32. Longest Valid Parentheses (JAVA)

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

Example 1:

Input: "(()"
Output: 2
Explanation: The longest valid parentheses substring is "()"

Example 2:

Input: ")()())"
Output: 4
Explanation: The longest valid parentheses substring is "()()"

class Solution {
    public int longestValidParentheses(String s) {
        int[] dp = new int[s.length()]; //longest valid parentheses end with current index
        Stack<Integer> stack = new Stack<>(); //index of each left parenthese
        int ret = 0;

        for(int i = 0; i < s.length(); i++){
            if(s.charAt(i) == '('){
                stack.push(i);
            }
            else if(!stack.empty()){ //')' and have left parenthese in the stack
                if(stack.peek() > 0)
                    dp[i] = dp[stack.peek()-1] + (i-stack.peek()+1);
                else //first index
                    dp[i] = i-stack.peek()+1;
                stack.pop();
            }
            else{ //')' and have no left parenthese in the stack
                stack.clear();
            }
        }

        for(int i = 0; i < s.length(); i++){
            if(dp[i]>ret) ret = dp[i];
        }
        return ret;
    }
}

最长有效括号不仅与当前stack的情况有关，也与有效做括号之前的stack情况有关，所以用动态规划。

使用一维动态规划记录以当前位置结束的最长有效括号。