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81 lines
2.9 KiB
Python
81 lines
2.9 KiB
Python
#ProjectEuler/Python/Problem14.py
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#Matthew Ellison
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# Created: 01-31-19
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#Modified: 03-28-19
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"""
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The following iterative sequence is defined for the set of positive integers:
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n → n/2 (n is even)
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n → 3n + 1 (n is odd)
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Which starting number, under one million, produces the longest chain?
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"""
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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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__topNum = 1000000 #The largest number that you will check against the chain
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#This function returns a list of numbers created by the chain
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def getChain(startNum: int) -> list:
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#Put the starting number in the list
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chain = [startNum]
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#Starting with the current number perform the correct opperations on the numbers until that number reaches 1
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while(startNum > 1):
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#Determine if the number is odd or even and perform the correct operation and add the new number to the list
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if((startNum % 2) == 0):
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startNum /= 2
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else:
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startNum = (3 * startNum) + 1
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#Add the new number to the chain
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chain.append(startNum)
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#Return the list
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return chain
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def Problem14():
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#Setup your variables
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largestChain = [] #Holds the longest chain of numbers
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#Start at 1 and run up to 1000000, checking how long the chain is when started with each number
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for startingNumber in range(1, __topNum):
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currentChain = getChain(startingNumber) #Get the chain
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#If the new chain is longer than the current longest chain replace it
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if(len(currentChain) > len(largestChain)):
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largestChain = currentChain.copy()
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#Print the results
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print("The longest chain with a starting number < " + str(__topNum) + " is " + str(largestChain[0]) + " with a length of " + str(len(largestChain)))
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#If you are running this file, automatically start the correct function
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if __name__ == "__main__":
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timer = Stopwatch() #Determines the algorithm's run time
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timer.start() #Start the timer
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Problem14() #Call the function that answers the question
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timer.stop() #Stop the timer
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#Print the results of the timer
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print("It took " + timer.getString() + " to run this algorithm")
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"""Results:
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The longest chain with a starting number < 1000000 is 837799 with a length of 525
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It took 28.893 seconds to run this algorithm
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"""
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