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 == 0){ return result; }

if (numerator == 0) { return "0"; }

//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 >= 0);

if ( n < 0 ){ n = -n; }

if ( d < 0 ){ 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 == 0){

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!=0; pos++, remainder=(remainder*10)%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*10)/d + '0');

}

return result;

}