<p>Given a string <code>s</code> representing a valid expression, implement a basic calculator to evaluate it, and return <em>the result of the evaluation</em>.</p>

<p><strong>Note:</strong> You are <strong>not</strong> allowed to use any built-in function which evaluates strings as mathematical expressions, such as <code>eval()</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;1 + 1&quot;
<strong>Output:</strong> 2
</pre>

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

<pre>
<strong>Input:</strong> s = &quot; 2-1 + 2 &quot;
<strong>Output:</strong> 3
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;(1+(4+5+2)-3)+(6+8)&quot;
<strong>Output:</strong> 23
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 3 * 10<sup>5</sup></code></li>
	<li><code>s</code> consists of digits, <code>&#39;+&#39;</code>, <code>&#39;-&#39;</code>, <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code>, and <code>&#39; &#39;</code>.</li>
	<li><code>s</code> represents a valid expression.</li>
	<li><code>&#39;+&#39;</code> is <strong>not</strong> used as a unary operation (i.e., <code>&quot;+1&quot;</code> and <code>&quot;+(2 + 3)&quot;</code> is invalid).</li>
	<li><code>&#39;-&#39;</code> could be used as a unary operation (i.e., <code>&quot;-1&quot;</code> and <code>&quot;-(2 + 3)&quot;</code> is valid).</li>
	<li>There will be no two consecutive operators in the input.</li>
	<li>Every number and running calculation will fit in a signed 32-bit integer.</li>
</ul>


class Solution {
public:
    int calculate(const std::string& s) {
        idx = 0;
        return calc(s);
    }

private:
    int idx;  // Index for parsing the string

    int calc(const std::string& s) {
        int num = 0, res = 0;
        int sign = 1;  // 1 for positive, -1 for negative

        while (idx < s.length()) {
            char c = s[idx++];
            
            // If it's a digit, construct the number
            if (c >= '0' && c <= '9') {
                num = num * 10 + (c - '0');
            } 
            // Handle open parenthesis
            else if (c == '(') {
                num = calc(s);  // Recursive call for the sub-expression
            } 
            // Handle close parenthesis
            else if (c == ')') {
                return res + num * sign;  // Return result when closing parenthesis is encountered
            } 
            // Handle operators
            else if (c == '+' || c == '-') {
                res += num * sign;  // Apply the previous number with its sign
                num = 0;            // Reset the number
                sign = (c == '-') ? -1 : 1;  // Update sign based on the current operator
            } 
            // Skip spaces
            else if (c == ' ') {
                continue;
            }
        }

        // Handle the last number after the loop ends
        res += num * sign;
        return res;
    }
};

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