Let T$($n$)$ denote the number of times that the recursive function DoSomething$($n$)$ prints $``$banana$."$

int DoSomething$($int n$)$

$\{$

for $($int i$=1$; i $<=$ n; i$=$i$+1)\{$ print "banana";$\}$

if $($n $<=2)$ return $1$;

else $\{$

x $=0$;

for $($int j$=1$; j$<=$ n; j$++)\{$ x $=$ x$+$DoSomething$($n$/2)$;$\}$

return x$*$x;

$\}$

$\}$

Give a recurrence relationship for T$($n$)?$ For simplicity you may assume that n is a power of $2.$

a$.$ T$($n$)=$ n$*$T$($n$/2)+$ n for n $>2$ and T$($n$)=$ n for n$<=2.$

b$.$ T$($n$)=$ n$*$T$($n$/2)+$ log n for n $>2$ and T$($n$)=1$ for n$<=2.$

c$.$T$($n$)=$ n$*$T$($n$/2)+$ n for n $>2$ and T$($n$)=0$ for n$<=2.$

d$.$ T$($n$)=2*$T$($n$/2)+$ n for n $>2$ and T$($n$)=0$ for n$<=2.$

e$.$ T$($n$)=$ T$($n$/2)+$ n for n $>2$ and T$($n$)=0$ for n$<=2.$

f$.$ T$($n$)=$ T$($n$/2)+$ log n for n $>2$ and T$($n$)=0$ for n$<=2.$