# Project Euler - Problem 14
# http://projecteuler.net/index.php?section=problems&id=14
#
# The following iterative sequence is defined for the set of positive
# integers:
#
# n → n/2 (n is even)
# n → 3n + 1 (n is odd)
#
# Using the rule above and starting with 13, we generate the following
# sequence:
# 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
#
# It can be seen that this sequence (starting at 13 and finishing at 1)
# contains 10 terms. Although it has not been proved yet (Collatz
# Problem), it is thought that all starting numbers finish at 1.
#
# Which starting number, under one million, produces the longest chain?
#
# NOTE: Once the chain starts the terms are allowed to go above one
# million.
 
def next_in_seq(n)
  if n.even?
    n / 2
  else
    3 * n + 1
  end
end
 
def seq_length(start)
  n = start
  l = 1
 
  begin
    n = next_in_seq(n)
    l += 1
  end while n != 1
 
  l
end
 
max_length = 0
max_start  = 0
 
(1...1_000_000).each do |n|
  l = seq_length(n)
  if l > max_length
    max_length = l
    max_start = n
  end
end
 
puts "Answer: #{max_start}"