Ruby Euler #3

gistfile1.rb

#print the largest prime factor a number

#this is the most elegant way and work ok for large numbers 
require 'prime'  

Prime.prime_division(big_number).max()

# Not using Prime which has pretty bad performance before 1.9 
# and using tail recursion which is cool as fast 

number = ARGV.first.to_i

def generate(n, largest = 1)
  return largest if n == 1
  new_factor = (2..n).find {|f| n % f == 0} 
  generate(n / new_factor, new_factor)
end

factor = generate(number)

puts "Largest factor of #{number} is #{factor}"

# This one is for really big numbers 100+ digits
# That Sqrt theorem is very interesting, I don't fully get the math but I believe the PhDs :D
# http://math.stackexchange.com/questions/102755/greatest-prime-factor-of-n-is-less-than-square-root-of-n-proof/102760#102760
# in my tests the performance is much worst than the native ruby Prime class
# the idea from the regexp prime checker comes from here https://github.com/fxn/math-with-regexps/blob/master/one-liners.sh

number = "10000000000"

def isPrimeRegexp n
  "1" * n =~ /^1?$|^(11+?)\1+$/
end

Math.sqrt(number).to_i.downto(2) do |n|
  if isPrimeRegexp(n) && number%n ==0
    puts "Largest factor of #{number} is #{n}"
    break
  end
end