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.
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 going to see a solution that works in O(1) for each query.
Idea is based on the Post length of the longest valid balanced substring If we marked indexes of all Balanced parentheses/bracket in a temporary array (here we named it BCP, BOP ) then we answer each query in O(1) time.
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 above idea.
Maximum Length Correct Bracket Subsequence between 5 and 11 = 6 Maximum Length Correct Bracket Subsequence between 4 and 5 = 2 Maximum Length Correct Bracket Subsequence between 1 and 5 = 2
Time complexity for each query is O(1).
- Range Queries for Longest Correct Bracket Subsequence
- Number of balanced bracket subsequence of length 2 and 4
- Array range queries over range queries
- Longest subsequence such that every element in the subsequence is formed by multiplying previous element with a prime
- Check if the bracket sequence can be balanced with at most one change in the position of a bracket | Set 2
- Find index of closing bracket for a given opening bracket in an expression
- RGYB(color) Slots Game to guess the correct color for the correct slot
- Longest Zig-Zag Subsequence
- Longest subsequence with no 0 after 1
- Longest subsequence with a given AND value | O(N)
- Longest subsequence with a given AND value
- Longest Bitonic Subsequence in O(n log n)
- Longest subsequence whose average is less than K
- Longest Increasing Odd Even Subsequence
- Longest Consecutive Subsequence
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.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.
Improved By : Raj Bansal