【leetcode】Longest Valid Parentheses

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.

 

设dp[i]表示从s[i]开始（包括s[i]），到达s[n-1]时，最长的有效括号对的长度。

 

如果s[i]=='('

我们需要检查j=dp[i+1]+i+1对应的s[j]位置的括号是否为")"，如果s[j]为')'则说明又组成了一对括号

故此时dp[i]=dp[i+1]+2

于此同时，我们还需要继续考虑dp[j+1]的值，如果j+1没有超出范围，则dp[i]=dp[i+1]+2+dp[j+1]

 

其他情况dp[i]=0;

 

 class Solution {
 public:
     int longestValidParentheses(string s) {
         int n=s.length();
         if(n==) return ;

         int *dp=new int[n];
         dp[n-]=;

         int result=;
         for(int i=n-;i>=;i--)
         {
             if(s[i]=='(')
             {
                 int j=dp[i+]+i+;

                 if(s[j]==')')
                 {
                     dp[i]=dp[i+]+;
                     if(j<n-) dp[i]+=dp[j+];
                 }
                 else
                 {
                     dp[i]=;
                 }

                 if(dp[i]>result)
                 {
                     result=dp[i];
                 }
             }
             else
             {
                 dp[i]=;
             }
         }
         delete [] dp;
         return result;
     }
 };