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., 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}

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++

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

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Java

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// 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<Integer, ArrayList<Integer>> 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<Integer> al = m.get(diff);
                    al.add(arr[i]);
                    m.put(diff, al);
                }
                else
                {
                        ArrayList<Integer> 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<Integer> 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

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Python3

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# 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

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Output

5 9 10 3 2 





Time Complexity: O(n Log n) 
Auxiliary Space: O(n)
This article is contributed by Sahil Chhabra. 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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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++

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// CPP program for the above approach
#include <bits/stdc++.h>
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[0]);
    int x = 7;
    rearrange(arr, n, x);
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    return 0;
}

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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).

This article is contributed by D. Mohit Varsha. 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. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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