From 7c04e9043cf1b1b962d4de0175240fe16171ce3f Mon Sep 17 00:00:00 2001
From: Matthew Ellison <m_ellison@ymail.com>
Date: Thu, 27 Sep 2018 13:33:45 -0400
Subject: [PATCH] Added program for problem 3

---
 ProjectEuler/C++/Problem3.cpp | 104 ++++++++++++++++++++++++++++++++++
 1 file changed, 104 insertions(+)
 create mode 100644 ProjectEuler/C++/Problem3.cpp

diff --git a/ProjectEuler/C++/Problem3.cpp b/ProjectEuler/C++/Problem3.cpp
new file mode 100644
index 0000000..16728f9
--- /dev/null
+++ b/ProjectEuler/C++/Problem3.cpp
@@ -0,0 +1,104 @@
+//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;
+}