<p>A <strong>boolean expression</strong> is an expression that evaluates to either <code>true</code> or <code>false</code>. It can be in one of the following shapes:</p>

<ul>
	<li><code>&#39;t&#39;</code> that evaluates to <code>true</code>.</li>
	<li><code>&#39;f&#39;</code> that evaluates to <code>false</code>.</li>
	<li><code>&#39;!(subExpr)&#39;</code> that evaluates to <strong>the logical NOT</strong> of the inner expression <code>subExpr</code>.</li>
	<li><code>&#39;&amp;(subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub>)&#39;</code> that evaluates to <strong>the logical AND</strong> of the inner expressions <code>subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub></code> where <code>n &gt;= 1</code>.</li>
	<li><code>&#39;|(subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub>)&#39;</code> that evaluates to <strong>the logical OR</strong> of the inner expressions <code>subExpr<sub>1</sub>, subExpr<sub>2</sub>, ..., subExpr<sub>n</sub></code> where <code>n &gt;= 1</code>.</li>
</ul>

<p>Given a string <code>expression</code> that represents a <strong>boolean expression</strong>, return <em>the evaluation of that expression</em>.</p>

<p>It is <strong>guaranteed</strong> that the given expression is valid and follows the given rules.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;&amp;(|(f))&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> 
First, evaluate |(f) --&gt; f. The expression is now &quot;&amp;(f)&quot;.
Then, evaluate &amp;(f) --&gt; f. The expression is now &quot;f&quot;.
Finally, return false.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;|(f,f,f,t)&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> The evaluation of (false OR false OR false OR true) is true.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;!(&amp;(f,t))&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> 
First, evaluate &amp;(f,t) --&gt; (false AND true) --&gt; false --&gt; f. The expression is now &quot;!(f)&quot;.
Then, evaluate !(f) --&gt; NOT false --&gt; true. We return true.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= expression.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li>expression[i] is one following characters: <code>&#39;(&#39;</code>, <code>&#39;)&#39;</code>, <code>&#39;&amp;&#39;</code>, <code>&#39;|&#39;</code>, <code>&#39;!&#39;</code>, <code>&#39;t&#39;</code>, <code>&#39;f&#39;</code>, and <code>&#39;,&#39;</code>.</li>
</ul>

#include <iostream>
#include <string>
#include <vector>
#include <stack>

class Solution {
public:
    bool parseBoolExpr(const std::string& expression) {
        std::stack<char> stk;

        for (char ch : expression) {
            if (ch == ',') {
                continue;  // Ignore commas
            } else if (ch != ')') {
                stk.push(ch);  // Push everything except closing parenthesis ')'
            } else {
                // We have encountered a closing parenthesis ')', process the expression
                std::vector<char> operands;
                while (stk.top() != '(') {
                    operands.push_back(stk.top());
                    stk.pop();
                }
                stk.pop();  // Remove the opening parenthesis '('

                char operatorChar = stk.top();
                stk.pop();  // Remove the operator character '!', '&', or '|'

                char result;
                if (operatorChar == '!') {
                    result = (operands[0] == 't') ? 'f' : 't';
                } else if (operatorChar == '&') {
                    result = 't';
                    for (char op : operands) {
                        if (op == 'f') {
                            result = 'f';
                            break;
                        }
                    }
                } else if (operatorChar == '|') {
                    result = 'f';
                    for (char op : operands) {
                        if (op == 't') {
                            result = 't';
                            break;
                        }
                    }
                }

                stk.push(result);  // Push the result of the evaluation back onto the stack
            }
        }

        // The final result will be the only element left in the stack
        return stk.top() == 't';
    }
};

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