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Leetcode 1984. Minimum Difference Between Highest and Lowest of K Scores

Problem Statement

You are given a list of integers scores representing the scores of a game and an integer k. Your task is to find the minimum difference between the highest and lowest scores in any k-subarray of scores. A k-subarray is a subarray of length k.

Constraints:

Clarifying Questions

  1. Is the array of scores always sorted?
    • No, the array of scores is not necessarily sorted.
  2. Can the array contain negative numbers?
    • According to constraints, all numbers are non-negative.
  3. Should we return the exact minimum difference or just any valid difference within a k-size subarray?
    • The goal is to return the exact minimum difference between the highest and lowest scores in any k-size subarray.

Strategy

To solve this problem, you’ll use the following steps:

  1. Sort the Array:
    • First, sort the array to simplify finding k-size subarrays with the minimum range.
  2. Sliding Window Technique:
    • Use a sliding window approach to find the minimum difference between the maximum and minimum values in each subarray of length k.

Code

Here is the Java implementation for the problem:

import java.util.Arrays;

public class MinimumDifferenceBetweenScores {
    public int minimumDifference(int[] scores, int k) {
        // If k is 1, the minimum difference is always 0
        if (k == 1) return 0;

        // Step 1: Sort the array
        Arrays.sort(scores);

        int minDifference = Integer.MAX_VALUE;

        // Step 2: Use sliding window approach
        for (int i = 0; i <= scores.length - k; i++) {
            int currentDifference = scores[i + k - 1] - scores[i];
            if (currentDifference < minDifference) {
                minDifference = currentDifference;
            }
        }

        return minDifference;
    }

    public static void main(String[] args) {
        MinimumDifferenceBetweenScores solution = new MinimumDifferenceBetweenScores();
        int[] scores = {9, 4, 1, 7};
        int k = 2;
        System.out.println(solution.minimumDifference(scores, k)); // Output: 2
    }
}

Time Complexity

Hence, the overall time complexity is dominated by the sorting step, resulting in O(n log n).

This should cover the problem comprehensively and provide a clear and efficient solution using Java.

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