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：

我第一反应是想到了栈（不像好多网友第一下想到DP, DP基础还是不够扎实。。。），但是没想到栈里存的是index。后来发现如果发生失配，那么就更新last，表示上一组匹配的括号的结束地址是什么，否则的话就用当前index减去栈顶的index。

代码：

    int max(int a, int b){
        if(a > b)
            return a;
        return b;
    }
    int longestValidParentheses(string s) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        int l = s.length();
        if(l < 2)
            return 0;
        int i;
        stack<int> Stack;
        int result = 0;
        int last = -1;
        for(i = 0; i < l; i++){
            if(s[i] == '('){
                Stack.push(i);
            }
            else{
                if(Stack.empty()){
                    last = i;   
                }
                else{
                    Stack.pop();
                    if(Stack.empty()){
                        result = max(result, i-last);
                    }
                    else{
                        result = max(result, i-Stack.top());
                    }
                }
            }
        }     
        return result;
    }