Q$1[15$ pts$.]$: Given the following key sequence $(5,23,8,14,13,2,7)$ build the dynamic binary

search tree WITHOUT BALANCING IT$.$ How many probes $($i$.$e$.,$ comparisons$)$ does it

take to determine that key $100$ is not in the tree? $($In this study case, the root is $5$; the next

element $23>5,$ so it goes to the right, etc$).$

Q$2[5$ pts$.]$: How many leaves does a $3-$ary tree have if its depth is $7?($HINT: see the pattern for

a full binary tree of depth n and modify it$).$

Q$3[10$ pts$.]$: How many total nodes does a $5-$ary tree have if its depth is $6?$

Q$4[10$ pts$.]$: Given the preorder traversal of a tree is: a$,$b$,$c$,$d$,$e and the inoder traversal of the tree

is: b$,$a$,$e$,$d$,$c$.$ What is the POSTORDER traversal of that tree?

Q$5[15$ pts$.]$: Consider a binary tree containing n nodes.

$($a$)$ What is the theta value for the preorder traversal of this tree?

$($b$)$ What is the theta value for the inorder traversal of this tree?

$($c$)$ What is the theta value for the postorder traversal of this tree?

Q$6[15$ pts$.]$: Hash the given file $(5,23,8,14,13,2,7)$ and use linear probing and the table size of

$11.$ How many total collisions occurred? What is the loading density of the table?

Q$7[15$ pts$.]$: Hash the given file $(5,23,8,14,13,2,7)$ and use overflow chaining. How many

comparisons are needed to determine whether key value $12$ is in the table?

Q$8[15$ pts$.]$: What should the loading factor be $($on ANY HASH TABLE$)$ if you want to have an

average of $1\mathrm{.}3$ comparisons per search if LINEAR PROBING?

I need proper answers for all the questions but not AI generated. Also should be handwritten if necessary.

Thanks.