In writing pseudocode for the divide$-$into$-$three algorithm for the fake$-$coin problem, you do all these except.

a$.$ Make sure that your algorithm handles properly all values of n$,$ not only those that are multiples of $3.$

b$.$ You must take a look at the time efficiency class of Russian peasant multiplication

c$.$ 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 $=3$k$.$

d$.$ 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$.$