PATB1034.有理数的四则运算

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本文介绍了一个C++程序，用于实现分数的加法、减法、乘法和除法运算，并提供分数简化的功能。程序中定义了分数结构体并实现了求最大公约数的方法，通过这些方法实现了分数的输入、输出及四则运算。

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知识点笔记：

AC代码：

#include <iostream>
#include <cmath>
using namespace std;
typedef long long ll;
struct Fraction{
	ll up,down; //分子 分母
};

//求最大公约数
ll gcd(ll a,ll b){
	if(b==0) return a;
	else return gcd(b,a%b);
}

//分数化简
Fraction reduction(Fraction result){
	if(result.down<0){   //分母为负数，令分子和分母都变为相反数
		result.up = -result.up;
		result.down = -result.down;
	}

	if(result.up==0)  //如果分子为0
		result.down=1; //令分母等于1
	else{				//如果分子不为0，进行约分，同除以最大公约数
		int d = gcd(abs(result.up),abs(result.down));
		result.up/=d;
		result.down/=d;
	}
	return result;
}

//分数的输出
void showResult(Fraction r){
	r = reduction(r);
	if(r.up<0) printf("(");
	if(r.down==1) printf("%lld",r.up);
	else if(abs(r.up)>abs(r.down)){
		//假分数
		printf("%lld %lld/%lld",r.up/r.down,abs(r.up)%r.down,r.down);
	}else{ //真分数
		 printf("%lld/%lld",r.up,r.down);
	}
	if(r.up<0) printf(")");
}

//分数的加法
Fraction add(Fraction f1,Fraction f2){
	Fraction result;
	result.up=f1.up*f2.down+f2.up*f1.down;
	result.down=f1.down*f2.down;
	return reduction(result);
}

//分数的减法
Fraction minu(Fraction f1,Fraction f2){
	Fraction result;
	result.up=f1.up*f2.down-f2.up*f1.down;
	result.down=f1.down*f2.down;
	return reduction(result);
}

//分数的乘法
Fraction multi(Fraction f1,Fraction f2){
	Fraction result;
	result.up=f1.up*f2.up;
	result.down=f1.down*f2.down;
	return reduction(result);
}

//分数的除法
Fraction divide(Fraction f1,Fraction f2){
	Fraction result;
	result.up=f1.up*f2.down;
	result.down=f1.down*f2.up;
	return reduction(result);
}

int main() {
	Fraction f1,f2;
	f1=reduction(f1);
	f2=reduction(f2);
	scanf("%lld/%lld %lld/%lld",&f1.up,&f1.down,&f2.up,&f2.down);

	showResult(f1);
	printf(" + ");
	showResult(f2);
	printf(" = ");
	showResult(add(f1,f2));
	printf("\n");

	showResult(f1);
	printf(" - ");
	showResult(f2);
	printf(" = ");
	showResult(minu(f1,f2));
	printf("\n");

	showResult(f1);
	printf(" * ");
	showResult(f2);
	printf(" = ");
	showResult(multi(f1,f2));
	printf("\n");

	showResult(f1);
	printf(" / ");
	showResult(f2);
	printf(" = ");
	if(f2.up==0) printf("Inf");
	else showResult(divide(f1,f2));

	return 0;
}