1088 Rational Arithmetic

题意：

给出两个分式(a1/b1 a2/b2)，分子、分母的范围为int型，且确保分母不为0。计算两个分数的加减乘除，结果化为最简的形式，即"k a/b"，其中若除数为0的话，输出Inf。

思路：

分数四则运算的模板题。分析详见：基础数学问题

代码：

#include <stdio.h>
#include <string.h>
#include <stdlib.h>//abs()
typedef long long LL;
struct Fraction{
    LL up;//分子
    LL down;//分母
    Fraction():up(),down(){}//默认初始化
    Fraction(int up_,int down_):up(up_),down(down_){}
};

//求最大公约数
int gcd(LL a,LL b){
    ) return a;
    else return gcd(b,a%b);
}

//分数化简
void simplify(Fraction& a){
    ) {
        a.down = -a.down;
        a.up = -a.up;
    }
    ){
        a.down=;
    }else{
        int commonFractor=gcd(abs(a.up), abs(a.down));//注意要加绝对值！！！
        a.up/=commonFractor;
        a.down/=commonFractor;
    }
}
//打印分数
void printFraction(Fraction a){
    simplify(a);
    ) printf("(");
    ) printf("%lld",a.up);//如果分母为1，则只打印分子即可
    else{
        if(abs(a.up)>abs(a.down))
            printf("%lld %lld/%lld",a.up/a.down,abs(a.up)%a.down,a.down);
        else
            printf("%lld/%lld",a.up,a.down);
    }
    ) printf(")");
}

//分数相加
Fraction add(Fraction a,Fraction b){
    Fraction c;
    c.down=a.down*b.down;
    c.up=a.up*b.down+a.down*b.up;
    simplify(c);
    return c;
}
//分数相减
Fraction sub(Fraction a,Fraction b){
    Fraction c;
    c.down=a.down*b.down;
    c.up=a.up*b.down-a.down*b.up;
    simplify(c);
    return c;
}
//分数相乘
Fraction multiply(Fraction a,Fraction b){
    Fraction c;
    c.down=a.down*b.down;
    c.up=a.up*b.up;
    simplify(c);
    return c;
}
//分数相除
Fraction divide(Fraction a,Fraction b){
    Fraction c;
    c.down=a.down*b.up;
    c.up=a.up*b.down;
    simplify(c);
    return c;
}

void showEquation(Fraction a,Fraction b,const char* op)
{
    bool flag=true;
    Fraction ans;
    printFraction(a);
    ){
        printf(" + ");
        ans=add(a,b);
    }){
        printf(" - ");
        ans=sub(a,b);
    }){
        printf(" * ");
        ans=multiply(a,b);
    }else {
        printf(" / ");
        ) flag=false;
        else ans=divide(a,b);
    }
    printFraction(b);
    printf(" = ");
    if(flag) printFraction(ans);
    else printf("Inf");
    printf("\n");
}

int main()
{
    LL a1,b1,a2,b2;
    scanf("%lld/%lld %lld/%lld",&a1,&b1,&a2,&b2);
    Fraction a(a1,b1);
    Fraction b(a2,b2);
    showEquation(a,b,"add");
    showEquation(a,b,"sub");
    showEquation(a,b,"multiply");
    showEquation(a,b,"divide");
    ;
}