suppose that you are given a binary tree T with vertices V and edges E$,$

in adjacency list format. Assume that there is a designated root node x$.$ For

two nodes u$,$ v in V $,$ u is an ancestor of v if the path from the root x to v

passes through u$.$ If u is an ancestor of v$,$ then v is said to be a descendant

of u$.$

Suppose that in addition to the tree T$,$ you are given an array P$,$ where P$($u$)$

contains a value associated with each node u$.($The meaning of these values is

unimportant.$)$ Define array Z such that Z$($u$)$ contains the maximum of the

P values of all of u$$s descendants $($including u itself$).$ Propose a linear$-$time

algorithm to compute Z$.$