Divide and Conquer (15 points) Suppose you have a set of n identical coins, one of which is a counterfeit. The coins all look the same, however the counterfeit coin is lighter by an unknown amount. You have a rudimentary weighing scale which you can use to compare the weight of two sets of objects. The scale tells you if its two sides weigh equal or tells you which side is lighter. a) Design a divide-and-conquer algorithm (either in plain English or in pseudo-code) to determine the counterfeit coin. (10 points) b) Write down the recurrence relation for the runtime complexity and solve it by the master theorem. (5 points)