<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) {
        vector<char> pos;
        vector<int> eval;
        int i = 0;
        while (i < s.length()){
            // cout << "hi0 " << s[i] << endl;
            if (s[i] == '(') {
                pos.push_back('(');
                i++;
            }
            else if (s[i] == '+') {
                pos.push_back('+');
                i++;
            }
            else if (s[i] == '-') {
                pos.push_back('-');
                i++;
            }
            else if ( '0' <= s[i] && s[i] <= '9') { 
                string N = "";
                N += s[i];
                while (i+1 < s.length() && '0' <= s[i+1] && s[i+1] <= '9'){
                    N += s[i+1];
                    i++;
                    // cout << "hi" << endl;
                }
                i++;
                // cout << N << " " << N.length() << endl;
                int n = stoi(N);
                int top = pos.size()-1;
                int etop = eval.size()-1;
                if (top < 0){
                    eval.push_back(n);
                    pos.push_back('n');
                }
                else if (pos[top] == '+'){
                    eval[etop] += n;
                    pos.pop_back();
                }
                else if (pos[top] == '-'){
                    if (top-1 >= 0 && pos[top-1] == 'n'){
                        eval[etop] -= n;
                        pos.pop_back();
                    }
                    else {
                        eval.push_back(-n);
                        pos.pop_back();
                        pos.push_back('n');
                    }
                }
                else {
                    pos.push_back('n');
                    eval.push_back(n);
                }
            }
            else if (s[i] == ')'){
                int top = pos.size()-3;
                int etop = eval.size()-1;
                int n = eval[etop];
                i++;
                pos.pop_back();
                pos.pop_back();
                eval.pop_back();
                // cout << "hel " << n << " " << top << endl;
                if (top < 0){
                    // cout << top << " k " << etop << endl;
                    eval.push_back(n);
                    pos.push_back('n');
                }
                else if (pos[top] == '+'){
                    eval[etop-1] += n;
                    pos.pop_back();
                }
                else if (pos[top] == '-'){
                    if (top - 1 >= 0 && pos[top-1] == 'n'){
                        eval[etop-1] -= n;
                        pos.pop_back();
                    }
                    else {
                        eval.push_back(-n);
                        pos.pop_back();
                        pos.push_back('n');
                    }
                }
                else {
                    pos.push_back('n');
                    eval.push_back(n);
                }
            }
            else i++;
            // for (int h = 0; h < eval.size(); h++){
            //     cout << eval[h] << " ";
            // }
            // cout << endl;
            // for (int h = 0; h < pos.size(); h++){
            //     cout << pos[h] << " ";
            // }
            // cout << endl;
        }
        return eval[0];
    }
};
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