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85 lines
2.9 KiB
Python
85 lines
2.9 KiB
Python
#ProjectEuler/Python/Problem26.py
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#Matthew Ellison
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# Created: 07-29-19
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#Modified: 08-02-19
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#Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
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#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
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"""
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Copyright (C) 2019 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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"""
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from Stopwatch import Stopwatch
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import Algorithms
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__topNumber = 999 #The largest denominator to be checked
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def Problem26():
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longestCycle = 0
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longestNumber = 1
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#Start with 1/2 and find out how long the longest cycle is by checking the remainders
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#Loop through every number from 2-999 and use it for the denominator
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for denominator in range(2, __topNumber):
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remainderList = [] #Holds the list of remainders
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endFound = False #Holds whether we have found an end to the number (either a cycle or a 0 for remainder)
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cycleFound = False #Holds whether a cycle was detected
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numerator = 1 #The numerator that will be divided
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while(not endFound):
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#Get the remainder after the division
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remainder = numerator % denominator
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#Check if the remainder is 0
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#If it is set the flag
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if(remainder == 0):
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endFound = True
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#Check if the remainder is in the list
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#If it is in the list, set the appropriate flags
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elif remainder in remainderList:
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endFound = True
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cycleFound = True
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#Else add it to the list
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else:
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remainderList.append(remainder)
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#Multiply the remainder by 10 to continue finding the next remainder
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numerator = remainder * 10
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#If a cycle was found check the size of the list against the largest cycle
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if(cycleFound):
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#If it is larger than the largest, set it as the new largest
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if(len(remainderList) > longestCycle):
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longestCycle = len(remainderList)
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longestNumber = denominator
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#Print the results
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print("The longest cycle is " + str(longestCycle) + " digits long")
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print("It is started with the number " + str(longestNumber))
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#This calls the appropriate functions if the script is called stand along
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if __name__ == "__main__":
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timer = Stopwatch()
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timer.start()
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Problem26()
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timer.stop()
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print("It took " + timer.getString() + " to run this algorithm")
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""" Results:
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The longest cycle is 982 digits long
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It is started with the number 983
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It took 182.704 milliseconds to run this algorithm
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"""
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