大数的分数的四则运算(C++)

骑猪看日落 2023-05-30 09:18 13阅读 0赞

主要包括一下几个方面：  
1、分数的表示

struct Fraction          //结构来存储 分子分母
    { 
    	ll up, down;
    };

2、分数的化简

Fraction Reducation(Fraction result)  //化简操作
    { 
    	ll d;
    	if (result.down < 0)   //为负数的时候
    	{ 
    		result.up = -result.up;
    		result.down = -result.down;
    	}
    	if (result.up == 0)
    		result.down = 1;
    	else if(result.down==0)
          printf("error");
    	else
    	{ 
    		d = gcd(abs(result.up), abs(result.down));   //化简假分数，通过调用最大公约数
    		result.up /= d;
    		result.down /= d;
    	}
    	return result;
    }

3、分数的加减乘除

Fraction add(Fraction f1, Fraction f2) //加法运算 f1,f2为两个数，通过结构体来调用分子分母
    {
    	Fraction result;
    	result.up = f1.up*f2.down + f2.up*f1.down; 
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction jian(Fraction f1, Fraction f2) //减法运算
    {
    	Fraction result;
    	result.up = f1.up*f2.down - f2.up*f1.down;
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction chen(Fraction f1, Fraction f2) //乘法运算
    {
    	Fraction result;
    	result.up = f1.up*f2.up;
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction chu(Fraction f1, Fraction f2) //除法运算
    {
    	Fraction result;
    	result.up = f1.up*f2.down;
    	result.down = f1.down*f2.up;
    	return Reducation(result);
    }cpp

4、分数的输出

void showResult(Fraction r)
    { 
    	r = Reducation(r);
    	if (r.down == 1) //分母为1
    		printf("%lld", r.up);
    	else if (fabs(r.up) > 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);
    }

5、总的代码

#include <iostream>
    #include<string.h>
    #include<cstdio>
    #include<math.h>
    #define _CRT_SECURE_NO_WARNINGS
    
    typedef long long ll;   //由于乘法和除法的过程中可能使分子或分母超过int型的表示范围
    					  //因此一般情况，分子分母应当使用long long 型存储
    using namespace std;
    
    struct Fraction          //结构来存储 分子分母
    { 
    	ll up, down;
    };
    
    int  gcd(ll a, ll b)
    { 
    	
    	if (b == 0)
    		return a;
    	else
    		return gcd(b, a%b);
    }
    Fraction Reducation(Fraction result)  //化简操作
    { 
    	ll d;
    	if (result.down < 0)   //为负数的时候
    	{ 
    		result.up = -result.up;
    		result.down = -result.down;
    	}
    	if (result.up == 0)
    		result.down = 1;
    	else if(result.down==0)
          printf("error");
    	else
    	{ 
    		d = gcd(abs(result.up), abs(result.down));   //化简假分数，通过调用最大公约数
    		result.up /= d;
    		result.down /= d;
    	}
    	return result;
    }
    Fraction add(Fraction f1, Fraction f2) //加法运算 f1,f2为两个数，通过结构体来调用分子分母
    { 
    	Fraction result;
    	result.up = f1.up*f2.down + f2.up*f1.down; 
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction jian(Fraction f1, Fraction f2) //减法运算
    { 
    	Fraction result;
    	result.up = f1.up*f2.down - f2.up*f1.down;
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction chen(Fraction f1, Fraction f2) //乘法运算
    { 
    	Fraction result;
    	result.up = f1.up*f2.up;
    	result.down = f1.down*f2.down;
    	return Reducation(result);
    }
    Fraction chu(Fraction f1, Fraction f2) //除法运算
    { 
    	Fraction result;
    	result.up = f1.up*f2.down;
    	result.down = f1.down*f2.up;
    	return Reducation(result);
    }
    
    void showResult(Fraction r)
    { 
    	r = Reducation(r);
    	if (r.down == 1) //分母为1
    		printf("%lld", r.up);
    	else if (fabs(r.up) > 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);
    }
    int main()
    { 
    
    	Fraction f1,f2 ;
    	Fraction result;
    	char x;
    	printf("input two fraction:\n");
    	scanf_s("%lld/%lld ",&f1.up,&f1.down);
    	scanf_s("%c",&x);
    	scanf_s("%lld/%lld",&f2.up,&f2.down);
    	switch (x)
    	{ 
    	case '+':
    		result = add(f1, f2);
    		break;
    	case '-':
    		result = jian(f1, f2);
    		break;
    	case '*':
    		result = chen(f1, f2);
    		break;
    	case '/':
    		result = chu(f1, f2);
    	}
    	showResult(result);
    	system("pause");
    	return 0;
    }