We can use a stack to store the indices of characters. We push the index of ( and when we see ), we pop. The length is current_index - stack[-1]. We seed the stack with -1 to handle the base starting case.

1. stack = [-1], max_len = 0.
2. Iterate i from 0 to len(s) - 1:
   • If s[i] == '(': stack.append(i).
   • Else (s[i] == ')'):
     • stack.pop().
     • If stack is empty, this ) is a breaker. Push current i as the new ground.
     • Else, current valid length is i - stack[-1]. Update max_len.

• Time Complexity: O(N).
• Space Complexity: O(N).

def longest_valid_parentheses(s):
    stack = [-1]
    max_len = 0
    
    for i in range(len(s)):
        if s[i] == '(':
            stack.append(i)
        else:
            stack.pop()
            if not stack:
                stack.append(i)
            else:
                max_len = max(max_len, i - stack[-1])
                
    return max_len