#ProjectEuler/Python/Problem14.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
"""
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Which starting number, under one million, produces the longest chain?
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
	Copyright (C) 2019  Matthew Ellison

	This program is free software: you can redistribute it and/or modify
	it under the terms of the GNU Lesser General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU Lesser General Public License for more details.

	You should have received a copy of the GNU Lesser General Public License
	along with this program.  If not, see <https://www.gnu.org/licenses/>.
"""


from Stopwatch import Stopwatch

__topNum = 1000000	#The largest number that you will check against the chain


#This function returns a list of numbers created by the chain
def getChain(startNum: int) -> list:
	#Put the starting number in the list
	chain = [startNum]

	#Starting with the current number perform the correct opperations on the numbers until that number reaches 1
	while(startNum > 1):
		#Determine if the number is odd or even and perform the correct operation and add the new number to the list
		if((startNum % 2) == 0):
			startNum /= 2
		else:
			startNum = (3 * startNum) + 1
		#Add the new number to the chain
		chain.append(startNum)

	#Return the list
	return chain

def Problem14():
	#Setup your variables
	largestChain = []	#Holds the longest chain of numbers

	#Start at 1 and run up to 1000000, checking how long the chain is when started with each number
	for startingNumber in range(1, __topNum):
		currentChain = getChain(startingNumber)	#Get the chain
		#If the new chain is longer than the current longest chain replace it
		if(len(currentChain) > len(largestChain)):
			largestChain = currentChain.copy()

	#Print the results
	print("The longest chain with a starting number < " + str(__topNum) + " is " + str(largestChain[0]) + " with a length of " + str(len(largestChain)))


#If you are running this file, automatically start the correct function
if __name__ == "__main__":
	timer = Stopwatch()	#Determines the algorithm's run time
	timer.start()	#Start the timer
	Problem14()		#Call the function that answers the question
	timer.stop()	#Stop the timer
	#Print the results of the timer
	print("It took " + timer.getString() + " to run this algorithm")

"""Results:
The longest chain with a starting number < 1000000 is 837799 with a length of 525
It took 28.893 seconds to run this algorithm
"""