Give a decision tree lower bound for the (worst case) number of weighings that must be performed by any algorithm solving this problem. b. Design an algorithm that solves this problem with (worst case) number of weighings equal to the lower bound you found in (a). Present your algorithm by drawing a decision tree, rather than pseudo-code. c. Alter the problem slightly to allow the possibility that all 12 bars are pure gold. Thus there is one additional possible verdict: "all gold". Make a minor change to your algorithm in part (b) so that it gives a correct answer to this more general problem.