# Range Queries for Longest Correct Bracket Subsequence Set | 2

Given a bracket sequence or in other words a string S of length n, consisting of characters ‘(‘ and ‘)’. Find the length of the maximum correct bracket subsequence of sequence for a given query range. Note: A correct bracket sequence is the one that has matched bracket pairs or which contains another nested correct bracket sequence. For e.g (), (()), ()() are some correct bracket sequence.
Examples:

```Input : S = ())(())(())(
Start Index of Range = 0,
End Index of Range = 11
Output : 10
Explanation:  Longest Correct Bracket Subsequence is ()(())(())

Input : S = ())(())(())(
Start Index of Range = 1,
End Index of Range = 2
Output : 0

```

Approach: In the Previous post (SET 1) we discussed a solution that works in O(long) for each query, now is this post we will go to see a solution that works in O(1) for each query.
The idea is based on the Post length of the longest valid balanced substring If we marked indexes of all Balanced parentheses/brackets in a temporary array (here we named it BCP[], BOP[] ) then we answer each query in O(1) time.
Algorithm :

```stack is used to get the index of balance bracket.
Travese a string from 0 ..to n
IF we seen a closing bracket,
( i.e., str[i] = ')' && stack is not empty )

Then mark both "open & close" bracket indexes as 1.
BCP[i] = 1;
BOP[stk.top()] = 1;

And At last, stored cumulative sum of BCP[] & BOP[]
Run a loop from 1 to n
BOP[i] +=BOP[i-1], BCP[i] +=BCP[i-1]

```

Now you can answer each query in O(1) time

```(BCP[e] - BOP[s-1]])*2;

```

Below is the implementation of the above idea.

## C++

 `// CPP code to answer the query in constant time` `#include ` `using` `namespace` `std;`   `/*` `BOP[] stands for "Balanced open parentheses" ` `BCP[] stands for "Balanced close parentheses"`   `*/`   `// function for precomputation` `void` `constructBlanceArray(``int` `BOP[], ``int` `BCP[],` `                          ``char``* str, ``int` `n)` `{`   `    ``// Create a stack and push -1 as initial index to it.` `    ``stack<``int``> stk;`   `    ``// Initialize result` `    ``int` `result = 0;`   `    ``// Traverse all characters of given string` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// If opening bracket, push index of it` `        ``if` `(str[i] == ``'('``)` `            ``stk.push(i);`   `        ``else` `// If closing bracket, i.e., str[i] = ')'` `        ``{` `            ``// If closing bracket, i.e., str[i] = ')'` `            ``// && stack is not empty then mark both` `            ``// "open & close" bracket indexs as 1 .` `            ``// Pop the previous opening bracket's index` `            ``if` `(!stk.empty()) {` `                ``BCP[i] = 1;` `                ``BOP[stk.top()] = 1;` `                ``stk.pop();` `            ``}`   `            ``// If stack is empty.` `            ``else` `                ``BCP[i] = 0;` `        ``}` `    ``}`   `    ``for` `(``int` `i = 1; i < n; i++) {` `        ``BCP[i] += BCP[i - 1];` `        ``BOP[i] += BOP[i - 1];` `    ``}` `}`   `// Function return output of each query in O(1)` `int` `query(``int` `BOP[], ``int` `BCP[],` `          ``int` `s, ``int` `e)` `{` `    ``if` `(BOP[s - 1] == BOP[s]) {` `        ``return` `(BCP[e] - BOP[s]) * 2;` `    ``}`   `    ``else` `{` `        ``return` `(BCP[e] - BOP[s] + 1) * 2;` `    ``}` `}`   `// Driver program to test above function` `int` `main()` `{`   `    ``char` `str[] = ``"())(())(())("``;` `    ``int` `n = ``strlen``(str);`   `    ``int` `BCP[n + 1] = { 0 };` `    ``int` `BOP[n + 1] = { 0 };`   `    ``constructBlanceArray(BOP, BCP, str, n);`   `    ``int` `startIndex = 5, endIndex = 11;`   `    ``cout << ``"Maximum Length Correct Bracket"` `            ``" Subsequence between "` `         ``<< startIndex << ``" and "` `<< endIndex << ``" = "` `         ``<< query(BOP, BCP, startIndex, endIndex) << endl;`   `    ``startIndex = 4, endIndex = 5;` `    ``cout << ``"Maximum Length Correct Bracket"` `            ``" Subsequence between "` `         ``<< startIndex << ``" and "` `<< endIndex << ``" = "` `         ``<< query(BOP, BCP, startIndex, endIndex) << endl;`   `    ``startIndex = 1, endIndex = 5;` `    ``cout << ``"Maximum Length Correct Bracket"` `            ``" Subsequence between "` `         ``<< startIndex << ``" and "` `<< endIndex << ``" = "` `         ``<< query(BOP, BCP, startIndex, endIndex) << endl;`   `    ``return` `0;` `}`

