Minimum Difference Between Highest and Lowest of K Scores

Problem Description

You are given a 0-indexed integer array nums, where nums[i] represents the score of the i-th student. You are also given an integer k. Pick the scores of any k students from the array so that the difference between the highest and the lowest of the k scores is minimized. Return the minimum possible difference.

Key Insights

• The problem requires selecting k scores to minimize the difference between the maximum and minimum scores.
• Sorting the array allows for easier calculation of the differences of contiguous subarrays.
• The minimum difference will always be found in a contiguous subarray of size k after sorting the array.

Space and Time Complexity

Time Complexity: O(n log n) - due to the sorting of the array.
Space Complexity: O(1) - no additional space is used apart from a few variables.

Solution

To solve the problem, we can use the following steps:

1. Sort the Input Array: This allows us to work with contiguous elements easily.
2. Iterate Through the Array: Check every possible subarray of length k in the sorted array.
3. Calculate Differences: For each subarray, calculate the difference between the maximum and minimum values.
4. Track the Minimum Difference: Keep updating the minimum difference found during the iterations.

The algorithm primarily uses sorting and a simple iteration, making it efficient and straightforward.

Code Solutions