Given a balanced bracket sequence as a string str containing character ‘(‘ or ‘)’, the task is to find the next lexicographical order balanced sequence if possible else print -1.
Input: str = “(())”
Input: str = “((()))”
Approach: First find the rightmost opening bracket which we can replace it by a closing bracket to get the lexicographically larger bracket string. The updated string might not be balanced, we can fill the remaining part of the string with the lexicographically minimal one: i.e. first with as much opening brackets as possible, and then fill up the remaining positions with closing brackets. In other words we try to leave a long as possible prefix unchanged, and the suffix gets replaced by the lexicographically minimal one.
To find this position, we can iterate over the character from right to left, and maintain the balance depth of open and closing brackets. When we meet an opening brackets, we will decrement depth, and when we meet a closing bracket, we increase it. If we are at some point meet an opening bracket, and the balance after processing this symbol is positive, then we have found the rightmost position that we can change. We change the symbol, compute the number of opening and closing brackets that we have to add to the right side, and arrange them in the lexicographically minimal way.
If we find no suitable position, then this sequence is already the maximal possible one, and there is no answer.
Below is the implementation of the above approach:
- Check if the bracket sequence can be balanced with at most one change in the position of a bracket
- Convert an unbalanced bracket sequence to a balanced sequence
- Print the balanced bracket expression using given brackets
- Number of balanced bracket subsequence of length 2 and 4
- Number of closing brackets needed to complete a regular bracket sequence
- Find the minimum value to be added so that array becomes balanced
- Lexicographical smallest alternate Array
- Lexicographical concatenation of all substrings of a string
- Lexicographical Maximum substring of string
- Find the subsequence with given sum in a superincreasing sequence
- Find the Kth position element of the given sequence
- Print all the combinations of a string in lexicographical order
- Sort the words in lexicographical order in Python
- Find minimum length sub-array which has given sub-sequence in it
- Print all longest common sub-sequences in lexicographical order
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