Implement a program that calculates the following function based on a value n entered by a user. Write a recursive function that computes n $*$ n$/3*$ n$/9*$ n$/27*$ n$/81...$ where n is a nonnegative integer, n$/$x is integer division and the quotient is always a multiple of $3$ from the previous quotient. The sequence repeats as long as n$/$x $>0.$ For example:

for n$=27$ : $27*9*3*1=729$

for n$=8$ : $8*2=16$

for n$=100$: $100*33*11*3*1=108900$

The function prototype should be: int recursive$($unsigned int n$)$;

Sample run $1$:

Input: $27$

Result: $729$

Sample run $2$:

Input: $1$

Result: $1$

Solution

Note: The following code optimizes the solution to avoid any final recursive call that multiplies the result by $1.$

int recursive$($unsigned int n$)$

$\{$

if

$($

n $<=$

$3)$

$\{$

return $1$

;

$\}$

return

;

$\}$