You are given a string, s, that contains:
Lowercase English letters
Opening '(' and closing ')' parentheses
A string is considered valid if:
All opening parentheses '(' are closed properly by a matching ')'.
The parentheses are in the correct order and nesting.
Letters can appear anywhere and do not affect validity.
Return all possible valid strings that can be formed by removing the minimum number of invalid parentheses. The answer must be a list of unique strings, in any order.
Constraints:
s.length
s consists of lowercase English letters and parentheses '(' and ')'.
There will be at most 20 parentheses in s.
The algorithm aims to generate all possible valid strings by removing the minimum number of invalid parentheses. It starts with a preprocessing step to determine how many opening and closing parentheses need to be removed. As it scans the string, it increments a counter for each opening parenthesis. For each closing parenthesis, it tries to match it with an opening one. If no match is found, it marks the closing parenthesis as unmatched. This ensures the algorithm knows the minimum number of each type of parenthesis to remove.
Once the number of invalid parentheses is known, the algorithm uses recursive backtracking to explore all valid combinations. It processes the string one character at a time and considers several choices:
If the character is an opening parenthesis (, the algorithm considers two choices: skip it to reduce the number of unmatched openings, or add it to the expression and increase the open count.
If it’s a closing parenthesis ), it can be skipped to reduce unmatched closings, or added to the expression—but only if more opening parentheses are already added, to keep the expression balanced.
If it’s ...
You are given a string, s, that contains:
Lowercase English letters
Opening '(' and closing ')' parentheses
A string is considered valid if:
All opening parentheses '(' are closed properly by a matching ')'.
The parentheses are in the correct order and nesting.
Letters can appear anywhere and do not affect validity.
Return all possible valid strings that can be formed by removing the minimum number of invalid parentheses. The answer must be a list of unique strings, in any order.
Constraints:
s.length
s consists of lowercase English letters and parentheses '(' and ')'.
There will be at most 20 parentheses in s.
The algorithm aims to generate all possible valid strings by removing the minimum number of invalid parentheses. It starts with a preprocessing step to determine how many opening and closing parentheses need to be removed. As it scans the string, it increments a counter for each opening parenthesis. For each closing parenthesis, it tries to match it with an opening one. If no match is found, it marks the closing parenthesis as unmatched. This ensures the algorithm knows the minimum number of each type of parenthesis to remove.
Once the number of invalid parentheses is known, the algorithm uses recursive backtracking to explore all valid combinations. It processes the string one character at a time and considers several choices:
If the character is an opening parenthesis (, the algorithm considers two choices: skip it to reduce the number of unmatched openings, or add it to the expression and increase the open count.
If it’s a closing parenthesis ), it can be skipped to reduce unmatched closings, or added to the expression—but only if more opening parentheses are already added, to keep the expression balanced.
If it’s ...