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111 lines
3.0 KiB
C++
111 lines
3.0 KiB
C++
//ProjectEuler/C++/Source/Problem27.cpp
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//Matthew Ellison
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// Created: 09-14-19
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//Modified: 09-14-19
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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/myClasses
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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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#include <string>
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#include <sstream>
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#include <cinttypes>
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#include "Algorithms.hpp"
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#include "../Headers/Problem27.hpp"
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Problem27::Problem27(){
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topA = topB = topN = 0;
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primes = mee::getPrimes((int64_t)(12000));
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}
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void Problem27::solve(){
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//If the problem has already been solved do nothing and end the function
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if(solved){
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return;
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}
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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(int64_t 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(int64_t 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 with concecutive n's
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int64_t n = 0;
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int64_t quadratic = (n * n) + (a * n) + b;
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while(mee::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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//Throw a flag to show the problem is solved
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solved = true;
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}
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std::string Problem27::getString() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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std::stringstream results;
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results << "The greatest number of primes found is " << topN
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<< "\nIt was found with A = " << topA << ", B = " << topB
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<< "\nThe product of A and B is " << topA * topB;
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return results.str();
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}
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int64_t Problem27::getTopA() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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return topA;
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}
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int64_t Problem27::getTopB() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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return topB;
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}
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int64_t Problem27::getTopN() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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return topN;
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}
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