Question

Use Ocaml language writing a bunch of simple functions in a file called warmups.ml. Write these functions in a pure functional style only: no assignment statements, no explicit loops, and no arrays!

Write a function to compute fibonacci numbers (in the sequence 0, 1, 1, 2, 3, 5, ... where each number is the sum of the previous two numbers on the list). Use pattern matching but no if/then/else statements. Use a tail recursive solution to make sure the function doesn't take exponential time. Call your function fibonacci. Test it by computing the 44th fibonacci number. What happens when you try to compute larger fibonacci numbers? Why? Indicate the answer in a comment in your code.

Answer 1

let fib n =
  let rec fib_aux n a b =
    match n with
    | 0 -> a
    | _ -> fib_aux (n-1) b (a+b)
  in
  fib_aux n 0 1

fib(44)

below is image for above code and out:

# let fib n # let rec fib-aux n a b match n with 0- a I _-fib_aux (n-1) b (a+b) #in tfib aux n 15 val fib : int-> int = <fun» # fib(3);; -:int 2 # fib(4);; # fib(5);; -:int = 5 # fib(44);; - : int = 701408733