#ProjectEuler/Python/Problem26.py
#Matthew Ellison
# Created: 07-29-19
#Modified: 08-02-19
#Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
#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
import Algorithms


__topNumber = 999	#The largest denominator to be checked


def Problem26():
	longestCycle = 0
	longestNumber = 1
	#Start with 1/2 and find out how long the longest cycle is by checking the remainders
	#Loop through every number from 2-999 and use it for the denominator
	for denominator in range(2, __topNumber):
		remainderList = []	#Holds the list of remainders
		endFound = False	#Holds whether we have found an end to the number (either a cycle or a 0 for remainder)
		cycleFound = False	#Holds whether a cycle was detected
		numerator = 1	#The numerator that will be divided
		while(not endFound):
			#Get the remainder after the division
			remainder = numerator % denominator
			#Check if the remainder is 0
			#If it is set the flag
			if(remainder == 0):
				endFound = True
			#Check if the remainder is in the list
			#If it is in the list, set the appropriate flags
			elif remainder in remainderList:
				endFound = True
				cycleFound = True
			#Else add it to the list
			else:
				remainderList.append(remainder)

			#Multiply the remainder by 10 to continue finding the next remainder
			numerator = remainder * 10
		#If a cycle was found check the size of the list against the largest cycle
		if(cycleFound):
			#If it is larger than the largest, set it as the new largest
			if(len(remainderList) > longestCycle):
				longestCycle = len(remainderList)
				longestNumber = denominator

	#Print the results
	print("The longest cycle is " + str(longestCycle) + " digits long")
	print("It is started with the number " + str(longestNumber))


#This calls the appropriate functions if the script is called stand along
if __name__ == "__main__":
	timer = Stopwatch()
	timer.start()
	Problem26()
	timer.stop()
	print("It took " + timer.getString() + " to run this algorithm")

""" Results:
The longest cycle is 982 digits long
It is started with the number 983
It took 182.704 milliseconds to run this algorithm
"""