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## to Palindrome Products in the Ruby Track

Published at Jan 02 2021 · 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``````
``````require 'matrix'

class Palindromes

def initialize (min_factor: 1, max_factor:)
@min_factor = min_factor
@max_factor = max_factor
@palindromes ||= generate
end

def generate
range = (@min_factor..@max_factor).to_a
Matrix
.build(range.count) { |i, j| range[i] * range[j] }
.flat_map { |x| x }
.uniq
.select(&:palindrome?)
end

def largest
Largest.new(@palindromes, @min_factor, @max_factor)
end

def smallest
Smallest.new(@palindromes, @min_factor, @max_factor)
end
end

class Integer
def palindrome?
c = to_s
c.reverse.eql? c
end

def factors(min, max)
factor_range = (min..max)

factor_candidates = factor_range.select do |i|
(self % i).zero?
end

factor_candidates = factor_candidates.inject([]) do |f, i|
f << i
f << self / i unless i == self / i
f
end

factor_candidates.sort
end

# https://stackoverflow.com/a/21165002/4341322
def paired_up_factors(min, max)
factor_range = (min..max)
a = factors(min, max)
l = a.length

factor_pairs = if (l % 2).zero?
a[0, l / 2].zip(a[-l / 2, l / 2].reverse)
else
a[0, l / 2].zip(a[-l / 2 + 1, l / 2].reverse) + [[a[l / 2], a[l / 2]]]
end

factor_pairs
.uniq
.select do |p|
factor_range.include? p and factor_range.include? p
end
end
end

class Factor
def initialize(palindromes, min_factor, max_factor)
@palindromes = palindromes
@min_factor = min_factor
@max_factor = max_factor
end

def factors
value.paired_up_factors(@min_factor, @max_factor)
end
end

class Largest < Factor
def value
@palindromes.max
end
end

class Smallest < Factor
def value
@palindromes.min
end
end``````

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