<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> oper_stack;
        vector<string> num_stack;
        vector<string> rpn;

        map<char, int> prec = {{'N', 4}, {'+', 2}, {'-', 2}, {'*', 3}, {'/', 3}};
        string stoi_tmp;
        bool unary_flag = true;

        for(const auto &c : s) {
            if(c == ' ' || c == '\n') {
                continue;
            }

            if(isdigit(c)) {
                stoi_tmp = stoi_tmp + c;
                unary_flag = false;
            } else {
                if(unary_flag && c == '-') {
                    oper_stack.push_back('N');
                    continue;
                }
                if(stoi_tmp != "") {
                    rpn.push_back(stoi_tmp);
                    stoi_tmp = "";
                }
                if(oper_stack.size() != 0 && c != '(' && c != ')') {
                    if(prec[c] <= prec[oper_stack.back()]) {
                        while(oper_stack.size() != 0 && prec[c] <= prec[oper_stack.back()]) {
                            if(oper_stack.back() == '(' || oper_stack.back() == ')') break;
                            rpn.push_back(string(1, oper_stack.back()));
                            oper_stack.pop_back();
                        }
                    } 
                    oper_stack.push_back(c);
                } else if(c == ')') {
                    while(oper_stack.back() != '(') {
                        rpn.push_back(string(1, oper_stack.back()));
                        oper_stack.pop_back();
                    }
                    oper_stack.pop_back();
                    if(oper_stack.size() != 0 && oper_stack.back() == 'N') {
                        rpn.push_back(string(1, 'N'));
                        oper_stack.pop_back();
                    }
                } else {
                    oper_stack.push_back(c);
                }
                if(c == '+' || c == '-' || c == '*' || c == '/' || c == '(') {
                    unary_flag = true;
                } else {
                    unary_flag = false;
                }
            }
        }
        

        if(stoi_tmp != "") {
            rpn.push_back(stoi_tmp);
        }

        while(oper_stack.size() != 0) {
            rpn.push_back(string(1, oper_stack.back()));
            oper_stack.pop_back();
        }

        vector<int> cal_stack;

        for(auto a : rpn) {
            cout << a << " ";
            if(a != "+" && a != "-" && a != "*" && a != "/" && a != "N") {
                cal_stack.push_back(stoi(a));
            } else if(a == "N") {
                int tmp = -cal_stack.back();
                cal_stack.pop_back();
                cal_stack.push_back(tmp);
            } else {
                int suffix = cal_stack.back();
                cal_stack.pop_back();
                int prefix = cal_stack.back();
                cal_stack.pop_back();
                int pb;
                if(a == "+") {
                    pb = prefix + suffix;
                } else if(a == "-") {
                    pb = prefix - suffix;
                } else if(a == "/") {
                    pb = prefix / suffix;
                } else if(a == "*"){
                    pb = prefix * suffix;
                }
                cal_stack.push_back(pb);
            }
        }

        return cal_stack.back();
    }
};
30931