a$)$ Write a 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

b$)$Set up a recurrence relation for the number of weighings in the divide into$-$three

algorithm for the fake$-$coin problem and solve it for n $=3$k$.$