<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(string s) {
        stack<char> st;
        vector<string> rpn;
        char ch;
        char prev = '(';

        for (int i = 0; i < s.length(); i++) {
            ch = s[i];
            if (ch == ' ') {
                continue;
            }

            switch (ch) {
                case '(':
                    st.push(ch);
                    break;
                case ')':
                    st.pop();
                    if (!st.empty() && st.top() != '(') {
                        rpn.push_back(string(1, st.top()));
                        st.pop();
                    }
                    break;
                case '+':
                    st.push(ch);
                    break;
                case '-':
                    if (rpn.empty() || prev == '(') {
                        rpn.push_back("0");
                    }
                    st.push(ch);
                    break;
                default:
                    if (prev >= '0' && prev <= '9') {
                        rpn.back() += ch;
                    } else {
                        rpn.push_back(string(1, ch));
                    }

                    if ((i == s.length() - 1 || (s[i + 1] < '0' || s[i + 1] > '9')) && 
                        (!st.empty() && st.top() != '(')) {
                        rpn.push_back(string(1, st.top()));
                        st.pop();
                    }
                    break;
            }

            prev = ch;
        }

        return evalRPN(rpn);
    }

    int evalRPN(vector<string>& tokens) {
        stack<int> operands;
        int num1 = 0;
        int num2 = 0;
        int result = 0;

        for (int i = 0; i < tokens.size(); i++) {
            if (tokens[i] == "+" || tokens[i] == "-") {
                num2 = operands.top();
                operands.pop();
                num1 = operands.top();
                operands.pop();

                switch (tokens[i][0]) {
                    case '+':
                        result = num1 + num2;
                        break;
                    case '-':
                        result = num1 - num2;
                        break;
                    case '*':
                        result = num1 * num2;
                        break;
                    case '/':
                        result = num1 / num2;
                        break;
                    default:
                        break;
                }

                operands.push(result);
            } else {
                operands.push(stoi(tokens[i]));
            }
        }

        return operands.top();
    }
};
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