# Minimizing Unfairness: A Hackerrank Challenge Explained

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## Chapter 1: Understanding the Max Min Problem

The Max Min challenge on Hackerrank presents a fascinating problem involving a list of integers. Given an array arr and an integer k, your goal is to create a sub-array of length k such that the unfairness is minimized. Unfairness is defined as the difference between the maximum and minimum values of the chosen sub-array, denoted as arr'.

For example, consider the array:

arr = [1, 4, 7, 2]

k = 2

By selecting the elements 4 and 7 to form arr', the unfairness can be calculated as:

unfairness = max(4, 7) - min(4, 7) = 7 - 4 = 3

However, testing all possible pairs shows that selecting [1, 2] results in a minimum unfairness of 1.

It’s crucial to recognize that the number of combinations grows significantly with larger arrays. Thus, we need an efficient approach to tackle this issue.

### Section 1.1: Sorting the Array

To streamline our calculations, sorting the array is beneficial. If we have three values, a, b, and c, the maximum and minimum values can be easily identified once sorted. The maximum will be the last element, while the minimum will be the first.

#### Subsection 1.1.1: Selecting k Elements

After sorting, our next challenge is to efficiently select k elements. Instead of examining all possible combinations, we can focus on the minimum and maximum values of our selected subsets. By extracting segments of length k from the sorted array, we can evaluate all possible combinations without redundancy.

### Section 1.2: Finalizing the Solution

With our sorted segments, the final step is straightforward: calculate the difference between the first and last elements of each segment and determine the minimum difference. This results in the optimal unfairness.

## Chapter 2: Implementation

Now that we have a strategy, let's look at the code implementation.

The first video, "HackerRank Interview Prep: Max Min - Greedy Algorithm Solution," provides a comprehensive walkthrough of the algorithm.

Continuing with our approach, here's the code breakdown:

- Sort the array.
- Initialize a variable to track the minimum unfairness found.
- If the array length equals k, simply return the difference of the last and first elements.
- Loop through the array from the start to the (length - k + 1) index and compute the differences, updating the minimum value as necessary.

Here’s a sample JavaScript implementation:

// Sort the integer array

array.sort((a, b) => {

return a - b;

});

// Using arrow function notation

(a, b) => {

return a - b;

}

// Traditional function definition

function(a, b) {

return a - b;

}

The second video, "188 - Max Min | Greedy | Hackerrank Solution | Python," dives deeper into the solution using Python, showcasing alternative coding techniques.

By following this structured approach, you can effectively minimize unfairness in the Max Min challenge on Hackerrank.