有理数的四则运算

链接：http://www.nowcoder.com/pat/6/problem/4060

题目描述

本题要求编写程序，计算2个有理数的和、差、积、商。

输入描述:

输入在一行中按照“a1/b1 a2/b2”的格式给出两个分数形式的有理数，其中分子和分母全是整型范围内的整数，负号只可能出现在分子前，分

母不为0。

输出描述:

分别在4行中按照“有理数1 运算符 有理数2 = 结果”的格式顺序输出2个有理数的和、差、积、商。注意输出的每个有理数必须是该有理数的

最简形式“k a/b”，其中k是整数部分，a/b是最简分数部分；若为负数，则须加括号；若除法分母为0，则输出“Inf”。题目保证正确的输出中

没有超过整型范围的整数。

输入例子:

5/3 0/6

输出例子:

1 2/3 + 0 = 1 2/3

1 2/3 - 0 = 1 2/3

1 2/3 * 0 = 0

1 2/3 / 0 = Inf

思路：多加几个变量保存输入的有理数，1.用来保存最简形式 2.用来保存计算形式，就是通分过的形式。代码写起来比较复杂，还有输入格式的要求也比较多。

浮点错误：出现了除以0的情况。

#include "iostream"
#include <iomanip>
#include <string.h>
#include <string>
#include <vector>
#include <cmath>
#include <cctype>
#include <algorithm>
using namespace std;
 
typedef struct YLS{
    int z;
    int fz;
    int fm;
}YLS;
 
void change(YLS &yls)
{
    if(yls.fm == 0) return;
    if(yls.fz/yls.fm != 0)
    {
        yls.z += yls.fz/yls.fm;
        yls.fz = yls.fz%yls.fm;
    }
}
void tongFen(YLS &yls1, YLS &yls2)
{
     
            int t1, t2;
            t1 = yls1.fm;
            t2 = yls2.fm;
            yls1.fz *= t2;
            yls1.fm *= t2;
            yls2.fz *= t1;
            yls2.fm *= t1;
}
void output1(YLS yls1)
{
    int mark = 0;
    if(yls1.z<0 || yls1.fz<0 ||yls1.fm<0)
    {
        mark = 1;
        cout <<'(';
    }
    if(yls1.fz==0 && yls1.z==0)
    {
        cout <<0;
    }
    else
    {
        if(yls1.z == 0)
        {
            if(yls1.fm < 0)
            {
                yls1.fm = -yls1.fm;
                yls1.fz = -yls1.fz;
            }
            cout <<yls1.fz <<"/" <<yls1.fm;
        }
        else
        {
            if(yls1.fz == 0)
            {
                cout <<yls1.z;
            }
            else
            {
                if(yls1.fm < 0)
                {
                    yls1.fm = -yls1.fm;
                    yls1.fz = -yls1.fz;
                }
                if(yls1.fz < 0)
                {
                    if(yls1.z > 0)   yls1.z = -yls1.z;
                    yls1.fz = - yls1.fz;
                }
                cout <<yls1.z <<" " <<yls1.fz <<"/" <<yls1.fm;
            }
        }
    }
    if(mark == 1)   cout <<')';
    cout <<" " <<"/" <<" ";
    cout <<0;
    cout <<" " <<"=" <<" ";
    cout <<"Inf";
}
void output(YLS yls1, YLS yls2, char c, YLS yls3)
{
    int mark = 0;
    if(yls1.z<0 || yls1.fz<0 || yls1.fm<0)
    {  
        mark = 1;
        cout <<'(';
    }
    if(yls1.fz==0 && yls1.z==0)
    {
        cout <<0;
    }
    else
    {
        if(yls1.z == 0)
        {
            if(yls1.fm < 0)
            {
                yls1.fm = -yls1.fm;
                yls1.fz = -yls1.fz;
            }
            cout <<yls1.fz <<"/" <<yls1.fm;
        }
        else
        {
            if(yls1.fz == 0)
            {
                cout <<yls1.z;
            }
            else
            {
                if(yls1.fm < 0)
                {
                    yls1.fm = -yls1.fm;
                    yls1.fz = -yls1.fz;
                }
                if(yls1.fz < 0)
                {
                    if(yls1.z > 0)   yls1.z = -yls1.z;
                    yls1.fz = - yls1.fz;
                }
                cout <<yls1.z <<" " <<yls1.fz <<"/" <<yls1.fm;
            }
        }
    }
    if(mark == 1)   cout <<')';
    cout <<" " <<c <<" ";
    mark = 0;
    if(yls2.z<0 || yls2.fz<0 || yls2.fm<0)
    {  
        mark = 1;
        cout <<'(';
    }
    if(yls2.fz==0 && yls2.z==0)
    {
        cout <<0;
    }
    else
    {
        if(yls2.z == 0)
        {
            if(yls2.fm < 0)
            {
                yls2.fm = -yls2.fm;
                yls2.fz = -yls2.fz;
            }      
            cout <<yls2.fz <<"/" <<yls2.fm;
        }
        else
        {
            if(yls2.fz == 0)
            {
                cout <<yls2.z;
            }
            else
            {
                if(yls2.fm < 0)
                {
                    yls2.fm = -yls2.fm;
                    yls2.fz = -yls2.fz;
                }
                if(yls2.fz < 0)
                {
                    if(yls2.z > 0)   yls2.z = -yls2.z;
                    yls2.fz = - yls2.fz;
                }
                cout <<yls2.z <<" " <<yls2.fz <<"/" <<yls2.fm;
            }
        }
    }
    if(mark == 1)   cout <<')';
    cout <<" " <<"=" <<" ";
    mark = 0;
    if(yls3.z<0 || yls3.fz<0 || yls3.fm<0)
    {
        mark = 1;
        cout <<'(';
    }
    if(yls3.fz==0 && yls3.z==0)
    {
        cout <<0;
    }
    else
    {
        if(yls3.z == 0)
        {
            if(yls3.fm < 0)
            {
                yls3.fm = -yls3.fm;
                yls3.fz = -yls3.fz;
            }
            cout <<yls3.fz <<"/" <<yls3.fm;
        }
        else
        {
            if(yls3.fz == 0)
            {
                cout <<yls3.z;
            }
            else
            {
                if(yls3.fm < 0)
                {
                    yls3.fm = -yls3.fm;
                    yls3.fz = -yls3.fz;
                }
                if(yls3.fz < 0)
                {
                    if(yls3.z > 0)   yls3.z = -yls3.z;
                    yls3.fz = -yls3.fz;
                }
                cout <<yls3.z <<" " <<yls3.fz <<"/" <<yls3.fm;
            }
        }
    }
    if(mark == 1)   cout <<')';
}
int gcd(int x, int y)
{
    if(y != 0)
    {if(x%y == 0)
    {
        return y;
    }
    else
    {
        return gcd(y, x%y);
    }}
}
int main()
{
    YLS yls1, yls2, yls3, yls4;
    yls1.z = 0;
    cin >>yls1.fz;
    getchar();
    cin >>yls1.fm;
    yls2.z = 0;
    cin >>yls2.fz;
    getchar();
    cin >>yls2.fm;
 
