# Divide array in two Subsets such that sum of square of sum of both subsets is maximum

Given an integer array arr[], the task is to divide this array into two non-empty subsets such that the sum of the square of the sum of both the subsets is maximum and sizes of both the subsets must not differ by more than 1.

Examples:

Input: arr[] = {1, 2, 3}
Output: 26
Explanation:
Sum of Subset Pairs are as follows
(1)2 + (2 + 3)2 = 26
(2)2 + (1 + 3)2 = 20
(3)2 + (1 + 2)2 = 18
Maximum among these is 26, Therefore the required sum is 26

Input: arr[] = {7, 2, 13, 4, 25, 8}
Output: 2845

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The task is to maximize the sum of a2 + b2 where a and b are the sum of the two subsets and a + b = C (constant), i.e., the sum of the entire array. The maximum sum can be achieved by sorting the array and dividing the first N/2 – 1 smaller elements in one subset and the rest N/2 + 1 elements in the other subset. In this way, the sum can be maximized while keeping the difference in size at most 1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to return the maximum sum of the ` `// square of the sum of two subsets of an array ` `int` `maxSquareSubsetSum(``int``* A, ``int` `N) ` `{ ` `    ``// Initialize variables to store ` `    ``// the sum of subsets ` `    ``int` `sub1 = 0, sub2 = 0; ` ` `  `    ``// Sorting the array ` `    ``sort(A, A + N); ` ` `  `    ``// Loop through the array ` `    ``for` `(``int` `i = 0; i < N; i++) { ` ` `  `        ``// Sum of the first subset ` `        ``if` `(i < (N / 2) - 1) ` `            ``sub1 += A[i]; ` ` `  `        ``// Sum of the second subset ` `        ``else` `            ``sub2 += A[i]; ` `    ``} ` ` `  `    ``// Return the maximum sum of ` `    ``// the square of the sum of subsets ` `    ``return` `sub1 * sub1 + sub2 * sub2; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 7, 2, 13, 4, 25, 8 }; ` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << maxSquareSubsetSum(arr, N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// Function to return the maximum sum of the  ` `    ``// square of the sum of two subsets of an array  ` `    ``static` `int` `maxSquareSubsetSum(``int` `[]A, ``int` `N)  ` `    ``{  ` `        ``// Initialize variables to store  ` `        ``// the sum of subsets  ` `        ``int` `sub1 = ``0``, sub2 = ``0``;  ` `     `  `        ``// Sorting the array  ` `        ``Arrays.sort(A);  ` `     `  `        ``// Loop through the array  ` `        ``for` `(``int` `i = ``0``; i < N; i++)  ` `        ``{  ` `     `  `            ``// Sum of the first subset  ` `            ``if` `(i < (N / ``2``) - ``1``)  ` `                ``sub1 += A[i];  ` `     `  `            ``// Sum of the second subset  ` `            ``else` `                ``sub2 += A[i];  ` `        ``}  ` `     `  `        ``// Return the maximum sum of  ` `        ``// the square of the sum of subsets  ` `        ``return` `sub1 * sub1 + sub2 * sub2;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``int` `arr[] = { ``7``, ``2``, ``13``, ``4``, ``25``, ``8` `};  ` `        ``int` `N = arr.length;  ` `     `  `        ``System.out.println(maxSquareSubsetSum(arr, N)); ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the maximum sum of the  ` `# square of the sum of two subsets of an array  ` `def` `maxSquareSubsetSum(A, N) : ` ` `  `    ``# Initialize variables to store  ` `    ``# the sum of subsets  ` `    ``sub1 ``=` `0``; sub2 ``=` `0``; ` `     `  `    ``# Sorting the array ` `    ``A.sort(); ` ` `  `    ``# Loop through the array  ` `    ``for` `i ``in` `range``(N) : ` ` `  `        ``# Sum of the first subset  ` `        ``if` `(i < (N ``/``/` `2``) ``-` `1``) : ` `            ``sub1 ``+``=` `A[i];  ` ` `  `        ``# Sum of the second subset  ` `        ``else` `: ` `            ``sub2 ``+``=` `A[i];  ` ` `  `    ``# Return the maximum sum of  ` `    ``# the square of the sum of subsets  ` `    ``return` `sub1 ``*` `sub1 ``+` `sub2 ``*` `sub2;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``arr ``=` `[ ``7``, ``2``, ``13``, ``4``, ``25``, ``8` `];  ` `    ``N ``=` `len``(arr);  ` ` `  `    ``print``(maxSquareSubsetSum(arr, N));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// Function to return the maximum sum of the  ` `    ``// square of the sum of two subsets of an array  ` `    ``static` `int` `maxSquareSubsetSum(``int` `[]A, ``int` `N)  ` `    ``{  ` `        ``// Initialize variables to store  ` `        ``// the sum of subsets  ` `        ``int` `sub1 = 0, sub2 = 0;  ` `     `  `        ``// Sorting the array  ` `        ``Array.Sort(A);  ` `     `  `        ``// Loop through the array  ` `        ``for` `(``int` `i = 0; i < N; i++)  ` `        ``{  ` `     `  `            ``// Sum of the first subset  ` `            ``if` `(i < (N / 2) - 1)  ` `                ``sub1 += A[i];  ` `     `  `            ``// Sum of the second subset  ` `            ``else` `                ``sub2 += A[i];  ` `        ``}  ` `     `  `        ``// Return the maximum sum of  ` `        ``// the square of the sum of subsets  ` `        ``return` `sub1 * sub1 + sub2 * sub2;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main() ` `    ``{  ` `        ``int` `[]arr = { 7, 2, 13, 4, 25, 8 };  ` `        ``int` `N = arr.Length;  ` `     `  `        ``Console.WriteLine(maxSquareSubsetSum(arr, N)); ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```2845
```

Time Complexity: O(N*log(N))

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : AnkitRai01

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.