## Java

 `// Java code to answer the query in constant time` `import` `java.util.*;`   `class` `GFG{`   `/*` `BOP[] stands for "Balanced open parentheses" ` `BCP[] stands for "Balanced close parentheses"`   `*/`   `// Function for precomputation` `static` `void` `constructBlanceArray(``int` `BOP[], ``int` `BCP[],` `                                ``String str, ``int` `n)` `{` `    `  `    ``// Create a stack and push -1` `    ``// as initial index to it.` `    ``Stack stk = ``new` `Stack<>();;`   `    ``// Traverse all characters of given String` `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{` `        `  `        ``// If opening bracket, push index of it` `        ``if` `(str.charAt(i) == ``'('``)` `            ``stk.add(i);` `            `  `        ``// If closing bracket, i.e., str[i] = ')'` `        ``else` `        ``{` `            `  `            ``// If closing bracket, i.e., str[i] = ')'` `            ``// && stack is not empty then mark both` `            ``// "open & close" bracket indexs as 1 .` `            ``// Pop the previous opening bracket's index` `            ``if` `(!stk.isEmpty())` `            ``{` `                ``BCP[i] = ``1``;` `                ``BOP[stk.peek()] = ``1``;` `                ``stk.pop();` `            ``}`   `            ``// If stack is empty.` `            ``else` `                ``BCP[i] = ``0``;` `        ``}` `    ``}`   `    ``for``(``int` `i = ``1``; i < n; i++)` `    ``{` `        ``BCP[i] += BCP[i - ``1``];` `        ``BOP[i] += BOP[i - ``1``];` `    ``}` `}`   `// Function return output of each query in O(1)` `static` `int` `query(``int` `BOP[], ``int` `BCP[],` `                 ``int` `s, ``int` `e)` `{` `    ``if` `(BOP[s - ``1``] == BOP[s])` `    ``{` `        ``return` `(BCP[e] - BOP[s]) * ``2``;` `    ``}` `    ``else` `    ``{` `        ``return` `(BCP[e] - BOP[s] + ``1``) * ``2``;` `    ``}` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{`   `    ``String str = ``"())(())(())("``;` `    ``int` `n = str.length();`   `    ``int` `BCP[] = ``new` `int``[n + ``1``];` `    ``int` `BOP[] = ``new` `int``[n + ``1``];`   `    ``constructBlanceArray(BOP, BCP, str, n);`   `    ``int` `startIndex = ``5``, endIndex = ``11``;` `    ``System.out.print(``"Maximum Length Correct "` `+ ` `                     ``"Bracket Subsequence between "` `+ ` `                     ``startIndex + ``" and "` `+ endIndex +` `                     ``" = "` `+ query(BOP, BCP, startIndex,` `                                   ``endIndex) + ``"\n"``);`   `    ``startIndex = ``4``;` `    ``endIndex = ``5``;` `    ``System.out.print(``"Maximum Length Correct "` `+  ` `                     ``"Bracket Subsequence between "` `+ ` `                     ``startIndex + ``" and "` `+ endIndex +` `                     ``" = "` `+ query(BOP, BCP, startIndex,` `                                   ``endIndex) + ``"\n"``);`   `    ``startIndex = ``1``;` `    ``endIndex = ``5``;` `    ``System.out.print(``"Maximum Length Correct "` `+` `                     ``"Bracket Subsequence between "` `+` `                     ``startIndex + ``" and "` `+ endIndex +` `                     ``" = "` `+ query(BOP, BCP, startIndex,` `                                   ``endIndex) + ``"\n"``);` `}` `}`   `// This code is contributed by 29AjayKumar`

