# Sort elements of an array in increasing order of absolute difference of adjacent elements

Given an array arr[], the task is to arrange the array in such a way that the absolute difference between the adjacent elements is in increasing order.

Examples:

Input: arr[] = {8, 1, 2, 3, 0}
Output: 2 3 1 8 0
Explanation:
|2-3| = 1, |3-1| = 2, |1-8| = 7, |8-0| = 8
The absolute difference between the adjacent elements is in increasing order.

Input: -1 -2 3 4 5
Output: 3 4 -1 5 -2
Explanation:
|3-4| = 1, |4-(-1)| = 5, |-1-5| = 6, |5-(-2)| = 7

Approach: The idea is to sort the elements of the array and then take the middle element of the array and then repeat this step until the array is not empty. Below is an illustration of the approach with the help of an example:

```Given Array be - {8, 1, 2, 3, 0}

After Sorting the array - {0, 1, 2, 3, 8}

Array          Middle Ele     Output Array
---------------    -------------  ---------------
{0, 1, 2, 3, 8}    5//2 = 2, 2          2
{0, 1, 3, 8}       4//2 = 2, 3        2, 3
{0, 1, 8}          3//2 = 1, 1       1, 2, 3
{0, 8}             2//2 = 1, 8      1, 2, 3, 8
{0}                1//2 = 0, 0     1, 2, 3, 8, 0```

## C++

 `// C++ implementation to sort ` `// the elements of the array in ` `// such a way that absolute  ` `// difference between the adjacent ` `// elements are in increasing order ` `#include ` `using` `namespace` `std; ` `     `  `// Function to sort the elements ` `// of the array by difference ` `void` `sortDiff(vector<``int``> arr,  ` `              ``int` `n)  ` `{    ` `    ``// Sorting the array ` `    ``sort(arr.begin(), arr.end()); ` `     `  `    ``// Array to store the ` `    ``// elements of the array ` `    ``vector<``int``> out; ` `     `  `    ``// Iterating over the length ` `    ``// of the array to include  ` `    ``// each middle element of array ` `    ``while``(n > 0) ` `    ``{       ` `        ``// Appending the middle  ` `        ``// element of the array ` `        ``out.push_back(arr[n / 2]); ` `        ``arr.erase(arr.begin() + n / 2); ` `        ``n = n - 1; ` `    ``} ` `    ``for``(``auto` `i : out) ` `        ``cout << i << ``" "``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `  ``vector<``int``> a = {8, 1, 2, 3, 0}; ` `  ``int` `n = 5; ` `  ``sortDiff(a, n); ` `} ` ` `  `// This code is contributed by Chitranayal`

## Java

 `// Java implementation to sort ` `// the elements of the array in ` `// such a way that absolute  ` `// difference between the adjacent ` `// elements are in increasing order ` `import` `java.util.*; ` ` `  `class` `GFG{ ` `     `  `// Function to sort the elements ` `// of the array by difference ` `static` `void` `sortDiff(Vector arr, ``int` `n)  ` `{ ` `     `  `    ``// Sorting the array ` `    ``Collections.sort(arr); ` `     `  `    ``// Array to store the ` `    ``// elements of the array ` `    ``Vector out = ``new` `Vector(); ` `     `  `    ``// Iterating over the length ` `    ``// of the array to include  ` `    ``// each middle element of array ` `    ``while``(n > ``0``) ` `    ``{ ` `         `  `        ``// Appending the middle  ` `        ``// element of the array ` `        ``out.add(arr.get(n / ``2``)); ` `        ``arr.remove(n / ``2``); ` `        ``n = n - ``1``; ` `    ``} ` `    ``for``(``int` `i : out) ` `        ``System.out.print(i + ``" "``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``Integer []a = { ``8``, ``1``, ``2``, ``3``, ``0` `}; ` `    ``Vector arr = ``new` `Vector(Arrays.asList(a)); ` `    ``int` `n = ``5``; ` `    ``sortDiff(arr, n); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python implementation to sort ` `# the elements of the array in ` `# such a way that absolute  ` `# difference between the adjacent ` `# elements are in increasing order ` ` `  `# Function to sort the elements ` `# of the array by difference ` `def` `sortDiff(arr, n): ` `     `  `    ``# Sorting the array ` `    ``arr.sort() ` `     `  `    ``# Array to store the ` `    ``# elements of the array ` `    ``out ``=` `[] ` `     `  `    ``# Iterating over the length ` `    ``# of the array to include  ` `    ``# each middle element of array ` `    ``while` `n: ` `         `  `        ``# Appending the middle  ` `        ``# element of the array ` `        ``out.append(arr.pop(n``/``/``2``)) ` `        ``n``=``n``-``1` `     `  `    ``print``(``*``out) ` `    ``return` `out ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``arr ``=` `[``8``, ``1``, ``2``, ``3``, ``0``] ` `     `  `    ``n ``=` `5` `    ``sortDiff(arr, n) `

## C#

 `// C# implementation to sort ` `// the elements of the array in ` `// such a way that absolute  ` `// difference between the adjacent ` `// elements are in increasing order ` `using` `System; ` `using` `System.Collections.Generic; ` `class` `GFG{ ` `     `  `// Function to sort the elements ` `// of the array by difference ` `static` `void` `sortDiff(List<``int``> arr, ``int` `n)  ` `{ ` `     `  `    ``// Sorting the array ` `    ``arr.Sort(); ` `     `  `    ``// Array to store the ` `    ``// elements of the array ` `    ``List<``int``> Out = ``new` `List<``int``>(); ` `     `  `    ``// Iterating over the length ` `    ``// of the array to include  ` `    ``// each middle element of array ` `    ``while``(n > 0) ` `    ``{ ` `         `  `        ``// Appending the middle  ` `        ``// element of the array ` `        ``Out.Add(arr[n / 2]); ` `        ``arr.RemoveAt(n / 2); ` `        ``n = n - 1; ` `    ``} ` `    ``foreach``(``int` `i ``in` `Out) ` `        ``Console.Write(i + ``" "``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]a = { 8, 1, 2, 3, 0 }; ` `    ``List<``int``> arr = ``new` `List<``int``>(a); ` `    ``int` `n = 5; ` `    ``sortDiff(arr, n); ` `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

## Javascript

 ` `

Output:

`2 3 1 8 0`

Time Complexity: O(n2) as erase function takes O(n) time in the worst case.
Auxiliary Space: O(n)

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