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to Palindrome Products in the Ruby Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

Detect palindrome products in a given range.

A palindromic number is a number that remains the same when its digits are reversed. For example, 121 is a palindromic number but 112 is not.

Given a range of numbers, find the largest and smallest palindromes which are products of numbers within that range.

Your solution should return the largest and smallest palindromes, along with the factors of each within the range. If the largest or smallest palindrome has more than one pair of factors within the range, then return all the pairs.

Example 1

Given the range [1, 9] (both inclusive)...

And given the list of all possible products within this range: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 15, 21, 24, 27, 20, 28, 32, 36, 25, 30, 35, 40, 45, 42, 48, 54, 49, 56, 63, 64, 72, 81]

The palindrome products are all single digit numbers (in this case): [1, 2, 3, 4, 5, 6, 7, 8, 9]

The smallest palindrome product is 1. Its factors are (1, 1). The largest palindrome product is 9. Its factors are (1, 9) and (3, 3).

Example 2

Given the range [10, 99] (both inclusive)...

The smallest palindrome product is 121. Its factors are (11, 11). The largest palindrome product is 9009. Its factors are (91, 99).


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 palindrome_products_test.rb

To include color from the command line:

ruby -r minitest/pride palindrome_products_test.rb

Source

Problem 4 at Project Euler http://projecteuler.net/problem=4

Submitting Incomplete Solutions

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

palindrome_products_test.rb

require 'minitest/autorun'
require_relative 'palindrome_products'

class PalindromesTest < Minitest::Test
  def test_largest_palindrome_from_single_digit_factors
    palindromes = Palindromes.new(max_factor: 9)
    palindromes.generate
    largest = palindromes.largest
    assert_equal 9, largest.value
    assert_includes [[[3, 3], [1, 9]], [[1, 9], [3, 3]]], largest.factors
  end

  def test_largest_palindrome_from_double_digit_factors
    skip
    palindromes = Palindromes.new(max_factor: 99, min_factor: 10)
    palindromes.generate
    largest = palindromes.largest
    assert_equal 9009, largest.value
    assert_equal [[91, 99]], largest.factors
  end

  def test_smallest_palindrome_from_double_digit_factors
    skip
    palindromes = Palindromes.new(max_factor: 99, min_factor: 10)
    palindromes.generate
    smallest = palindromes.smallest
    assert_equal 121, smallest.value
    assert_equal [[11, 11]], smallest.factors
  end

  def test_largest_palindrome_from_triple_digit_factors
    skip
    palindromes = Palindromes.new(max_factor: 999, min_factor: 100)
    palindromes.generate
    largest = palindromes.largest
    assert_equal 906_609, largest.value
    assert_equal [[913, 993]], largest.factors
  end

  def test_smallest_palindrome_from_triple_digit_factors
    skip
    palindromes = Palindromes.new(max_factor: 999, min_factor: 100)
    palindromes.generate
    smallest = palindromes.smallest
    assert_equal 10_201, smallest.value
    assert_equal [[101, 101]], smallest.factors
  end
end
class Palindromes
  def initialize(min_factor: 0, max_factor:)
    @range = (min_factor..max_factor).to_a
  end

  def generate
    @products = generate_palindrome_products
  end

  def largest
    @largest ||= palindrome(:max)
  end

  def smallest
    @smallest ||= palindrome(:min)
  end

  private

  attr_reader :range, :products

  def generate_palindrome_products
    range
      .product(range)
      .map { |x, y| x * y }
      .uniq
      .select { |product| palindrome?(product) }
  end

  def palindrome?(number)
    number == number.to_s.reverse.to_i
  end

  def palindrome(method)
    Palindrome.new(range, products.public_send(method))
  end

  class Palindrome
    attr_reader :factors, :value

    def initialize(range, value)
      @value = value
      @factors = generate_factors(range)
    end

    private

    def generate_factors(range)
      range
        .repeated_combination(2)
        .to_a
        .select { |x, y| x * y == value }
    end
  end
  private_constant :Palindrome
end

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