//Java/JavaClasses/Algorithms.java
//Matthew Ellison
// Created: 03-02-19
//Modified: 03-02-19
//This class holds many algorithms that I have found it useful to keep around
//As such all of the functions in here are static and meant to be used as stand alone functions
/*
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/>.
*/


package mattrixwv;


import java.util.Arrays;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Collections;


public class Algorithms{
	//This function returns a list with all the prime numbers <= goalNumber
	public static ArrayList<Integer> getPrimes(Integer goalNumber){
		ArrayList<Integer> primes = new ArrayList<Integer>();	//Holds the prime numbers
		Boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the numebr is 0 or negative return an empty list
		if(goalNumber <= 1){
			return primes;
		}
		//Otherwise the number is at least 2, so 2 should be added to the list
		else{
			primes.add(2);
		}

		//We cna now start at 3 and skipp all even numbers, because they cannot be prime
		for(int possiblePrime = 3;possiblePrime <= goalNumber;possiblePrime += 2){
			//Check all current primes, up to sqrt(possiblePrime), to see if there is a divisor
			Double topPossibleFactor = Math.ceil(Math.sqrt(possiblePrime));
			//We can safely assume that there will be at least 1 element in the primes list because of 2 being added before this
			for(int primesCnt = 0;primes.get(primesCnt) <= topPossibleFactor.intValue();){
				if((possiblePrime % primes.get(primesCnt)) == 0){
					foundFactor = true;
					break;
				}
				else{
					++primesCnt;
				}
				//Check if the index has gone out of range
				if(primesCnt >= primes.size()){
					break;
				}
			}

			//If you didn't find a factor then the current number must be prime
			if(!foundFactor){
				primes.add(possiblePrime);
			}
			else{
				foundFactor = false;
			}
		}

		//Sort the list before returning it
		Collections.sort(primes);
		return primes;
	}
	public static ArrayList<BigInteger> getPrimes(BigInteger goalNumber){
		ArrayList<BigInteger> primes = new ArrayList<BigInteger>();	//Holds the prime numbers
		Boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the numeber is 1, 0 or negative return an empty list
		if(goalNumber.compareTo(BigInteger.valueOf(1)) <= 0){
			return primes;
		}
		//Otherwise the number is at least 2, so 2 should be added to the list
		else{
			primes.add(BigInteger.valueOf(2));
		}

		//We cna now start at 3 and skipp all even numbers, because they cannot be prime
		for(BigInteger possiblePrime = BigInteger.valueOf(3);possiblePrime.compareTo(goalNumber) <= 0;possiblePrime = possiblePrime.add(BigInteger.valueOf(2))){
			//Check all current primes, up to sqrt(possiblePrime), to see if there is a divisor
			BigInteger topPossibleFactor = possiblePrime.sqrt().add(BigInteger.valueOf(1));
			//We can safely assume that there will be at least 1 element in the primes list because of 2 being added before this
			for(int primesCnt = 0;primes.get(primesCnt).compareTo(topPossibleFactor) <= 0;){
				if((possiblePrime.mod(primes.get(primesCnt))) == BigInteger.valueOf(0)){
					foundFactor = true;
					break;
				}
				else{
					++primesCnt;
				}
				//Check if the index has gone out of range
				if(primesCnt >= primes.size()){
					break;
				}
			}

			//If you didn't find a factor then the current number must be prime
			if(!foundFactor){
				primes.add(possiblePrime);
			}
			else{
				foundFactor = false;
			}
		}

		//Sort the list before returning it
		Collections.sort(primes);
		return primes;
	}
	//This function gets a certain number of primes
	public static ArrayList<Integer> getNumPrimes(int numberOfPrimes){
		ArrayList<Integer> primes = new ArrayList<Integer>();	//Holds the prime numbers
		Boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the numebr is 0 or negative return an empty list
		if(numberOfPrimes <= 1){
			return primes;
		}
		//Otherwise the number is at least 2, so 2 should be added to the list
		else{
			primes.add(2);
		}

		//We cna now start at 3 and skipp all even numbers, because they cannot be prime
		for(int possiblePrime = 3;primes.size() < numberOfPrimes;possiblePrime += 2){
			//Check all current primes, up to sqrt(possiblePrime), to see if there is a divisor
			Double topPossibleFactor = Math.ceil(Math.sqrt(possiblePrime));
			//We can safely assume that there will be at least 1 element in the primes list because of 2 being added before this
			for(int primesCnt = 0;primes.get(primesCnt) <= topPossibleFactor.intValue();){
				if((possiblePrime % primes.get(primesCnt)) == 0){
					foundFactor = true;
					break;
				}
				else{
					++primesCnt;
				}
				//Check if the index has gone out of range
				if(primesCnt >= primes.size()){
					break;
				}
			}

