eulerproblems.cpp

#include <iostream>
#include <cmath>
#include <string>

using namespace std;

void projecteuler1();
void projecteuler2();
void projecteuler3();
void projecteuler4();
void projecteuler5();
void projecteuler6();

int main() {
	projecteuler6();
	return 0;
}

/*
projecteuler.net Problem 1
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
*/
void projecteuler1(){
	int sum = 0;
	int num = 0;
	for (int i = 0; i < 1000; i++) {
		if (i % 3 == 0 || i% 5 == 0) {
			num = i;
			sum += num;
			}
	}
	cout << "The sum of all the multiples of 3 or 5 below 1000 is " << sum << endl;
}

/*
projecteuler.net Problem 2
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
*/
void projecteuler2() {
	//generate the fibonnacci sequence
	unsigned int sum = 0;
	int storage; //to store the previous number temporarily
	int prevnum = 0;
	int fibonacci = 1;
	bool fourmil = false;
	while (fourmil == false) {
		if (fibonacci < 4000000) {
			storage = fibonacci;
			fibonacci += prevnum;
			prevnum = storage;
			if (fibonacci % 2 == 0) {
				sum += fibonacci;
			}
		}
		else {
			fourmil = true;
		}
		
	}
	cout << "The sum of all even terms in the Fibonacci sequence whose values do not exceed four million are: " << sum << endl;
}
/*
projecteuler.net Problem 3
What is the largest prime factor of the number 600,851,475,143 ?
*/
void projecteuler3() {

	const long long number = 600851475143;
	long long tempnum = number;
	long long largestprime = 0;

	int counter = 2;
	while (counter * counter <= tempnum) {
		if (tempnum % counter == 0) {
			tempnum = tempnum / counter;
			largestprime = counter;
		}
		else {
			counter = (counter == 2) ? 3 : counter + 2;
		}
	}
	if (tempnum > largestprime) { // the remainder is a prime number
		largestprime = tempnum;
	}
	cout << "The largest prime factor of 600,851,475,143 is " << largestprime << endl;
}
/*
projecteuler.net Problem 4 
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.
*/
void projecteuler4() {
	int num, first, second, backup;
	int inv = 0;
	int palindromei = 0;
	for (first = 999; first > 100; first--) {
		for (second = 999; second > 100; second--) {
			num = first * second;
			backup = num;
			do {
				int digit;
				digit = num % 10;
				inv = (inv * 10) + digit;
				num = num / 10;
			} while (num != 0);
			
			if (backup == inv) {
				if (backup > palindromei) {
					palindromei = backup;
				}
			}
			inv = 0;
		}
	}
	cout << "The largest palindrome from two 3 digit integers is: " << palindromei << endl;
}
/*
projecteuler.net	Problem 5
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
*/
void projecteuler5() {
	bool small = true;
	int number = 0;
	while (small==true)
	{
		number++;
		for (int i = 1; i <= 20; i++) {
			if (number%i == 0) {
				if (i == 20) {
					small = false;
				}
			}
			else {
				i = 21;
			}
		}
	}
	cout << "The smallest number that can be divided by the numbers 1-20 is: " << number << endl;
}
/*
projecteuler.net Problem 6
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
*/
void projecteuler6() {
	int sumofsquare = 0;
	int square;
	int squareofsum = 0;
	for (int i = 1; i <= 100; i++) {
		square = i*i;
		sumofsquare += square;
		squareofsum += i;
	}
	squareofsum = squareofsum*squareofsum;
	square = squareofsum - sumofsquare;
	cout << "The difference between the sum of the squares and the square of the sum is: " << square << endl;
}