/*分数ライブラリ*/
#ifndef YAMAGIWA_FRAC
#define YAMAGIWA_FRAC

#include<stdio.h>
#include<assert.h>

typedef struct fraction{
	int numerator;
	int denominator;
}FRAC;

/*最大公約数*/
int gcd(int m,int n){
	if(m<=0 || n<=0)return 0;
	if(m<n){
		int temp;
		temp=m;
		m=n;
		n=temp;
	}
	while(n!=0){
		int r=m%n;
		m=n;
		n=r;
	}
	return m;
}
/*最小公倍数*/
int lcm(int m,int n){
	int d = gcd(m,n);
	if( d == 0) return 0;
	return ( m*n/gcd(m,n) );
}
/*分子取得*/
int getNume(FRAC *a){
	return (a->numerator);
}
/*分母取得*/
int getDenom(FRAC * a){
	return (a->denominator);
}
/*約分*/
FRAC* reduce(FRAC* a){
	int d = gcd(a->numerator,a->denominator);
	if(d==0)return NULL;
	a->numerator /= d;
	a->denominator /= d;
	/*分母が負のとき分子分母に-1をかける*/
	if(getDenom(a)<0){
		a->numerator *= -1;
		a->denominator *= -1;
	}
	return a;
}
/*値を設定*/
FRAC setFrac(int num,int denom){
	FRAC temp;
	temp.numerator=num;
	temp.denominator=denom;
	reduce(&temp);/*約分*/
	return temp;
}
/*整数を分数変数へ変換*/
FRAC *int2Frac(int n){
	static FRAC c;
	c = setFrac(n,1);
	return &c;
}
/*有理数を分数変数へ変換*/
FRAC *double2Frac(double r){
	static FRAC c;
	int t=1;/**/
	while(r-(int)r != 0){
		r*=10;
		t*=10;
	}
	c = setFrac((int)r,t);
	return &c;
}
/*表示*/
void showFrac(FRAC* a){
	printf("%d/%d",a->numerator,a->denominator);
}
/*浮動小数点で表す*/
double frac2Double(FRAC* a){
	assert(a->denominator!=0);
	//if(a->denominator!=0) abort();/*0割終了*/
	return ((double)(a->numerator)/(a->denominator));
}
/*足し算*/
FRAC addFrac(FRAC *a,FRAC *b){
	FRAC c;
	int na = getNume(a);
	int nb = getNume(b);
	int m  = getDenom(a);
	if(getDenom(a)!=getDenom(b)){
		m = lcm(getDenom(a),getDenom(b));
		na = getNume(a) * m/getDenom(a);
		nb = getNume(b) * m/getDenom(b);
	}
	c = setFrac(na+nb,m);
	reduce(&c);
	return c;
}
FRAC difFrac(FRAC *a,FRAC *b){
	FRAC c;
	int na = getNume(a);
	int nb = getNume(b);
	int m  = getDenom(a);
	if(getDenom(a)!=getDenom(b)){
		m = lcm(getDenom(a),getDenom(b));
		na = getNume(a) * m/getDenom(a);
		nb = getNume(b) * m/getDenom(b);
	}
	c = setFrac(na-nb,m);
	reduce(&c);
	return c;
}
/*掛け算*/
FRAC multiFrac(FRAC *a,FRAC *b){
	FRAC c;
	c = setFrac(getNume(a)*getNume(b),getDenom(a)*getDenom(b));
	reduce(&c);
	return c;
}
/*割り算*/
FRAC divFrac(FRAC *a,FRAC *b){
	FRAC c;
	c = setFrac(getNume(a)*getDenom(b),getDenom(a)*getDenom(b));
	reduce(&c);
	return c;
}
/*比較 aが大きければ正,bが大きければ負,等しければ0を返す*/
double compFrac(FRAC *a,FRAC *b){
	FRAC c;
	double r;
	c=difFrac(a,b);/*差*/
	r=frac2Double(&c);
	return r;
}

#endif