Consider the BST built from the items $($:$32,24,17,47,53,24,19,8,32,26$:$)$ on the pre$-$

vious assignment.

$($a$)(4$ pts$.)$ Find floor$(25)$ and ceiling$(25).$ Indicate the comparisons, which subtree

you continue searching, and which values you get as potential floor or ceiling

during the search.

$($b$)(4$ pts$.)$ In the BST above, at every vertex indicate the size of the subtree

starting at that vertex, including the vertex itself. Indicate how you compute

these values.

$($c$)(4$ pts$.)$ Use the above values to find Select$(4).$ Indicate which cases you en$-$

counter and the values of $t$ and $k$ as you

$($d$)(4$ pts$.)$ Find Rank$(30)$ in the above BST$.$ Indicate which cases you encounter

and what values contribute to the total.

$($e$)(4$ pts$.)$ Insert $35$ into this BST$,$ then remove $32.$ Explain what steps you need

to do$.$