# Sort an array according to absolute difference with given value

• Difficulty Level : Medium
• Last Updated : 28 Jun, 2021

Given an array of n distinct elements and a number x, arrange array elements according to the absolute difference with x, i. e., an element having minimum difference comes first, and so on.
Note: If two or more elements are at equal distance arrange them in the same sequence as in the given array.
Examples :

```Input : arr[] : x = 7, arr[] = {10, 5, 3, 9, 2}
Output : arr[] = {5, 9, 10, 3, 2}
Explanation:
7 - 10 = 3(abs)
7 - 5 = 2
7 - 3 = 4
7 - 9 = 2(abs)
7 - 2 = 5
So according to the difference with X,
elements are arranged as 5, 9, 10, 3, 2.

Input : x = 6, arr[] = {1, 2, 3, 4, 5}
Output :  arr[] = {5, 4, 3, 2, 1}

Input : x = 5, arr[] = {2, 6, 8, 3}
Output :  arr[] = {6, 3, 2, 8}```
Recommended Practice

The idea is to use a self-balancing binary search tree. We traverse the input array and for every element, we find its difference with x and store the difference as key and element as the value in a self-balancing binary search tree. Finally, we traverse the tree and print its inorder traversal which is the required output.
C++ Implementation :
In C++, self-balancing-binary-search-tree is implemented by set, map, and multimap. We can’t use set here as we have key-value pairs (not only keys). We also can’t directly use map also as a single key can belong to multiple values and map allows a single value for a key. So we use multimap which stores key-value pairs and can have multiple values for a key.

1. Store the values in the multimap with the difference with X as key.
2. In multimap, the values will be already in sorted order according to key i.e. difference with X because it implements self-balancing-binary-search-tree internally.
3. Update all the values of an array with the values of the map so that the array has the required output.

## C++

 `// C++ program to sort an array according absolute` `// difference with x.` `#include` `using` `namespace` `std;`   `// Function to sort an array according absolute` `// difference with x.` `void` `rearrange(``int` `arr[], ``int` `n, ``int` `x)` `{` `    ``multimap<``int``, ``int``> m;` `    ``multimap<``int` `,``int` `>:: iterator it;` `    ``// Store values in a map with the difference` `    ``// with X as key` `    ``for` `(``int` `i = 0 ; i < n; i++)` `        ``m.insert(make_pair(``abs``(x-arr[i]),arr[i]));`   `    ``// Update the values of array` `    ``int` `i = 0;` `    ``for` `(it = m.begin(); it != m.end(); it++)` `        ``arr[i++] = (*it).second ;` `}`   `// Function to print the array` `void` `printArray(``int` `arr[] , ``int` `n)` `{` `    ``for` `(``int` `i = 0 ; i < n; i++)` `        ``cout << arr[i] << ``" "``;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = {10, 5, 3, 9 ,2};` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr);` `    ``int` `x = 7;` `    ``rearrange(arr, n, x);` `    ``printArray(arr, n);` `    ``return` `0;` `}`

## Java

 `// Java program to sort an array according absolute ` `// difference with x. ` `import` `java.io.*;` `import` `java.util.*;`   `class` `GFG ` `{`   `    ``// Function to sort an array according absolute ` `    ``// difference with x.` `    ``static` `void` `rearrange(``int``[] arr, ``int` `n, ``int` `x)` `    ``{` `            ``TreeMap> m = ` `                                    ``new` `TreeMap<>();` `            `  `            ``// Store values in a map with the difference ` `            ``// with X as key` `            ``for` `(``int` `i = ``0``; i < n; i++)` `            ``{` `                ``int` `diff = Math.abs(x - arr[i]);` `                ``if` `(m.containsKey(diff)) ` `                ``{` `                    ``ArrayList al = m.get(diff);` `                    ``al.add(arr[i]);` `                    ``m.put(diff, al);` `                ``}` `                ``else` `                ``{` `                        ``ArrayList al = ``new` `                                       ``ArrayList<>();` `                        ``al.add(arr[i]);` `                        ``m.put(diff,al);` `                ``}` `            ``}`   `            ``// Update the values of array` `            ``int` `index = ``0``;` `            ``for` `(Map.Entry entry : m.entrySet()) ` `            ``{` `                ``ArrayList al = m.get(entry.getKey());` `                ``for` `(``int` `i = ``0``; i < al.size(); i++)` `                        ``arr[index++] = al.get(i); ` `            ``}` `    ``}`   `    ``// Function to print the array` `    ``static` `void` `printArray(``int``[] arr, ``int` `n)` `    ``{` `            ``for` `(``int` `i = ``0``; i < n; i++)` `                ``System.out.print(arr[i] + ``" "``);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String args[])` `    ``{` `            ``int``[] arr = {``10``, ``5``, ``3``, ``9` `,``2``};` `            ``int` `n = arr.length;` `            ``int` `x = ``7``;` `            ``rearrange(arr, n, x); ` `            ``printArray(arr, n); ` `    ``}` `}`   `// This code is contributed by rachana soma`

