<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>

#include <algorithm>
#include <iostream>
#include <iterator>
#include <string>
class Solution {
public:
    bool isNum(char c) {
        return '0' <= c && c <= '9';
    }

    vector<string> createTokens(string s) {
        vector<string> tokens;
    
        int start = 0, end = 0;
        if (s[0] == '-') {
            tokens.push_back("0");
        }
        while (end < s.length()) {
            if (s[start] == ' ') {
                start++;
                end++;
                continue;
            }
            if (!isNum(s[start])) {
                if (s[start] == '-' && tokens.back() == "(") {
                    tokens.push_back("0");
                }
                tokens.push_back(s.substr(start, 1));
                start++;
                end++;
                continue;
            }
            if (isNum(s[start]) && isNum(s[end])) {
                end++;
                continue;
            }
            if (isNum(s[start]) && !isNum(s[end])) {
                tokens.push_back(s.substr(start, end - start));
                start = end;
                continue;
            }
        }
        if (start < s.length()) {
            tokens.push_back(s.substr(start, end - start));
        }

        return tokens;
    }

    vector<string> createReversePolishNotation(vector<string> tokens) {
        vector<string> reversePolishTokens;
        stack<string> operators;
        
        for (string token : tokens) {
            if (isNum(token[0])) {
                reversePolishTokens.push_back(token);
            }
            else if (token == "(") {
                operators.push(token);
            }
            else if (token == ")") {
                while (operators.top() != "(") {
                    reversePolishTokens.push_back(operators.top());
                    operators.pop();
                }
                operators.pop();
            }
            else if (token == "+" || token == "-") {
                while (!operators.empty() && operators.top() != "(") {
                    reversePolishTokens.push_back(operators.top());
                    operators.pop();
                }
                operators.push(token);
            }
        }
        while (!operators.empty()) {
            reversePolishTokens.push_back(operators.top());
            operators.pop();
        }

        return reversePolishTokens;
    }

    int evaluateReversePolishNotation(vector<string> reversePolishTokens) {
        stack<string> operands;
        for (string token : reversePolishTokens) {
            if (isNum(token[0])) {
                operands.push(token);
                continue;
            }
            int num2 = stoi(operands.top());
            operands.pop();
            int num1 = stoi(operands.top());
            operands.pop();
            if (token == "+") {
                operands.push(to_string(num1 + num2));
            }
            else if (token == "-") {
                operands.push(to_string(num1 - num2));
            }
        }

        return stoi(operands.top());
    }

    int calculate(string s) {
        vector<string> tokens;
        vector<string> reversePolishTokens;
        int res;

        tokens = createTokens(s);
        // std::cout << "Created Tokens\n";
        // for (auto token : tokens) {
        //     std::cout << token << ", ";
        // }
        // std::cout << std::endl;
        reversePolishTokens = createReversePolishNotation(tokens);
        // std::cout << "Created Reverse Polish Notation\n";
        // for (auto token : reversePolishTokens) {
        //     std::cout << token << ", ";
        // }
        // std::cout << std::endl;
        res = evaluateReversePolishNotation(reversePolishTokens);

        return res;
    }
};
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