# Split array into K subsets to maximize sum of their second largest elements

Given an array arr[] consisting of N integers and an integer K, the task is to split the array into K subsets (N % K = 0) such that the sum of second largest elements of all subsets is maximized.

Examples:

Input: arr[] = {1, 3, 1, 5, 1, 3}, K = 2
Output: 4
Explanation: Splitting the array into the subsets {1, 1, 3} and {1, 3, 5} maximizes the sum of second maximum elements in the two arrays.

Input: arr[] = {1, 2, 5, 8, 6, 4, 3, 4, 9}, K = 3
Output: 17

Approach: The idea is to sort the array and keep adding every second element encountered while traversing the array in reverse, starting from the second largest element in the array, exactly K times. Follow the steps below to solve the problem:

Below is the implementation of the above approach:

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to split array into` `// K subsets having maximum` `// sum of their second maximum elements` `void` `splitArray(``int` `arr[], ``int` `n, ``int` `K)` `{` `    ``// Sort the array` `    ``sort(arr, arr + n);`   `    ``int` `i = n - 1;`   `    ``// Stores the maximum possible` `    ``// sum of second maximums` `    ``int` `result = 0;`   `    ``while` `(K--) {`   `        ``// Add second maximum` `        ``// of current subset` `        ``result += arr[i - 1];`   `        ``// Proceed to the second` `        ``// maximum of next subset` `        ``i -= 2;` `    ``}`   `    ``// Print the maximum` `    ``// sum obtained` `    ``cout << result;` `}`   `// Driver Code` `int` `main()` `{` `    ``// Given array arr[]` `    ``int` `arr[] = { 1, 3, 1, 5, 1, 3 };`   `    ``// Size of array` `    ``int` `N = ``sizeof``(arr)` `            ``/ ``sizeof``(arr);`   `    ``int` `K = 2;`   `    ``// Function Call` `    ``splitArray(arr, N, K);`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach ` `import` `java.io.*; ` `import` `java.util.Arrays; ` `  `  `class` `GFG` `{ ` `  `  `// Function to split array into` `// K subsets having maximum` `// sum of their second maximum elements` `static` `void` `splitArray(``int` `arr[], ``int` `n, ``int` `K)` `{` `    ``// Sort the array` `    ``Arrays.sort(arr);` ` `  `    ``int` `i = n - ``1``;` ` `  `    ``// Stores the maximum possible` `    ``// sum of second maximums` `    ``int` `result = ``0``;` ` `  `    ``while` `(K-- != ``0``) ` `    ``{` ` `  `        ``// Add second maximum` `        ``// of current subset` `        ``result += arr[i - ``1``];` ` `  `        ``// Proceed to the second` `        ``// maximum of next subset` `        ``i -= ``2``;` `    ``}` ` `  `    ``// Print the maximum` `    ``// sum obtained` `    ``System.out.print(result);` `}` `  `  `// Drive Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``// Given array arr[]` `    ``int``[] arr = { ``1``, ``3``, ``1``, ``5``, ``1``, ``3` `};` ` `  `    ``// Size of array` `    ``int` `N = arr.length;` ` `  `    ``int` `K = ``2``;` ` `  `    ``// Function Call` `    ``splitArray(arr, N, K);` `} ` `} `   `// This code is contributed by sanjoy_62.`

## Python3

 `# Python3 program to implement` `# the above approach`   `# Function to split array into K ` `# subsets having maximum sum of ` `# their second maximum elements` `def` `splitArray(arr, n, K):` `    `  `    ``# Sort the array` `    ``arr.sort()`   `    ``i ``=` `n ``-` `1`   `    ``# Stores the maximum possible` `    ``# sum of second maximums` `    ``result ``=` `0`   `    ``while` `(K > ``0``):`   `        ``# Add second maximum` `        ``# of current subset` `        ``result ``+``=` `arr[i ``-` `1``]`   `        ``# Proceed to the second` `        ``# maximum of next subset` `        ``i ``-``=` `2` `        ``K ``-``=` `1`   `    ``# Print the maximum` `    ``# sum obtained` `    ``print``(result)`   `# Driver Code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``# Given array arr[]` `    ``arr ``=` `[ ``1``, ``3``, ``1``, ``5``, ``1``, ``3` `]`   `    ``# Size of array` `    ``N ``=` `len``(arr)`   `    ``K ``=` `2`   `    ``# Function Call` `    ``splitArray(arr, N, K)`   `# This code is contributed by chitranayal`

## C#

 `// C# program for the above approach ` `using` `System;` `class` `GFG` `{ ` `  `  `// Function to split array into` `// K subsets having maximum` `// sum of their second maximum elements` `static` `void` `splitArray(``int` `[]arr, ``int` `n, ``int` `K)` `{` `    ``// Sort the array` `    ``Array.Sort(arr);` ` `  `    ``int` `i = n - 1;` ` `  `    ``// Stores the maximum possible` `    ``// sum of second maximums` `    ``int` `result = 0;` ` `  `    ``while` `(K-- != 0) ` `    ``{` ` `  `        ``// Add second maximum` `        ``// of current subset` `        ``result += arr[i - 1];` ` `  `        ``// Proceed to the second` `        ``// maximum of next subset` `        ``i -= 2;` `    ``}` ` `  `    ``// Print the maximum` `    ``// sum obtained` `    ``Console.Write(result);` `}` `  `  `// Drive Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``// Given array []arr` `    ``int``[] arr = { 1, 3, 1, 5, 1, 3 };` ` `  `    ``// Size of array` `    ``int` `N = arr.Length;` ` `  `    ``int` `K = 2;` ` `  `    ``// Function Call` `    ``splitArray(arr, N, K);` `} ` `} `   `// This code is contributed by shikhasingrajput`

## Javascript

 ``

Output:

`4`

Time complexity: O(N logN)
Auxiliary Space: O(N)

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