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124 lines
4.1 KiB
Python
124 lines
4.1 KiB
Python
#ProjectEuler/Python/Problem27.py
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#Matthew Ellison
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# Created: 09-15-19
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#Modified: 07-24-21
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#Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0.
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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) 2020 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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import NumberAlgorithms
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class Problem27(Problem):
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#Functions
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#Constructor
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def __init__(self) -> None:
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super().__init__("Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0")
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self.topA = 0 #The A for the most n's generated
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self.topB = 0 #The B for the most n's generated
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self.topN = 0 #The most n's generated
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self.primes = [] #A list of all primes that could possibly be generated with this formula
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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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#Get the primes
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primes = NumberAlgorithms.getPrimes(12000) #A list of all primes that could possibly be generated with this formula
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#Start with the lowest possible A and check all possibilities after that
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for a in range(-999, 999):
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#Start with the lowest possible B and check all possibilities after that
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for b in range(-1000, 1000):
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#Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
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n = 0
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quadratic = (n * n) + (a * n) + b
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while(quadratic in primes):
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n += 1
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quadratic = (n * n) + (a * n) + b
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n -= 1 #Negate an n because the last formula failed
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#Set all the largest numbers if this created more primes than any other
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if(n > self.topN):
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self.topN = n
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self.topB = b
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self.topA = a
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#Stop the timer
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self.timer.stop()
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#Save the results
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self.result = "The greatest number of primes found is " + str(self.topN)
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self.result += "\nIt was found with A = " + str(self.topA) + ", B = " + str(self.topB)
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self.result += "\nThe product of A and B is " + str(self.topA * self.topB)
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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.topA = 0
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self.topB = 0
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self.topN = 0
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self.primes.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 greatest number of primes found is {self.topN}\n" \
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f"It was found with A = {self.topA}, B = {self.topB}\n" \
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f"The product of A and B is {self.topA * self.topB}"
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#Returns the top A that was generated
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def getTopA(self) -> int:
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self.solvedCheck("largest A")
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return self.topA
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#Returns the top B that was generated
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def getTopB(self) -> int:
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self.solvedCheck("largest B")
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return self.topA
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#Returns the top N that was generated
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def getTopN(self) -> int:
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self.solvedCheck("largest N")
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return self.topA
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#Returns the product of A and B for the answer
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def getProduct(self) -> int:
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self.solvedCheck("product of A and B")
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return self.topA * self.topB
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""" Results:
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The greatest number of primes found is 70
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It was found with A = -61, B = 971
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The product of A and B is -59231
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It took an average of 49.963 seconds to run this problem through 100 iterations
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"""
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