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【C/C++】分数

作者:雨泽 / 发布于2016/4/21/ 714

struct frac{
	int num,den;
};

double fabs(double x){
	return x>0?x:-x;
}

int gcd(int a,int b){
	int t;
	if (a<0)
		a=-a;
	if (b<0)
		b=-b;
	if (!b)
		return a;
	while (t=a%b)
		a=b,b=t;
	return b;
}

void simplify(frac& f){
	int t;
	if (t=gcd(f.num,f.den))
		f.num/=t,f.den/=t;
	else
		f.den=1;
}

frac f(int n,int d,int s=1){
	frac ret;
	if (d<0)
		ret.num=-n,ret.den=-d;
	else
		ret.num=n,ret.den=d;
	if (s)
		simplify(ret);
	return ret;
}

frac convert(double x){
	frac ret;
	for (ret.den=1;fabs(x-int(x))>1e-10;ret.den*=10,x*=10);
	ret.num=(int)x;
	simplify(ret);
	return ret;
}

int fraqcmp(frac a,frac b){
	int g1=gcd(a.den,b.den),g2=gcd(a.num,b.num);
	if (!g1||!g2)
		return 0;
	return b.den/g1*(a.num/g2)-a.den/g1*(b.num/g2);
}

frac add(frac a,frac b){
	int g1=gcd(a.den,b.den),g2,t;
	if (!g1)
		return f(1,0,0);
	t=b.den/g1*a.num+a.den/g1*b.num;
	g2=gcd(g1,t);
	return f(t/g2,a.den/g1*(b.den/g2),0);
}

frac sub(frac a,frac b){
	return add(a,f(-b.num,b.den,0));
}

frac mul(frac a,frac b){
	int t1=gcd(a.den,b.num),t2=gcd(a.num,b.den);
	if (!t1||!t2)
		return f(1,1,0);
	return f(a.num/t2*(b.num/t1),a.den/t1*(b.den/t2),0);
}

frac div(frac a,frac b){
	return mul(a,f(b.den,b.num,0));
}

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