Write a recursive algorithm to find the maximum element in an array of n

elements. Analyze its time efficiency.

$(8)(8$ marks$)$ Consider the following algorithm and answer the related questions.

Input: a nonnegative integer n

xyz$($n$)\{$

x $=0$;

for i $=1$ to n do $\{$

x $=$ x $+$ i $*$ i

$\}$

$\}$

$($a$)$ What does this algorithm compute?

$($b$)$ What are the basic operations in this algorithm?

$($c$)$ What is its time efficiency in terms of the number of basic operations that are

executed?

$($d$)$ Can you improve its time efficiency? Provide your solution.