There are n stacks of n identical-looking coins. All of the coins in one of these stacks are counterfeit, while all the coins in the other stacks are genuine. Every genuine coin weighs 10 grams; every fake weighs 11 grams. You have an analytical scale that can determine the exact weight of any number of coins. a. Devise a brute-force algorithm to identify the stack with the fake coins and determine its worst-case efficiency class. b. Find a constant time algorithm to identify the stack with the fake coins. Hint: It can be done in only one weighting.

Consider a variation of the Bucket Sort algorithm which uses an unknown number of buckets. We're given that the worst-case runtime of the algorithm is O(n.), Let the number of buckets be n* (n to the power of x). Fill in the following box with the proper numeric value of x such that the algorithm has the given runtime. For example, you could fill in 0, 1, 2, 3, 3.14 4.2, etc. Recall that we use Insertion Sort to sort each bucket. Answer:

Given is a list of K distinct coin denominations (V1,...,Vk) and the total sum S>0. Find the minimum number of coins whose sum is equal to S (we can use as many coins of one type as we want), or report that it’s not possible to select coins in such a way that they sum up to S. Justify your explanation!