//JavaClasses/src/main/java/mattrixwv/NumberAlgorithms.java
//Matthew Ellison
// Created: 07-03-21
//Modified: 06-25-22
//This class contains algorithms for numbers that I've found it useful to keep around
/*
	Copyright (C) 2022  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 com.mattrixwv;


import java.math.BigInteger;
import java.security.InvalidParameterException;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;

import com.mattrixwv.exceptions.InvalidResult;


public class NumberAlgorithms{
	private NumberAlgorithms(){}

	public static final String FACTORIAL_NEGATIVE_MESSAGE = "n! cannot be negative";

	//This function returns a list with all the prime numbers <= goalNumber
	public static List<Integer> getPrimes(int goalNumber){
		return ArrayAlgorithms.longToInt(getPrimes((long) goalNumber));
	}
	public static List<Long> getPrimes(long goalNumber){
		ArrayList<Long> primes = new ArrayList<>();	//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(2L);
		}

		//We cna now start at 3 and skipp all even numbers, because they cannot be prime
		for(long possiblePrime = 3L;possiblePrime <= goalNumber;possiblePrime += 2L){
			//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;(primesCnt < primes.size()) && (primes.get(primesCnt) <= topPossibleFactor.intValue());++primesCnt){
				if((possiblePrime % primes.get(primesCnt)) == 0){
					foundFactor = true;
					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 List<BigInteger> getPrimes(BigInteger goalNumber){
		ArrayList<BigInteger> primes = new ArrayList<>();	//Holds the prime numbers
		boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the number 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 can now start at 3 and skip 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;(primesCnt < primes.size()) && (primes.get(primesCnt).compareTo(topPossibleFactor) <= 0);++primesCnt){
				if((possiblePrime.mod(primes.get(primesCnt))) == BigInteger.valueOf(0)){
					foundFactor = true;
					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 List<Integer> getNumPrimes(int numberOfPrimes){
		return ArrayAlgorithms.longToInt(getNumPrimes((long)numberOfPrimes));
	}
	public static List<Long> getNumPrimes(long numberOfPrimes){
		ArrayList<Long> primes = new ArrayList<>();	//Holds the prime numbers
		boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the number 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(2L);
		}

		//We can now start at 3 and skip all even numbers, because they cannot be prime
		for(long possiblePrime = 3L;primes.size() < numberOfPrimes;possiblePrime += 2L){
			//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;(primesCnt < primes.size()) && (primes.get(primesCnt) <= topPossibleFactor.intValue());++primesCnt){
				if((possiblePrime % primes.get(primesCnt)) == 0){
					foundFactor = true;
					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 List<BigInteger> getNumPrimes(BigInteger numberOfPrimes){
		ArrayList<BigInteger> primes = new ArrayList<>();	//Holds the prime numbers
		boolean foundFactor = false;	//A flag for whether a factor of the current number has been found

		//If the number 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 can now start at 3 and skip 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;(primesCnt < primes.size()) && (primes.get(primesCnt).compareTo(topPossibleFactor) <= 0);++primesCnt){
				if((possiblePrime.mod(primes.get(primesCnt))) == BigInteger.valueOf(0)){
					foundFactor = true;
					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 return true if the value passed to it is prime
	public static boolean isPrime(long possiblePrime){
		if(possiblePrime <= 3){
			return possiblePrime > 1;
		}
		else if(((possiblePrime % 2) == 0) || ((possiblePrime % 3) == 0)){
			return false;
		}
		for(long cnt = 5;(cnt * cnt) <= possiblePrime;cnt += 6){
			if(((possiblePrime % cnt) == 0) || ((possiblePrime % (cnt + 2)) == 0)){
				return false;
			}
		}
		return true;
	}
	public static boolean isPrime(BigInteger possiblePrime){
		if(possiblePrime.compareTo(BigInteger.valueOf(3)) <= 0){
			return possiblePrime.compareTo(BigInteger.ONE) > 0;
		}
		else if(possiblePrime.mod(BigInteger.TWO).equals(BigInteger.ZERO) || possiblePrime.mod(BigInteger.valueOf(3)).equals(BigInteger.ZERO)){
			return false;
		}
		for(BigInteger cnt = BigInteger.valueOf(5);(cnt.multiply(cnt)).compareTo(possiblePrime) <= 0;cnt = cnt.add(BigInteger.valueOf(6))){
			if(possiblePrime.mod(cnt).equals(BigInteger.ZERO) || possiblePrime.mod(cnt.add(BigInteger.TWO)).equals(BigInteger.ZERO)){
				return false;
			}
		}
		return true;
	}


	//This function returns all factors of goalNumber
	public static List<Integer> getFactors(int goalNumber) throws InvalidResult{
		return ArrayAlgorithms.longToInt(getFactors((long)goalNumber));
	}
	public static List<Long> getFactors(long goalNumber) throws InvalidResult{
		//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));
		List<Long> primes = getPrimes(topPossiblePrime.longValue());
		ArrayList<Long> factors = new ArrayList<>();

		//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.isEmpty()){
			factors.add(goalNumber);
			goalNumber /= goalNumber;
		}

		//If for some reason the goalNumber is not 1 throw an error
		if(goalNumber != 1){
			if(isPrime(goalNumber)){
				factors.add(goalNumber);
			}
			else{
				throw new InvalidResult("The factor was not 1: " + goalNumber);
			}
		}

