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1.
Introduction
2.
Solution
2.1.
Approach
2.2.
Code
3.
3.1.
How to find the maximum difference between a group of k-elements and the rest of the array?
3.2.
How to calculate the absolute value in Python?
3.3.
What is the time complexity of the solution for â€śMaximum difference between a group of k-elements and rest of the array?â€ť
3.4.
How to find the last k elements in an array using python?
3.5.
Why did we define an additional calculate_sum() method?
4.
Conclusion
Last Updated: Mar 27, 2024

# Maximum difference between a group of k-elements and rest of the array

Roadmap to SDE career at Amazon
Speaker
Anubhav Sinha
SDE-2 @
25 Jun, 2024 @ 01:30 PM

## Introduction

For this current problem, we are given an array of elements and a value k. We need to find the maximum difference between a group of k-elements and the rest of the array for the given array. We need to first divide the array into two groups such that one group must contain k-elements and the other group must contain the rest of the array elements. The idea here is to select the best k-element group elements such that the maximum difference between this group and the group of remaining elements must be high.

Also see,  Rabin Karp Algorithm

## Solution

### Approach

Letâ€™s have some simple examples to understand this problem.

Example1:

Say, we are provided with an array of elements as a = [1,3,2,4,6,5], k = 2.

Then we can divide the array as g1 = [1,2] and g2 = [3,4,5,6]. Thus we get the maximum difference between these two groups will be abs(sum(g2) - sum(g1)) = 18-3, i.e15. Here the main problem is to select the best possible elements for the k-element group.

Example2:

Say, we are provided with an array of elements as a = [1, -2, -3, -1, 3], k = 2.

Then we can divide the array as g1 = [-1, -2, -3] and g2 = [1, 3]. Thus we get the maximum difference between these two groups will be abs(sum(g2) - sum(g1)) = 4- (-6), i.e 10. The main problem is selecting the best possible elements for the k-element group.

Here we can observe mainly two cases to get the optimal solution. In the first case, we can group all the k-smallest elements and the rest of the elements as another group. Similarly, in the second case, we can group all the k-largest elements and the rest of the elements as another group. So sorting the array might help us to solve the problem easily.

In this problem, we just need to print the maximum difference and not the groups. So we can follow the below algorithm:

Step1: Sort the given array.

Step2: Calculate the sum of the whole array of elements.

Step3: As discussed, find the sum of the first k-smallest elements.

Step4: calculate the difference as d1 = abs( arraySum - 2*k_Smallest_sum)

Step5: Another case, find the sum of first k-largest elements.

Step6:   calculate the new difference as d2 = abs( arraySum - 2*k_largest_sum)

Step7: Finally, display the max(d1, d2) as output.

### Code

Python:

``````def calculate_sum(arr, n):          #Calculating the sum of the given array up to n elements.
sum = 0
for i in range(n):
sum = sum + arr[i]
return sum

def solution(arr, k):

#Step1: Sorting the array

arr.sort()

#Step2: calculating the whole array sum

arr_total_sum = calculate_sum(arr, len(arr))

#Step3:  find the sum of the first k-smallest elements.

K_smallest = calculate_sum(arr, k)

#Step4: calculate the difference as d1

d1 = abs( arr_total_sum - 2*K_smallest)

#Step5: find the sum of first k-largest elements.

K_largest = calculate_sum(arr[-k:], k)

#Step6: calculate the new difference as d2

d2 = abs( arraySum - 2*K_largest)

#Step7: Finally, display the max(d1, d2) as output.

return max(d1, d2)

arr =  [1,3,2,4,6,5]
k = 2
print(solution(arr, k) ``````

Output: 15

The time complexity for this python solution code is O(n).

You can find this solution in different languages by referring to this GFG blog.

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## Frequently Asked Questions

#### How to find the maximum difference between a group of k-elements and the rest of the array?

You can find the maximum difference by just sorting the array, calculating the sum of array elements, calculating the sum of the first k-smallest elements, and finding the absolute difference between them. Similarly, follow the same for the k-largest elements. Then return a maximum of d1 and d2.

#### How to calculate the absolute value in Python?

In Python, we can use a built-in method called abs(). It can calculate the absolute difference for you. You can also use a simple if-else block to calculate the absolute difference.

#### What is the time complexity of the solution for â€śMaximum difference between a group of k-elements and rest of the array?â€ť

The time complexity for the problem â€śMaximum difference between a group of k-elements and the rest of the arrayâ€ť is O(n) as we are traversing the whole array at least once for calculating the whole array sum.

#### How to find the last k elements in an array using python?

In python, we can use list slicing to get the last k-elements from the array. For example, if you have an array a, then we can say a[-k:] to the last k-elements.

#### Why did we define an additional calculate_sum() method?

The calculate_sum() method acts as a helper function that takes the array elements and the number of elements and calculates the sum of the array elements up to a number of elements variable value. It just calculates the sum of the n array elements.

## Conclusion

This article extensively discussed the problem "Maximum difference between a group of k-elements and the rest of the array" and also about the sum of two arrays. We start with a brief introduction, then discuss the problem with some simple examples.

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