Draw what a binary search tree would look like if the following values were added to an initially empty tree in this order:

$50,20,75,98,80,31,150,39,23,11,77.$

What are the outputs of a pre$-$order and post$-$order traversal of the final binary search tree drawn in question $1?$

If a search was conducted for the value $37$ in the final binary search tree from question #$1,$ which nodes would get visited? $($List them in the order they get visited.$)$

Delete $31$ and $98$ from the Tree, insert on the new Tree $92,65,$ then Delete $150.$

Add the NIL leaves on the final binary search tree from question #$4$ and color the nodes such that the black$-$height of the resulting red$-$ black tree is $2.$

Insert $90$ on the resulting R$-$B tree and fix$-$up the tree if any property is violated. Compute the black$-$height of the new tree.