[Leetcode] Longest Valid Parentheses

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.

 

很多人会说这道题用动规，可是用动规每次匹配后还要向前到上一个匹配跟这个匹配是否连接，时间复杂度为O(n^2)，其实可以换个想法，用一个bool数组来标记已经匹配过的字符，找到最长的连续标记的长度就是所求的结果。只要遍历两遍数组，时间复杂度为O(n)。

 1 class Solution {

 2 public:

 3     int longestValidParentheses(string s) {

 4         bool *a = new bool[s.length()];

 5         memset(a, false, s.length());

 6         stack<int> st;

 7         for (int i = 0; i < s.length(); ++i) {

 8             if (s[i] == '(') {

 9                 st.push(i);

10             } else if (s[i] == ')' && !st.empty()) {

11                 a[i] = true;

12                 a[st.top()] = true;

13                 st.pop();

14             }

15         }

16         int max_len = 0, cur_len = 0;

17         for (int i = 0; i < s.length(); ++i) {

18             if (a[i]) ++cur_len;

19             else cur_len = 0;

20             max_len = max(max_len, cur_len);

21         }

22         return max_len;

23     }

24 };