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109 lines
3.5 KiB
Python
109 lines
3.5 KiB
Python
#ProjectEuler/Python/Problem29.py
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#Matthew Ellison
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# Created: 10-10-19
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#Modified: 07-24-21
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#How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
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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) 2021 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 Problems.Problem import Problem
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class Problem29(Problem):
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#Variables
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__bottomA = 2 #The lowest possible value for A
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__topA = 100 #The highest possible value for A
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__bottomB = 2 #The lowest possible value for B
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__topB = 100 #The highest possible value for B
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#Functions
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#Constructor
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def __init__(self) -> None:
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super().__init__("How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?")
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self.unique = []
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#Operational functions
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#Solve the problem
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def solve(self) -> None:
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#If the problem has already been solved do nothing and end the function
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if(self.solved):
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return
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#Start the timer
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self.timer.start()
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#Start with the first A and move towards the top
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for currentA in range(self.__bottomA, self.__topA + 1):
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#Start with the first B and move towards the top
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for currentB in range(self.__bottomB, self.__topB + 1):
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#Get the new number
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currentNum = currentA ** currentB
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#If the new number isn't in the list add it
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if currentNum not in self.unique:
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self.unique.append(currentNum)
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#Stop the timer
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self.timer.stop()
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#Throw a flag to show the problem is solved
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self.solved = True
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#Reset the problem so it can be run again
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def reset(self) -> None:
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super().reset()
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self.unique.clear()
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#Gets
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#Returns the result of solving the problem
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def getResult(self) -> str:
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self.solvedCheck("result")
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return f"The number of unique values generated by a^b for {self.__bottomA} <= a < = {self.__topA} and {self.__bottomB} <= b <= {self.__topB} is {len(self.unique)}"
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#Returns the lowest possible value for a
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def getBottomA(self) -> int:
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self.solvedCheck("lowest a")
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return self.__bottomA
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#Returns the lowest possible value for a
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def getTopA(self) -> int:
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self.solvedCheck("highest a")
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return self.__topA
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#Returns the lowest possible value for a
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def getBottomB(self) -> int:
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self.solvedCheck("lowest b")
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return self.__bottomB
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#Returns the lowest possible value for a
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def getTopB(self) -> int:
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self.solvedCheck("highest b")
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return self.__topB
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#Returns a list of all unique values for a^b
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def getUnique(self) -> list:
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self.solvedCheck("unique values for a^b")
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return self.unique
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#Returns the number of unique values for a^b
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def getNumUnique(self) -> int:
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self.solvedCheck("number of unique values for a^b")
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return len(self.unique)
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""" Results:
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The number of unique values generated by a^b for 2 <= a < = 100 and 2 <= b <= 100 is 9183
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It took an average of 304.306 milliseconds to run this problem through 100 iterations
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"""
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