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

		//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.isEmpty()){
			factors.add(goalNumber);
			goalNumber = goalNumber.divide(goalNumber);
		}

		//If for some reason the goalNumber is not 1 throw an error
		if(!goalNumber.equals(BigInteger.ONE)){
			throw new InvalidResult("The factor was not 1: " + goalNumber);
		}

		//Return the list of factors
		return factors;
	}


	//This function returns all the divisors of goalNumber
	public static List<Integer> getDivisors(int goalNumber){
		return ArrayAlgorithms.longToInt(getDivisors((long)goalNumber));
	}
	public static List<Long> getDivisors(long goalNumber){
		HashSet<Long> divisors = new HashSet<>();
		//Start by checking that the number is positive
		if(goalNumber <= 0){
			return new ArrayList<>();
		}
		else{
			divisors.add(1L);
			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(long possibleDivisor = 2L;possibleDivisor <= topPossibleDivisor;++possibleDivisor){
			//If you find one add it and the number it creates to the list
			if((goalNumber % possibleDivisor) == 0){
				long possibleDivisor2 = goalNumber / possibleDivisor;
				divisors.add(possibleDivisor);
				divisors.add(possibleDivisor2);
			}
		}

		ArrayList<Long> divisorList = new ArrayList<>(divisors);
		//Sort the list before returning it for neatness
		Collections.sort(divisorList);
		//Return the list
		return divisorList;
	}
	public static List<BigInteger> getDivisors(BigInteger goalNumber){
		HashSet<BigInteger> divisors = new HashSet<>();
		//Start by checking that the number is positive
		if(goalNumber.compareTo(BigInteger.valueOf(0)) <= 0){
			return new ArrayList<>();
		}
		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.TWO;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))){
				BigInteger possibleDivisor2 = goalNumber.divide(possibleDivisor);
				divisors.add(possibleDivisor);
				divisors.add(possibleDivisor2);
			}
		}

		ArrayList<BigInteger> divisorList = new ArrayList<>(divisors);
		//Sort the list before returning it for neatness
		Collections.sort(divisorList);
		//Return the list
		return divisorList;
	}

	//This function returns the goalSubscript'th Fibonacci number
	public static int getFib(int goalSubscript){
		return (int)getFib((long)goalSubscript);
	}
	public static long getFib(long goalSubscript){
		//Setup the variables
		long[] fibNums = {1L, 1L, 0L};	//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 0L;
		}

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

		//Return the proper 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
		int fibLoc;
		for(fibLoc = 2;goalSubscript.compareTo(BigInteger.valueOf(fibLoc)) > 0;++fibLoc){
			fibNums[fibLoc % 3] = fibNums[(fibLoc - 1) % 3].add(fibNums[(fibLoc - 2) % 3]);
		}

		//Return the proper 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 List<Integer> getAllFib(int goalNumber){
		return ArrayAlgorithms.longToInt(getAllFib((long) goalNumber));
	}
	public static List<Long> getAllFib(long goalNumber){
		//Setup the variables
		ArrayList<Long> fibNums = new ArrayList<>();	//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(1L);
		fibNums.add(1L);

		//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 List<BigInteger> getAllFib(BigInteger goalNumber){
		//Setup the variables
		ArrayList<BigInteger> fibNums = new ArrayList<>();	//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 factorial of the number passed to it
	public static int factorial(int num) throws InvalidParameterException{
		return (int)factorial((long)num);
	}
	public static long factorial(long num) throws InvalidParameterException{
		long fact = 1L;	//The value of the factorial

		//If the number passed in is < 0 throw an exception
		if(num < 0){
			throw new InvalidParameterException(FACTORIAL_NEGATIVE_MESSAGE);
		}
		//Loop through every number up to and including num and add the product to the factorial
		for(long cnt = 2L;cnt <= num;++cnt){
			fact *= cnt;
		}

		return fact;
	}
	public static BigInteger factorial(BigInteger num) throws InvalidParameterException{
		BigInteger fact = BigInteger.valueOf(1L);

		//If the number passed in is < 0 throw an exception
		if(num.compareTo(BigInteger.ZERO) < 0){
			throw new InvalidParameterException(FACTORIAL_NEGATIVE_MESSAGE);
		}
		//Loop through every number up to and including num and add the product to the factorial
		for(BigInteger cnt = BigInteger.TWO;cnt.compareTo(num) <= 0;cnt = cnt.add(BigInteger.ONE)){
			fact = fact.multiply(cnt);
		}

		return fact;
	}

	//This function returns the GCD of the two numbers sent to it
	public static int gcd(int num1, int num2){
		return (int)gcd((long)num1, (long)num2);
	}
	public static long gcd(long num1, long num2){
		while((num1 != 0) && (num2 != 0)){
			if(num1 > num2){
				num1 %= num2;
			}
			else{
				num2 %= num1;
			}
		}
		return num1 | num2;
	}
	public static BigInteger gcd(BigInteger num1, BigInteger num2){
		while(!num1.equals(BigInteger.ZERO) && !num2.equals(BigInteger.ZERO)){
			if(num1.compareTo(num2) > 0){
				num1 = num1.mod(num2);
			}
			else{
				num2 = num2.mod(num1);
			}
		}
		return num1.or(num2);
	}

	//Converts a number to its binary equivalent
	public static String toBin(long num){
		//Convert the number to binary string
		return Long.toBinaryString(num);
	}
	public static String toBin(BigInteger num){
		//Conver the number to binary string
		return num.toString(2);
	}
}