1088 Rational Arithmetic （20 分）

1088 Rational Arithmetic （20 分）

For two rational numbers, your task is to implement the basic arithmetics, that is, to calculate their sum, difference, product and quotient.

Input Specification:

Each input file contains one test case, which gives in one line the two rational numbers in the format a1/b1 a2/b2. The numerators and the denominators are all in the range of long int. If there is a negative sign, it must appear only in front of the numerator. The denominators are guaranteed to be non-zero numbers.

Output Specification:

For each test case, print in 4 lines the sum, difference, product and quotient of the two rational numbers, respectively. The format of each line is number1 operator number2 = result. Notice that all the rational numbers must be in their simplest form k a/b, where k is the integer part, and a/b is the simplest fraction part. If the number is negative, it must be included in a pair of parentheses. If the denominator in the division is zero, output Inf as the result. It is guaranteed that all the output integers are in the range of long int.

Sample Input 1:

2/3 -4/2

Sample Output 1:

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

Sample Input 2:

5/3 0/6

Sample Output 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
思路：
　　刚开始在四则运算之前没有化简，第三个测试点通不过，然后在计算之前添加了化简语句后能通过，我猜可能是发生了溢出。

#include<iostream>
#include<vector>
#include<algorithm>
#include<map>
#include<set>
#include<cmath>
#include<climits>
#include<sstream>
#include<cstdio>
#include<string.h>
#include<unordered_map>
using namespace std;
struct Fraction
{
   long long int up;
   long long int down;
};
int gcd(long long int a,long long int b)
{
    if(b==0)
        return a;
    return gcd(b,a%b);
}
void reduction(Fraction &temp)
{
    if(temp.up==0)
    {
        temp.down=1;
        return;
    }
    if(temp.down<0)
    {
        temp.up=-temp.up;
        temp.down=-temp.down;
    }
    int t=gcd(abs(temp.up),abs(temp.down));
    temp.up/=t;
    temp.down/=t;
}

void add(Fraction &sum,Fraction &temp,Fraction& result)
{

    result.up=sum.up*temp.down+sum.down*temp.up;
    result.down=sum.down*temp.down;
    reduction(result);
}

void diff(Fraction &A,Fraction &B,Fraction &result)
{
    result.up=A.up*B.down-A.down*B.up;
    result.down=A.down*B.down;
    reduction(result);
}

void product(Fraction &A,Fraction &B,Fraction &result)
{
    result.up=A.up*B.up;
    result.down=A.down*B.down;
    reduction(result);
}

bool quotient(Fraction &A,Fraction &B,Fraction &result)
{
    if(B.up==0)
        return false;
    result.up=A.up*B.down;
    result.down=A.down*B.up;
    reduction(result);
    return true;
}

void print(Fraction A)
{
    int num=A.up/A.down;
    if(num>0)
    {
        printf("%d",num);
        A.up=A.up%A.down;
        if(A.up>0)
        {
            printf(" %lld/%lld",A.up,A.down);
        }
    }
    else if(num==0)
    {
        if(A.up<0)
        {
            printf("(%lld/%lld)",A.up,A.down);
        }
        else if (A.up==0)
            printf("0");
        else
            printf("%lld/%lld",A.up,A.down);
    }
    else
    {
        printf("(%d",num);
        A.up=abs(A.up)%A.down;
        if(A.up>0)
        {
            printf(" %lld/%lld)",A.up,A.down);
        }
        else
            printf(")");
    }
}



void output(char sign,Fraction A,Fraction B,Fraction result)
{
    print(A);
    printf(" %c ",sign);
    print(B);
    printf(" = ");
    print(result);
    printf("
");

}

int main()
{
    Fraction A,B,result;
    scanf("%lld/%lld%lld/%lld",&A.up,&A.down,&B.up,&B.down);
    reduction(A);
    reduction(B);
    add(A,B,result);
    output('+',A,B,result);
    diff(A,B,result);
    output('-',A,B,result);
    product(A,B,result);
    output('*',A,B,result);
    if(quotient(A,B,result))
    {
        output('/',A,B,result);
    }
    else
    {
        print(A);
        printf(" / ");
        print(B);
        printf(" = ");
        printf("Inf");
    }

    return 0;
}