<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:
    struct ASTNode {
        ASTNode(char op_, const std::shared_ptr<ASTNode> &arg1_, const std::shared_ptr<ASTNode> &arg2_)
            : op {op_}, value {0}, arg1 {arg1_}, arg2 {arg2_}
        {}
        ASTNode(char op_, const std::shared_ptr<ASTNode> &arg1_)
            : op {op_}, value {0}, arg1 {arg1_}
        {}
        ASTNode(char op_, int value_ = 0)
            : op {op_}, value {value_}
        {}

        char op;
        int value = 0;
        std::shared_ptr<ASTNode> arg1 = nullptr;
        std::shared_ptr<ASTNode> arg2 = nullptr;
    };

    static inline int eval(const std::shared_ptr<ASTNode> &node) {
        switch(node->op) {
        case '=': return node->value;
        case '+': return eval(node->arg1) + eval(node->arg2);
        case '-': return eval(node->arg1) - eval(node->arg2);
        default: return 0;
        }
    }

    static inline std::shared_ptr<ASTNode> parse_ast(const std::string &s, int &pos);
    static inline std::shared_ptr<ASTNode> parse_term(const std::string &s, int &pos);
    static inline std::shared_ptr<ASTNode> parse_digit(const std::string &s, int &pos);

    static inline void skip_spaces(const std::string &s, int &pos) {
        while(pos < s.size() && s[pos] == ' ') {
            ++pos;
        }
    }

    int calculate(string s) {
        int pos = 0;
        auto node = parse_ast(s, pos);
        return eval(node);
    }
};

    inline std::shared_ptr<Solution::ASTNode> Solution::parse_term(const std::string &s, int &pos) {
        skip_spaces(s, pos);
        if(s[pos] == '(') {
            ++pos;
            auto node = parse_ast(s, pos);
            skip_spaces(s, pos);
            if(s[pos++] != ')') {
                //TODO: handle this
            }
            return node;
        }
        return parse_digit(s, pos);
    }

    inline std::shared_ptr<Solution::ASTNode> Solution::parse_ast(const std::string &s, int &pos) {
        std::shared_ptr<ASTNode> node = nullptr;
        skip_spaces(s, pos);
        if(s[pos] == '-') {
            ++pos;
            node = std::make_shared<ASTNode>(
                '-',
                std::make_shared<ASTNode>('='),
                parse_term(s, pos)
            );
        } else {
            node = parse_term(s, pos);
        }

        skip_spaces(s, pos);
        while(pos < s.size() && (s[pos] == '+' || s[pos] == '-')) {
            auto new_node = std::make_shared<ASTNode>(
                s[pos++],
                node
            );

            new_node->arg2 = parse_term(s, pos);
            node = new_node;
        }

        return node;
    }

    inline std::shared_ptr<Solution::ASTNode> Solution::parse_digit(const std::string &s, int &pos) {
        skip_spaces(s, pos);

        std::ostringstream stream;
        while(pos < s.size() && (s[pos] >= '0' && s[pos] <= '9')) {
            stream << s[pos++];
        }

        skip_spaces(s, pos);
        auto val = std::stoi(stream.str());
        return std::make_shared<ASTNode>('=', val);
    }

44993