# Sort integers in array according to their distance from the element K

• Difficulty Level : Easy
• Last Updated : 17 Nov, 2021

Given an array arr[] of N integers and an integer K, the task is to sort these integers according to their distance from given integer K. If more than 1 element is at the same distance, print them in increasing order.
Note: Distance between two elements in the array is measured as the difference between their index.
Note: The integer K is always present in array arr[] and is unique.

Examples:

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Input: arr[] = {12, 10, 102, 31, 15}, K = 102
Output: 102 10 31 12 15
Explanation:
Elements at their respective distance from K are,
At distance 0: 102
At distance 1: 10, 31 in sorted form.
At distance 2: 12, 15 in sorted form.
Hence, our resultant array is [ 102, 10, 31, 12, 15 ]

Input: arr[] = {14, 1101, 10, 35, 0}, K = 35
Output: 35 0 10 1101 14
Explanation:
Elements at their respective distance from K are,
At distance 0: 35
At distance 1: 10, 0 and in sorted form we have 0, 10.
At distance 2: 1101
At distance 3: 14
Hence, our resultant array is [ 35, 0, 10, 1101, 14 ]

Approach :
To solve the problem mentioned above we create an auxiliary vector to store elements at any distance from K. Then find the position of given integer K in the array arr[] and insert the element K at position 0 in the auxiliary vector. Traverse the array in the left direction from K and insert those elements in the vector at their distance from K. Repeat the above process for the right side elements of K. Finally, print the array elements from distance 0 in sorted order.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to Sort the integers in``// array according to their distance from given``// element K present in the array``#include ``using` `namespace` `std;` `// Function to get sorted array based on``// their distance from given integer K``void` `distanceSort(``int` `arr[], ``int` `K, ``int` `n)``{``    ``// Vector to store respective elements``    ``// with their distance from integer K``    ``vector<``int``> vd[n];` `    ``// Find the position of integer K``    ``int` `pos;` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(arr[i] == K) {``            ``pos = i;``            ``break``;``        ``}``    ``}` `    ``// Insert the elements with their``    ``// distance from K in vector` `    ``int` `i = pos - 1, j = pos + 1;` `    ``// Element at distance 0``    ``vd.push_back(arr[pos]);` `    ``// Elements at left side of K``    ``while` `(i >= 0) {``        ``vd[pos - i].push_back(arr[i]);``        ``--i;``    ``}` `    ``// Elements at right side of K``    ``while` `(j < n) {``        ``vd[j - pos].push_back(arr[j]);``        ``++j;``    ``}` `    ``// Print the vector content in sorted order``    ``for` `(``int` `i = 0; i <= max(pos, n - pos - 1); ++i) {` `        ``// Sort elements at same distance``        ``sort(begin(vd[i]), end(vd[i]));` `        ``// Print elements at distance i from K``        ``for` `(``auto` `element : vd[i])``            ``cout << element << ``" "``;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `arr[] = {14, 1101, 10, 35, 0 }, K = 35;` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``distanceSort(arr, K, n);` `    ``return` `0;``}`

## Java

 `// Java implementation to Sort the integers in``// array according to their distance from given``// element K present in the array``import` `java.util.*;` `class` `GFG{``    ` `// Function to get sorted array based on``// their distance from given integer K``@SuppressWarnings``(``"unchecked"``)``static` `void` `distanceSort(``int` `arr[], ``int` `K, ``int` `n)``{``    ` `    ``// Vector to store respective elements``    ``// with their distance from integer K``    ``Vector vd[] = ``new` `Vector[n];``    ` `    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``        ``vd[i] = ``new` `Vector();``    ``}``    ` `    ``// Find the position of integer K``    ``int` `pos = ``0``;`` ` `    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``        ``if` `(arr[i] == K)``        ``{``            ``pos = i;``            ``break``;``        ``}``    ``}`` ` `    ``// Insert the elements with their``    ``// distance from K in vector``    ``int` `i = pos - ``1``, j = pos + ``1``;`` ` `    ``// Element at distance 0``    ``vd[``0``].add(arr[pos]);`` ` `    ``// Elements at left side of K``    ``while` `(i >= ``0``)``    ``{``        ``vd[pos - i].add(arr[i]);``        ``--i;``    ``}`` ` `    ``// Elements at right side of K``    ``while` `(j < n)``    ``{``        ``vd[j - pos].add(arr[j]);``        ``++j;``    ``}`` ` `    ``// Print the vector content in sorted order``    ``for``(i = ``0``; i <= Math.max(pos, n - pos - ``1``); ++i)``    ``{``        ` `        ``// Sort elements at same distance``        ``Collections.sort(vd[i]);`` ` `        ``// Print elements at distance i from K``        ``for` `(j = ``0``; j < vd[i].size(); j++)``        ``{``            ``int` `element = (``int``)vd[i].get(j);``            ``System.out.print(element + ``" "``);``        ``}``    ``}``}``    ` `// Driver Code``public` `static` `void` `main(String s[])``{``    ``int` `arr[] = {``14``, ``1101``, ``10``, ``35``, ``0` `};``    ``int` `K = ``35``;` `    ``int` `n = arr.length;` `    ``distanceSort(arr, K, n);``}   ``}` `// This code is contributed by rutvik_56`

