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HARD

Longest Valid Parentheses

Given a string containing just the characters '(' and ')', find the length of the longest valid (well-formed) parentheses substring.

Example

Input:

s = ")()())"

Output:

4

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

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Constraints

• 0 ≤ s.length ≤ 3 × 10⁴
• s[i] is '(' or ')'.

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Solution: Dynamic Programming

• Time Complexity: O(n)
• Space Complexity: O(n)

C++

class Solution {
public:
    int longestValidParentheses(string s) {
        int n = s.size();
        vector<int> dp(n, 0);
        int ans = 0;
        for (int i = 1; i < n; i++) {
            if (s[i] == ')') {
                if (s[i - 1] == '(') {
                    dp[i] = (i >= 2 ? dp[i - 2] : 0) + 2;
                } else if (i - dp[i - 1] > 0 && s[i - dp[i - 1] - 1] == '(') {
                    dp[i] = dp[i - 1] +
                            ((i - dp[i - 1]) >= 2 ? dp[i - dp[i - 1] - 2] : 0) +
                            2;
                }
                ans = max(ans, dp[i]);
            }
        }
        return ans;
    }
};