166. Fraction to Recurring Decimal -- 将除法的商表示成字符串（循环节用括号表示）

Given two integers representing the numerator and denominator of a fraction, return the fraction in string format.

If the fractional part is repeating, enclose the repeating part in parentheses.

For example,

• Given numerator = 1, denominator = 2, return "0.5".
• Given numerator = 2, denominator = 1, return "2".
• Given numerator = 2, denominator = 3, return "0.(6)".

string fractionToDecimal(int numerator, int denominator) {

    string result;

    //deal with the `ZERO` cases

    if (denominator == ){ return result; }

    if (numerator == ) { return ""; }

    //using long long type make sure there has no integer overflow

    long long n = numerator;

    long long d = denominator;

    //deal with negtive cases 

    bool sign = ((float)numerator/denominator >= );

    if ( n <  ){ n = -n; }

    if ( d <  ){ d = -d; }

    if (sign == false){

        result.push_back('-');

    }

    long long remainder = n % d;

    long long division = n / d;

    ostringstream oss;

    oss << division;

    result += oss.str();

    if (remainder == ){

        return result;

    }

    //remainder has value, the result is a float

    result.push_back('.');

    //using a map to record all of reminders and their position.

    //if the reminder appeared before, which means the repeated loop begin, 

    //then, get the place from map to insert "(".

    //(In C++11, it's better to use unordered_map )

    map<long long, int> rec;

    for (int pos=result.size(); remainder!=; pos++, remainder=(remainder*)%d ) {

        if (rec.find(remainder) != rec.end()) {

            result.insert(result.begin()+rec[remainder], '(');

            result.push_back(')');

            return result;

        }

        rec[remainder] = pos;

        result.push_back((remainder*)/d + '');

    }

    return result;

}