## Python3

 `# Python3 program to sort an` `# array according absolute` `# difference with x.`   `# Function to sort an array ` `# according absolute difference ` `# with x.` `def` `rearrange(arr, n, x):`   `    ``m ``=` `{}`   `    ``# Store values in a map` `    ``# with the difference` `    ``# with X as key` `    ``for` `i ``in` `range``(n):` `        ``m[arr[i]] ``=` `abs``(x ``-` `arr[i])`   `    ``m ``=` `{k : v ``for` `k, v ``in` `sorted``(m.items(), ` `         ``key ``=` `lambda` `item : item[``1``])}`   `    ``# Update the values of array` `    ``i ``=` `0`   `    ``for` `it ``in` `m.keys():` `        ``arr[i] ``=` `it` `        ``i ``+``=` `1`   `# Function to print the array` `def` `printArray(arr, n):`   `    ``for` `i ``in` `range``(n):` `        ``print``(arr[i], end ``=` `" "``)` `        `  `# Driver code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``arr ``=` `[``10``, ``5``, ``3``, ``9``, ``2``]` `    ``n ``=` `len``(arr)` `    ``x ``=` `7` `    ``rearrange(arr, n, x)` `    ``printArray(arr, n)`   `# This code is contributed by Chitranayal`

## C#

 `// C# program to sort an array according absolute ` `// difference with x. ` `using` `System;` `using` `System.Collections.Generic;`   `public` `class` `GFG` `{`   `  ``// Function to sort an array according absolute ` `  ``// difference with x.` `  ``static` `void` `rearrange(``int``[] arr, ``int` `n, ``int` `x)` `  ``{` `    ``SortedDictionary<``int``,List<``int``>> m = ``new` `SortedDictionary<``int``,List<``int``>>();`   `    ``// Store values in a map with the difference ` `    ``// with X as key` `    ``for` `(``int` `i = 0; i < n; i++)` `    ``{` `      ``int` `diff = Math.Abs(x - arr[i]);` `      ``if` `(m.ContainsKey(diff)) ` `      ``{` `        ``List<``int``> al = m;` `        ``al.Add(arr[i]);` `        ``m = al;` `      ``}` `      ``else` `      ``{` `        ``List<``int``> al = ``new`  `List<``int``>();` `        ``al.Add(arr[i]);` `        ``m.Add(diff, al);` `      ``}` `    ``}` `    ``// Update the values of array` `    ``int` `index = 0;` `    ``foreach``(``int` `entry ``in` `m.Keys) ` `    ``{` `      ``List<``int``> al = m[entry];` `      ``for` `(``int` `i = 0; i < al.Count; i++)` `        ``arr[index++] = al[i]; ` `    ``}` `  ``}`   `  ``// Function to print the array` `  ``static` `void` `printArray(``int``[] arr, ``int` `n)` `  ``{` `    ``for` `(``int` `i = 0; i < n; i++)` `      ``Console.Write(arr[i] + ``" "``);` `  ``}`   `  ``// Driver code` `  ``static` `public` `void` `Main (){` `    ``int``[] arr = {10, 5, 3, 9 ,2};` `    ``int` `n = arr.Length;` `    ``int` `x = 7;` `    ``rearrange(arr, n, x); ` `    ``printArray(arr, n); ` `  ``}` `}`   `// This code is contributed by avanitrachhadiya2155`

## Javascript

 ``

Output

`5 9 10 3 2 `

Time Complexity: O(n Log n)
Auxiliary Space: O(n)
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C++ STL based Implementation: In C++, we can use stable_sort(), and write a lambda expression for the custom comparator function. This solution is elegant and far easier to understand. The only challenge in writing the lambda expression is to send the value ‘x’ into the lambda expression to be able to use it inside the expression. This can be achieved either by operator overloading with the help of a class or using a much simpler capture.

## C++

 `// CPP program for the above approach` `#include ` `using` `namespace` `std;`   `void` `rearrange(``int` `arr[], ``int` `n, ``int` `x)` `{` `    ``/*` `        ``We can send the value x into ` `        ``lambda expression as` `        ``follows: [capture]()` `        ``{` `            ``//statements` `            ``//capture value can be used inside` `        ``}` `    ``*/` `    ``stable_sort(arr, arr + n, [x](``int` `a, ``int` `b) ` `    ``{` `        ``if` `(``abs``(a - x) < ``abs``(b - x))` `            ``return` `true``;` `        ``else` `            ``return` `false``;` `    ``});` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 10, 5, 3, 9, 2 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``int` `x = 7;` `    ``rearrange(arr, n, x);` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``cout << arr[i] << ``" "``;` `    ``return` `0;` `}`

Output

`5 9 10 3 2 `

Time Complexity: since we are using a stable sort of STL, which uses a variation of merge sort the time complexity is O(n logn).