PAT-A1088/B1034 Rational Arithmetic/有理数四则运算 题目内容及题解

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

本题要求编写程序，计算 2 个有理数的和、差、积、商。

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.

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。

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.

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。

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

解题思路

分解问题：

1. 建立结构体保存有理数；
2. 读入数字并预处理；
3. 分别建立加减乘除的函数（需要注意除法的边界条件）；
4. 建立输出函数处理不同情况的结果（是否加括号、输出格式等）；
5. 按照题目要求格式输出；
6. 返回零值。

代码

#include<stdio.h>

struct Rational{
    long long sign,numerator,denominator;
}num[2],ans;

long long gcd(long long a,long long b){
    if(b==0){
        return a;
    }else{
        return gcd(b,a%b);
    }
}

void Print1(struct Rational a){
    long long pub;
    if(a.numerator==0){
        printf("0");
    }else{
        if(a.numerator/a.denominator){
            printf("%d",a.numerator/a.denominator);
            a.numerator%=a.denominator;
            if(a.numerator==0){
                return;
            }else{
                printf(" ");
            }
        }
        pub=gcd(a.numerator,a.denominator);
        printf("%d/%d",a.numerator/pub,a.denominator/pub);
    }
}

void Print(struct Rational a){
    if(a.sign==-1){
        printf("(-");
        Print1(a);
        printf(")");
    }else{
        Print1(a);
    }
}
void Add(){
    long long a,b,pub;
    pub=gcd(num[0].denominator,num[1].denominator);
    a=num[0].denominator/pub;
    b=num[1].denominator/pub;
    ans.denominator=a*b*pub;
    ans.numerator=num[0].sign*num[0].numerator*b+num[1].sign*num[1].numerator*a;
    if(ans.numerator<0){
        ans.sign=-1;
        ans.numerator=-ans.numerator;
    }else{
        ans.sign=1;
    } 
    pub=gcd(ans.numerator,ans.denominator);
    ans.denominator/=pub;
    ans.numerator/=pub;
}

void Minus(){
    long long a,b,pub;
    pub=gcd(num[0].denominator,num[1].denominator);
    a=num[0].denominator/pub;
    b=num[1].denominator/pub;
    ans.denominator=a*b*pub;
    ans.numerator=num[0].sign*num[0].numerator*b-num[1].sign*num[1].numerator*a;
    if(ans.numerator<0){
        ans.sign=-1;
        ans.numerator=-ans.numerator;
    }else{
        ans.sign=1;
    }
    pub=gcd(ans.numerator,ans.denominator);
    ans.denominator/=pub;
    ans.numerator/=pub;
}

void Multi(){
    long long pub;
    ans.denominator=num[0].denominator*num[1].denominator;
    ans.numerator=num[0].numerator*num[1].numerator;
    if(ans.numerator==0){
        ans.sign=1;
    }else{
        ans.sign=num[0].sign*num[1].sign;
    }
    pub=gcd(ans.numerator,ans.denominator);
    ans.denominator/=pub;
    ans.numerator/=pub;
}

void Devide(){
    long long pub;
    ans.denominator=num[0].denominator*num[1].numerator;
    ans.numerator=num[0].numerator*num[1].denominator;
    if(ans.numerator==0){
        ans.sign=1;
    }else{
        ans.sign=num[0].sign*num[1].sign;
    }
    pub=gcd(ans.numerator,ans.denominator);
    ans.denominator/=pub;
    ans.numerator/=pub;
}

int main(){
    int i;
    long long a,b,pub;
    for(i=0;i<2;i++){
        scanf("%lld/%lld",&a,&b);
        if(a<0){
            num[i].sign=-1;
            a=-a;
        }else{
            num[i].sign=1;
        }
        pub=gcd(a,b);
        num[i].numerator=a/pub;
        num[i].denominator=b/pub;
    }
    Print(num[0]);
    printf(" + ");
    Print(num[1]);
    printf(" = ");
    Add();
    Print(ans);
    printf("\n");
    Print(num[0]);
    printf(" - ");
    Print(num[1]);
    printf(" = ");
    Minus();
    Print(ans);
    printf("\n");
    Print(num[0]);
    printf(" * ");
    Print(num[1]);
    printf(" = ");
    Multi();
    Print(ans);
    printf("\n");
    Print(num[0]);
    printf(" / ");
    Print(num[1]);
    printf(" = ");
    if(num[1].numerator==0){
        printf("Inf");
    }else{
        Devide();
        Print(ans);
        
    }
    printf("\n");
}

运行结果