Euler Project Problem #014

euler14.rb

# Solution to Project Euler's fourteenth problem
# http://projecteuler.net/index.php?section=problems&id=14
# Find the longest Collatz conjecture chain starting with a number under one million.
def find_lengths(ceiling=999999)
	numbers = (1..ceiling).to_a
	terms = Array.new(ceiling, 1)
	numbers.each_with_index do |n, i|
		if n%16==15 or n%16==7 or n%16==11 or n%16==9 or n%16==1 then #to improve the search speed, filter out all hexadecimal numbers not ending in 15, 7, 11, 9, or 1, in that order for all numbers % 16 greater than 64, the remainder is either 15, 7, 11, 9, or 1, with a greater frequency on the fifteens and then the sevens.
			until n == 1
				if n.even? then
					n = n/2
					terms[i] +=1
				else
					n = 3*n+1
					terms[i] +=1
				end
			end
		end
	end
	return terms
end
def index_of_longest(lengths)
	longest, index = 0, -1
	lengths.each_with_index do |l, i| 
		if longest < l then longest = l; index = i; p index + 1 end
	end
	return index
end

a = Time.new
lengths = find_lengths
index = index_of_longest(lengths)
p index + 1
b = Time.new - a
p b