Problem $2.$ Write down a recurrence relation that models the worst case running time of Quicksort, i$.$e$.$ the case where PARTITION selects the last element at each iteration. What is the worst$-$case running time of QuickSort? Be sure to write both the recurrence relation and the runtime. You may use either the Unrolling Method or the Recursion$-$Tree Method.

Answer.

$T(n)=\{\begin{array}{ccc}& \text{Y}\text{o}\text{u}\text{r}\text{a}\text{n}\text{s}\text{w}\text{e}\text{r}\text{,}if& n\text{d}\text{o}\text{t}\text{s}\text{,}\\ & \text{Y}\text{o}\text{u}\text{r}\text{a}\text{n}\text{s}\text{w}\text{e}\text{r}\text{,}if& n>\text{d}\text{o}\text{t}\text{s}\end{array}$

The worst$-$case running time of QuickSort is$....$