Consider a tree storing $100,000$ entries. What is the worst$-$case height of

in the following cases?

$($a$)$

is a binary search tree.

$($b$)$

is an AVL tree.

$($c$)$

is a splay tree.

$($d$)$

is a $(2,4)$ tree.

$($e$)$

is a red$-$black tree.