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Yes, this problem or similar time-enumeration problems can appear in technical interviews. It tests skills like string manipulation, edge case handling, and understanding small bounded search spaces.
A hash set is useful for storing the digits from the original time. It allows constant-time checks to verify whether each digit in a candidate time is valid. This keeps the validation step simple and efficient.
Yes, backtracking can generate all possible combinations of the allowed digits to form candidate times. After generating them, you filter valid times and choose the smallest one greater than the current time. Because the digit count is small, the search space remains manageable.
A common optimal approach is to simulate time minute by minute from the current time. At each step, convert the time back to HH:MM and verify that every digit belongs to the allowed digit set. Since there are only 1440 minutes in a day, the search is very efficient.