Project Euler 74

class P74

  def initialize
    @max = 1000000
    @factorials = make_factorial
    @sum_factorials = []
    @num_loops = []
  end

  def main
    each_loop_num.size
  end

  def each_loop_num
    ( 0 .. @max ).select do |base|
      @num_loops[base] = find_num_loop( base, tmp_array = [] )
      @num_loops[base] == 60
    end
  end

  def find_num_loop( base, stack )

    return @num_loops[base] if @num_loops[base]
    return 0 if stack.include?( base )

    find_num_loop( sum_factorial( base ), stack << base ) + 1
  end

  def sum_factorial( base )
    if @sum_factorials[base]
      @sum_factorials[base]
    else
      @sum_factorials[base] = base.to_s.each_char.inject(0)  { |sum, ch| sum + @factorials[ ch.to_i ] }
    end
  end

  def make_factorial
    ( 0..9 ).map do |n|
      ( 1 .. n ).inject(1) { |result, i| result * i }
    end
  end
end