[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)。

class Solution {
public:
    int longestValidParentheses(string s) {
        bool *a = new bool[s.length()];
        memset(a, false, s.length());
        stack<int> st;
        for (int i = 0; i < s.length(); ++i) {
            if (s[i] == '(') {
                st.push(i);
            } else if (s[i] == ')' && !st.empty()) {
                a[i] = true;
                a[st.top()] = true;
                st.pop();
            }
        }
        int max_len = 0, cur_len = 0;
        for (int i = 0; i < s.length(); ++i) {
            if (a[i]) ++cur_len;
            else cur_len = 0;
            max_len = max(max_len, cur_len);
        }
        return max_len;
    }
};