Remove Invalid Parentheses - Solution & Explanation

This approach uses a BFS technique. The idea is to start with the original string and try to remove each parenthesis at each level, generating a new state each time. We are looking for the shortest valid string, hence the BFS approach ensures that we explore the minimum removal solution first.

The critical parts of the approach are:

• Use a queue to store intermediate states of string removal.
• Use a set to keep track of visited states to avoid redundant work.
• Level by level, try removing each parentheses '(' or ')' and check if the remaining string is valid.
• Once a valid state is found, further remove operations are ceased at that level since BFS ensures minimum operations are performed.

This Python function uses a queue to explore each possible state of the string. For each invalid state, we remove one parenthesis at each position and check the new state. A visited set is used to avoid processing the same string multiple times, ensuring more efficient performance.

DFS with backtracking is a common technique in situations where all combinations must be explored. In this problem, we explore each possible configuration and backtrack when we identify that no valid state can follow the current configuration.

The primary characteristics of this approach are:

• Recursively explore each character, either remove or keep it, leading to a valid configuration.
• Ensure the counting of invalid parentheses removal is minimized using backtracking.

This JavaScript function utilizes DFS and backtracking to explore each state's depth, leveraging a pruning strategy to skip duplicate configurations and strings that exceed the minimum removal already encountered. The use of a Set avoids duplicates in the final result.