<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:
  map<string, int> OPS = {
    {"+", 1},
    {"-", 1},
    {"UNARY_NEGATE", 2},
    {"(", 3},
    {")", 3},
  };

  vector<string> getTokens(string& s) {
    int idx = 0;
    vector<string> tokens;
    while (idx < s.size()) {
      while (idx < s.size() && isspace(s[idx])) idx++;
      if (idx < s.size()) {
        string token = "";
        if (isdigit(s[idx])) {
          while (idx < s.size() && isdigit(s[idx])) {
            token += s[idx++];
          }
        } else {
          token += s[idx++];
        }
        if (token == "-" && (tokens.empty() || tokens.back() == "(")) {
          token = "UNARY_NEGATE";
        } 
        tokens.push_back(token);
      }
    }
    return tokens;
  }

  vector<string> convertToRPN(string& s) {
    vector<string> rpn;
    stack<string> opsStack;

    for (auto& token : getTokens(s)) {
      if (OPS.find(token) != end(OPS)) {
        if (token == "(") {
          opsStack.push(token);
        } else if (token == ")") {
          while (opsStack.top() != "(") {
            rpn.push_back(opsStack.top());
            opsStack.pop();
          }
          opsStack.pop();
        } else if (opsStack.empty() || OPS[opsStack.top()] < OPS[token]) {
          opsStack.push(token);
        } else {
          while (!opsStack.empty() && opsStack.top() != "(") {
            rpn.push_back(opsStack.top());
            opsStack.pop();
          }
          opsStack.push(token);
        }
      } else {
        rpn.push_back(token);
      }
    }

    while (!opsStack.empty()) { 
      rpn.push_back(opsStack.top());
      opsStack.pop();
    }

    return rpn;
  }

  int evalRPN(vector<string>& rpn) {
    stack<int> st;

    for (const auto& token : rpn) {
      if (OPS.find(token) != end(OPS)) {
        if (token == "UNARY_NEGATE") {
          int b = st.top();
          st.pop();
          st.push(-b);
        } else {
          int b = st.top();
          st.pop();

          int a = 0;
          if (!st.empty()) {
            a = st.top();
            st.pop();
          }

          st.push(token[0] == '+' ? a + b : a - b);
        }
      } else {
        st.push(stoi(token));
      }
    }    

    return st.top();
  }

  int calculate(string s) {
    auto rpn = convertToRPN(s);
    return evalRPN(rpn);
  }
};
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