How to write 2**n - 1 as a recursive function?

Question

I need a function that takes n and returns 2ⁿ - 1 . It sounds simple enough, but the function has to be recursive. So far I have just 2ⁿ:

def required_steps(n):     if n == 0:         return 1     return 2 * req_steps(n-1) 

The exercise states: "You can assume that the parameter n is always a positive integer and greater than 0"

Answer 1

2**n -1 is also 1+2+4+...+2^n-1 which can made into a single recursive function (without the second one to subtract 1 from the power of 2).

Hint: 1+2*(1+2*(...))

Solution below, don't look if you want to try the hint first.

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This works if n is guaranteed to be greater than zero (as was actually promised in the problem statement):

def required_steps(n):     if n == 1: # changed because we need one less going down         return 1     return 1 + 2 * required_steps(n-1) 

A more robust version would handle zero and negative values too:

def required_steps(n):     if n < 0:         raise ValueError("n must be non-negative")     if n == 0:         return 0     return 1 + 2 * required_steps(n-1) 

(Adding a check for non-integers is left as an exercise.)