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ProjectEulerPython/Problems/Problem26.py

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#ProjectEuler/Python/Problem26.py
#Matthew Ellison
# Created: 07-29-19
#Modified: 07-19-20
#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) 2020 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 Problems.Problem import Problem
from Stopwatch import Stopwatch
from Unsolved import Unsolved
import Algorithms
class Problem26(Problem):
#Variables
__topNumber = 999 #The largest denominator to be checked
#Function
#Constructor
def __init__(self):
super().__init__("Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.")
self.longestCycle = 0
self.longestNumber = 0
#Operational function
#Solve the problem
def solve(self):
#If the problem has already been solved do nothing and end the function
if(self.solved):
return
#Start the timer
self.timer.start()
#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, self.__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) > self.longestCycle):
self.longestCycle = len(remainderList)
self.longestNumber = denominator
#Stop the timer
self.timer.stop()
#Print the results
self.result = "The longest cycle is " + str(self.longestCycle) + " digits long" + "\nIt is started with the number " + str(self.longestNumber)
#Throw a flag to show the problem is solved
self.solved = True
#Reset the problem so it can be run again
def reset(self):
super().reset()
self.longestCycle = 0
self.longestNumber = 0
#Gets
#Returns the length of the longest cycle
def getLongestCycle(self) -> int:
#If the problem hasn't been solved throw an exception
if(not self.solved):
raise Unsolved("You must solve the problem before can you see the length of the longest cycle")
return self.longestCycle
#Returns the denominator that starts the longest cycle
def getLongestNumber(self) -> int:
#If the problem hasn't been solved throw an exception
if(not self.solved):
raise Unsolved("You must solve the problem before can you see the denominaotr that started the cycle")
return self.longestNumber
#This calls the appropriate functions if the script is called stand along
if __name__ == "__main__":
problem = Problem26()
print(problem.getDescription()) #Print the description
problem.solve() #Call the function that answers the problem
#Print the results
print(problem.getResult())
print("It took " + problem.getTime() + " to solve 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
"""