## C#

 `// C# code to answer the query` `// in constant time` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{`   `    ``/*` `    ``BOP[] stands for "Balanced open parentheses"` `    ``BCP[] stands for "Balanced close parentheses"` `    ``*/`   `    ``// Function for precomputation` `    ``static` `void` `constructBlanceArray(``int``[] BOP, ``int``[] BCP,` `                                     ``String str, ``int` `n)` `    ``{`   `        ``// Create a stack and push -1` `        ``// as initial index to it.` `        ``Stack<``int``> stk = ``new` `Stack<``int``>();;`   `        ``// Traverse all characters of given String` `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``{`   `            ``// If opening bracket, push index of it` `            ``if` `(str[i] == ``'('``)` `                ``stk.Push(i);`   `            ``// If closing bracket, i.e., str[i] = ')'` `            ``else` `            ``{`   `                ``// If closing bracket, i.e., str[i] = ')'` `                ``// && stack is not empty then mark both` `                ``// "open & close" bracket indexs as 1 .` `                ``// Pop the previous opening bracket's index` `                ``if` `(stk.Count != 0) ` `                ``{` `                    ``BCP[i] = 1;` `                    ``BOP[stk.Peek()] = 1;` `                    ``stk.Pop();` `                ``}`   `                ``// If stack is empty.` `                ``else` `                    ``BCP[i] = 0;` `            ``}` `        ``}`   `        ``for` `(``int` `i = 1; i < n; i++) ` `        ``{` `            ``BCP[i] += BCP[i - 1];` `            ``BOP[i] += BOP[i - 1];` `        ``}` `    ``}`   `    ``// Function return output of each query in O(1)` `    ``static` `int` `query(``int``[] BOP, ``int``[] BCP, ``int` `s, ``int` `e)` `    ``{` `        ``if` `(BOP[s - 1] == BOP[s]) ` `        ``{` `            ``return` `(BCP[e] - BOP[s]) * 2;` `        ``}` `        ``else` `        ``{` `            ``return` `(BCP[e] - BOP[s] + 1) * 2;` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``String str = ``"())(())(())("``;` `        ``int` `n = str.Length;` `        ``int``[] BCP = ``new` `int``[n + 1];` `        ``int``[] BOP = ``new` `int``[n + 1];` `        ``constructBlanceArray(BOP, BCP, str, n);` `        ``int` `startIndex = 5, endIndex = 11;` `        ``Console.Write(``"Maximum Length Correct "` `+ ` `                      ``"Bracket Subsequence between "` `+ ` `                       ``startIndex + ``" and "` `+ endIndex + ``" = "` `+ ` `                       ``query(BOP, BCP, startIndex, endIndex) + ``"\n"``);`   `        ``startIndex = 4;` `        ``endIndex = 5;` `        ``Console.Write(``"Maximum Length Correct "` `+ ` `                      ``"Bracket Subsequence between "` `+ ` `                       ``startIndex + ``" and "` `+ endIndex + ``" = "` `+` `                       ``query(BOP, BCP, startIndex, endIndex) + ``"\n"``);`   `        ``startIndex = 1;` `        ``endIndex = 5;` `        ``Console.Write(``"Maximum Length Correct "` `+ ` `                      ``"Bracket Subsequence between "` `+ ` `                       ``startIndex + ``" and "` `+ endIndex + ``" = "` `+ ` `                       ``query(BOP, BCP, startIndex, endIndex) + ``"\n"``);` `    ``}` `}`   `// This code is contributed by Amit Katiyar`

Output:

```Maximum Length Correct Bracket Subsequence between 5 and 11 = 4
Maximum Length Correct Bracket Subsequence between 4 and 5 = 0
Maximum Length Correct Bracket Subsequence between 1 and 5 = 2

```

The time complexity for each query is O(1).

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.