Consider the following algorithm.

Preconditions:

X $=\{$x$1,$ x$2,...,$ xn$\}$ N$.$

i $1$

t $0$

while

i $$ n

do$$

s $1$

$$

j $1$

while

j $$ i

do$$

s $$ s $$ xi

$$

j $$ j $+1$

t $$ t $+$ s

i $$ i $+1$

$($a$)$ Compute the number of times the algorithm performs a multiplication operation $($in terms of n$).$

Preconditions:

X $=\{$x$1,$ x$2,...,$ xn$\}$ N$.$

i $1$

t $0$

while

i $$ n

do$$

s $1$

$$

j $1$

while

j $$ i

do$$

s $$ s $$ xi

$$

j $$ j $+1$

t $$ t $+$ s

i $$ i $+1$

$($a$)$ Compute the number of times the algorithm performs a multiplication operation $($in terms of n$).$

Reverse$($prewt$)$

using a top$-$down evaluation.