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# Find K elements whose absolute difference with median of array is maximum

Given an array arr[] and an integer K, the task is to find the K elements of the array whose absolute difference with median of array is maximum.
Note: If two elements have equal difference then the maximum element is taken into consideration.

Examples:

Input : arr[] = {1, 2, 3, 4, 5}, k = 3
Output : {5, 1, 4}
Explanation :
Median m = 3,
Difference of each array elements from median,
1 ==> diff(1-3) = 2
2 ==> diff(2-3) = 1
3 ==> diff(3-3) = 0
4 ==> diff(4-3) = 1
5 ==> diff(5-3) = 2
First K elements are 5, 1, 4 in this array.

Input: arr[] = {1, 2, 3}, K = 2
Output: {3, 1}

Approach:

• Sort the array and find the median of the array
• Create a difference array to store the difference of each element with the median of the sorted array.
• Highest difference elements will be the corner elements of the array. Therefore, initialize the two pointers as both the corner elements of the array that is 0 and N – 1.
• Finally include the elements of the array one by one with the maximum difference with the median.

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find first K``// elements whose difference with the ``// median of array is maximum`` ` `#include ``using` `namespace` `std;`` ` `// Function for calculating median ``double` `findMedian(``int` `a[], ``int` `n) ``{``    ``// check for even case ``    ``if` `(n % 2 != 0) ``       ``return` `(``double``)a[n/2]; ``       ` `    ``return` `(``double``)(a[(n-1)/2] + a[n/2])/2.0; ``} `` ` `// Function to find the K maximum absolute``// difference with the median of the array``void` `kStrongest(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// Sort the array.``    ``sort(arr, arr + n);`` ` `    ``// Store median``    ``double` `median = findMedian(arr, n);``    ``int` `diff[n];`` ` `    ``// Find and store difference``    ``for` `(``int` `i = 0; i < n; i++) {``        ``diff[i] = ``abs``(median - arr[i]);``    ``}`` ` `    ``int` `i = 0, j = n - 1;``    ``while` `(k > 0) {``         ` `        ``// If diff[i] is greater print it``        ``// Else print diff[j]``        ``if` `(diff[i] > diff[j]) {``            ``cout << arr[i] << ``" "``;``            ``i++;``        ``}``        ``else` `{``            ``cout << arr[j] << ``" "``;``            ``j--;``        ``}``        ``k--;``    ``}``}`` ` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 3, 4, 5 };``    ``int` `k = 3;``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);`` ` `    ``kStrongest(arr, n, k);``    ``return` `0;``}`

## Java

 `// Java implementation to find first K``// elements whose difference with the ``// median of array is maximum``import` `java.util.*;``class` `GFG{``  ` `// Function for calculating median ``static` `double` `findMedian(``int` `a[], ``int` `n) ``{``    ``// check for even case ``    ``if` `(n % ``2` `!= ``0``) ``       ``return` `(``double``)a[n / ``2``]; ``        ` `    ``return` `(``double``)(a[(n - ``1``) / ``2``] + ``                    ``a[n / ``2``]) / ``2.0``; ``} ``  ` `// Function to find the K maximum absolute``// difference with the median of the array``static` `void` `kStrongest(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// Sort the array.``    ``Arrays.sort(arr);``  ` `    ``// Store median``    ``double` `median = findMedian(arr, n);``    ``int` `[]diff = ``new` `int``[n];``  ` `    ``// Find and store difference``    ``for` `(``int` `i = ``0``; i < n; i++) ``    ``{``        ``diff[i] = (``int``)Math.abs(median - arr[i]);``    ``}``  ` `    ``int` `i = ``0``, j = n - ``1``;``    ``while` `(k > ``0``) ``    ``{``          ` `        ``// If diff[i] is greater print it``        ``// Else print diff[j]``        ``if` `(diff[i] > diff[j])``        ``{``            ``System.out.print(arr[i] + ``" "``);``            ``i++;``        ``}``        ``else` `        ``{``            ``System.out.print(arr[j] + ``" "``);``            ``j--;``        ``}``        ``k--;``    ``}``}``  ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5` `};``    ``int` `k = ``3``;``    ``int` `n = arr.length;``  ` `    ``kStrongest(arr, n, k);``}``}``// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 program to find first K``# elements whose difference with the``# median of array is maximum`` ` `# Function for calculating median``def` `findMedian(a, n):``     ` `    ``# Check for even case``    ``if` `(n ``%` `2` `!``=` `0``):``        ``return` `a[``int``(n ``/` `2``)]``         ` `    ``return` `(a[``int``((n ``-` `1``) ``/` `2``)] ``+` `            ``a[``int``(n ``/` `2``)]) ``/` `2.0`` ` `# Function to find the K maximum ``# absolute difference with the ``# median of the array``def` `kStrongest(arr, n, k):``     ` `    ``# Sort the array``    ``arr.sort()``     ` `    ``# Store median``    ``median ``=` `findMedian(arr, n)``    ``diff ``=` `[``0``] ``*` `(n)``     ` `    ``# Find and store difference``    ``for` `i ``in` `range``(n):``        ``diff[i] ``=` `abs``(median ``-` `arr[i])``         ` `    ``i ``=` `0``    ``j ``=` `n ``-` `1``     ` `    ``while` `(k > ``0``):``         ` `        ``# If diff[i] is greater print ``        ``# it. Else print diff[j]``        ``if` `(diff[i] > diff[j]):``            ``print``(arr[i], end ``=` `" "``)``            ``i ``+``=` `1``        ``else``:``            ``print``(arr[j], end ``=` `" "``)``            ``j ``-``=` `1``         ` `        ``k ``-``=` `1``     ` `# Driver code``arr ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5` `]``k ``=` `3``n ``=` `len``(arr)`` ` `kStrongest(arr, n, k)`` ` `# This code is contributed by sanjoy_62`

