1. 題目：

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 "()()"

2. 思路

初始思路

從字符串中每個位置開始，求以該位置開始的最長合法字串長度，然後從這些字串中選出最長的。時間復雜度O(n^2)

改進

可以利用前面已經產生的結果，減少匹配不必要的匹配

 1 class Solution {
 2         public int longestValidParentheses(String s) {
 3             int[] records = new int[s.length()];
 4             int max = 0;
 5             for (int
 
 i = 1; i < s.length(); i++) {
 6                 boolean match = false;
 7                 if ( s.charAt(i) == ‘)‘) {
 8                     if (s.charAt(i-1) == ‘(‘) {
 9                         records[i] = 2;
10                         match = true;
11                     }
12                     else
 
 if (records[i-1] > 0 && i - records[i-1] > 0 && s.charAt(i - records[i-1] - 1) == ‘(‘) {
13                         records[i] = records[i - 1] + 2;
14                         match = true;
15                     }
16                     if  (match) {
17                         if (i - records[i] >=  0 && records[i - records[i]] > 0) {
18                             records[i] += records[i - records[i]];
19                         }
20                         max = max > records[i] ? max :  records[i];
21                     }
22                 }
23             }
24             return max;
25         }
26     }

LeetCode:32 Longest Valid Parentheses