Number of Valid Clock Times

Problem Description

You are given a string of length 5 called time, representing the current time on a digital clock in the format "hh:mm". The earliest possible time is "00:00" and the latest possible time is "23:59". In the string time, the digits represented by the ? symbol are unknown, and must be replaced with a digit from 0 to 9. Return an integer answer, the number of valid clock times that can be created by replacing every ? with a digit from 0 to 9.

Key Insights

• The first two characters represent hours and must be in the range of "00" to "23".
• The last two characters represent minutes and must be in the range of "00" to "59".
• Each ? can be replaced by any digit from 0 to 9, but must adhere to the valid hour and minute constraints.
• The total number of valid times can be computed by enumerating all possible replacements for ? and filtering valid combinations.

Space and Time Complexity

Time Complexity: O(1) - The operations are constant in terms of input size, as the string length is fixed at 5. Space Complexity: O(1) - We use a fixed amount of space for variables regardless of input.

Solution

To find the number of valid clock times, we will:

1. Parse the string to identify the positions of ?.
2. For each ?, determine the valid digit replacements based on their positions (hours or minutes).
3. Count the total combinations of valid replacements and return the result.

We will use simple conditional checks to ensure the replacements yield valid hour and minute values.

Code Solutions