Fibonacci Iterator
10 Points
interfaces
Instructions
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, ...
Elements are defined by these rules:
a₁ = a₂ = 1
aₙ = aₙ₋₁ + aₙ₋₂For example
- the third element would be
a₃ = a₁ + a₂ = 1 + 1 = 2 - the fourth would be
a₄ = a₂ + a₃ = 1 + 2 = 3 - and so on.
Note
Some sources define the first elements as a₀ = 0 and a₁ = 1.
However in the context of this exercise, we define the sequence without a 0th element.
1. Define the Fiberator type
Define the Fiberator type with a constructor that takes an integer n as the argument.
julia> Fiberator(10)
Fiberator(10)2. Implement iterate method(s)
Define both of the necessary iterate methods.
- The single argument method should take a
Fiberatortype. - The two-argument method should take a
Fiberatortype and a state (with type of your choosing).
Iteration should terminate after the first n Fibonacci numbers.
julia> for a in Fiberator(10)
println(a)
end
1
1
2
3
5
8
13
21
34
55Note
You can ignore integer overflow in your implementation.
The tests will only use n small enough to not cause overflow problems.
3. Make collect work
Functionality like collect and comprehensions require more information than just iteration.
Define the appropriate length method to make these work.
julia> collect(Fiberator(10))
10-element Vector{Any}:
1
1
2
3
5
8
13
21
34
554. Enable type inference
It is more performant/efficient to help Julia infer the type of the iterator.
Define the appropriate eltype method to allow for this.
julia> collect(Fiberator(10))
10-element Vector{Int64}:
1
1
2
3
5
8
13
21
34
55Fibonacci Iterator
10 Points
interfaces
Instructions
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, ...
Elements are defined by these rules:
a₁ = a₂ = 1
aₙ = aₙ₋₁ + aₙ₋₂For example
- the third element would be
a₃ = a₁ + a₂ = 1 + 1 = 2 - the fourth would be
a₄ = a₂ + a₃ = 1 + 2 = 3 - and so on.
Note
Some sources define the first elements as a₀ = 0 and a₁ = 1.
However in the context of this exercise, we define the sequence without a 0th element.
1. Define the Fiberator type
Define the Fiberator type with a constructor that takes an integer n as the argument.
julia> Fiberator(10)
Fiberator(10)2. Implement iterate method(s)
Define both of the necessary iterate methods.
- The single argument method should take a
Fiberatortype. - The two-argument method should take a
Fiberatortype and a state (with type of your choosing).
Iteration should terminate after the first n Fibonacci numbers.
julia> for a in Fiberator(10)
println(a)
end
1
1
2
3
5
8
13
21
34
55Note
You can ignore integer overflow in your implementation.
The tests will only use n small enough to not cause overflow problems.
3. Make collect work
Functionality like collect and comprehensions require more information than just iteration.
Define the appropriate length method to make these work.
julia> collect(Fiberator(10))
10-element Vector{Any}:
1
1
2
3
5
8
13
21
34
554. Enable type inference
It is more performant/efficient to help Julia infer the type of the iterator.
Define the appropriate eltype method to allow for this.
julia> collect(Fiberator(10))
10-element Vector{Int64}:
1
1
2
3
5
8
13
21
34
55