PAT1034

本题要求编写程序，计算2个有理数的和、差、积、商。

输入格式：

# include<iostream>
# include<algorithm>
# include<stdio.h>
# include<string>
using namespace std;
bool ISint(int a,int b)
{
    double c = a*1.0 / b;
    if(c - (int)c == 0)
    {
        return true;
    }
    else
    {
        return false;
    }
}
int gcd(int a,int b)//a da
{
    int t;
    if(a<b)
    {
        t=a;a=b;b=t;
    }
    
    if(b==0)
    {
        return 0;
    }
    else
    {
        while(b!=0)
        {
            t = a % b;
            a = b;
            b = t;
        }
        return a;
    }
}

int gbs(int x,int y)
{
    return (x*y)/gcd(x,y);
}

void printhe(int he,int gb,int a1,int b1,int a2,int b2)
{
    if( ISint(a1,b1) && a1>=0)
    {
        cout<<a1/b1;
    }
    else if(ISint(a1,b1) && a1<0 )
    {
        cout<<"("<<a1/b1<<")";
    }
    else if(!ISint(a1,b1) && a1>=0)
    {
        int t1 = gcd(a1,b1);
        a1 = a1 /t1;
        b1 = b1 /t1;
        if(a1>b1)
        {
            int k1=0;
            while(a1>b1)
            {
                a1 = a1 - b1;
                k1++;
            }
        cout<<k1<<" "<<a1<<"/"<<b1;
         }
         else
         {
             cout<<a1<<"/"<<b1;
         }
    }
    else
    {
            a1 = -a1;
            int t1 = gcd(a1,b1);
        a1 = a1 /t1;
        b1 = b1 /t1;
        if(a1>b1)
        {
            int k1=0;
            while(a1>b1)
            {
                a1 = a1 - b1;
                k1++;
            }
                  cout<<"(-"<<k1<<" "<<a1<<"/"<<b1<<")";
         }
         else
         {
                  cout<<"(-"<<a1<<"/"<<b1<<")";
            }
        
    }
    cout<<" + ";
    if( ISint(a2,b2) && a2>=0)
    {
        cout<<a2/b2;
    }
    else if(ISint(a2,b2) && a2<0 )
    {
        cout<<"("<<a2/b2<<")";
    }
    else if(!ISint(a2,b2) && a2>=0)
    {
        int t2 = gcd(a2,b2);
        a2 = a2 /t2;
        b2 = b2 /t2;
        if(a2>b2)
        {
            int k2=0;
            while(a2>b2)
            {
                a2 = a2 - b2;
                k2++;
            }
        cout<<k2<<" "<<a2<<"/"<<b2;
         }
         else
         {
             cout<<a2<<"/"<<b2;
         }
    }
    else
    {
            a2 = -a2;
            int t2 = gcd(a2,b2);
        a2 = a2 /t2;
        b2 = b2 /t2;
        if(a2>b2)
        {
            int k2=0;
            while(a2>b2)
            {
                a2 = a2 - b2;
                k2++;
            }
                  cout<<"("<<-k2<<" "<<a2<<"/"<<b2<<")";
              }
         else
          {
                 cout<<"(-"<<a2<<"/"<<b2<<")";
         }
        
    }
    cout<<" = ";
    if(he>=0)
    {
        if(ISint(he,gb))
        {
                cout<<he;
        }
        else
        {
            int t = gcd(he,gb);
            he = he /t;
            gb = gb /t;
            if(he>gb)
            {
                int k=0;
                while(he>gb)
                {
                    he = he - gb;
                    k++;
                }
                cout<<k<<" "<<he<<"/"<<gb;
            }
            else
            {
                cout<<he<<"/"<<gb;
            }
        }
    }
    else
    {
        he = - he;
        if(ISint(he,gb))
        {
                cout<<"(-"<<he/gb<<")";
        }
        else
        {
            int t = gcd(he,gb);
            he = he /t;
            gb = gb /t;
            if(he>gb)
            {
                int k=0;
                while(he>gb)
                {
                    he = he - gb;
                    k++;
                }
                cout<<"("<<-k<<" "<<he<<"/"<<gb<<")";
            }
            else
            {
                cout<<"("<<-he<<"/"<<gb<<")";
            }
        }
    }
    cout<<endl;
}

