11002

题目

实现分数结构体，并实现其加减乘除运算。要求输出的结果为最简分数。

解析

1. 定义结构体
2. 约分：gcd 函数
3. 运算：加减乘除

答案

typedef struct {
    int numerator;    // 分子
    int denominator;  // 分母
} fraction;

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

void simplify(fraction *frac) {
    int common = gcd(abs(frac->numerator), abs(frac->denominator));
    frac->numerator /= common;
    frac->denominator /= common;

    // 确保分母为正数，负号放在分子上
    if (frac->denominator < 0) {
        frac->numerator = -frac->numerator;
        frac->denominator = -frac->denominator;
    }
}

fraction add(fraction a, fraction b) {
    fraction result;
    result.numerator = a.numerator * b.denominator + b.numerator * a.denominator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

fraction subtract(fraction a, fraction b) {
    fraction result;
    result.numerator = a.numerator * b.denominator - b.numerator * a.denominator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

fraction multiply(fraction a, fraction b) {
    fraction result;
    result.numerator = a.numerator * b.numerator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

fraction divide(fraction a, fraction b) {
    assert(b.denominator != 0);
    fraction result;
    result.numerator = a.numerator * b.denominator;
    result.denominator = a.denominator * b.numerator;
    simplify(&result);
    return result;
}

fraction create_fraction(int numerator, int denominator = 1) {
    assert(denominator != 0);
    fraction result;
    result.numerator = numerator;
    result.denominator = denominator;
    simplify(&result);
    return result;
}