C语言分数加减乘除化简操作集(含测试源码)

本博文源于胡凡老师的《算法笔记》，书上给出了，一套分数的表示操作集，为了加深印象，写了这篇博文。

1.分数表示

分数由分子up和分母downn表示。

struct Fraction{int up,down;
};

2. 分数加法

假设两个分数f1,f2,其计算公式为
result=f1.up∗f2.down+f2.up∗f1.downf1.down∗f2.downresult = \frac{f1.up*f2.down+f2.up*f1.down}{f1.down*f2.down} result=f1.down∗f2.downf1.up∗f2.down+f2.up∗f1.down

Fraction add(Fraction f1,Fraction f2){Fraction res;res.up = f1.up * f2.down + f2.up * f1.down;res.down = f1.down * f2.down;return reduction(res);
}

3.分数减法

假设两个分数f1和f2，其减法计算公式
result=f1.up∗f2.down−f2.up∗f1.downf1.down∗f2.downresult = \frac{f1.up*f2.down-f2.up*f1.down}{f1.down*f2.down} result=f1.down∗f2.downf1.up∗f2.down−f2.up∗f1.down

Fraction minu(Fraction f1,Fraction f2){Fraction res;res.up = f1.up * f2.down - f2.up*f1.down;//分数差的分子res.down = f1.down * f2.down; //分数差的分母return reduction(res);}

4.分数乘法

对两个分数f1和f2,其乘法计算公式为
result=f1.up∗f2.upf1.down∗f2.downresult = \frac{f1.up*f2.up}{f1.down*f2.down} result=f1.down∗f2.downf1.up∗f2.up,

Fraction multi(Fraction f1,Fraction f2){Fraction r;r.up = f1.up * f2.up;r.down = f1.down * f2.down;return reduction(r);
}

5.分数除法

对两个分数f1和f2,其除法计算公式为
result=f1.up∗f2.downf1.down∗f2.upresult = \frac{f1.up*f2.down}{f1.down*f2.up} result=f1.down∗f2.upf1.up∗f2.down

Fraction divide(Fraction f1,Fraction f2){Fraction r;r.up = f1.up * f2.down;r.down = f1.down * f2.down;return reduction(r);
}

3.分数化简

如果分母down为负数，那么令分子up和分母down都变为相反数
如果分子up为0，那么令分母down为1
约分:求出分子绝对值与分母绝对值的最大公约数d，然后令分子分母同时除以d

Fraction reduction(Fraction result){if(result.down <0){//字母为负数，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0result.down = 1; //令分母为1}else{//如果分子不为0，进行约分int d = gcd(abs(result.up),abs(result.down));//分子分母的最大公约数result.up /= d;result.down /= d;}return result;
}

4.分数显示

输出分数前，需要先对其进行化简
如果分数r的分母down为1，说明该分数是整数,一般来说题目会要求直接输出分子，而省略分母的输出。
如果分数r的分子up的绝对值大于分母down，说明该分数是假分数，
如果以上都不满足，那就原样输出。

void showResult(Fraction r){r = reduction(r);if(r.down == 1) printf("%lld\n",r.up); //整数else if(abs(r.up) > r.down) { //假分数printf("%d %d/%d\n",r.up/r.down,abs(r.up)%r.down,r.down);}else{printf("%d/%d\n",r.up,r.down);}
}

完整代码

#include<stdio.h>
#include<math.h>
struct Fraction{int up,down;
};
int gcd(int a,int b){if(b==0) return a;else return gcd(b,a%b);
}
Fraction reduction(Fraction result){if(result.down <0){//字母为负数，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0result.down = 1; //令分母为1}else{//如果分子不为0，进行约分int d = gcd(abs(result.up),abs(result.down));//分子分母的最大公约数result.up /= d;result.down /= d;}return result;
}
//分数的加法运算
Fraction add(Fraction f1,Fraction f2){Fraction res;res.up = f1.up * f2.down + f2.up * f1.down;res.down = f1.down * f2.down;return reduction(res);
}//分数的减法运算
Fraction minu(Fraction f1,Fraction f2){Fraction res;res.up = f1.up * f2.down - f2.up*f1.down;//分数差的分子res.down = f1.down * f2.down; //分数差的分母return reduction(res);}//分数逇乘法运算
Fraction multi(Fraction f1,Fraction f2){Fraction r;r.up = f1.up * f2.up;r.down = f1.down * f2.down;return reduction(r);
}//分数的除法
Fraction divide(Fraction f1,Fraction f2){Fraction r;r.up = f1.up * f2.down;r.down = f1.down * f2.down;return reduction(r);
}void showResult(Fraction r){r = reduction(r);if(r.down == 1) printf("%lld\n",r.up); //整数else if(abs(r.up) > r.down) { //假分数printf("%d %d/%d\n",r.up/r.down,abs(r.up)%r.down,r.down);}else{printf("%d/%d\n",r.up,r.down);}
}int main()
{//测试分数的显示包含化简Fraction res;res.down = 12;res.up = 6;showResult(res);//测试分数的加法，减法，乘法，除法Fraction op1{3,7};Fraction op2{4,9};showResult(add(op1,op2));showResult(minu(op1,op2));showResult(multi(op1,op2));showResult(divide(op1,op2));return 0;}

测试效果