# Partition the array into two odd length groups with minimized absolute difference between their median

Given an array arr[] of positive integers of even length, the task is to partition these elements of arr[] into two groups each of odd length such that the absolute difference between the median of the two groups is minimized.
Examples:

Input: arr[] = { 1, 2, 3, 4, 5, 6 }
Output:
Explanation:
Group 1 can be [2, 4, 6] with median 4
Group 2 can be [1, 3, 5] with median 3.
The absolute difference between the two medians is 4 – 3 = 1, which can’t be minimized further with any kind of groupings formed.
Input: arr[] = { 15, 25, 35, 50 }
Output: 10
Explanation:
Group 1 can be [15, 25, 50] with median 25
Group 2 can be [35] with median 35.
The absolute difference between the two medians is 35 – 25 = 10, which can’t be minimized further with any kind of groupings formed.

Approach:

• If the given array arr[] is sorted, the middle elements of arr[] will give the minimum difference.
• So divide the arr[] in such a way that these two elements will be the median of two new arrays of odd length.
• Therefore, put the n/2th element of the arr[] in the first group and the (n/2 â€“ 1)th element of the arr[] in the second group as a median respectively.
• Then abs(arr[n/2] – arr[(n/2)-1]) is the minimum difference between the two new arrays.

Below is the implementation of the above approach:

## C++

 `// C++ program to minimize the` `// median between partition array`   `#include "bits/stdc++.h"` `using` `namespace` `std;`   `// Function to find minimize the` `// median between partition array` `int` `minimizeMedian(``int` `arr[], ``int` `n)` `{` `    ``// Sort the given array arr[]` `    ``sort(arr, arr + n);`   `    ``// Return the difference of two` `    ``// middle element of the arr[]` `    ``return` `abs``(arr[n / 2] - arr[(n / 2) - 1]);` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 15, 25, 35, 50 };`   `    ``// Size of arr[]` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);`   `    ``// Function that returns the minimum` `    ``// the absolute difference between` `    ``// median of partition array` `    ``cout << minimizeMedian(arr, n);` `    ``return` `0;` `}`

## Java

 `// Java program to minimise the ` `// median between partition array` `import` `java.util.*;`   `class` `GFG ` `{`   `    ``// Function to find minimise the ` `    ``// median between partition array ` `    ``static` `int` `minimiseMedian(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Sort the given array arr[] ` `        ``Arrays.sort(arr); ` `    `  `        ``// Return the difference of two ` `        ``// middle element of the arr[] ` `        ``return` `Math.abs(arr[n / ``2``] - arr[(n / ``2``) - ``1``]); ` `    ``} ` `    `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``15``, ``25``, ``35``, ``50` `}; ` `    `  `        ``// Size of arr[] ` `        ``int` `n = arr.length; ` `    `  `        ``// Function that returns the minimum ` `        ``// the absolute difference between ` `        ``// median of partition array ` `        ``System.out.println(minimiseMedian(arr, n)); ` `    ``} ` `}`   `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program to minimise the ` `# median between partition array `   `# Function to find minimise the ` `# median between partition array ` `def` `minimiseMedian(arr, n) : `   `    ``# Sort the given array arr[] ` `    ``arr.sort();` `    `  `    ``# Return the difference of two` `    ``# middle element of the arr[]` `    ``ans ``=` `abs``(arr[n ``/``/` `2``] ``-` `arr[(n ``/``/` `2``) ``-` `1``]);` `    `  `    ``return` `ans; `   `# Driver Code ` `if` `__name__ ``=``=` `"__main__"` `: `   `    ``arr ``=` `[ ``15``, ``25``, ``35``, ``50` `]; `   `    ``# Size of arr[] ` `    ``n ``=` `len``(arr); `   `    ``# Function that returns the minimum ` `    ``# the absolute difference between ` `    ``# median of partition array ` `    ``print``(minimiseMedian(arr, n)); ` `    `  `# This code is contributed by AnkitRai01`

## C#

 `// C# program to minimise the ` `// median between partition array` `using` `System;`   `class` `GFG ` `{`   `    ``// Function to find minimise the ` `    ``// median between partition array ` `    ``static` `int` `minimiseMedian(``int` `[]arr, ``int` `n) ` `    ``{ ` `        ``// Sort the given array []arr ` `        ``Array.Sort(arr); ` `    `  `        ``// Return the difference of two ` `        ``// middle element of the []arr ` `        ``return` `Math.Abs(arr[n / 2] - arr[(n / 2) - 1]); ` `    ``} ` `    `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``int` `[]arr = { 15, 25, 35, 50 }; ` `    `  `        ``// Size of []arr ` `        ``int` `n = arr.Length; ` `    `  `        ``// Function that returns the minimum ` `        ``// the absolute difference between ` `        ``// median of partition array ` `        ``Console.WriteLine(minimiseMedian(arr, n)); ` `    ``} ` `}`   `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`10`

Time Complexity: O(N*log N)
Auxiliary Space: O(1)

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