For $($a$)$ and $($b$),$ select the recurrence representing the recursive runtimes of each method in terms of n$.$ Assume that any $+,-,*,/,\%$ operations and

System.out.println$()$calls take constant runtime. Don't worry about finding the exact constants for the non$-$recursive term. For example, if the running time is

T$($n$)=4$T$($n$/3)+25$n$,$ you need to get the $4$ and the $3$ right but you don't have to worry about getting the $25$ right.

Question $1\mathrm{.}1$ From Code to Reccurence

Q$1\mathrm{.}1$ From Code to Reccurence

$1$ Point

Grading comment:

Write the recurrence of the recursive case $($not the base case$)$ for

mystery$($n$,1),$ where the initial value of the parameter

step $=1$

$/*$

$*$ A mystery method

$*/$

public void mystery$($int n$,$ int step$)\{$

if $($n $<=$ step$)\{$

return;

$\}$

for $($int i $=0$; i $<$ n; i $+=$ step$)\{$

int a $=$ i $+$ n $/2$;

System.out.print$($a $*$ a $+"")$;

$\}$

System.out.println$()$;

mystery$($n$,$ step $*2)$;

mystery$($n$,$ step $*2)$;

$\}$

The following multiple$-$choice options contain math elements, so you may need to read them in your screen reader's $$reading$$ or $$browse$$ mode instead of $$forms$$ or $$focus$$ mode.

Choice $1$ of $4$:

T$($n$)=3$T$($n$/2)+$n

Choice $2$ of $4$:

T$($n$)=2$T$($n$/3)+25$

Choice $3$ of $4$:

T$($n$)=2$T$($n$/2)+$n

Choice $4$ of $4$:

T$($n$)=3$T$($n$/3)+25$