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82 lines
2.9 KiB
Java
82 lines
2.9 KiB
Java
//ProjectEuler/Java/Problem27.java
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//Matthew Ellison
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// Created: 09-15-19
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//Modified: 09-15-19
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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 non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/JavaClasses
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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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import mattrixwv.Stopwatch;
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import mattrixwv.Algorithms;
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import java.util.ArrayList;
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public class Problem27{
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private static Integer topA = 0; //The A for the most n's generated
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private static Integer topB = 0; //The B for the most n's generated
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private static Integer topN = 0; //The most n's generated
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private static ArrayList<Integer> primes = Algorithms.getPrimes(12000); //A list of all primes that could possibly be generated with this formula
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public static void main(String[] args){
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//Setup the variables
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Stopwatch timer = new Stopwatch();
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//Start the timer
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timer.start();
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//Start with the lowest possible A and check all possibilities after that
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for(Integer a = -999;a <= 999;++a){
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//Start with the lowest possible B and check all possibilities after that
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for(Integer b = -1000;b <=1000;++b){
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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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Integer n = 0;
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Integer quadratic = (n * n) + (a * n) + b;
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while(Algorithms.isFound(primes, quadratic)){
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++n;
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quadratic = (n * n) + (a * n) + b;
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}
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--n; //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 > topN){
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topN = n;
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topB = b;
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topA = a;
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}
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}
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}
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//Stop the timer
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timer.stop();
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//Print the restuls
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System.out.printf("The greatest number of primes found is %d", topN);
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System.out.printf("\nIt was found with A = %d, B = %d", topA, topB);
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System.out.printf("\nThe product of A and B is %d\n", topA * topB);
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System.out.println("It took " + timer.getStr() + " to run this algorithm");
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}
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}
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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 4.765 seconds to run this algorithm
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*/
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