This question is about red$-$black trees $($RBT$).$

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

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

$$

$($b$)$ Assume that you have a red$-$black 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 $]["$O$(1)","$O$($log n$)","$O$($n$)",$ "None of them"$]$

$$

$($c$)$ Assume that you have a red$-$black 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$(1)","$O$($log n$)","$O$($n$)",$ "None of them"$]$

$$

$($d$)$ Assume that you have a red$-$black tree T$$ with n nodes. What is the maximum tree height? Select the most accurate asymptotic notation in the dropdown.

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

$$

$($e$)$ Assume that you have a red$-$black 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$(1)",$ "Omega$($log n$)",$ "Omega$($n$)",$ "None of them"$]$