花花酱 LeetCode 1984. Minimum Difference Between Highest and Lowest of K Scores

You are given a 0-indexed integer array nums, where nums[i] represents the score of the ith 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.

Example 1:

Input: nums = [90], k = 1
Output: 0
Explanation: There is one way to pick score(s) of one student:
- [90]. The difference between the highest and lowest score is 90 - 90 = 0.
The minimum possible difference is 0.

Example 2:

Input: nums = [9,4,1,7], k = 2
Output: 2
Explanation: There are six ways to pick score(s) of two students:
- [9,4,1,7]. The difference between the highest and lowest score is 9 - 4 = 5.
- [9,4,1,7]. The difference between the highest and lowest score is 9 - 1 = 8.
- [9,4,1,7]. The difference between the highest and lowest score is 9 - 7 = 2.
- [9,4,1,7]. The difference between the highest and lowest score is 4 - 1 = 3.
- [9,4,1,7]. The difference between the highest and lowest score is 7 - 4 = 3.
- [9,4,1,7]. The difference between the highest and lowest score is 7 - 1 = 6.
The minimum possible difference is 2.

Constraints:

• 1 <= k <= nums.length <= 1000
• 0 <= nums[i] <= 105

Solution: Sliding Window

Sort the array, to minimize the difference, k numbers must be consecutive (i.e, from a subarray). We use a sliding window size of k and try all possible subarrays.
Ans = min{(nums[k – 1] – nums[0]), (nums[k] – nums[1]), … (nums[n – 1] – nums[n – k])}

Time complexity: O(nlogn)
Space complexity: O(1)