Longest Valid Parentheses

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问题描述

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：考虑()的嵌套：((()))和循环()()()

想法：动态规划

1、考虑嵌套时，dp[i] = dp[i] + dp[i + 1] 如果s.charAt(i - 1) = s.charAt(i);
2、考虑循环时，dp[i]的前一个()的标号位i - dp[i], 如：()()((()));

代码：

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

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