# Longest Valid parentheses

Source: Internet
Author: User

Given A string containing just the characters `‘(‘` `‘)‘` and, find the length of the longest valid (well-formed) parenthe SES substring.

`"(()"`for, the longest valid parentheses substring `"()"` are, which has length = 2.

Another example `")()())"` is, where the longest valid parentheses substring `"()()"` are, which has length = 4.

The problem uses the dynamic programming thought

My first thought was to use a two-dimensional array to hold the length, and X, y of the two-dimensional array to be the string subscript, preserving the length of the substring between them.

But I can't find a simple formula to show the relationship between big and small problems, which is quite complicated, I've found 36 cases and I want to list them all, but there are 36 other things. As a result I gave up this method.

So I searched the internet for other people's algorithms, and found that only one-dimensional arrays can be solved

The value of this one-dimensional array means the longest valid matching brace substring length from s[i] to s[s.length-1] containing s[i]

To tell the truth, the meaning is not easy to imagine, and if I think about it, I first think of the longest valid matching bracket string that does not contain s[i]. is based on what kind of thinking to get such a result. Why can't I just think about it? I do not believe that it is my IQ problem, it must be that I do too few problems. Continue to brush the question, quantitative change will always have a qualitative change that day.

`intLongestvalidparentheses (strings) {intLen =s.size (); if(Len <2)        return 0; intMaxLen =0; intF[len];  for(inti =0; i < Len; ++i)//initialized to 0 F[i]=0;  for(inti = len-2; I >=0; --i) {if(S[i] = ='(')//Since it contains s[i], then s[i] must be ' (' to form a matching bracket {intj = i +1+ f[i+1]; The next "Maybe" cannot match the position of the parenthesesif(J < len && S[j] = =')')//This "maybe" can be checked to match {F[i]= f[i+1] +2; if(j +1<len)//Beware if there is a matching brace in the back, the length is added f[i]+ = f[j+1]; }            if(F[i] >maxlen)//Maximum length maxlen=F[i]; }            }    returnMaxLen;}`

Longest Valid parentheses

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