#1106

Hard

auto_awesomeStack-based state management

LeetCode Problem Workspace

Parsing A Boolean Expression

Solve the "Parsing A Boolean Expression" problem by evaluating boolean expressions using stack-based state management, recursion, and string operations.

string stack recursion

Problem Statement

You are given a string expression representing a boolean expression. Your task is to evaluate and return the result of this expression. The expression is guaranteed to be valid and consists of boolean operations: AND ('&'), OR ('|'), NOT ('!'), and literals 't' (true) and 'f' (false). Operations are grouped by parentheses, and the expression is properly balanced.

You need to implement a function to evaluate the expression. This function should make use of helper functions for evaluating each operation type, handling recursion, and managing the operations' precedence. The expression can be complex, with multiple nested operations, so an efficient solution is required.

Examples

Example 1

Input: expression = "&(|(f))"

Output: false

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

The evaluation of (false OR false OR false OR true) is true.

Example 3

Input: expression = "!(&(f,t))"

Output: true

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 ','.

Solution Approach

Using Stack for State Management

A stack-based approach allows us to evaluate boolean expressions efficiently. We push intermediate states and results onto the stack to manage the nested operations. This helps handle the expression's complexity and ensures the correct order of operations.

Recursive Evaluation of Subexpressions

Each operation, such as AND, OR, or NOT, can be evaluated recursively. This allows the algorithm to break down complex expressions into smaller, manageable subexpressions. Recursion ensures that we correctly evaluate the boolean operations in a nested manner.

Optimized Parsing with Helper Functions

By writing helper functions like 'parse_or', 'parse_and', and 'parse_not', we simplify the logic of evaluating each operation. These functions handle specific boolean operations and help break down the main expression into smaller, more focused parts.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity is O(n) because we process each character in the expression exactly once, where n is the length of the expression. The space complexity is also O(n) due to the space required for the stack to hold intermediate results during evaluation.

What Interviewers Usually Probe

Candidate effectively demonstrates understanding of stack-based state management.
Candidate uses recursion in a clear and effective way to handle nested operations.
Candidate implements helper functions that make the solution modular and readable.

Common Pitfalls or Variants

Common pitfalls

Failing to correctly manage nested operations in the expression, leading to incorrect results.
Not properly handling edge cases with multiple nested parentheses or complex operator combinations.
Overcomplicating the solution by missing the stack's role in managing the expression's state.

Follow-up variants

Change the expression format to include additional boolean operations or nested expressions.
Implement this problem with different recursion depths or constraints, such as limiting parentheses.
Extend the problem to support more complex boolean operations like XOR or conditional (if-else).

FAQ

What is the main challenge in solving "Parsing A Boolean Expression"?

The main challenge is correctly evaluating the boolean expression, especially when dealing with nested operations and parentheses using a stack-based approach.

How can recursion be used to solve the "Parsing A Boolean Expression" problem?

Recursion helps break down the expression into smaller subexpressions, allowing for proper evaluation of each operation in the correct order, especially within nested parentheses.

What is the time complexity of the solution to the "Parsing A Boolean Expression" problem?

The time complexity is O(n), where n is the length of the expression, since each character is processed once during evaluation.

What is the role of stack-based state management in "Parsing A Boolean Expression"?

The stack is used to keep track of the state during evaluation, storing intermediate results for nested expressions and ensuring correct operation order.

What helper functions are needed for solving "Parsing A Boolean Expression"?

Helper functions like 'parse_or', 'parse_and', and 'parse_not' are essential to evaluate the respective boolean operations recursively and manage the complexity of the expression.

terminal

Solution

Solution 1: Stack

For this type of expression parsing problem, we can use a stack to assist.

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class Solution:
    def parseBoolExpr(self, expression: str) -> bool:
        stk = []
        for c in expression:
            if c in 'tf!&|':
                stk.append(c)
            elif c == ')':
                t = f = 0
                while stk[-1] in 'tf':
                    t += stk[-1] == 't'
                    f += stk[-1] == 'f'
                    stk.pop()
                match stk.pop():
                    case '!':
                        c = 't' if f else 'f'
                    case '&':
                        c = 'f' if f else 't'
                    case '|':
                        c = 't' if t else 'f'
                stk.append(c)
        return stk[0] == 't'

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