i just need help with part c$)$

The problem of finding the heaviest coin:

$($a$)$ Suppose that we have $9$ identical$-$looking coins numbered from $1$ to $9$ and only one of

the coins is heavier than the others. Also, suppose that you have one balance scale and are

allowed only $2$ weighings. Provide a method for finding the heavier coin.

$($b$)$ Suppose we now have n coins and only one is heavier than others. Also suppose that n

is a power of $3$ and you are allowed for logn$3($log base $3,$ of n$)$ wighings to determine the

heavier coin. Discuss an algorithm to solve this problem.

$($c$)$ Implement the algorithm and analyze its complexity.