Assiume the tree$/$levels table below represents the worst$-$case number of times a diamond operation is performed in an algorithm.

A$)$ What $T(n)$ expression best represents the worst$-$case number of diamond operations performed in the algorithm?

$T(n)=0+{\displaystyle \underset{i=0}{\overset{k-1}{}}}(4^i\frac{n}{4^i}+2)$

none of these expressions is correct

$T(n)=4^k+{\displaystyle \underset{i=0}{\overset{k-1}{}}}(n+24^i)$

$T(n)=4^k+{\displaystyle \underset{i=0}{\overset{k}{}}}(n+24^i)$

$T(n)=n+{\displaystyle \underset{i=0}{\overset{k}{}}}(n+4^i)$

$T(n)=4^k+{\displaystyle \underset{i=1}{\overset{k}{}}}(4^i\frac{n}{4^i}+2)$

$T(n)=4^k+{\displaystyle \underset{i=1}{\overset{k-1}{}}}(n+24^i)$

$T(n)=4^k+{\displaystyle \underset{i=1}{\overset{k-1}{}}}(n+24^i)$

B$)$ What is the worst$-$case runtime growth rate of the algorithm?

$(1)$

$(lo{g}_{4}n)$

$(n)$

$(nlo{g}_{4}n)$

$(n^2)$

$(n^3)$

$(n^k)$

$(4^n)$

$(4^k)$

$(n!)$