539. Minimum Time Difference

Difficulty: Medium

Topics: Array, Math, String, Sorting

Given a list of 24-hour clock time points in "HH:MM" format, return the minimum minutes difference between any two time-points in the list.

Example 1:

• Input: timePoints = ["23:59","00:00"]
• Output: 1

Example 2:

• Input: timePoints = ["00:00","23:59","00:00"]
• Output: 0

Constraints:

• 2 <= timePoints.length <= 2 * 104
• timePoints[i] is in the format "HH:MM".

Solution:

The approach can be broken down as follows:

Approach:

1. Convert time points to minutes:
   Each time point is in "HH:MM" format, so we can convert it into the total number of minutes from 00:00. For example, "23:59" would be 23 * 60 + 59 = 1439 minutes.

2. Sort the time points:
   Once all the time points are converted into minutes, sort them to calculate the differences between consecutive time points.

3. Handle the circular nature of the clock:
   The difference between the first and last time points also needs to be considered, because of the circular nature of the clock. This can be handled by adding 1440 (24 hours) to the last time point and comparing it with the first time point.

4. Find the minimum difference:
   After sorting, find the minimum difference between consecutive time points, including the difference between the first and last time points.

Let's implement this solution in PHP: 539. Minimum Time Difference

<?php
/**
 * @param String[] $timePoints
 * @return Integer
 */
function findMinDifference($timePoints) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */

}

// Example 1:
$timePoints1 = ["23:59", "00:00"];
echo findMinDifference($timePoints1) . "\n";  // Output: 1

// Example 2:
$timePoints2 = ["00:00", "23:59", "00:00"];
echo findMinDifference($timePoints2) . "\n";  // Output: 0
?>

Explanation:

1. array_map(): This function is used to convert each time point from "HH:MM" format into the total number of minutes from 00:00.
2. sort($minutes): After converting the time points into minutes, we sort them to calculate the difference between consecutive time points.
3. Calculate consecutive differences: The difference between consecutive time points is computed and tracked as the minimum difference.
4. Circular difference: The difference between the last and the first time point is calculated as 1440 - last + first, which ensures that the circular nature of the clock is accounted for.

Time Complexity:

• Sorting the array takes O(n log n), where *n * is the number of time points.
• Comparing consecutive time points takes O(n).
• Overall time complexity: O(n log n), which is efficient for n up to 20,000 (as given in the constraints).

This solution should work efficiently within the given problem constraints.

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