**π‘ Problem Formulation:** We wish to determine the earliest palindromic time that comes after a given input time. A time is palindromic when it reads the same backward as forward (e.g., 12:21 or 05:50). Given an input time, say 22:58, we would expect to find the next palindromic time, which in this case would be 23:32.

## Method 1: Brute Force Iteration

The brute force iteration method involves continuously adding one minute to the input time until we find a time that forms a palindrome. It uses simple iterations and checks to find the next palindromic time.

Here’s an example:

from datetime import datetime, timedelta def is_palindrome(time): return time == time[::-1] def next_palindromic_time(time_str): time = datetime.strptime(time_str, '%H:%M') while True: time += timedelta(minutes=1) if is_palindrome(time.strftime('%H:%M')): return time.strftime('%H:%M') print(next_palindromic_time('22:58'))

Output:

23:32

This function converts the input string to a datetime object and continuously adds one minute while checking if the result is a palindrome. When a palindromic time is found, it’s formatted and returned as a string.

## Method 2: Increment Hour and Minute Separately

This method increments the minutes and, when required, the hours separately. When the minutes reach 60, they roll over to 00 and the hour is incremented. This might result in faster convergence in some cases.

Here’s an example:

def next_palindromic_time(time_str): hours, minutes = map(int, time_str.split(':')) while True: minutes += 1 if minutes == 60: minutes = 0 hours = 0 if hours == 23 else hours + 1 time = f'{hours:02d}:{minutes:02d}' if time == time[::-1]: return time print(next_palindromic_time('22:58'))

Output:

23:32

Here, we split the hours and minutes, then increment them while checking for palindromes. This approach avoids creating datetime objects, potentially increasing the function’s performance.

## Method 3: Using a Precomputed List of Palindromic Times

This method uses an optimization technique: precomputing all palindromic times. Given a time, it finds the next palindromic time from the list, making the lookup instantaneous.

Here’s an example:

palindromic_times = [ '00:00', '01:10', '02:20', '03:30', '04:40', '05:50', '10:01', '11:11', '12:21', '13:31', '14:41', '15:51', '20:02', '21:12', '22:22', '23:32' ] def next_palindromic_time(time_str): for pal_time in palindromic_times: if time_str < pal_time: return pal_time return palindromic_times[0] # Return the first palindromic time of the next day print(next_palindromic_time('22:58'))

Output:

23:32

This snippet searches for the first palindromic time that is greater than the input time within the precomputed list. It’s efficient since it avoids recalculating palindrome conditions.

## Method 4: Calculating the Next Time Directly

By understanding the nature of palindromic times, we can construct an algorithm that jumps directly to the next palindromic time without iteration, based on the current time’s digits.

Here’s an example:

def next_palindromic_time(time_str): # This is a simplified version for illustration and may not handle all edge cases hour, minute = time_str.split(':') reverse_hour = hour[::-1] if minute < reverse_hour and hour < "23": return f"{hour}:{reverse_hour}" new_hour = str(int(hour) + 1).zfill(2) return f"{new_hour}:{new_hour[::-1]}" print(next_palindromic_time('22:58'))

Output:

23:32

This code strategically calculates the next palindromic time by analyzing the hour and minute components and checking against their reversals. This method can minimize iterations, optimizing time to reach the result.

## Bonus One-Liner Method 5: List Comprehension with Range

This one-liner method makes use of Python’s list comprehension along with the range function to generate a palindromic time in a single statement, given a starting time.

Here’s an example:

from datetime import datetime, timedelta start = '22:58' dt = datetime.strptime(start, '%H:%M') + timedelta(minutes=1) next_pal_time = next((dt + timedelta(minutes=i)).strftime('%H:%M') for i in range(1440) if str((dt + timedelta(minutes=i)).strftime('%H:%M')) == str((dt + timedelta(minutes=i)).strftime('%H:%M'))[::-1]) print(next_pal_time)

Output:

23:32

This one-liner uses a generator expression within a call to the built-in `next()`

function, generating and checking times in a single step until it finds a palindromic time.

## Summary/Discussion

**Method 1:**Brute Force Iteration. Straightforward. Might be slow for times close to ’23:59′.**Method 2:**Increment Hour and Minute Separately. More complex logic. Generally faster than Method 1.**Method 3:**Precomputed List of Palindromic Times. Instant lookup. Limited to known patterns and lacks flexibility.**Method 4:**Calculating Next Time Directly. Optimal performance. Requires careful handling of edge cases.**Method 5:**One-Liner List Comprehension. Elegant and concise. Can be inefficient due to potential checking of 1,440 times (all minutes in a day).