Longest Collatz Sequence with comments.

collatz.rb

# n → n/2 (n is even)
# n → 3n + 1 (n is odd)	
# Write a method to determine a number's collatz sequence.
# Find the number (1 to 1,000,000) with the longest sequence.


# collatz method defined below with (n) as an argument.

def collatz(n)

	# longest_sequence will serve as an empty array to 
	# store the longest collatz sequence. 

	longest_sequence = []

	# next, we loop through each number (1 through 1,000,000). 
	# sequence = [x] <-- this means that for 1, 2, 3, and so on
	# each number '[x]' will be run through the loop, and the resulting 
	# collatz values of that number will be pushed into the 
	# sequence array, UNTIL the sequence ends at 1.  

	(1..n).each do |x|
		sequence = [x]

		until sequence.last === 1
			if sequence.last.even?
				sequence.push(sequence.last / 2)
			else
				sequence.push(sequence.last * 3 + 1)
			end
		end # <-- until statement ends here.  

		# now we check to see how long the sequence is.  
		# if it's longer than the previous sequence, 
		# this block will push it into the 
		# 'longest_sequence' array.

		if sequence.length > longest_sequence.length
			longest_sequence = sequence
		end
	end

# then, we print the values of the longest sequence.
p "#{longest_sequence[0]} produces the longest Collatz sequence, with a length of #{longest_sequence.length}!"

end

# last, we call the method with an argument of 1,000,000 
# which is the max number required for the lesson. 

collatz(1000000)