Balanced Parentheses (Generative)

To solve the balanced parentheses problem efficiently, I would use a backtracking approach with a recursive helper function. The core idea is to build the solution character by character while maintaining strict constraints on the number of open and close brackets available. First, I initialize a list to store results and start the recursion with an empty string, zero open brackets, and zero close brackets. The base case occurs when the current string reaches a length of 2*n; at this point, we have a valid combination and add it to our result set. For the recursive step, there are two conditional branches. First, if the count of open brackets used is less than n, we can safely append an opening parenthesis '(' and recurse. This ensures we don't exceed the total pairs allowed. Second, and more critically, we can only append a closing parenthesis ')' if the count of close brackets is strictly less than the count of open brackets. This condition guarantees that every closing bracket has a matching preceding open bracket, preventing invalid sequences like ')('. I would implement this using a StringBuilder to ensure efficient memory usage during string construction. Regarding complexity, while the output size is exponential, the pruning logic ensures we never explore invalid paths. This approach aligns well with Google's focus on algorithmic efficiency and clean, logical code structure in their engineering roles.