utils.rb

class Utils

  def Utils.get_primes n
    max_non_prime = Integer(Math.sqrt(n))
    primes = Array(2..n)
    primes.each do |p|
      if p > max_non_prime
        break
      end
      primes.delete_if { |x| x != p && x % p == 0 }
    end
    primes
  end

  def Utils.get_factors n
    max_factor = Math.sqrt(n)
    initial_factors = (1..max_factor).select { |x| n % x == 0 }
    factors = initial_factors.clone
    initial_factors.each do |x|
      factors.push(n / x)
    end
    factors.sort
  end

  def Utils.factorial n
    if n <= 1
      return 1
    else
      return n * factorial(n - 1)
    end
  end

  def Utils.is_prime? n
    n > 1 && !(2..n - 1).any? { |x| n % x == 0 }
  end

  def Utils.get_nth_prime n
    (1..Infinity).lazy_select { |x| Utils.is_prime? x }.take(n).last
  end

  def Utils.get_pandigitals first, last
    (first..last).to_a.permutation(last - first + 1).to_a.select{|x| x[0] != 0}.collect{|x| Integer(x.join)}.sort
  end

  def Utils.strip_leading_zero x
    x.sub(/^0/, "")
  end

  def Utils.strip_leading_zeroes x
    x.sub(/^0+/, "")
  end

  def Utils.is_triangle_number n
    (-1 + Math.sqrt(1 + 8 * n)) / 2 % 1 == 0
  end

  def Utils.is_pentagonal_number n
    (1 + Math.sqrt(1 + 24 * n)) / 6 % 1 == 0
  end
  
  def Utils.get_pentagonal_number n
    n * (3 * n - 1) / 2
  end
  
  def Utils.get_reverse n
    Integer(strip_leading_zeroes(n.to_s.reverse))
  end
  
  def Utils.is_palindrome n
    n.to_s == n.to_s.reverse
  end
end

module Enumerable
  def lazy_select
    Enumerator.new do |yielder|
      each do |obj|
        yielder.yield(obj) if yield(obj)
      end
    end
  end
end

module Constants
  INFINITY = 1.0 / 0
end