Problem Statement
Parentheses Validator
You are a software engineer working on a code editor that needs to validate nested parentheses in programming languages. The editor needs to identify the longest valid substring of parentheses to help users fix syntax errors.
Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.
A valid parentheses substring is one where every opening parenthesis '(' has a matching closing parenthesis ')', and they are properly nested.
Examples
Example 1:
Input: s = "(()"
Output: 2
Explanation: The longest valid parentheses substring is '()'.
Example 2:
Input: s = ")()())"
Output: 4
Explanation: The longest valid parentheses substring is '()()'.
Example 3:
Input: s = ""
Output: 0
Explanation: The input string is empty, so there are no valid parentheses.
Constraints
- The input string consists of only '(' and ')'.
- The length of the input string is between 0 and 3 × 10^4.
- The solution should handle nested parentheses correctly.
Problem Breakdown
To solve this problem, we need to:
- A valid parentheses substring must have an equal number of opening and closing parentheses, and they must be properly nested.
- We can use a stack to keep track of the indices of unmatched parentheses.
- Dynamic programming can be used to build up the solution by considering one character at a time.
- We can also solve this problem using a two-pass approach with constant extra space.
String Problems
Learning Objective
Apply string manipulation concepts to solve a real-world problem.
Parentheses Validator
You are a software engineer working on a code editor that needs to validate nested parentheses in programming languages. The editor needs to identify the longest valid substring of parentheses to help users fix syntax errors.
Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.
A valid parentheses substring is one where every opening parenthesis '(' has a matching closing parenthesis ')', and they are properly nested.
Examples
Example 1:
The longest valid parentheses substring is '()'.
Example 2:
The longest valid parentheses substring is '()()'.
Example 3:
The input string is empty, so there are no valid parentheses.
Problem Breakdown
Constraints:
- The input string consists of only '(' and ')'.
- The length of the input string is between 0 and 3 × 10^4.
- The solution should handle nested parentheses correctly.
Key Insights:
A valid parentheses substring must have an equal number of opening and closing parentheses, and they must be properly nested.
We can use a stack to keep track of the indices of unmatched parentheses.
Dynamic programming can be used to build up the solution by considering one character at a time.
We can also solve this problem using a two-pass approach with constant extra space.
Real-World Application
This problem has several practical applications:
Code Editors
Validating syntax in programming languages to highlight errors and provide suggestions.
Document Parsing
Checking for well-formed XML or HTML documents with properly nested tags.
Expression Evaluation
Evaluating mathematical expressions with nested parentheses in calculators and spreadsheets.