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
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:
To include color from the command line:
ruby -r minitest/pride perfect_numbers_test.rb
Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
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
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.