There are two algorithms A and B for solving the same problem.

Algorithm A has a worst$-$case time complexity $T_A(n)$ that satisfies the recurrence relation

$T_A(n)=7T_A(\frac{n}{2})+200n^2,$ where $n$ is the input size.

Algorithm B has a worst$-$case time complexity $T_B(n)$ that satisfies the recurrence relation

$T_B(n)=a{T}_B(\frac{n}{4})+10n^2,$ where $n$ is the input size and $a$ is a positive integer.

Answer the following questions.

In the dropdown lists, $\backslash$Theta stands for $\frac{,}{{\mathit{l}\mathit{o}\mathit{g}}_b}$ a stands for $lo{g}_{b}a,$ and $n^{{?}^{{?}^{?}}}x$ stands for $n^x$

$($a$)$ Which case of the Master method applies when solving for $T_A(n)?$

$($b$)$ What is the asymptotic notation of $T_A(n)?$

$($c$)$ Assume that $a=16.$ Which case of the Master method applies when solving for $T_B(n)$

$?$

$[$ Select $]$

$($d$)$ Assume that $a=16.$ What is the asymptotic notation of $T_B(n)?$

$($e$)$ Assume that Which case of the Master method applies when solving for $T_B(n)$

$?$

$($f$)$ Assume that What is the asymptotic notation of $T_B(n)?$

$[$ Selec

$($g$)$ Assume that $a>16.$ Which case of the Master method applies when solving for $T_B(n)$

$?$

$($h$)$ Assume that $a>16.$ What is the asymptotic notation of $T_B(n)?$

$($i$)$ What is the largest integer a such that Algorithm B is asymptotically faster than Algorithm

A$?$

$[$Selec

$($j$)$ What is the smallest integer a such that Algorithm B is asymptotically slower than

Algorithm A$?$