<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>

class Solution {
public:
  void solve(string& ans, long long numerator, long long denominator) {
    unordered_map<long long, int> pos;  // To store the positions of remainders
    string fractionalPart;
    int index = 0;

    // Start processing fractional part
    fractionalPart += '.';

    while (numerator != 0) {
        // If the current remainder has been seen before, insert parentheses
        if (pos.find(numerator) != pos.end()) {
            int repeatStart = pos[numerator];
            fractionalPart.insert(repeatStart + 1, "(");
            fractionalPart += ")";
            break;
        }

        // Record the position of the current remainder
        pos[numerator] = index;

        numerator *= 10;
        fractionalPart += (numerator / denominator) + '0';  // Convert digit to character
        numerator %= denominator;
        index++;
    }

    ans += fractionalPart;
}

string fractionToDecimal(int numerator, int denominator) {
    string ans;

    // Handle case where numerator is zero
    if (numerator == 0) {
        return "0";
    }

    // Handle sign of the result
    if ((numerator < 0) ^ (denominator < 0)) {
        ans += '-';
    }

    // Use absolute values to simplify the division and remainder calculations
    long long absNumerator = abs(static_cast<long long>(numerator));
    long long absDenominator = abs(static_cast<long long>(denominator));

    // Integer part of the result
    ans += to_string(absNumerator / absDenominator);

    // Calculate remainder
    long long remainder = absNumerator % absDenominator;
    if (remainder != 0) {
        solve(ans, remainder, absDenominator);
    }

    return ans;
    }
};
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