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Leetcode 2437. Number of Valid Clock Times Let’s go through solving the problem step by step.

Problem Statement

Given a string time in the form “HH:MM”, representing the hour and minutes on a 24-hour clock, some of the digits are hidden (represented by ‘?’). We need to compute how many distinct valid times can be represented by such a string.

Clarifying Questions

1. Q: Can both ‘H’ and ‘M’ be given as ‘?’ at the same time? A: Yes, each digit may independently be ‘?’.

2. Q: Should we only consider valid 24-hour times? A: Yes, what counts as valid times here are those that can exist in a 24-hour format.

3. Q: Is the input always going to be valid in terms of format (i.e., only ‘?’ and numeric characters, specifically in the form “HH:MM”)? A: Yes, you can assume that the input format is always valid.

Strategy

1. Identify Positions: We’ll be working with positions HH:MM.
   • ‘H1’, ‘H2’ for hours and ‘M1’, ‘M2’ for minutes.
2. Brute Force: Use nested loops to generate all potential valid times by replacing ‘?’ with all possible valid digits (0-9). Check each generated value to see if it forms a valid hour (00 through 23) and minute (00 through 59).

Time Complexity

• The time complexity of this brute-force approach primarily depends on the number of possible combinations tested. With each ‘?’ being replaceable by 10 possible digits:
  • Worst case, ‘HH:MM’ like ‘??:??’ would generate 10^4 possibilities, which translates to 10,000 combinations to check.

Code

public class ValidClockTimes {
    public int countValidTimes(String time) {
        int validTimeCount = 0;
        for (int h1 = 0; h1 < 3; h1++) {
            if (time.charAt(0) != '?' && time.charAt(0) - '0' != h1) continue;
            for (int h2 = 0; h2 < 10; h2++) {
                if (time.charAt(1) != '?' && time.charAt(1) - '0' != h2) continue;
                if (h1 * 10 + h2 >= 24) break;
                for (int m1 = 0; m1 < 6; m1++) {
                    if (time.charAt(3) != '?' && time.charAt(3) - '0' != m1) continue;
                    for (int m2 = 0; m2 < 10; m2++) {
                        if (time.charAt(4) != '?' && time.charAt(4) - '0' != m2) continue;
                        if (true) { // All given conditions met
                            validTimeCount++;
                        }
                    }
                }
            }
        }
        return validTimeCount;
    }

    public static void main(String[] args) {
        ValidClockTimes vct = new ValidClockTimes();
        String time = "1?:?2";
        System.out.println(vct.countValidTimes(time));  // Outputs the count of valid times
    }
}

Explanation of the Code

1. Nested Loops: Each possible digit for hours (first and second places) and minutes (third and fourth places) are considered.
2. Conditions: Within the loops, conditions ensure ‘?’ placements are replaced correctly.
3. Validation: Valid hour and minute combinations are identified by checking if they fall within the respective ranges.

By following this method, we ensure all potential valid time combinations are checked and counted appropriately.

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