## Python3

 `# Python3 implementation to Sort the integers in``# array according to their distance from given``# element K present in the array` `# Function to get sorted array based on``# their distance from given integer K``def` `distanceSort(arr,K,n):``    ``# Vector to store respective elements``    ``# with their distance from integer K``    ``vd ``=` `[[] ``for` `i ``in` `range``(n)]` `    ``# Find the position of integer K` `    ``for` `i ``in` `range``(n):``        ``if` `(arr[i] ``=``=` `K):``            ``pos ``=` `i``            ``break` `    ``# Insert the elements with their``    ``# distance from K in vector` `    ``i ``=` `pos ``-` `1``    ``j ``=` `pos ``+` `1` `    ``# Element at distance 0``    ``vd[``0``].append(arr[pos])` `    ``# Elements at left side of K``    ``while` `(i >``=` `0``):``        ``vd[pos ``-` `i].append(arr[i])``        ``i ``-``=` `1` `    ``# Elements at right side of K``    ``while` `(j < n):``        ``vd[j ``-` `pos].append(arr[j])``        ``j ``+``=` `1` `    ``# Print the vector content in sorted order``    ``for` `i ``in` `range``(``max``(pos, n ``-` `pos ``-` `1``) ``+` `1``):` `        ``# Sort elements at same distance``        ``vd[i].sort(reverse``=``False``)` `        ``# Print elements at distance i from K``        ``for` `element ``in` `vd[i]:``            ``print``(element,end ``=` `" "``)` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=`  `[``14``, ``1101``, ``10``, ``35``, ``0``]``    ``K ``=` `35` `    ``n ``=` `len``(arr)` `    ``distanceSort(arr, K, n)` `# This code is contributed by Surendra_Gangwar`

## C#

 `// C# implementation to Sort the integers in``// array according to their distance from given``// element K present in the array``using` `System;``using` `System.Collections.Generic;``class` `GFG{``    ` `// Function to get sorted array based on``// their distance from given integer K``static` `void` `distanceSort(``int` `[]arr,``                         ``int` `K, ``int` `n)``{   ``    ``// List to store respective elements``    ``// with their distance from integer K``    ``List<``int``> []vd = ``new` `List<``int``>[n];``    ``int` `i ;``    ``for``(i = 0; i < n; i++)``    ``{``        ``vd[i] = ``new` `List<``int``>();``    ``}``    ` `    ``// Find the position of integer K``    ``int` `pos = 0;`` ` `    ``for``(i = 0; i < n; i++)``    ``{``        ``if` `(arr[i] == K)``        ``{``            ``pos = i;``            ``break``;``        ``}``    ``}`` ` `    ``// Insert the elements with their``    ``// distance from K in vector``    ``int` `j = pos + 1;``     ``i = pos - 1;``  ` `    ``// Element at distance 0``    ``vd.Add(arr[pos]);`` ` `    ``// Elements at left side of K``    ``while` `(i >= 0)``    ``{``        ``vd[pos - i].Add(arr[i]);``        ``--i;``    ``}`` ` `    ``// Elements at right side of K``    ``while` `(j < n)``    ``{``        ``vd[j - pos].Add(arr[j]);``        ``++j;``    ``}`` ` `    ``// Print the vector content in sorted order``    ``for``(i = 0; i <= Math.Max(pos,``                             ``n - pos - 1); ++i)``    ``{       ``        ``// Sort elements at same distance``        ``vd[i].Sort();`` ` `        ``// Print elements at distance i from K``        ``for` `(j = 0; j < vd[i].Count; j++)``        ``{``            ``int` `element = (``int``)vd[i][j];``            ``Console.Write(element + ``" "``);``        ``}``    ``}``}``    ` `// Driver Code``public` `static` `void` `Main(String []args)``{``    ``int` `[]arr = {14, 1101, 10, 35, 0};``    ``int` `K = 35;``    ``int` `n = arr.Length;``    ``distanceSort(arr, K, n);``}   ``}` `// This code is contributed by shikhasingrajput`
Output:
`35 0 10 1101 14`

Time Complexity: O(N)

Auxiliary Space: O(N)

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