Consider the following algorithm segment. Assume that $n$ is a positive integer.

for $i$:$=1ton$

for $j$:$={|}_{{?}_{?}}\frac{i+1}{2_{{?}_{?}}}|ton$

$,x$:$=i*j$

next $j$

next $i$

$($a$)$ What is the actual number of elementary operations $($additions$,$ subtractions, multiplications, divisions, and compariso ignore those implied by for$-$next loops. Express your answer in terms of $n.($Hint: See Example $11\mathrm{.}3\mathrm{.}4$ and Exercise $11$

For odd $n$ the number of operations is

For even $n$ the number of operations is

$($b$)$ Apply the theorem on polynomial orders to the expressions in part $($a$)$ to find that an order for the algorithm segment