Code360 powered by Coding Ninjas X Naukri.com. Code360 powered by Coding Ninjas X Naukri.com
Table of contents
1.
Introduction
2.
Solution
2.1.
Approach
2.2.
Code
3.
Frequently Asked Questions
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 “Maximum difference between a group of k-elements and rest of the array?”
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

Let’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.

Get the tech career you deserve, faster!
Connect with our expert counsellors to understand how to hack your way to success
User rating 4.7/5
1:1 doubt support
95% placement record
Akash Pal
Senior Software Engineer
326% Hike After Job Bootcamp
Himanshu Gusain
Programmer Analyst
32 LPA After Job Bootcamp
After Job
Bootcamp

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 “Maximum difference between a group of k-elements and rest of the array?”

The time complexity for the problem “Maximum difference between a group of k-elements and the rest of the array” 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.

Recommended problems -

 

After reading about this problem, are you not feeling excited to read/explore more articles on similar problems? Don't worry; Coding Ninjas has you covered. Refer to our Guided Path on Coding Ninjas Studio to improve yourself in Competitive Programming, Data Structures and Algorithms, JavaScript, System Design, and many more! If you want to test your confidence in coding, you may check out the contests and participate in the mock test series hosted on Coding Ninjas Studio! But suppose you have just started your learning process and are looking for questions asked by tech giants like Amazon, Microsoft, Uber, etc. In that case, you must look at the problems, interview bundle, and interview experiences for placement preparations.

Nevertheless, you can consider our paid courses to give your career improvement an edge over others!

Do upvote our blogs and articles if you find them helpful and engaging!

Happy Learning!

 

Previous article
Program for Mean and Median of an unsorted array
Next article
Maximum difference between two elements such that larger element appears after the smaller number
Live masterclass