$(1$ point$)$

Assume $n$ is a positive integer. Our goal is to find a power function $g(n)=n^p$ such that the algorithm below is $O(n^p).$

$x$:$=30$

for $i$:$={|}_{{?}_{?}}\frac{n}{2_{{?}_{?}}}|ton$

$,x$:$=n-1$

next $i$

The number of operations performed by this algorithm depends on whether $n$ is even or odd.

Case $1$: $n$ is even

There are

operations performed in each run of the loop and the loop runs

times, so the total number of operations performed in this loop is

Case $2$: $n$ is odd

There are

operations performed in each run of the loop and the loop runs

times, so the total number of operations performed in this loop is

$.$

In either case, by the order of a polynomial theorem, we have that this algorithm is $O($

$.$