euler12b.rb

# http://johnnycoder.com/blog/2010/07/05/project-euler-12-ruby/

# Euler 12
# http://projecteuler.net/index.php?section=problems&id=12
# The sequence of triangle numbers is generated by adding 
# the natural numbers. So the 7th triangle number would be 
# 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms 
# would be:
# 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
# Let us list the factors of the first seven triangle 
# numbers:
#  1: 1
#  3: 1,3
#  6: 1,2,3,6
# 10: 1,2,5,10
# 15: 1,3,5,15
# 21: 1,3,7,21
# 28: 1,2,4,7,14,28
# We can see that 28 is the first triangle number to have 
# over five divisors. What is the value of the first 
# triangle number to have over five hundred divisors?
require 'mathn'
 
timer_start = Time.now
 
# http://mathschallenge.net/index.php?section=faq
#    &ref=number/number_of_divisors
# If n=48, then prime factors are 3^1 2^4, and divisor 
# count is calculated by adding 1 to each power and then
# multiplying the results together. 
# For 48, we have (1+1)(4+1) = 10
class Integer
  def divisor_count
    sum = 1
    # prime_division return two dimensional array.
    # for 48, [3,1], [2,4] is the result
    self.prime_division.each do |x| 
      sum *= (x[1] + 1)  
    end
    sum
  end
end
 
# Define the counter and first triangle number
i, triangle_number = 1, 1
while(triangle_number.divisor_count <= 500)  
  i += 1
  triangle_number += i  
end 
 
puts triangle_number
 
puts "Elapsed Time: #{(Time.now - timer_start)*1000} milliseconds"