<p>Given two integers representing the <code>numerator</code> and <code>denominator</code> of a fraction, return <em>the fraction in string format</em>.</p>

<p>If the fractional part is repeating, enclose the repeating part in parentheses.</p>

<p>If multiple answers are possible, return <strong>any of them</strong>.</p>

<p>It is <strong>guaranteed</strong> that the length of the answer string is less than <code>10<sup>4</sup></code> for all the given inputs.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> numerator = 1, denominator = 2
<strong>Output:</strong> &quot;0.5&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> numerator = 2, denominator = 1
<strong>Output:</strong> &quot;2&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> numerator = 4, denominator = 333
<strong>Output:</strong> &quot;0.(012)&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>-2<sup>31</sup> &lt;=&nbsp;numerator, denominator &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>denominator != 0</code></li>
</ul>

typedef long long ll;

class Solution {
public:
  ll sign(ll x) {
    if (x < 0) return -1;
    else if (x > 0) return 1;
    else assert(false);
  }
  
  string add_sign(string str, ll sign_res) {
    if (str != "0" && sign_res < 0) return "-" + str;
    else return str;
  }
  
  string fractionToDecimal(int numerator_, int denominator_) {
    ll numerator = numerator_;
    ll denominator = denominator_;
    
    if (numerator == 0) return "0";
    
    ll sign_res = sign(numerator) / sign(denominator);    
    numerator = abs(numerator);
    denominator = abs(denominator);
    
    ll whole = numerator / denominator;
    numerator %= denominator;
    
    if (numerator == 0) return add_sign(to_string(whole), sign_res);
    
    string f;
    unordered_map<int,int> index;
    
    for (int i = 0; true; ++i) {
      index[numerator] = i;
        
      numerator *= 10;
      ll d = numerator / denominator;
      numerator = numerator % denominator;
      f.push_back('0' + d);
      
      if (index.count(numerator) > 0) {
        f.insert(index[numerator], 1, '(');
        f.push_back(')');
        break;
      }
      
      if (numerator == 0) break;
    }
    
    return add_sign(to_string(whole) + "." + f, sign_res);
  }
};
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