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Problem26.py

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+#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
+"""