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to Perfect Numbers in the Ruby Track

Published at May 19 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.


For installation and learning resources, refer to the Ruby resources page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby perfect_numbers_test.rb

To include color from the command line:

ruby -r minitest/pride perfect_numbers_test.rb

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.rb

require 'minitest/autorun'
require_relative 'perfect_numbers'

class PerfectNumberTest < Minitest::Test
  def test_initialize_perfect_number
    assert_raises RuntimeError do
      PerfectNumber.classify(-1)
    end
  end

  def test_classify_deficient
    assert_equal 'deficient', PerfectNumber.classify(13)
  end

  def test_classify_perfect
    assert_equal 'perfect', PerfectNumber.classify(28)
  end

  def test_classify_abundant
    assert_equal 'abundant', PerfectNumber.classify(12)
  end
end
# frozen_string_literal: true

module PerfectNumber
  EQUAL = 0
  private_constant :EQUAL
  GREATER = 1
  private_constant :GREATER

  module_function

  def classify(number)
    raise RuntimeError unless number.positive?

    case aliquot_sum(number) <=> number
    when GREATER
      "abundant"
    when EQUAL
      "perfect"
    else
      "deficient"
    end
  end

  def aliquot_sum(number)
    (1...number)
      .each
      .with_object(number)
      .each_with_object([], &method(:add_factor))
      .sum
  end
  private_class_method :aliquot_sum

  def add_factor((candidate_factor, number), acc)
    acc << candidate_factor if factor?(candidate_factor, number)
  end
  private_class_method :add_factor

  def factor?(candidate_factor, number)
    number
      .modulo(candidate_factor)
      .zero?
  end
  private_class_method :factor?
end

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