$(30$ points$)$ Divide$-$and$-$Conquer. The Pancake Flipping Problem: Given a randomly

assorted stack of pancakes, each with a different diameter, rearrange the pancakes in

ascending order with the largest pancake on the bottom and the smallest one on top.

You are allowed to insert the spatula under any pancake and flip the entire stack above

that pancake over.

a$.$ Write a divide$-$and$-$conquer, pseudo$-$code algorithm that solves the Pancake Flip$-$

ping problem.

b$.$ What is the run$-$time efficiency of your algorithm?

c$.$ Apply your algorithm to the following instance of the problem. Be sure to show all

of your work.

$4$