$2$ Analyze Code I: Independent nested loops

$2\mathrm{.}1$ Problem $4[15pts]$

Problem $4.$ Analyze the worst$-$case runtime of the following algorithm:

Clearly derive the runtime complexity function $T(n)$ for this algorithm.

Using the formal definition of Big$-$Theta $(),$ find a tight asymptotic bound for $T(n),$ that is$,$ find a

function $f(n)$ such that $T(n)=(f(n)).$

Avoid heuristic arguments from CSCI $2270/2824$ such as multiplying the complexities of nested loops.

Answer.