$($b$)$ Assume that you have a binary search tree T with n nodes. What is the worst$-$case time complexity for insertion into the tree? Select the most accurate asymptotic notation in the dropdown.

$[$ Select $]["$None of them", $"$O$(1)","$O$($n$)","$O$($log n$)"]$

$$

$($c$)$ Assume that you have a binary search tree T with n nodes. What is the worst$-$case time complexity for deletion from the tree? Select the most accurate asymptotic notation in the dropdown.

$[$ Select $]["$O$($log n$)","$O$(1)","$O$($n$)",$ "None of them"$]$

$$

$($d$)$ Assume that you have a binary search tree T with n nodes. What is the minimum tree height? Select the most accurate asymptotic notation in the dropdown. Here we use Omega to denote $.$

$[$ Select $]["$Omega$($n$)",$ "None of them", "Omega$($log n$)",$ "Omega$(1)"]$

$$

$($e$)$

Is there a binary search tree $($BST$)$ T and a query value X such that the search for X in T visits the following sequence of key values in the given order?

$100,40,70,101,141$