Problem $1,(30$ points$)$ Answer the following problems. For each problem, consider the binary tree in Figure $1$ where $n_i$ for $i=0,1,$cdots,$8$ denotes the memory address of a node.

$($a$)(10$ points$)$ Show the output that the following method will produce when it is executed with its parameter node set to $n_0.$Briefly justify your answer.$($b$)(10$ points$)$ Show the output that the following method will produce when it is executed with its parameter node set to n$\_(0).$Brielly justify your answer$1($c$)(10$ points$)$ Show the output that the following method will produce when it is executed with its parameter node set to no$.$Brielly justify your answer:

Problem $2.(36$ points$)$ Answer each of the following problems assuming that Figure $1$ shows an AVL tree In Figure $1,n_i$ for $i=0,1,$dots,$8$ denotes the memory address of a node.

$($a$)(9$ points$)$ Assume that $t$ refers to the AVL tree shown in Figure $1.$ Draw the tree that would result from executing $t,$ add $(1),$ Justify your answer.

$($b$)(9$ points$)$ Assume that $t$ refen to the AVL tree ahowa in Figure $1.$ Draw the tree that would result from execuliag $t,$ add $(4),$ Justify your answer

$($c$)(9$ points$)$ Assume that $t$ refers to the AVL tree shown in Figure $1.$ Draw the tres that would result from exercutiag $2,$ reaove $(6),$ Justify your answer.

$($d$)$ points$)$ Assume that trefers to the AVL tree ulown is Figure $1.$ Draw the tre that would nersens