$1.[2$ marks$]$ The following is a recursive algorithm for a postorder binary tree traversal. Determine the worst$-$case runtime of this algorithm where the proper binary tree $\backslash ($ T $\backslash )$ has $\backslash ($ n $\backslash )$ internal nodes. Do this by specifying the recurrence equation for the runtime $\backslash ($ T$($n$)\backslash )$ and then deriving the closed form. Count the call $\backslash ($ T $\backslash ).$ isInternal $\backslash (($v$)\backslash )$ as $1$ primary operation and the call processNode $\backslash (($v$)\backslash )$ as $\backslash ($ c $\backslash )$ primary operations, where $\backslash ($ c $\backslash )$ is some constant. Assume that for each internal node $\backslash ($ v $\backslash ),$ its right child is an external node.

$```$

Algorithm postorder$($Tree T$,$ Node v$)$

Input: Binary tree T of size n and node v of T

Output: None

if T$.$ isInternal $($ v$)$ then

postorder$($T$,$T$.$leftChild$($v$))$

postorder$($T$,$T$.$rightChild$($v$))$

processNode$($v$)$

end

end

$```$