			//If you didn't find a factor then the current number must be prime
			if(!foundFactor){
				primes.add(possiblePrime);
			}
			else{
				foundFactor = false;
			}
		}

		//Sort the list before returning it
		Collections.sort(primes);
		return primes;
	}
	public static ArrayList<BigInteger> getNumPrimes(BigInteger numberOfPrimes){
		ArrayList<BigInteger> primes = new ArrayList<BigInteger>();	//Holds the prime numbers
		Boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the numebr is 0 or negative return an empty list
		if(numberOfPrimes.compareTo(BigInteger.valueOf(1)) <= 0){
			return primes;
		}
		//Otherwise the number is at least 2, so 2 should be added to the list
		else{
			primes.add(BigInteger.valueOf(2));
		}

		//We cna now start at 3 and skipp all even numbers, because they cannot be prime
		for(BigInteger possiblePrime = BigInteger.valueOf(3);numberOfPrimes.compareTo((BigInteger.valueOf(primes.size()))) > 0;possiblePrime = possiblePrime.add(BigInteger.valueOf(2))){
			//Check all current primes, up to sqrt(possiblePrime), to see if there is a divisor
			BigInteger topPossibleFactor = possiblePrime.sqrt().add(BigInteger.valueOf(1));
			//We can safely assume that there will be at least 1 element in the primes list because of 2 being added before this
			for(int primesCnt = 0;primes.get(primesCnt).compareTo(topPossibleFactor) <= 0;){
				if((possiblePrime.mod(primes.get(primesCnt))) == BigInteger.valueOf(0)){
					foundFactor = true;
					break;
				}
				else{
					++primesCnt;
				}
				//Check if the index has gone out of range
				if(primesCnt >= primes.size()){
					break;
				}
			}

			//If you didn't find a factor then the current number must be prime
			if(!foundFactor){
				primes.add(possiblePrime);
			}
			else{
				foundFactor = false;
			}
		}

		//Sort the list before returning it
		Collections.sort(primes);
		return primes;
	}
	//This function returns all factors of goalNumber
	public static ArrayList<Integer> getFactors(int goalNumber){
		//You need to get all the primes that could be factors of this number so you can test them
		Double topPossiblePrime = Math.ceil(Math.sqrt(goalNumber));
		ArrayList<Integer> primes = getPrimes(topPossiblePrime.intValue());
		ArrayList<Integer> factors = new ArrayList<Integer>();

		//You need to step through each prime and see if it is a factor in the number
		for(int cnt = 0;cnt < primes.size();){
			//If the prime is a factor you need to add it to the factor list
			if((goalNumber % primes.get(cnt)) == 0){
				factors.add(primes.get(cnt));
				goalNumber /= primes.get(cnt);
			}
			//Otherwise advance the location in primes you are looking at
			//By not advancing if the prime is a factor you allow for multiple of the same prime number as a factor
			else{
				++cnt;
			}
		}

		//If you didn't get any factors the number itself must be a prime
		if(factors.size() == 0){
			factors.add(goalNumber);
			goalNumber /= goalNumber;
		}

		//If for some reason the goalNumber is not 1 throw an error
		///Need to add the appropriate error here

		//Return the list of factors
		return factors;
	}
	public static ArrayList<BigInteger> getFactors(BigInteger goalNumber){
		//You need to get all the primes that could be factors of this number so you can test them
		BigInteger topPossiblePrime = goalNumber.sqrt();
		ArrayList<BigInteger> primes = getPrimes(topPossiblePrime);
		ArrayList<BigInteger> factors = new ArrayList<BigInteger>();

		//You need to step through each prime and see if it is a factor in the number
		for(int cnt = 0;cnt < primes.size();){
			//If the prime is a factor you need to add it to the factor list
			if((goalNumber.mod(primes.get(cnt))).compareTo(BigInteger.valueOf(0)) == 0){
				factors.add(primes.get(cnt));
				goalNumber = goalNumber.divide(primes.get(cnt));
			}
			//Otherwise advance the location in primes you are looking at
			//By not advancing if the prime is a factor you allow for multiple of the same prime number as a factor
			else{
				++cnt;
			}
		}

