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.

一维DP。

dp[i]表示[i， n-1]的最长距离，所以i从n-2开始逆向dp。

如果s[i]=‘（’，那么跳过中间dp[i+1] 已经求出的最长距离，到 j=i+1+dp[i+1]，如果dp[j]为‘）’且j<n，那么dp[i]=dp[i+1]+2.

接下来还需要一步计算：如果j+1<n，[i, j]已经求出了最大距离，还需要加上dp[j+1]. 相当于最终的值=新匹配的（）-> 2+dp[i+1]+dp[j+1]

int longestValidParentheses(string s){    int dp[65536];    int longest=0;    int n=s.size();    memset(dp, 0, 65536);    for(int i=n-2; i>=0; i--)    {        if(s[i]=='(')        {            int j=i+1+dp[i+1];            if(j<n && s[j]==')')            {                dp[i]=dp[i+1]+2;                if(j+1<n)                    dp[i]+=dp[j+1];            }        }        longest=max(longest, dp[i]);    }    return longest;}