You are given the following pseudocode for a recursive algorithm.

Algorithm $1$ Recursive Function $1$

$1$: Algorithm RecFunc$($n$)$

Input: Integer n

$2$: if n $=1$ then

$3$: return $1$

$4$: else if n is even then

$5$: return $2$n $+$ RecFunc$($n $1)$

$6$: else if n is odd then

$7$: return n $+$ RecFunc$($n $1)$

$8$: end if

$9$: end Algorithm

a$.$ State the base and the recursive cases

b$.$ Draw the corresponding recursion tree when RecFunc$(5)$ is invoked.

c$.$ Compute the return value $($as an integer$)$ of the function call RecFunc$(5).$

d$.$ Determine its worst$-$case asymptotic running time in terms of n

e$.$ Determine its space complexity in terms of n