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Longest Valid Parentheses

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program to find the length of the longest valid (well-formed) parentheses substring in a given string containing just the characters '(' and ')'. A valid parentheses string is one where every opening parenthesis '(' has a matching closing parenthesis ')' and they are properly nested.

Example 1
    

  • Input: s = "(()"
    • 

  • Output: 2
    • 

  • Explanation: 
      

    • Step 1: Use a stack-based approach to track valid parentheses pairs.
      • 

    • Step 2: Process each character in the string, pushing indices of '(' onto the stack.
      • 

    • Step 3: When encountering ')', pop from stack and calculate the length of valid sequence.
      • 

    • Step 4: The longest valid parentheses substring is "()" with length 2.
      • 

    •
Example 2
    

  • Input: s = ")()())"
    • 

  • Output: 4
    • 

  • Explanation: 
      

    • Step 1: Use a stack-based approach to track valid parentheses pairs.
      • 

    • Step 2: Process each character in the string, pushing indices of '(' onto the stack.
      • 

    • Step 3: When encountering ')', pop from stack and calculate the length of valid sequence.
      • 

    • Step 4: The longest valid parentheses substring is "()()" with length 4.
      • 

    •
Constraints
    

  • 0 ≤ s.length ≤ 3 * 10^4
    • 

  • s[i] is '(' or ')'
    • 

  • Time Complexity: O(n) where n is the length of the string
    • 

  • Space Complexity: O(n)
    •
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Hint
Solution

Solution Hints

    
  
  • Consider using a stack to track opening parentheses
    • 
  
  • Another approach is using dynamic programming
    • 
  
  • You can also solve it with constant space using two passes
    • 
  
  • Track the current valid sequence length while scanning the string
    • 
  
  • Consider edge cases like empty strings or strings with only one type of parenthesis
    •

Steps to solve by this approach:

 Step 1: Initialize a stack and push -1 as a base index.
 Step 2: Iterate through each character in the string.
 Step 3: If the current character is '(', push its index onto the stack.
 Step 4: If the current character is ')', pop the top element from the stack.
 Step 5: If the stack becomes empty after popping, push the current index as the new base.
 Step 6: If the stack is not empty, calculate the length of the valid substring (current index - top of stack).
 Step 7: Update the maximum length found so far.

Submitted Code :