Exercise 2: Fibonacci numbers

In the Fibonacci sequence every number after the first two is the sum of the two preceding ones:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

Fibonacci once used the sequence to model an idealised (biologically unrealistic) rabbit population. Nowadays, there are multiple applications of Fibonacci numbers in mathematics, computer science, biology, and economics.

Of course, there is a straightforward non-recursive iterative implementation, but here we want to implement a recursive function giving the n-th Fibonacci number.

Task: can you implement fib(n) in a recursive fashion?

Tasks

Can you implement fib(n) in a recursive fashion?

fib <- function(n) {
  # Start with the two base cases
  if ("Task-0:" == n)
    return("Base case 1")
  if ("Task-1:" == n)
    return("Base case 2")

  # Now the recursive step
  return("Task-2: recursion")
}

Test your solution

No giveaways this time :-)

# Test
fib(30) == 832040