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ProjectEulerPython/Problem26.py

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2.9 KiB
Python

#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
"""