USACO Section 2.1 Ordered Fractions

/*
ID: lucien23
PROG: frac1
LANG: C++
*/

#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
using namespace std;

typedef struct Fraction
{
	int numerator;
	int denominator;
	Fraction(){}
	Fraction(int x, int y)
	{
		numerator = x;
		denominator = y;
	}
} Fraction;

bool isPrimes(int x, int y);

bool compFrac(Fraction frac1, Fraction frac2)
{
	if (frac1.numerator/(double)frac1.denominator < frac2.numerator/(double)frac2.denominator)
	{
		return true;
	}
	return false;
}

int main()
{
	ifstream infile("frac1.in");
	ofstream outfile("frac1.out");
	if(!infile || !outfile)
	{
		cout << "file operation failure!" << endl;
		return -1;
	}

	int N;
	infile >> N;

	vector<Fraction> fractions;
	fractions.push_back(Fraction(0, 1));
	fractions.push_back(Fraction(1, 1));

	for (int i=1; i<=N; i++)
	{
		for (int j=1; j<i; j++)
		{
			if (isPrimes(j, i))
			{
				fractions.push_back(Fraction(j, i));
			}
		}
	}

	sort(fractions.begin(), fractions.end(), compFrac);

	for (vector<Fraction>::iterator it=fractions.begin(); it!=fractions.end(); it++)
	{
		outfile << it->numerator << "/" <<it->denominator << endl;
	}

	return 0;
}

/*
 *推断两数是否互质
 */
bool isPrimes(int x, int y)
{
	for (int i=2; i<=x; i++)
	{
		if (x%i == 0 && y%i == 0)
		{
			return false;
		}
	}

	return true;
}