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Fibonacci Iterative vs Recursive

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Your question is Fibonacci Iterative vs Recursive. Start with the requirements on the right.

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Problem

Washington Staffing's coding evaluation needs a function that generates the Fibonacci series up to a specified limit. Implement both iterative and recursive approaches, returning every Fibonacci value less than or equal to the limit.

Formal Specification

Implement fibonacci_series(n, approach), where n is a non-negative integer and approach is either "iterative" or "recursive". Use the Fibonacci definition F(0) = 0, F(1) = 1, and F(k) = F(k - 1) + F(k - 2). Return a list beginning with 0, containing values in ascending sequence order, and excluding values greater than n.

The recursive implementation should avoid recomputing the same sequence values through exponential branching. Raise ValueError if approach is not one of the two supported strings.

Constraints

  • 0 <= n <= 10^9
  • approach is either "iterative" or "recursive"
  • Return all and only Fibonacci values less than or equal to n
  • The recursive approach must avoid exponential repeated computation

Function Signature

def fibonacci_series(n, approach):
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