//ProjectEuler/Java/Problem29.java
//Matthew Ellison
// Created: 10-09-19
//Modified: 10-09-19
//How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
//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 java.util.ArrayList;
import java.math.BigInteger;


public class Problem29{
	private static final Integer BOTTOM_A = 2;	//The lowest possible value for a
	private static final Integer TOP_A = 100;	//The highest possible value for a
	private static final Integer BOTTOM_B = 2;	//The lowest possible value for b
	private static final Integer TOP_B = 100;	//The highest possible value for b
	private static ArrayList<BigInteger> unique;	//Holds all unique values generated
	public static void main(String[] args){
		//Setup the variables
		Stopwatch timer = new Stopwatch();
		unique = new ArrayList<BigInteger>();

		//Start the time
		timer.start();

		//Start with the first A and move towards the top
		for(Integer currentA = BOTTOM_A;currentA <= TOP_A;++currentA){
			//Start with the first B and move towards the top
			for(Integer currentB = BOTTOM_B;currentB <= TOP_B;++currentB){
				//Get the new number
				BigInteger currentNum = BigInteger.valueOf(currentA).pow(currentB);
				//If the current number is not in the array add it
				if(!unique.contains(currentNum)){
					unique.add(currentNum);
				}
			}
		}

		//Stop the timer
		timer.stop();

		//Print the results
		System.out.printf("The number of unique values generated by a^b for %d <= a <= %d and %d <= b <= %d is %d\n", BOTTOM_A, TOP_A, BOTTOM_B, TOP_B, unique.size());
		System.out.println("It took " + timer.getStr() + " to run this algorithm");
	}
}

/* Results:
The number of unique values generated by a^b for 2 <= a <= 100 and 2 <= b <= 100 is 9183
It took 258.922 milliseconds to run this algorithm
*/