What is the time complexity of Minimum Difference Between Highest and Lowest of K Scores?

The optimal solution has a time complexity of O(n log n).

What data structures are used to solve Minimum Difference Between Highest and Lowest of K Scores?

This problem uses Array, Sliding Window, Sorting. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Minimum Difference Between Highest and Lowest of K Scores?

Insight 1: Sorting the array allows for efficient finding of the minimum and maximum scores within a sliding window of size k. Insight 2: A sliding window approach can effectively iterate through all possible k-sized subarrays without redundant calculations.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Minimum Difference Between Highest and Lowest of K Scores - LeetCode 1984 Solution

Q: Which companies ask LeetCode 1984. Minimum Difference Between Highest and Lowest of K Scores in interviews?

This problem is frequently asked at Tinkoff.

Minimum Difference Between Highest and Lowest of K Scores - Complete Solution Guide

Minimum Difference Between Highest and Lowest of K Scores is LeetCode problem 1984, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

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 . 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 =

Detailed Explanation

The problem asks you to find the minimum difference between the highest and lowest scores among any group of `k` students. You are given an array `nums` where each element represents a student's score, and an integer `k` representing the number of students to select. The goal is to select `k` students such that the difference between the maximum and minimum score within that group is as small as possible. The input is a 0-indexed integer array `nums` and an integer `k`. The output is a single integer representing the minimum possible difference.

Solution Approach

The provided solutions utilize a sorting algorithm followed by a sliding window technique. First, the input array `nums` is sorted in ascending order. Then, a sliding window of size `k` is iterated across the sorted array. For each window, the difference between the last and first element (representing the highest and lowest scores in that window) is calculated. The minimum difference encountered across all windows is stored and finally returned.

Step-by-Step Algorithm

Step 1: Sort the input array `nums` in ascending order. This ensures that the smallest and largest elements within any k-sized subarray will be easily accessible at the beginning and end of the subarray.
Step 2: Initialize a variable `min_diff` to a large value (infinity in Python, Integer.MAX_VALUE in Java, etc.). This variable will store the minimum difference found so far.
Step 3: Iterate through the sorted array using a sliding window of size `k`. The loop iterates from index 0 to `len(nums) - k + 1`.
Step 4: For each window, calculate the difference between the element at index `i + k - 1` (the maximum) and the element at index `i` (the minimum).
Step 5: Update `min_diff` with the minimum value between the current `min_diff` and the calculated difference.
Step 6: After iterating through all windows, return the value of `min_diff`.

Key Insights

Insight 1: Sorting the array allows for efficient finding of the minimum and maximum scores within a sliding window of size k.
Insight 2: A sliding window approach can effectively iterate through all possible k-sized subarrays without redundant calculations.
Insight 3: Handling the edge case where k equals 1 (the minimum difference will always be 0).

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(1)

Topics

This problem involves: Array, Sliding Window, Sorting.

Companies

Asked at: Tinkoff.

Minimum Difference Between Highest and Lowest of K Scores | LeetCode 1984

Easy

Array Sliding Window Sorting

Time: O(n log n)Space: O(1)

Solution Code

Available in:

import java.util.Arrays;

class Solution {
    public int minimumDifference(int[] nums, int k) {
        if (k == 1) {
            return 0;
        }
        Arrays.sort(nums);
        int minDifference = Integer.MAX_VALUE;
        for (int i = 0; i <= nums.length - k; i++) {
            int difference = nums[i + k - 1] - nums[i];
            minDifference = Math.min(minDifference, difference);
        }
        return minDifference;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 1984: Minimum Difference Between Highest and Lowest of K Scores - Detailed explanation and solution approaches.

Topics

Array Sliding Window Sorting

Companies

Tinkoff

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1984

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Sort the input array `nums` in ascending order. This ensures that the smallest and largest elements within any k-sized subarray will be easily accessible at the beginning and end of the subarray.
2
Step 2: Initialize a variable `min_diff` to a large value (infinity in Python, Integer.MAX_VALUE in Java, etc.). This variable will store the minimum difference found so far.
3
Step 3: Iterate through the sorted array using a sliding window of size `k`. The loop iterates from index 0 to `len(nums) - k + 1`.
4
Step 4: For each window, calculate the difference between the element at index `i + k - 1` (the maximum) and the element at index `i` (the minimum).
5
Step 5: Update `min_diff` with the minimum value between the current `min_diff` and the calculated difference.
6
Step 6: After iterating through all windows, return the value of `min_diff`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is the sorting of the array, which takes O(n log n) time using efficient algorithms like merge sort or quicksort. The sliding window iteration has a time complexity of O(n). The space complexity is O(1) because the algorithm uses a constant amount of extra space regardless of the input size. In-place sorting can also be implemented.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute-Force Approach

Generate all possible combinations of `k` students and compute the difference for each combination. This approach would require iterating through all combinations, which has a high time complexity.

Time: O(n^k)Space: O(k)

Trade-offs: This approach is less efficient than the sorting and sliding window approach, especially for larger values of `n` and `k`. It's only practical for very small input sizes.

✨

Key Insights

1Insight 1: Sorting the array allows for efficient finding of the minimum and maximum scores within a sliding window of size k.
2Insight 2: A sliding window approach can effectively iterate through all possible k-sized subarrays without redundant calculations.
3Insight 3: Handling the edge case where k equals 1 (the minimum difference will always be 0).

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Sliding Window

A moving "window" over data to process subsets efficiently.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: When `k` is 1, the minimum difference is always 0 because there's only one student selected. This is handled by a conditional check in the solutions.
Edge case 2: When all elements in `nums` are the same, the minimum difference will always be 0, which is correctly handled by the algorithm.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to sort the array before applying the sliding window. This will result in incorrect minimum differences.

✗Common mistake 2: Incorrectly handling the window boundaries in the sliding window loop. Off-by-one errors are common.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Optimizing resource allocation. Suppose you have `k` resources to allocate among `n` tasks, and each task has a certain score. You can use this algorithm to find the allocation that minimizes the difference in resource usage among tasks.

🏦Real-world scenario 2: Determining fair team composition. If you are forming teams of size `k` from `n` individuals with different skill scores, this algorithm can help form teams where skill levels are relatively balanced.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 5, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 13

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How do I determine the window size in sliding window problems?

For fixed-size windows (like max sum of k elements), window size is given. For variable-size windows (like smallest subarray with sum >= target), expand right pointer to meet condition, then shrink left pointer to find optimal. Track the best result during shrinking.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Minimum Difference Between Highest and Lowest of K Scores"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether sliding window techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?