<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 expNeg = false;
    int calculate(string s) {
        expNeg = false;
        vector<string> expression = getExpression(s);
        vector<string> postfix = getInfixToPostFixExpression(expression);
        // cout << "hi\n";
        return calculatePostFix(postfix) * (expNeg?-1:1);
    }
    
    vector<string> getExpression(string &exp) {
        string s = trimSpace(exp);
        vector<string> expression;
        string cur;
        bool neg = false;
        int i = 0;
        for (; i < s.length(); i++) {
           
            char c = s[i];
            if (c <= '9' && c >= '0') {
                cur.push_back(c);
                if (i == s.length()-1 || (s[i+1]<'0' || s[i+1] > '9')) {
                    expression.push_back((neg?"-":"")+cur);
                    cur = "";
                    neg = false;
                }
            } else if (c == '-' && (expression.empty() || expression.back() == "(")){
                expression.push_back("-1");
                expression.push_back("*");
            } else if(c == '+' || c == '-' || c == ')' || c == '(') {
                expression.push_back(string() + c);
            }
        }
        return expression;
    }
    
    string trimSpace(string s) {
        string trimmed = "";
        for (char c : s) {
            if (c != ' ' && c != '\t' && c != '\r') trimmed.push_back(c);
        }
        return trimmed;
    }
    
    vector<string> getInfixToPostFixExpression(vector<string> &exp) {
        vector<string> postfix;
        stack<string> oprtr;
        for (string s : exp) {
            // cout << s << endl;
            if (s == "+" || s == "-" || s == "*") {
                if (oprtr.empty() || prec(s) > prec(oprtr.top())) {
                    oprtr.push(s);
                } else {
                    while (!oprtr.empty() && prec(s) <= prec(oprtr.top())) {
                        postfix.push_back(oprtr.top());
                        oprtr.pop();
                    }
                    oprtr.push(s);
                }
            } else if (s == "(") {
                oprtr.push("(");
            } else if ( s == ")") {
                while (oprtr.top() != "(") {
                    postfix.push_back(oprtr.top());
                    oprtr.pop();
                }
                oprtr.pop();
            } else {
                postfix.push_back(s);
            }
        }
        while (!oprtr.empty()) {
            postfix.push_back(oprtr.top());
            oprtr.pop();
        }
        return postfix;
    }
    
    int calculatePostFix(vector<string> &exp) {
        stack<int> operand;
        for (string e : exp) {
            // cout << e << endl;
            if (e == "+" || e == "-" || e == "*") {
                int operand2 = operand.top(); operand.pop();
                int operand1 = operand.top(); operand.pop();
                operand.push(exec(operand1, operand2, e));
            } else {
                int val = stoi(e);
                operand.push(val);
            }
        }
        return operand.top();
    }
    
    int exec(int o1, int o2, string oprtr) {
        if (oprtr == "*") return o1 * o2;
        if (oprtr == "+") return o1 + o2;
        else return o1-o2;
    }
    
    int prec(string s) {
        if (s == "*") {
            return 2;
        }
        if (s == "+" || s == "-") {
            return 1;
        }
        return -1;
    }
};
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