    yls3 = yls1;
    yls4 = yls2;
    int gys = 0;
    if(yls2.fz != 0)
    {
        gys = gcd(yls2.fz, yls2.fm);
    }
    if(gys != 0)
    {yls2.fz /= gys;
    yls2.fm /= gys;}
    gys = 0;
    if(yls1.fz != 0)
    {
        gys = gcd(yls1.fz, yls1.fm);
    }
    if(gys != 0)
    {yls1.fz /= gys;
    yls1.fm /= gys;}
    change(yls1);
    change(yls2);
     
    YLS ylsX,ylsY,ylsZ;
    ylsX = yls3;
    ylsY = yls4;
    tongFen(ylsX, ylsY);
    ylsZ.z = ylsX.z+ylsY.z;
    ylsZ.fz = ylsX.fz+ylsY.fz;
    ylsZ.fm = ylsX.fm;
    gys = 0;
    if(ylsZ.fz != 0)
    {
        gys = gcd(ylsZ.fz, ylsZ.fm);
    }
    if(gys != 0)
    {ylsZ.fz /= gys;
    ylsZ.fm /= gys;}
    change(ylsZ);
    output(yls1, yls2, '+', ylsZ);
    cout <<endl;
 
    ylsZ.z = ylsX.z-ylsY.z;
    ylsZ.fz = ylsX.fz-ylsY.fz;
    ylsZ.fm = ylsX.fm;
    gys = 0;
    if(ylsZ.fz != 0)
    {
        gys = gcd(ylsZ.fz, ylsZ.fm);
    }
    if(gys != 0)
    {ylsZ.fz /= gys;
    ylsZ.fm /= gys;}
    change(ylsZ);
    output(yls1, yls2, '-', ylsZ);
    cout <<endl;
 
    ylsZ.z = 0;
    ylsZ.fz = yls3.fz*yls4.fz;
    ylsZ.fm = yls3.fm*yls4.fm;
    change(ylsZ);
    gys = 0;
    if(ylsZ.fz != 0)
    {
        gys = gcd(ylsZ.fz, ylsZ.fm);
    }
    if(gys != 0)
    {ylsZ.fz /= gys;
    ylsZ.fm /= gys;}
    output(yls1, yls2, '*', ylsZ);
    cout <<endl;
 
    YLS yls5;
    yls5.fm = yls4.fz;
    yls5.fz = yls4.fm;
    if(yls4.fz == 0)
    {
        output1(yls1);
        cout <<endl;
    }
    else
    {
        ylsZ.z = 0;
        ylsZ.fz = yls3.fz*yls5.fz;
        ylsZ.fm = yls3.fm*yls5.fm;
        change(ylsZ);
        gys = 0;
        if(ylsZ.fz != 0)
        {
            gys = gcd(ylsZ.fz, ylsZ.fm);
        }
        if(gys != 0)
        {ylsZ.fz /= gys;
        ylsZ.fm /= gys;}
        output(yls1, yls2, '/', ylsZ);
        cout <<endl;
    }
    return 0;
}