require 'prime'

class Integer
  def choose(k)
    factorial / (k.factorial * (self - k).factorial)
  end

  def divisors
    [].tap do |divisors|
      (1..Math.sqrt(self).to_i).each do |num|
        if self % num == 0
          divisors << num
          divisors << self / num
        end
      end
    end
  end

  def prime_factors
    self.prime_division.map(&:first)
  end

  def factorial
    (2..self).inject(:*)
  end

  def to_digit_list
    self.to_s.split('').map(&:to_i)
  end
end

module Euler

  class << self

    def from_digit_list(list)
      list.join('').to_i
    end

    def generate_pythagorean_triples(upper_bound)
      [].tap do |triples|
        (2..upper_bound).each do |a|
          (a..upper_bound).each do |b|
            c = Math.sqrt(a**2 + b**2)
            triples << [a, b, c.to_i] if c % 1 == 0
          end
        end
      end
    end

    def palindrome?(n)
      num = n.to_s
      (0..(num.length-1)/2).each do |i|
        if !(num[i] == num[num.length-1-i])
          return false
        end
      end
      true
    end

    def non_empty_subsets(list)
      (1..list.count).map { |x| list.combination(x).to_a }.flatten(1)
    end

    def powerset(list)
      (0..list.count).map { |x| list.combination(x).to_a }.flatten(1)
    end

  end
end