P4 (30pt): Eggs break when dropped from great enough height. Specifically, there must be a floor f in any sufficiently tall building such that an egg dropped from the fth floor breaks, but one dropped from the (f1)st floor will not. If the egg always breaks, then f=1. If the egg never breaks, then f=n+1. You seek to find the critical floor f using an n-story building. The only operation you can perform is to drop an egg off some floor and see what happens. You start out with k eggs, and seek to drop eggs as few times as possible. Broken eggs cannot be reused. Let Ek, n) be the minimum number of egg droppings that will always suffice. 2. (b) Show that E(k,n)=O(n/k). (Hint1: Try to recurse; Hint2:mathematical induc- tion on k. Hint3: treat variables as real numbers and minimize via derivative. ] P4 (30pt): Eggs break when dropped from great enough height. Specifically, there must be a floor f in any sufficiently tall building such that an egg dropped from the fth floor breaks, but one dropped from the (f1)st floor will not. If the egg always breaks, then f=1. If the egg never breaks, then f=n+1. You seek to find the critical floor f using an n-story building. The only operation you can perform is to drop an egg off some floor and see what happens. You start out with k eggs, and seek to drop eggs as few times as possible. Broken eggs cannot be reused. Let Ek, n) be the minimum number of egg droppings that will always suffice. 2. (b) Show that E(k,n)=O(n/k). (Hint1: Try to recurse; Hint2:mathematical induc- tion on k. Hint3: treat variables as real numbers and minimize via derivative. ]