$5.$ AVL Trees: $(30$ pts $)$

a$)$ Show the result $($draw the tree$)$ of inserting $2,1,4,5$ into an initially empty AVL Tree $(5$ pts$).$ Is the resulted tree balanced or not $(2$ pts $)?$

Answer:

b$)$ Show the result $($draw the tree$)$ of inserting $9$ into the AVL Tree. If the tree is unblanced, please indicate the violation case. Please show the rebalance steps and the resulted AVL tree. $(5$ pts$)$ Answer:

c$)$ Show the result $($draw the tree$)$ of inserting $3$ into the AVL Tree. If the tree is unblanced, please indicate the violation case. Please show the rebalance steps and the resulted AVL tree. $(5$ pts$)$

d$)$ Show the result $($draw the tree$)$ of inserting $6$ into the AVL Tree. If the tree is unblanced, please indicate the violation case. Please show the rebalance steps and the resulted AVL tree. $(5$ pts$)$

e$)$ Show the result $($draw the tree$)$ of inserting $7$ into the AVL Tree. If the tree is unblanced, please indicate the violation case. Please show the rebalance steps and the resulted AVL tree. $(3$ pts$)$

f$)$ Show the result $($draw the tree$)$ of deleting $1$ and $3$ from the AVL tree. $(5$ pts$)$