Problem $2$

In the worst$-$case linear$-$time order statistics algorithm SELECT $($Slide $16$ of Lecture $10),$ the input elements are divided into groups of $5$

a$)$ Using the analysis method from Lecture $10,$ prove that the algorithm still works in worst$-$case linear time if input elements are divided into groups of $7.$

b$)$ Using the same method, show that SELECT does not run in linear time if groups of $3$ are used