a. Write pseudocode for the divide-into-three algorithm for the fake-coin problem. Make sure that your algorithm handles properly all values of n, not only those that are multiples of 3.
b. Set up a recurrence relation for the number of weighings in the divide-intothree algorithm for the fake-coin problem and solve it for n = 3k.
c. For large values of n, about how many times faster is this algorithm than the one based on dividing coins into two piles? Your answer should not depend on n.
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