Given a string representing an expression of fraction addition and subtraction, you need to return the calculation result in string format. The final result should be irreducible fraction. If your final result is an integer, say 2, you need to change it to the format of fraction that has denominator 1. So in this case, 2 should be converted to 2/1.

Example 1:

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Input:"-1/2+1/2"
Output: "0/1"

Example 2:

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Input:"-1/2+1/2+1/3"
Output: "1/3"

Example 3:

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Input:"1/3-1/2"
Output: "-1/6"

Example 4:

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Input:"5/3+1/3"
Output: "2/1"

Note:

  1. The input string only contains '0' to '9', '/', '+' and '-'. So does the output.
  2. Each fraction (input and output) has format ±numerator/denominator. If the first input fraction or the output is positive, then '+'will be omitted.
  3. The input only contains valid irreducible fractions, where the numerator and denominator of each fraction will always be in the range [1,10]. If the denominator is 1, it means this fraction is actually an integer in a fraction format defined above.
  4. The number of given fractions will be in the range [1,10].
  5. The numerator and denominator of the final result are guaranteed to be valid and in the range of 32-bit int.

模拟分数的计算，我总是觉得好像做过类似的题。

其实就是单纯的模拟手算就可以了，一个分数有三个属性：

  1. 分子
  2. 分母
  3. 符号

依次地读取和计算就可以了，最后再求一个最大公约数（辗转相除法）。

为了实现的简洁优雅一些，并且提高代码复用性，我定义了一个Fraction类并重载了+运算符来进行分数的计算。

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class Fraction {
public:
    int numerator;
    int denominator;
    int sign;
    
    Fraction(int a, int b) : numerator(a), denominator(b), sign(1) {}
    Fraction(int a, int b, int s) : numerator(a), denominator(b), sign(s) {}
    Fraction() : numerator(0), denominator(1), sign(1) {} // 初始化为0(0/1)
    Fraction operator + (const Fraction& b) {
        int ta, tb; // ta分子，tb分母
        tb = denominator * b.denominator;
        
        if (this->sign == -1) ta = -numerator;
        else ta = numerator;
        
        ta *= b.denominator;
        
        if (b.sign == -1) ta += (-b.numerator * denominator);
        else ta += (b.numerator * denominator);
        
        return Fraction(abs(ta), tb, ta >= 0 ? 1 : -1);
    }
    
    void print() {
        printf("%s%d/%d\n", sign == 1 ? "" : "-", numerator, denominator);
    }
    
    string getString() {
        if (numerator == 0) denominator = 1;
        else {
            int gcd = getGcd(numerator, denominator);
            numerator /= gcd;
            denominator /= gcd;
        }
        string ans = (sign == 1 ? "" : "-");
        ans += (to_string(numerator) + "/" + to_string(denominator));
        return ans;
    }
    
    int getGcd(int a, int b) {
        if (a < b) swap(a, b);
        if (a % b == 0) return b;
        else return getGcd(b, a % b);
    }
};

class Solution {
public:
    string fractionAddition(string expression) {
        if (expression[0] != '-') {
            expression.insert(expression.begin(), '+');
        }
        Fraction ans;
        int p = 0;
        while (p < expression.size()) {
            Fraction next;
            p = readFraction(expression, p, next);
            ans  = ans + next;
        }
        return ans.getString();
    }
    
    int readFraction(const string& expression, int p, Fraction &frac) {
        if (expression[p++] == '-') {
            frac.sign = -1;
        }
        else {
            frac.sign = 1;
        }
        
        int nextP = p;
        while (nextP < expression.size() && isdigit(expression[nextP])) nextP++;
        frac.numerator = stoi(string(expression.begin() + p, expression.begin() + nextP));
        
        p = nextP + 1;
        nextP = p;
        while (nextP < expression.size() && isdigit(expression[nextP])) nextP++;
        frac.denominator = stoi(string(expression.begin() + p, expression.begin() + nextP));
        return nextP;
    }
};