<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:
    bool isOperator(string& s)
    {
        return (s == "+" || s == "-" || s == "*" || s == "/");
    }

    int evalRPN(vector<string>& tokens) {
        stack<int> integerStack{};
        for (auto s : tokens)
        {
            if (!isOperator(s))
            {
                integerStack.push(stoi(s));
            }
            else
            {
                const int operand2 = integerStack.top();
                integerStack.pop();
                const int operand1 = integerStack.top();
                integerStack.pop();
                int result{};
                if (s == "+")
                {
                    result = operand1 + operand2;
                }
                else if (s == "-")
                {
                    result = operand1 - operand2;
                }
                else if (s == "*")
                {
                    result = operand1 * operand2;
                }
                else
                {
                    result = operand1 / operand2;
                }
                integerStack.push(result);
            }
        }
        return integerStack.top();
    }

    int calculate(string s) {
        vector<string> postfixNotation{};
        stack<char> operatorStack{};
        string integer{};
        bool isLastTokenIntegerOrClosedParenthesis = false;
        for (int i = 0; i < s.size(); ++i)
        {
            while (i < s.size() && isdigit(s[i]))
            {
                integer += s[i++];
            }
            if (integer != "")
            {
                isLastTokenIntegerOrClosedParenthesis = true;
                postfixNotation.push_back(integer);
                integer = "";
            }
            if (i == s.size())
            {
                break;
            }
            if (s[i] == ' ')
            {
                continue;
            }
            else if (s[i] == '(')
            {
                isLastTokenIntegerOrClosedParenthesis = false;
                operatorStack.push(s[i]);
            }
            else if (s[i] == ')')
            {
                isLastTokenIntegerOrClosedParenthesis = true;
                while (operatorStack.top() != '(')
                {
                    postfixNotation.push_back(string{operatorStack.top()});
                    operatorStack.pop();
                }
                operatorStack.pop(); // Popping '('
            }
            else if (s[i] == '+')
            {
                isLastTokenIntegerOrClosedParenthesis = false;
                while (!operatorStack.empty() && operatorStack.top() != '(')
                {
                    postfixNotation.push_back(string{operatorStack.top()});
                    operatorStack.pop();
                }
                operatorStack.push(s[i]);
            }
            else // s[i] == '-'
            {
                if (!isLastTokenIntegerOrClosedParenthesis)
                {
                    postfixNotation.push_back("0");
                }
                isLastTokenIntegerOrClosedParenthesis = false;
                while (!operatorStack.empty() && operatorStack.top() != '(')
                {
                    postfixNotation.push_back(string{operatorStack.top()});
                    operatorStack.pop();
                }
                operatorStack.push(s[i]);
            } 
        }
        while (!operatorStack.empty())
        {
            postfixNotation.push_back(string{operatorStack.top()});
            operatorStack.pop();
        }

        return evalRPN(postfixNotation);
    }
};
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