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.

思路：最长有效的括号，可以看做能够匹配的最长扩展，只有当右括号匹配左括号时才是有效的，因此我们需要计算每个左括号被右括号匹配时可能得到的最长序列；

1. int longestValidParentheses(string s) {
2. int last = -1;
3. int max_len = 0;
4. stack<int> st;
5. int size = s.size();
6. if(size == 0) return 0;
7. int index = 0;
8. while(!s.empty() || index < size) {
9. if(s.at(index) == '(') {
10. st.push(index); // 记录待匹配的左括号下标
11. } else if (s.at(index) == ')') {
12. if(!st.empty()) {
13. st.pop();
14. if(!st.empty()) max_len = max(max_len,index-st.top()); //分两种情况讨论，1） 栈中有左括号
15. else max_len = max(max_len,index-last);   2）栈中无左括号
16. } else {
17. last = index; //记录未能匹配的右括号下标，之后重新开始匹配
18. }
19. }
20. index++;
21. if(index == size) break;
22. }
23. return max_len;
24. }