Next Closest Time

Problem Statement

Given a time string in the HH:MM format, the goal is to find the closest time possible by rearranging or reusing the digits in the given time string. The primary condition here is that we can reuse the same digits multiple times to form a valid future time. The time string provided is always valid and strictly adheres to the 24-hour format, ensuring two digits for both hours and minutes separated by a colon.

The key challenge is to determine the smallest time increment that can be made using only the digits present in the current time while navigating through the intricacies of time cycles, especially transitions around the midnight hour.

Examples

Example 1

Input:

time = "19:34"

Output:

"19:39"

Explanation:

The next closest time choosing from digits 1, 9, 3, 4, is 19:39, which occurs 5 minutes later.
It is not 19:33, because this occurs 23 hours and 59 minutes later.

Example 2

Input:

time = "23:59"

Output:

"22:22"

Explanation:

The next closest time choosing from digits 2, 3, 5, 9, is 22:22.
It may be assumed that the returned time is next day's time since it is smaller than the input time numerically.

Constraints

• time.length == 5
• time is a valid time in the form "HH:MM".
• 0 <= HH < 24
• 0 <= MM < 60

Approach and Intuition

• Understanding the mechanics behind this problem makes use of some essential steps and thought processes:

1. Extract and Use Digits: Begin by extracting the digits from the given time representation. For instance, from "19:34", the digits would be [1, 9, 3, 4].

2. Generate Time Possibilities: Using the identified digits, we need to generate possible valid time combinations. This step may involve combing through permutations and filtering out invalid times (those not adhering to the 24-hour format, such as "25:99").

3. Identify the Next Closest Time: After generating valid times, the aim is to find the smallest forward leap in time. This implies searching for the smallest increment, and if the original time is the latest in the day, the search wraps to the next day.

   • For instance, from "19:34", the valid next time that can be formed by rearranging or reusing [1, 9, 3, 4] is "19:39". This is because "19:39" is the immediate valid time increment and does not require a wrap around the 24-hour clock, unlike "19:33" which is technically 23 hours and 59 minutes ahead, leading into the next day.

4. Handle Edge Cases: Times such as "23:59" require resetting to an earlier hour; thus, understanding how to wrap around the clock is crucial. In this example, using the digits [2, 3, 5, 9], the next logically valid time is "22:22", which indulges the rollover to the next day due to military time constraints.

• The intuition behind solving this problem lies in understanding time as a cyclic entity and efficiently generating and checking probable times. Utilizing available digits for the most minor increment from the given time requires a combination of comprehension of time mechanisms and efficient combinatorial generation and filtering techniques.

Solutions

class Solution {
    public String findNextTime(String current) {
        int initialMinutes = 60 * Integer.parseInt(current.substring(0, 2));
        initialMinutes += Integer.parseInt(current.substring(3));
        int closestTime = initialMinutes;
        int timeDifference = 24 * 60;
        Set<Integer> validDigits = new HashSet();
        for (char c: current.toCharArray()) if (c != ':') {
            validDigits.add(c - '0');
        }
    
        for (int hourFirst: validDigits) for (int hourSecond: validDigits) if (hourFirst * 10 + hourSecond < 24) {
            for (int minuteFirst: validDigits) for (int minuteSecond: validDigits) if (minuteFirst * 10 + minuteSecond < 60) {
                int currentMinutes = 60 * (hourFirst * 10 + hourSecond) + (minuteFirst * 10 + minuteSecond);
                int relativeDifference = Math.floorMod(currentMinutes - initialMinutes, 24 * 60);
                if (0 < relativeDifference && relativeDifference < timeDifference) {
                    closestTime = currentMinutes;
                    timeDifference = relativeDifference;
                }
            }
        }
    
        return String.format("%02d:%02d", closestTime / 60, closestTime % 60);
    }
}