instructions.md

In this exercise you're going to write an iterator that iterates through the first n elements of the Fibonacci sequence.

Fibonacci sequence

The Fibonacci sequence is a sequence of numbers, where every element of the sequence is calculated by adding the two numbers that come before it. You can think of a sequence as a list of numbers in a certain order. The first two numbers of the sequence are set to $1$.

The start of the sequence is $1,~1,~2,~3,~5,~8,~13,~21,~34,~55,89,\dots$

In maths notation:

$$ a_1 = a_2 = 1\\ a_n = a_{n-1} + a_{n-2} $$

For example, the third element would be $a_3 = a_1 + a_2 = 1 + 1 = 2$, the fourth would be $a_4 = a_2 + a_3 = 1 + 2 = 3$, and so on.

!!! note Some sources define the first elements as $a_0 = 0$ and $a_1 = 1$. However in the context of this exercise, we define the sequence without a $0$-th element.

1. Define a Fib type with a constructor that takes n as argument

julia> Fib(10)
Fib(10)

2. Implement iterate methods

julia> for a in Fib(10)
           println(a)
       end
1
1
2
3
5
8
13
21
34
55

You can ignore integer overflow in your implementation. The tests will only test for n small enough to not cause overflow problems.

3. Define the optional methods that make collect work

julia> collect(Fib(10))
10-element Array{Any,1}:
  1
  1
  2
  3
  5
  8
 13
 21
 34
 55

4. Define the optional methods that are necessary for Julia to infer the type of the elements of the iterator

julia> collect(Fib(10))
10-element Array{Int64,1}:
  1
  1
  2
  3
  5
  8
 13
 21
 34
 55