Complete the following exercises:
1) Write a function that uses recursion that converts a decimal number to octal (base 8). The function should accept a single integer and return a String containing the base 8 equivalent.
2) Write a recursive function that implement the following functions:
a) x0 = 1
xn = x * xn-1 if n > 0
b) x0 = 1
xn = (xn/2)2 if n > 0 and n is even
xn = x * (xn/2)2 if n> 0 and n is odd
3) How many multiplications will the functions you wrote in problem 2 perform when computing 319? 332?
How many recursive calls will the functions make when computing 319? 332?
4) Write a recursive function that implements the following function:
f(1) = 1; f(2) = 1; f(3) = 1; f(4) = 3; f(5) = 5
f(n) = f(n-1) + 3 * f(n-5) for all n > 5
Make the function as efficient as possible.
5) Compute f(n) for n = 6, 7, 12, 15