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to Perfect Numbers in the Elixir Track

Published at Aug 27 2019 · 0 comments
Instructions
Test suite
Solution

Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.

The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their aliquot sum. The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9

  • Perfect: aliquot sum = number
    • 6 is a perfect number because (1 + 2 + 3) = 6
    • 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
  • Abundant: aliquot sum > number
    • 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
    • 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
  • Deficient: aliquot sum < number
    • 8 is a deficient number because (1 + 2 + 4) = 7
    • Prime numbers are deficient

Implement a way to determine whether a given number is perfect. Depending on your language track, you may also need to implement a way to determine whether a given number is abundant or deficient.

Running tests

Execute the tests with:

$ mix test

Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant @tag :pending with a # symbol.

For example:

# @tag :pending
test "shouting" do
  assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end

Or, you can enable all the tests by commenting out the ExUnit.configure line in the test suite.

# ExUnit.configure exclude: :pending, trace: true

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

perfect_numbers_test.exs

defmodule PerfectNumbersTest do
  use ExUnit.Case

  describe "Perfect numbers" do
    # @tag :pending
    test "Smallest perfect number is classified correctly" do
      assert PerfectNumbers.classify(6) == {:ok, :perfect}
    end

    @tag :pending
    test "Medium perfect number is classified correctly" do
      assert PerfectNumbers.classify(28) == {:ok, :perfect}
    end

    @tag :pending
    test "Large perfect number is classified correctly" do
      assert PerfectNumbers.classify(33_550_336) == {:ok, :perfect}
    end
  end

  describe "Abundant numbers" do
    @tag :pending
    test "Smallest abundant number is classified correctly" do
      assert PerfectNumbers.classify(12) == {:ok, :abundant}
    end

    @tag :pending
    test "Medium abundant number is classified correctly" do
      assert PerfectNumbers.classify(30) == {:ok, :abundant}
    end

    @tag :pending
    test "Large abundant number is classified correctly" do
      assert PerfectNumbers.classify(33_550_335) == {:ok, :abundant}
    end
  end

  describe "Deficient numbers" do
    @tag :pending
    test "Smallest prime deficient number is classified correctly" do
      assert PerfectNumbers.classify(2) == {:ok, :deficient}
    end

    @tag :pending
    test "Smallest non-prime deficient number is classified correctly" do
      assert PerfectNumbers.classify(4) == {:ok, :deficient}
    end

    @tag :pending
    test "Medium deficient number is classified correctly" do
      assert PerfectNumbers.classify(32) == {:ok, :deficient}
    end

    @tag :pending
    test "Large deficient number is classified correctly" do
      assert PerfectNumbers.classify(33_550_337) == {:ok, :deficient}
    end

    @tag :pending
    test "Edge case (no factors other than itself) is classified correctly" do
      assert PerfectNumbers.classify(1) == {:ok, :deficient}
    end
  end

  describe "Invalid inputs" do
    @tag :pending
    test "Zero is rejected (not a natural number)" do
      assert PerfectNumbers.classify(0) ==
               {:error, "Classification is only possible for natural numbers."}
    end

    @tag :pending
    test "Negative integer is rejected (not a natural number)" do
      assert PerfectNumbers.classify(-1) ==
               {:error, "Classification is only possible for natural numbers."}
    end
  end
end

test_helper.exs

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule PerfectNumbers do
  defguardp non_natural_number?(number) when number < 1

  @doc """
  Determine the aliquot sum of the given `number`, by summing all the factors
  of `number`, aside from `number` itself.

  Based on this sum, classify the number as:

  :perfect if the aliquot sum is equal to `number`
  :abundant if the aliquot sum is greater than `number`
  :deficient if the aliquot sum is less than `number`
  """
  @spec classify(number :: integer) :: {:ok, atom} | {:error, String.t()}

  def classify(number) when non_natural_number?(number) do
    {:error, "Classification is only possible for natural numbers."}
  end

  def classify(1), do: {:ok, :deficient}

  def classify(number) do
    aliquot_sum = aliquot_sum(number)

    classification =
      cond do
        aliquot_sum > number ->
          :abundant

        aliquot_sum == number ->
          :perfect

        true ->
          :deficient
      end

    {:ok, classification}
  end

  defp aliquot_sum(number) do
    1..(number - 1)
    |> Enum.reduce(0, &add_factor(number, &1, &2))
  end

  defp add_factor(number, candidate_factor, acc) do
    if factor?(number, candidate_factor) do
      acc + candidate_factor
    else
      acc
    end
  end

  defp factor?(number, candidate_factor) do
    rem(number, candidate_factor) == 0
  end
end

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