<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) {
        // Convert infix to postfix
        vector<string> postfix;
        stack<string> my_stack;
        string num = "";
        bool seen_num = false;
        for (int i = 0; i < s.length(); i++) {
            string c = s.substr(i, 1);
            if ('0' <= c[0] && c[0] <= '9') {
                num += c;
            } else if (num != "") {
                postfix.push_back(num);
                num = "";
                seen_num = true;
            }
            if (i == s.length() - 1 && num != "") {
                postfix.push_back(num);
            }
            if (c == "(") {
                my_stack.push(c);
                seen_num = false;
            } else if (c == ")") {
                while (!my_stack.empty() && my_stack.top() != "(") {
                    postfix.push_back(my_stack.top());
                    my_stack.pop();
                }
                my_stack.pop();
            } else if (c == "+" || c == "-") { // Operator
                while (!my_stack.empty() && (my_stack.top() == "+" || my_stack.top() == "-" || my_stack.top() == "u-")) {
                    postfix.push_back(my_stack.top());
                    my_stack.pop();
                }
                if (c == "-" && !seen_num) {
                    my_stack.push("u-");
                } else {
                    my_stack.push(c);
                }
            }
        }
        while (!my_stack.empty()) {
            postfix.push_back(my_stack.top());
            my_stack.pop();
        }
        // Evaluate postfix
        stack<string> eval_stack;
        for (int i = 0; i < postfix.size(); i++) {
            string token = postfix[i];
            if (token == "u-") {
                int num = stoi(eval_stack.top());
                eval_stack.pop();
                eval_stack.push(to_string(-num));
            } else if (token == "+" || token == "-") {
                int second = stoi(eval_stack.top());
                eval_stack.pop();
                int first = stoi(eval_stack.top());
                eval_stack.pop();
                if (token == "+") {
                    eval_stack.push(to_string(first + second));
                }
                if (token == "-") {
                    eval_stack.push(to_string(first - second));
                }
            } else {
                eval_stack.push(token);
            }
        }
        return stoi(eval_stack.top());
    }
};
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