$(3)$ Draw the $2-3$ three that results when you insert the keys YLPMXHCRAE

$S$ in that order into an initially empty tree.

$(4)$ Find an insertion order for the keys S E A R C HX M that leads to a $2-3$ tree of

height $1.$

$(5)$ The figure at right shows all the structurally different $2-3$ trees with $N$ keys, for $N$

from $1$ to $6($ignore the order of the subtrees$).$ Draw all the structurally different

trees for $N=7,8,9,$ and $10.$

$(6)$ Show all possible ways that one might represent a $4-$node with three $2-$nodes

bound together with red links $($not necessarily left$-$leaning$).$

$(7)$ Which of the following are red$-$black BSTs$?$

$(8)$ Draw the red$-$black BST that results when you insert items with the keys E A S

YQUTION in that order into an initially empty tree.

$(9)$ Draw the red$-$black BST that results when you insert items with the keys $YLP$

M X HCRAES in that order into an initially empty tree.

$(10)$ True or false: If you insert keys in increasing order into a red$-$black BST$,$ the tree

height is monotonically increasing.