<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:
    vector<string> tokenize(string s) {
        std::vector<string> result;

        bool is_bin_sub = false;
        
        for (int cursor = 0; cursor < s.length();) {

            // Skip preceeding whitespace.
            while (cursor < s.length() && s.at(cursor) == ' ') {
                cursor++;
            }
            if (cursor == s.length()) break;

            // Parse a token.
            string token;
            char c = s.at(cursor);
            if (c == '+' || c == '-' || c == '(' || c == ')') {
                if (c == '-') {
                    token = is_bin_sub ? "-" : "~";
                } else {
                    token = c;
                }
                cursor++;
                is_bin_sub = (c == ')');
            } else if (isdigit(c)) {
                while (isdigit(c)) {
                    token += c;
                    cursor++;
                    if (cursor >= s.length()) break;
                    c = s.at(cursor);
                }
                is_bin_sub = true;
            }

            result.push_back(token);
        }
        
        return result;
    }

    // shunting-yard
    vector<string> toRPN(const vector<string> tokens) {
        stack<string> operators;
        vector<string> output;
        for (string token : tokens) {
            if (token == "+" || token == "-" || token == "~") {
                // Note the real shunting-yard logic is more complicated, but we only have + and -.
                while (!operators.empty() && operators.top() != "(") {
                    output.push_back(operators.top());
                    operators.pop();
                }
                operators.push(token);
            } else if (token == "(") {
                operators.push(token);
            } else if (token == ")") {
                while (operators.top() != "(") {
                    output.push_back(operators.top());
                    operators.pop();
                }
                operators.pop(); // (
            } else {
                output.push_back(token);
            }
        }
        while (!operators.empty()) {
            output.push_back(operators.top());
            operators.pop();
        }
        return output;
    }

    int evalRPN(vector<string>& tokens) {
        stack<int> operands;
        for (string& token : tokens) {
            if (token == "+") {
                int b = operands.top();
                operands.pop();
                int a = operands.top();
                operands.pop();
                operands.push(a + b);
            } else if (token == "-") {
                int b = operands.top();
                operands.pop();
                int a = operands.top();
                operands.pop();
                operands.push(a - b);
            } else if (token == "~") {
                int a = operands.top();
                operands.pop();
                operands.push(-a);
            } else {
                operands.push(stoi(token));
            }
        }
        return operands.top();
    }

    int calculate(string s) {
        auto tokens = tokenize(s);
        auto rpn = toRPN(tokens);
        return evalRPN(rpn);
    }


};
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