Determine the processing time T$($n$)$ of the recursive algorithm:

$1$ int myTest$($ int n $)\{$

$2$ if $($ n $<=0)$ return $0$;

$3$ else $\{$

$4$ int i $=$ random$($ n $-1)$;

$5$ return myTest$($ i $)+$ myTest$($ n $-1-$ i $)$;

$6\}$

$7\}$

providing the algorithm random$($ int n $)$ spends one time unit to return a random integer value uniformly distributed in the range $[0,$ n$]$ whereas all other instructions spend a negligibly small time $($e$.$g$.,$ T $(0)=0).$

Hints: derive and solve the basic recurrence relating T$($n$)$ in average to T$($n$1),...,$ T$(0).$ You might need the equation $1+1++1=$ n for deriving the explicit formula for T $($n$).$