		//If you didn't get any factors the number itself must be a prime
		if(factors.size() == 0){
			factors.add(goalNumber);
			goalNumber.divide(goalNumber);
		}

		//If for some reason the goalNumber is not 1 throw an error
		///Need to add the appropriate error here

		//Return the list of factors
		return factors;
	}
	//This function returns all the divisors of goalNumber
	public static ArrayList<Integer> getDivisors(int goalNumber){
		ArrayList<Integer> divisors = new ArrayList<Integer>();
		//Start by checking that the number is positive
		if(goalNumber <= 0){
			return divisors;
		}
		//If the number is 1 return just itself
		else if(goalNumber == 1){
			divisors.add(1);
		}
		//Otherwise add 1 and itself to the list
		else{
			divisors.add(1);
			divisors.add(goalNumber);
		}

		//Start at 3 and loop through all numbers < sqrt(goalNumber) looking for a number that divides it evenly
		Double topPossibleDivisor = Math.ceil(Math.sqrt(goalNumber));
		for(Integer possibleDivisor = 2;possibleDivisor <= topPossibleDivisor;++possibleDivisor){
			//If you find one add it and the number it creates to the list
			if((goalNumber % possibleDivisor) == 0){
				divisors.add(possibleDivisor);
				//Accound for the possibility of sqrt(goalNumber) being a divisor
				if(possibleDivisor != topPossibleDivisor.intValue()){
					divisors.add(goalNumber / possibleDivisor);
				}
			}
		}

		//Sort the list before returning it for neatness
		Collections.sort(divisors);
		//Return the list
		return divisors;
	}
	public static ArrayList<BigInteger> getDivisors(BigInteger goalNumber){
		ArrayList<BigInteger> divisors = new ArrayList<BigInteger>();
		//Start by checking that the number is positive
		if(goalNumber.compareTo(BigInteger.valueOf(0)) <= 0){
			return divisors;
		}
		//If the number is 1 return just itself
		else if(goalNumber.equals(BigInteger.valueOf(1))){
			divisors.add(BigInteger.valueOf(1));
		}
		//Otherwise add 1 and itself to the list
		else{
			divisors.add(BigInteger.valueOf(1));
			divisors.add(goalNumber);
		}

		//Start at 3 and loop through all numbers < sqrt(goalNumber) looking for a number that divides it evenly
		BigInteger topPossibleDivisor = goalNumber.sqrt();
		for(BigInteger possibleDivisor = BigInteger.valueOf(2);possibleDivisor.compareTo(topPossibleDivisor) <= 0;possibleDivisor = possibleDivisor.add(BigInteger.valueOf(1))){
			//If you find one add it and the number it creates to the list
			if(goalNumber.mod(possibleDivisor).equals(BigInteger.valueOf(0))){
				divisors.add(possibleDivisor);
				//Accound for the possibility of sqrt(goalNumber) being a divisor
				if(!possibleDivisor.equals(topPossibleDivisor)){
					divisors.add(goalNumber.divide(possibleDivisor));
				}
			}
		}

		//Sort the list before returning it for neatness
		Collections.sort(divisors);
		//Return the list
		return divisors;
	}
	//This function returns all the divisors of goalNumber
	public static Integer getFib(int goalSubscript){
		//Setup the variables
		Integer[] fibNums = {1, 1, 0};	//A list to keep track of the Fibonacci numbers. It need only be 3 long because we only need the one we are working on and the last 2

		//If the number is <= 0 return 0
		if(goalSubscript <= 0){
			return 0;
		}

		//Loop through the list, generating Fibonacci numbers until it finds the correct subscript
		Integer fibLoc = 2;
		for(fibLoc = 2;fibLoc < goalSubscript;++fibLoc){
			fibNums[fibLoc % 3] = fibNums[(fibLoc - 1) % 3] + fibNums[(fibLoc - 2) % 3];
		}

		//Return the propper number. The location counter is 1 off of the subscript
		return fibNums[(fibLoc - 1) % 3];
	}
	public static BigInteger getFib(BigInteger goalSubscript){
		//Setup the variables
		BigInteger[] fibNums = {BigInteger.valueOf(1), BigInteger.valueOf(1), BigInteger.valueOf(0)};	//A list to keep track of the Fibonacci numbers. It need only be 3 long because we only need the one we are working on and the last 2

