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Consider the following algorithm?

ALGORITHM Mystery $(n)$

$//$Input: A nonnegative integer $n$

for

return $S$

a$)$ What does this algorithm compute?

b$)$ What is its basic operation?

c$)$ How many times is the basic operation executed? $($use a summation$)$

d$)$ What is the efficiency class of this algorithm?

e$)$ Suggest an improvement, or a better algorithm altogether, and indicate its efficiency class. If you cannot do it$,$ try to prove that, in fact, it cannot be done.