# 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: 1
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  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.

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

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 – 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 minimise the ` `// median between partition array ` ` `  `#include "bits/stdc++.h" ` `using` `namespace` `std; ` ` `  `// Function to find minimise the ` `// median between partition array ` `int` `minimiseMedian(``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); ` ` `  `    ``// Function that returns the minimum ` `    ``// the absolute difference between ` `    ``// median of partition array ` `    ``cout << minimiseMedian(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 `

Output:

```10
```

Time Complexity: O(N*log N)

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Improved By : AnkitRai01, 29AjayKumar