void printcha(int cha,int gb,int a1,int b1,int a2,int b2)
{
    if( ISint(a1,b1) && a1>=0)
    {
        cout<<a1/b1;
    }
    else if(ISint(a1,b1) && a1<0 )
    {
        cout<<"("<<a1/b1<<")";
    }
    else if(!ISint(a1,b1) && a1>=0)
    {
        int t1 = gcd(a1,b1);
        a1 = a1 /t1;
        b1 = b1 /t1;
        if(a1>b1)
        {
            int k1=0;
            while(a1>b1)
            {
                a1 = a1 - b1;
                k1++;
            }
        cout<<k1<<" "<<a1<<"/"<<b1;
         }
         else
         {
             cout<<a1<<"/"<<b1;
         }
    }
    else
    {
            a1 = -a1;
            int t1 = gcd(a1,b1);
        a1 = a1 /t1;
        b1 = b1 /t1;
        if(a1>b1)
        {
            int k1=0;
            while(a1>b1)
            {
                a1 = a1 - b1;
                k1++;
            }
                  cout<<"("<<-k1<<" "<<a1<<"/"<<b1<<")";
              }
         else
         {
                cout<<"(-"<<a1<<"/"<<b1<<")";
           }
    }
    cout<<" - ";
    if( ISint(a2,b2) && a2>=0)
    {
        cout<<a2/b2;
    }
    else if(ISint(a2,b2) && a2<0 )
    {
        cout<<"("<<a2/b2<<")";
    }
    else if(!ISint(a2,b2) && a2>=0)
    {
        int t2 = gcd(a2,b2);
        a2 = a2 /t2;
        b2 = b2 /t2;
        if(a2>b2)
        {
            int k2=0;
            while(a2>b2)
            {
                a2 = a2 - b2;
                k2++;
            }
        cout<<k2<<" "<<a2<<"/"<<b2;
         }
         else
         {
             cout<<a2<<"/"<<b2;
         }
    }
    else
    {
            a2 = -a2;
            int t2 = gcd(a2,b2);
        a2 = a2 /t2;
        b2 = b2 /t2;
        if(a2>b2)
        {
            int k2=0;
            while(a2>b2)
            {
                a2 = a2 - b2;
                k2++;
            }
                  cout<<"("<<-k2<<" "<<a2<<"/"<<b2<<")";
              }
         else
         {
                cout<<"(-"<<a2<<"/"<<b2<<")";
        }
    }
    cout<<" = ";
    if(cha>=0)
    {
        if(ISint(cha,gb))
        {
                cout<<cha;
        }
        else
        {
            int t = gcd(cha,gb);
            cha = cha /t;
            gb = gb /t;
            if(cha>gb)
            {
                int k=0;
                while(cha>gb)
                {
                    cha = cha - gb;
                    k++;
                }
                cout<<k<<" "<<cha<<"/"<<gb;
            }
            else
            {
                cout<<cha<<"/"<<gb;
            }
        }
    }
    else
    {
        cha = - cha;
        if(ISint(cha,gb))
        {
                cout<<"(-"<<cha/gb<<")";
        }
        else
        {
            int t = gcd(cha,gb);
            cha = cha /t;
            gb = gb /t;
            if(cha>gb)
            {
                int k=0;
                while(cha>gb)
                {
                    cha = cha - gb;
                    k++;
                }
                cout<<"("<<-k<<" "<<cha<<"/"<<gb<<")";
            }
            else
            {
                cout<<"("<<-cha<<"/"<<gb<<")";
            }
        }
    }
    cout<<endl;
}
int main()
{
    int a1,a2,b1,b2;
    scanf("%d/%d %d/%d",&a1,&b1,&a2,&b2);
    int gb,gy,he,cha;
    gb = gbs(b1,b2);
    he = a1 * gb / b1 + a2 * gb / b2;
    cha = a1 * gb / b1 - a2 * gb / b2;
    printhe(he,gb,a1,b1,a2,b2);
    printcha(cha,gb,a1,b1,a2,b2);
    return 0;
}

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。

输出格式：

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。

输入样例1：

2/3 -4/2

输出样例1：

2/3 + (-2) = (-1 1/3)
2/3 - (-2) = 2 2/3
2/3 * (-2) = (-1 1/3)
2/3 / (-2) = (-1/3)

输入样例2：

5/3 0/6

输出样例2：

1 2/3 + 0 = 1 2/3
1 2/3 - 0 = 1 2/3
1 2/3 * 0 = 0
1 2/3 / 0 = Inf