LeetCode: Longest Valid Parentheses

Given a string containing just the characters'('And')', Find

Length of the longest valid (well-formed) parentheses substring."(()",

Longest valid parentheses substring is"()", Which has length = 2.

Another example is")()())", Where the longest valid parentheses substring

Is"()()", Which has length = 4.

Solution:

You can use the stack or dp to solve this problem, but the O (N) solution written by the stack is not faster than dp. So let's talk about the dp idea.

First, let's look at the definition of the status:

Dp [I]: the maximum number of valid parentheses that can be composed of the I-th character.Through the above State definition, it is easy to get the following state transition equation:


The second state equation is obtained. When s [I] = ") ', tmp indicates the character corresponding to s [I ].
(Tmp> = 0 & s [tmp] = '(') indicates that tmp to I is a valid matching of parentheses, effective brackets may exist before tmp.
Configuration, so you need to add the two. Note that the boundary is located.
Solution code:

class Solution {public:    int longestValidParentheses(string s)     {        int n = s.size(), dp[n];        dp[0] = 0;        for (int i = 1; i < n; ++i)        {            int tmp = i - 1 - dp[i - 1];            if (s[i] == '(')                dp[i] = 0;            else if (tmp >= 0 && s[tmp] == '(')                dp[i] = dp[i - 1] + 2 + (tmp - 1 >= 0 ? dp[tmp - 1] : 0);            else                dp[i] = 0;        }        return *max_element(dp, dp + n);    }};