Lucas Numbers

Mix.install([
  {:jason, "~> 1.4"},
  {:kino, "~> 0.8.0", override: true},
  {:youtube, github: "brooklinjazz/youtube"},
  {:hidden_cell, github: "brooklinjazz/hidden_cell"}
])

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Lucas Numbers

This exercise was inspired by Exercism.io. It’s a fantastic platform for learning many languages including Elixir.

Lucas numbers are much like the fibonacci sequence where $fib(n) = fib(n - 1) + fib(n - 2)$ Numberphile has a great video that explains them in further detail,

YouTube.new("https://www.youtube.com/watch?v=PeUbRXnbmms")

Unlike Fibonacci, they start with a different initial 2 numbers.

Other than starting with two different numbers, the formula for a lucas number is still $L(n)=L(n-1)+L(n - 2)$.

In addition to generating the $nth$ lucas number, you’re also going to generate a sequence of lucas numbers.

Example Solution

defmodule Lucas do

  def number(0), do: 2
  def number(1), do: 1

  def number(n) do
    number(n - 1) + number(n - 2)
  end

  def sequence(length) do
    Enum.map(1..length, &number(&1 - 1)
  end
end

Lucas.sequence(10)

To avoid recomputing lucas numbers over and over, we can implement sequence/1 using Enum.reduce/3 instead.

def sequence(length) when length == 1 do
  [2]
end

def sequence(length) when length == 2 do
  [2, 1]
end

def sequence(length) when length > 2 do
  {_, _, list} =
    Enum.reduce(2..length-1, {2, 1, [1, 2]}, fn each, {prev2, prev1, list} ->
      current = prev2 + prev1
      {prev1, current, [current | list]}
    end)

  Enum.reverse(list)
end

Implement the Lucas module as documented.

defmodule Lucas do
  @doc """
  return the nth lucas number.

  ## Examples

    iex> Lucas.number(0)
    2

    iex> Lucas.number(1)
    1

    iex> Lucas.number(2)
    3

    iex> Lucas.number(3)
    4

    iex> Lucas.number(4)
    7
    
    iex> Lucas.number(5)
    11

    iex> Lucas.number(6)
    18

    iex> Lucas.number(20)
    15127
  """
  def number(n) do
  end

  @doc """
  Generate a list of lucas numbers with the given length.

  ## Examples

    iex> Lucas.sequence(1)
    [2]

    iex> Lucas.sequence(2)
    [2, 1]

    iex> Lucas.sequence(3)
    [2, 1, 3]

    iex> Lucas.sequence(4)
    [2, 1, 3, 4]

    iex> Lucas.sequence(10)
    [2, 1, 3, 4, 7, 11, 18, 29, 47, 76]
  """

  def sequence(length) do
  end
end

Mark As Completed

file_name = Path.basename(Regex.replace(~r/#.+/, __ENV__.file, ""), ".livemd")

save_name =
  case Path.basename(__DIR__) do
    "reading" -> "lucas_numbers_reading"
    "exercises" -> "lucas_numbers_exercise"
  end

progress_path = __DIR__ <> "/../progress.json"
existing_progress = File.read!(progress_path) |> Jason.decode!()

default = Map.get(existing_progress, save_name, false)

form =
  Kino.Control.form(
    [
      completed: input = Kino.Input.checkbox("Mark As Completed", default: default)
    ],
    report_changes: true
  )

Task.async(fn ->
  for %{data: %{completed: completed}} <- Kino.Control.stream(form) do
    File.write!(
      progress_path,
      Jason.encode!(Map.put(existing_progress, save_name, completed), pretty: true)
    )
  end
end)

form

Commit Your Progress

Run the following in your command line from the curriculum folder to track and save your progress in a Git commit. Ensure that you do not already have undesired or unrelated changes by running git status or by checking the source control tab in Visual Studio Code.

$ git checkout -b lucas-numbers-exercise
$ git add .
$ git commit -m "finish lucas numbers exercise"
$ git push origin lucas-numbers-exercise

Create a pull request from your lucas-numbers-exercise branch to your solutions branch. Please do not create a pull request to the DockYard Academy repository as this will spam our PR tracker.

DockYard Academy Students Only:

Notify your teacher by including @BrooklinJazz in your PR description to get feedback. You (or your teacher) may merge your PR into your solutions branch after review.

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