collatz.rb

class Collatz
  def initialize(min, max)
    @min = min
    @max = max
    @cache = Array.new(max, 0)
  end

  def longest_length
    max_n, max_length = 0, 0

    (@min..@max).each do |n|
      length = length_for(n)

      if length > max_length
        max_n, max_length = n, length
      end
    end

    [max_n, max_length]
  end

  private def length_for(n)
    @cache[n - 1] = next_for(n)
  end

  private def next_for(n)
    return 1 if n == 1
    return @cache[n - 1] if n <= @max && @cache[n - 1] != 0

    if n.even?
      1 + next_for(n / 2)
    else
      1 + next_for(n * 3 + 1)
    end
  end
end

collatz = Collatz.new(1, 1_000_000)
max_n, max_length = collatz.longest_length

puts "Number with longest Collatz sequence: #{max_n}"
puts "Longest sequence length: #{max_length}"