<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 isDigit(char c) {
        return '0' <= c && c <= '9';
    }
    int calculate(string s) {
        s = "(" + s + ")"; // trigger top-level evaluation
        vector<string> tokenize;
        for (int i = 0; i < s.size(); /* manual update */) {
            char c = s[i];
            if (isDigit(c)) {
                string num = "";
                for (; i < s.size(); i++) {
                    char c = s[i];
                    if (isDigit(c)) {
                        num += c;
                    } else {
                        break;
                    }
                }
                tokenize.push_back(num);
            } else if (c == '+') {
                tokenize.push_back("+");
                i++;
            } else if (c == '-') {
                tokenize.push_back("-");
                i++;
            } else if (c == '(') {
                tokenize.push_back("(");
                i++;
            } else if (c == ')') {
                tokenize.push_back(")");
                i++;
            } else {
                i++;
            }
        }
        reverse(tokenize.begin(), tokenize.end());
        deque<string> steak;
        for (int i = 0; i < tokenize.size(); i++) {
            const string& cur = tokenize[i];
            if (cur == ")") {
                steak.push_back(cur);
            } else if (cur == "(") {
                int value = 0;
                char prior_op = '+';
                while (true) {
                    string top = steak.back();
                    steak.pop_back();
                    if (top == ")") {
                        steak.push_back(to_string(value));
                        break;
                    } else if (top == "-") {
                        prior_op = '-';
                    } else if (top == "+") {
                        prior_op = '+';
                    } else {
                        if (prior_op == '+') {
                            value += stoi(top);
                        } else {
                            value -= stoi(top);
                        }
                    }
                }
            } else if (cur == "+") {
                steak.push_back(cur);
            } else if (cur == "-") {
                steak.push_back(cur);
            } else {
                steak.push_back(cur);
            }
        }
        return stoi(steak[0]);
    }
};
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