//ProjectEuler/C++/Problem3.cpp
//Matthew Ellison
// Created: 9-28-18
//Modified: 9-28-18
//The largest prime factor of 600851475143


#include <iostream>
#include <cmath>
#include <vector>
#include <chrono>

std::vector<unsigned long long> generatePrimes(const unsigned long long number);
unsigned long long findLargest(const std::vector<unsigned long long> list);


int main(){
	const unsigned long long goalNumber = 600851475143;	//The number you are trying to find the factors of
	std::vector<unsigned long long> primes;	//Holds the list of prime numbers
	std::vector<unsigned long long> factors;	//Holds the factors of goalNumber
	unsigned long long number = goalNumber;	//The number that is left after taking the prime numbers out
	bool found = false;


	std::chrono::high_resolution_clock::time_point startTime = std::chrono::high_resolution_clock::now();
	//Generate the primes
	primes = generatePrimes(ceil(sqrt(goalNumber)));
	//Check the primes against the number
	//62113 numbers at this point
	while(!found){
		//Loop through the list of primes
		for(int cnt = 0;cnt < primes.size();){
			//See if after dividing a prime out it is left with a whole number
			if((number % primes.at(cnt)) == 0){
				number /= primes.at(cnt);
				factors.push_back(primes.at(cnt));
			}
			//If you didn't find a prime then advance to the next possible number
			//If you did find a prime then stay where you are in the list incase it occurs more than once
			else{
				++cnt;
			}
		}
		//If the remaining number is 1 then you just added the last number to the factors
		if(number == 1){
			found = true;
		}
	}

	//Look for the largest number in the vector
	unsigned long long maxNum = findLargest(factors);

	//Calculate the amount of time it took to run the algorithm
	std::chrono::high_resolution_clock::time_point endTime = std::chrono::high_resolution_clock::now();
	std::chrono::high_resolution_clock::duration dur = std::chrono::duration_cast<std::chrono::milliseconds>(endTime - startTime);

	//Print the results
	std::cout << "The largest factor of the number " << goalNumber << " is " << maxNum
			<< "\nIt took " << dur.count() << " milliseconds to run this algorith" << std::endl;

	//Pause before exiting
	std::cin.get();
	return 0;
}

std::vector<unsigned long long> generatePrimes(const unsigned long long goalNumber){
	std::vector<unsigned long long> primes;
	bool foundFactor = false;

	//Start at 2 so we can skip 1
	if(goalNumber >= 2){
		primes.push_back(2);
	}
	//We can skip all of the even numbers
	for(unsigned long long possiblePrime = 3;possiblePrime < goalNumber;possiblePrime += 2){
		//Step through every element in the current primes. If you don't find anything that divides it, it must be a prime itself
		for(int cnt = 0;(cnt < primes.size()) && ((primes.at(cnt) * primes.at(cnt)) < goalNumber);++cnt){
			if(fmod(((double)possiblePrime / primes.at(cnt)), 1) == 0){
				foundFactor = true;
				break;
			}
		}
		//If you didn't find a factor then it must be prime
		if(!foundFactor){
			primes.push_back(possiblePrime);
		}
		//If you did find a factor you need to reset the flag
		else{
			foundFactor = false;
		}
	}
	return primes;
}

unsigned long long findLargest(const std::vector<unsigned long long> list){
	unsigned long long maxNum = 0;
	for(unsigned long long num : list){
		if(num > maxNum){
			maxNum = num;
		}
	}

	return maxNum;
}