Complete the following exercises:
1) prepare 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) prepare a recursive function that implement the following functions:
a) x^{0} = 1
x^{n }= x * x^{n-1} if n > 0
b) x0 = 1
x^{n }= (x^{n/2})^{2} if n > 0 and n is even
x^{n} = x * (x^{n/2})^{2} if n> 0 and n is odd
3) How many multiplications will the functions you wrote in problem 2 perform when computing 3^{19}? 3^{32}?
How many recursive calls will the functions make when computing 3^{19}? 3^{32}?
4) prepare 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