Q$2.($a$)$ Model traffic control at a turning point using an appropriate data structure. Show using

pseudocodes how will you implement entry and exit of traffic.

$($b$)$ Consider a string consisting of all the letters of your firstname and lastname. Ensure that the

string consists of a minimum of $10$ and a maximum of $20$ characters. You may append alphabets

by repeating from your firstname and lastname or truncate alphabets from your firstname and

lastname. Represent this string using a binary tree with the first character as the root. Your goal

should be to make this tree as complete as possible. Examine if your final tree is i$)$ almost

complete binary and ii$)$ height$-$balanced.

$($c$)$ Show a problem where a graph representation of data can be beneficial. You should clearly

define the problem and the representation.Answer all questions

Q$1.($a$)$ Differentiate between a linear and a non$-$linear data structure with one example in each

category.

$($b$)$ Define a strictly binary tree with an example. Prove using mathematical induction that a

strictly binary tree with $n$ leaves contains $(2n-1)$ nodes.

$($c$)$ Define a linear linked list. How can you represent a node in a i$)$ a singly connected linear

linked list and ii$)$ a doubly connected linear linked list?

$($d$)$ Prove or disprove: A connected graph is always complete.