The Number of Full Rounds You Have Played - Solution & Explanation

Problem Overview: You receive two timestamps in HH:MM format representing when a player logged in and logged out. A game round lasts exactly 15 minutes. The task is to count how many complete 15‑minute rounds were fully played between those two times. If the logout time is earlier than the login time, the session crossed midnight and continues into the next day.

Approach 1: Convert Times to Minutes and Calculate (Time: O(1), Space: O(1))

The straightforward strategy converts both timestamps into total minutes from midnight. Parse the string, compute hours * 60 + minutes, and handle overnight sessions by adding 24 * 60 minutes when the logout time is smaller than the login time. Once both values are normalized, round the start time up to the next 15‑minute boundary and round the end time down to the previous boundary. The number of full rounds equals (endRounded - startRounded) / 15 if the result is positive.

This approach works because a valid round must start and end exactly on multiples of 15 minutes. By shifting the login time upward and the logout time downward, only fully completed rounds remain in the interval. The implementation mainly uses simple arithmetic and string parsing, which makes it easy to implement in any language. Problems like this rely heavily on math operations combined with basic string parsing.

Approach 2: Utilize Modulo for Round Calculation (Time: O(1), Space: O(1))

This version performs the same logic but uses modulo arithmetic to align timestamps to valid round boundaries. After converting both times to minutes, adjust the login time using (15 - start % 15) % 15 to move it to the next multiple of 15. Adjust the logout time using end - (end % 15) to snap it to the previous boundary. Handle the overnight case by adding 1440 minutes when the logout time occurs the next day.

Once aligned, compute the difference and divide by 15 to get the total rounds. The modulo trick removes conditional rounding logic and keeps the calculation concise. This method is often preferred in interviews because it shows comfort with arithmetic transformations and edge cases such as midnight wrap‑around.

Recommended for interviews: Interviewers typically expect the minute‑conversion strategy combined with rounding to 15‑minute boundaries. It demonstrates clean reasoning about time intervals and edge cases like crossing midnight. The modulo variant is equally optimal and often considered a cleaner implementation once you recognize that every valid round aligns to multiples of 15.