<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>

static const int Nothing = 0;
static const int AND = 1;
static const int OR = 2;
static const int NOT = 3;
class Solution {
public:
    bool proc(bool ret,bool another,int op){
        if(op == AND){
            return ret && another;
        }
        else if(op == OR){
            return ret || another;
        }
        return !ret;
    }
    bool parse(const string& str,int start,int prefix,int& end){
        bool ret;
        bool init = false;
        for(int i = start;i < str.length();++i){
            char c = str[i];
            int next = 0;
            if(c == '&'){
                if(!init){
                    init = true;
                    ret = parse(str,i+2,AND,next);
                    if(prefix == NOT){
                        ret = !ret;
                    }
                }
                else{

                    bool cur = parse(str,i+2,AND,next);
                    ret = proc(ret,cur,prefix);
                }
                i = next;
            }
            else if(c == '|'){
                if(!init){
                    init = true;
                    ret = parse(str,i+2,OR,next);
                    if(prefix == NOT){
                        ret = !ret;
                    }
                }
                else{
                    bool cur = parse(str,i+2,OR,next);
                    ret = proc(ret,cur,prefix);
                }
                i = next;
            }
            else if(c == '!'){
                if(!init){
                    init = true;
                    ret = parse(str,i+2,NOT,next);
                    if(prefix == NOT){
                        ret = !ret;
                    }
                }
                else{
                    bool cur = parse(str,i+2,NOT,next);
                    ret = proc(ret,cur,prefix);
                }
                i = next;

            }

            else if(c == ','){}
            else if(c == '('){}
            else if(c == ')'){
                end = i;
                return ret;
            }
            else{
                if(!init){
                    init = true;
                    ret = (c == 't');
                    if(prefix == NOT){
                        ret = !ret;
                    }
                }
                else{
                    bool cur = (c=='t');
                    ret = proc(ret,cur,prefix);


                }
            }
        }
        return ret;
    }
    bool parseBoolExpr(string expression) {
        int end = 0;
        return parse(expression,0,0,end);
    }
};
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