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.

stack是解这种valid pari的不二法宝。。。

1. 维护一个stack, 只存 ‘（’ 的index

2. 同时维护一个start,记录最开始有效的位子。 

3. 每遇到‘）’，如果stk不为空 pop 并求最长 （根据是否为空） ， 如果为空，那么不是valid， 更新 start.

O(n)

class Solution {
public:
    int longestValidParentheses(string s) {
        int len=s.size();
        int maxLen=0, start=0;
        stack<int> stk;
        for (int i=0; i<len; i++){
            if (s[i]=='(')
                stk.push(i);
            else{
                if (stk.empty()){
                    start=i+1;
                } else{
                    stk.pop();
                    maxLen=max(maxLen, stk.empty()? i-start+1: i-stk.top());
                }
            }
        }
        return maxLen;
    }
};