1197. Parsing A Boolean Expression

Hard

A boolean expression is an expression that evaluates to either true or false. It can be in one of the following shapes:

't' that evaluates to true.
'f' that evaluates to false.
'!(subExpr)' that evaluates to the logical NOT of the inner expression subExpr.
'&(subExpr₁, subExpr₂, ..., subExpr_n)' that evaluates to the logical AND of the inner expressions subExpr₁, subExpr₂, ..., subExpr_n where n >= 1.
'|(subExpr₁, subExpr₂, ..., subExpr_n)' that evaluates to the logical OR of the inner expressions subExpr₁, subExpr₂, ..., subExpr_n where n >= 1.

Given a string expression that represents a boolean expression, return the evaluation of that expression.

It is guaranteed that the given expression is valid and follows the given rules.

Example 1:

Input: expression = "&(|(f))"
Output: false
Explanation: 
First, evaluate |(f) --> f. The expression is now "&(f)".
Then, evaluate &(f) --> f. The expression is now "f".
Finally, return false.

Example 2:

Input: expression = "|(f,f,f,t)"
Output: true
Explanation: The evaluation of (false OR false OR false OR true) is true.

Example 3:

Input: expression = "!(&(f,t))"
Output: true
Explanation: 
First, evaluate &(f,t) --> (false AND true) --> false --> f. The expression is now "!(f)".
Then, evaluate !(f) --> NOT false --> true. We return true.

Constraints:

1 <= expression.length <= 2 * 10⁴
expression[i] is one following characters: '(', ')', '&', '|', '!', 't', 'f', and ','.