Longest Valid Parentheses

問題描述

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

For “(()(()”, the longest valid parentheses substring is “()”, which has length = 2.

Another example is “)()())”, where the longest valid parentheses substring is “()()”, which has length = 4.

思考：考慮()的嵌套：((()))和循環()()()

想法：動態規劃

• 1、考慮嵌套時，dp[i] = dp[i] + dp[i + 1] 如果s.charAt(i - 1) = s.charAt(i);
• 2、考慮循環時，dp[i]的前一個()的標號位i - dp[i], 如：()()((()));

代碼：

public class Solution {
    public int longestValidParentheses(String s) {
        int toMatch = 0;
        int max = 0;
        int[] dp = new int[s.length() + 1];
        for(int i = 1 ; i <= s.length(); i++){
            if(s.charAt(i - 1) == '(')
                toMatch++;
            else{
                if(toMatch > 0){
                    toMatch--;
                    dp[i] = 2;

                    if(s.charAt(i - 2) == ')')//the "((()))",嵌套
                        dp[i] += dp[i - 1];

                    dp[i] += dp[i - dp[i]]; //()()()循環

                    if(dp[i] > max)
                        max = dp[i];
                }
            }
        }
        return max;
    }
}