There arek identical mugs and a n-story building. There is some value x between 1 and n such that if a mug is dropped from a floor ≥x, it breaks (aka. it's guaranteed that the mug breaks when dropped from floor x or higher). You want to find this value of x by dropping the fewest number of mugs. The only allowed operation is to drop a mug from some floor: if the mug breaks when you drop it, you cannot reuse it again, otherwise, it can be reused. Your goal is to devise a dynamic programming algorithm to determine the minimum number of drops needed to determine x in the worst case.
a)Suppose you are given 1 mug for a 5-story building (k=1,n=5). What is the minimum number of drops you have to make from which you are guaranteed to find the lowest floor where the mug breaks?