# Sort an array according to absolute difference with given value

Given an array of n distinct elements and a number x, arrange array elements according to the absolute difference with x, i. e., element having minimum difference comes first and so on.
Note : If two or more elements are at equal distance arrange them in 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: Please solve it on “PRACTICE ” first, before moving on to the solution.

The idea is to use a self balancing binary search tree. We traverse input array and for every element, we find its difference with x and store the difference as key and element as value in self balancing binary search tree. Finally we traverse the tree and print its inorder traversal which is required output.

C++ Implementation :
In C++, self-balancing-bianry-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 multiimap, the values will be already in sorted order according to key i.e. difference with X because it implements self-balancing-bianry-search-tree internally.
3. Update all the values of array with the values of map so that array has the required output.
```// C++ program to sort an array according absolute
// difference with x.
#include<bits/stdc++.h>
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;

// 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 (auto 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[0]);
int x = 7;
rearrange(arr, n, x);
printArray(arr, n);
return 0;
}
```

Output:

```5 9 10 3 2
```

Time Complexity : O(n Log n)
Auxiliary Space : O(n)

This article is contributed by Sahil Chhabra (KILLER). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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