		//If the number is <= 0 return 0
		if(goalSubscript.compareTo(BigInteger.valueOf(0)) <= 0){
			return BigInteger.valueOf(0);
		}

		//Loop through the list, generating Fibonacci numbers until it finds the correct subscript
		Integer fibLoc = 2;
		for(fibLoc = 2;goalSubscript.compareTo(BigInteger.valueOf(fibLoc)) > 0;++fibLoc){
			fibNums[fibLoc % 3] = fibNums[(fibLoc - 1) % 3].add(fibNums[(fibLoc - 2) % 3]);
		}

		//Return the propper number. The location counter is 1 off of the subscript
		return fibNums[(fibLoc - 1) % 3];
	}
	//This function returns a list of all Fibonacci numbers <= goalNumber
	public static ArrayList<Integer> getAllFib(int goalNumber){
		//Setup the variables
		ArrayList<Integer> fibNums = new ArrayList<Integer>();	//A list to save the Fibonacci numbers

		//If the number is <= 0 return an empty list
		if(goalNumber <= 0){
			return fibNums;
		}

		//This means that at least 2 1's are elements
		fibNums.add(1);
		fibNums.add(1);

		//Loop to generate the rest of the Fibonacci numbers
		while(fibNums.get(fibNums.size() - 1) <= goalNumber){
			fibNums.add(fibNums.get(fibNums.size() - 1) + fibNums.get(fibNums.size() - 2));
		}

		//At this point the most recent number is > goalNumber, so remove it and return the rest of the list
		fibNums.remove(fibNums.size() - 1);
		return fibNums;
	}
	public static ArrayList<BigInteger> getAllFib(BigInteger goalNumber){
		//Setup the variables
		ArrayList<BigInteger> fibNums = new ArrayList<BigInteger>();	//A list to save the Fibonacci numbers

		//If the number is <= 0 return an empty list
		if(goalNumber.compareTo(BigInteger.valueOf(0)) <= 0){
			return fibNums;
		}

		//This means that at least 2 1's are elements
		fibNums.add(BigInteger.valueOf(1));
		fibNums.add(BigInteger.valueOf(1));

		//Loop to generate the rest of the Fibonacci numbers
		while(fibNums.get(fibNums.size() - 1).compareTo(goalNumber) <= 0){
			fibNums.add(fibNums.get(fibNums.size() - 1).add(fibNums.get(fibNums.size() - 2)));
		}

		//At this point the most recent number is > goalNumber, so remove it and return the rest of the list
		fibNums.remove(fibNums.size() - 1);
		return fibNums;
	}
	//This function returns the sum of all elements in the list
	public static int getSum(ArrayList<Integer> nums){
		//If a blank list was passed to the function return 0 as the sum
		if(nums.size() == 0){
			return 0;
		}

		//Setup the variables
		Integer sum = 0;

		//Loop through every element in the list and add them together
		for(Integer num : nums){
			sum += num;
		}

		//Return the sum of all elements
		return sum;
	}
	public static BigInteger getBigSum(ArrayList<BigInteger> nums){
		//If a blank list was passed to the function return 0 as the sum
		if(nums.size() == 0){
			return BigInteger.valueOf(0);
		}

		//Setup the variables
		BigInteger sum = BigInteger.valueOf(0);

		//Loop through every element in the list and add them together
		for(BigInteger num : nums){
			sum = sum.add(num);
		}

		//Return the sum of all elements
		return sum;
	}
	//This function returns the product of all elements in the list
	public static int getProd(ArrayList<Integer> nums){
		//If a blank list was passed tot he fuction return 0 as the product
		if(nums.size() == 0){
			return 0;
		}

		//Setup the variables
		Integer product = 1;	//Start at 1 because x * 1 = x

		//Loop through every element in the list and multiply them together
		for(Integer num : nums){
			product *= num;
		}

		//Return the product of all elements
		return product;
	}
	public static BigInteger getBigProd(ArrayList<BigInteger> nums){
		//If a blank list was passed tot he fuction return 0 as the product
		if(nums.size() == 0){
			return BigInteger.valueOf(0);
		}

		//Setup the variables
		BigInteger product = BigInteger.valueOf(1);	//Start at 1 because x * 1 = x

		//Loop through every element in the list and multiply them together
		for(BigInteger num : nums){
			product = product.multiply(num);
		}

		//Return the product of all elements
		return product;
	}
}