Recurrence Relations $(20$ pts$)$

Provide runtime complexity for the following functions using tree method or

substitution method:

$($a$)T(n)=2T(\frac{n}{5})+cn$

$($b$)T(n)=7T(\frac{n}{3})+c{n}^{{?}^{{?}^{?}}}3$

$($c$)T(n)=T(\frac{n}{2})+n$

$($d$)$

int fact$($int $N$

if $)$ return $1$ ;

return $N^{**}$ fact$(\{$:$N-1)$;

$\}$