Consider the following two algorithms A and B$.$ For A$($n$),$ let its time be tA$($n$).$ Give a recurrence

for tA$($n$)($don$$t forget the initial condition$)$ and solve it using the recursion tree method. For B$($n$),$ let its

time be tB$($n$).$ What is tB$($n$)$ and why? Correct solution to incorrect recurrence will get little credit.

A$($x$,$ n$)$ B$($n$)$

if n $=0$ for i$=1$ to n

return x$*$x for j$=1$ to i

else print A$($n$,$ n$*$n$)$

return x$*$x$*$x$*$A$($x$,$ n$-1)$ print A$($n$,$ n$*$n$)$

end A end B

$2.$