1. Pancake aesthetics. A diner serves a breakfast plate which simply consists of n pancakes A very bad cook fills the order. He proceeds by making n pancakes-all of different sizes and all with one side burnt. He then piles the pancakes onto a plate to create a tower of pancakes. Mr. Waiter picks up the plate and immediately realizes that he has to make the plate presentable. He wants to (i) sort the pancakes from smallest to largest with the largest pancake at the bottom of the plate, and (ii) hide the burnt side of each pancake. Now he only has one move available to him push a spatula underneath one of the pancakes and then flip the entire subtower of pancakes above the spatula upside down. His goal is to use this move repeatedly until his goals are accomplished. How many moves does he need? Let's create a mathematical model for this problem. Represent the ith smallest pancake as i if the pancake has its good side facing up and as -i if its burnt side is facing up Let the array .. .. n] store the pancakes on the plate created by the bad cook. In particular, Plj] refers to the jth pancake from the top. Thus, for n 5 the input array can look like this: P-3, 2,4, -1,-5] Let flip(i), 1 i