Give a complete problem formulation for each of the following problems. You are not restricted by any formalism, but you should make sure that your formulation is sufficiently precise so as to be implementable. So for example, you can use specify your problem formulation in terms of Initial State, Goal State, Subroutines, Cost/Utility Function, etc. c. Suppose you have a computer program that, when fed a file of input records, outputs the message "Illegal Input Record" if there is indeed an illegal input record in that file. Assuming that the processing of each input record is independent of each other, explain how you would go about figuring out which one (or ones) of the input records in that file is (or are) illegal. d. Suppose you have three jugs - 3 gallons, 8 gallons, and 12 gallons - and a water faucet from which you can fill up these jugs. The only legal operations for you are: - Fill up a jug completely, either from the faucet or from another jug - Dump out a jug completely, either to the sink or to another jug. Explain how, in the fewest possible number of moves, you would measure out exactly 1 gallon of water. Note that, if you dump out a jug, you have to dump it out completely, That means it is illegal to, for example, fill up the 12-gallon jug and then dump it into both the 3-gallon jug and the 8-gallon to leave behind 1 gallon in the 12-gallon jug