//ProjectEuler/Java/Problem27.java
//Matthew Ellison
// Created: 09-15-19
//Modified: 09-15-19
//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.
//Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/JavaClasses
/*
	Copyright (C) 2019  Matthew Ellison

	This program is free software: you can redistribute it and/or modify
	it under the terms of the GNU Lesser General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	This program is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU Lesser General Public License for more details.

	You should have received a copy of the GNU Lesser General Public License
	along with this program.  If not, see <https://www.gnu.org/licenses/>.
*/


import mattrixwv.Stopwatch;
import mattrixwv.Algorithms;

import java.util.ArrayList;


public class Problem27{
	private static Integer topA = 0;	//The A for the most n's generated
	private static Integer topB = 0;	//The B for the most n's generated
	private static Integer topN = 0;	//The most n's generated
	private static ArrayList<Integer> primes = Algorithms.getPrimes(12000);	//A list of all primes that could possibly be generated with this formula
	public static void main(String[] args){
		//Setup the variables
		Stopwatch timer = new Stopwatch();

		//Start the timer
		timer.start();

		//Start with the lowest possible A and check all possibilities after that
		for(Integer a = -999;a <= 999;++a){
			//Start with the lowest possible B and check all possibilities after that
			for(Integer b = -1000;b <=1000;++b){
				//Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
				Integer n = 0;
				Integer quadratic = (n * n) + (a * n) + b;
				while(Algorithms.isFound(primes, quadratic)){
					++n;
					quadratic = (n * n) + (a * n) + b;
				}
				--n;	//Negate an n because the last formula failed

				//Set all the largest numbers if this created more primes than any other
				if(n > topN){
					topN = n;
					topB = b;
					topA = a;
				}
			}
		}

		//Stop the timer
		timer.stop();

		//Print the restuls
		System.out.printf("The greatest number of primes found is %d", topN);
		System.out.printf("\nIt was found with A = %d, B = %d", topA, topB);
		System.out.printf("\nThe product of A and B is %d\n", topA * topB);
		System.out.println("It took " + timer.getStr() + " to run this algorithm");
	}
}

/* Results:
The greatest number of primes found is 70
It was found with A = -61, B = 971
The product of A and B is -59231
It took 4.765 seconds to run this algorithm
*/