## C#

 `// C# implementation to find first K``// elements whose difference with the ``// median of array is maximum``using` `System;`` ` `class` `GFG{`` ` `// Function for calculating median ``static` `double` `findMedian(``int` `[]a, ``int` `n) ``{``    ``// Check for even case ``    ``if` `(n % 2 != 0) ``        ``return` `(``double``)a[n / 2]; ``         ` `    ``return` `(``double``)(a[(n - 1) / 2] + ``                    ``a[n / 2]) / 2.0; ``} `` ` `// Function to find the K maximum absolute``// difference with the median of the array``static` `void` `kStrongest(``int` `[]arr, ``int` `n,``                                  ``int` `k)``{``     ` `    ``// Sort the array.``    ``Array.Sort(arr);``     ` `    ``int` `i = 0;``     ` `    ``// Store median``    ``double` `median = findMedian(arr, n);``    ``int` `[]diff = ``new` `int``[n];`` ` `    ``// Find and store difference``    ``for``(i = 0; i < n; i++) ``    ``{``       ``diff[i] = (``int``)Math.Abs(median - arr[i]);``    ``}`` ` `    ``int` `j = n - 1;``    ``i = 0;``    ``while` `(k > 0) ``    ``{``         ` `        ``// If diff[i] is greater print it``        ``// Else print diff[j]``        ``if` `(diff[i] > diff[j])``        ``{``            ``Console.Write(arr[i] + ``" "``);``            ``i++;``        ``}``        ``else``        ``{``            ``Console.Write(arr[j] + ``" "``);``            ``j--;``        ``}``        ``k--;``    ``}``}`` ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 1, 2, 3, 4, 5 };``    ``int` `k = 3;``    ``int` `n = arr.Length;`` ` `    ``kStrongest(arr, n, k);``}``}`` ` `// This code is contributed by Rohit_ranjan`

## Javascript

 ``

Output

`5 1 4 `

Time Complexity: O(nlogn), where nlogn is the time complexity required to sort the given array
Auxiliary Space: O(n), extra space used to create a diff array

Another Approach:- In this approach we will se how we can reduce the space complexity to O(N)->O(1)

• There is no need to take difference array as in the above approach
• As we came to know that the difference will be maximum with corner values so no need to store the difference just take 2 pointer on start and end.
• Print the one which have greater difference and move that pointer

Implementation:-

## C++

 `// C++ implementation to find first K``// elements whose difference with the ``// median of array is maximum`` ` `#include ``using` `namespace` `std;`` ` `// Function for calculating median ``double` `findMedian(``int` `a[], ``int` `n) ``{``    ``// check for even case ``    ``if` `(n % 2 != 0) ``       ``return` `(``double``)a[n/2]; ``       ` `    ``return` `(``double``)(a[(n-1)/2] + a[n/2])/2.0; ``} `` ` `// Function to find the K maximum absolute``// difference with the median of the array``void` `kStrongest(``int` `arr[], ``int` `n, ``int` `k)``{``    ``// Sort the array.``    ``sort(arr, arr + n);`` ` `    ``// Store median``    ``double` `median = findMedian(arr, n);`` ` `    ``int` `i = 0, j = n - 1;``    ``while` `(k) {``       ` `          ``//if difference of element at i with K is greater than element at j``        ``if` `(``abs``(median-arr[i]) > ``abs``(median-arr[j])) {``            ``cout << arr[i] << ``" "``;``            ``i++;``        ``}``        ``else` `{``            ``cout << arr[j] << ``" "``;``            ``j--;``        ``}``        ``k--;``    ``}``}`` ` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 3, 4, 5 };``    ``int` `k = 3;``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);`` ` `    ``kStrongest(arr, n, k);``    ``return` `0;``}`

## Java

 `// Java implementation to find first K``// elements whose difference with the``// median of array is maximum`` ` `import` `java.util.*;`` ` `public` `class` `GFG {`` ` `    ``// Function for calculating median``    ``public` `static` `double` `findMedian(``int``[] a, ``int` `n)``    ``{``        ``// check for even case``        ``if` `(n % ``2` `!= ``0``) {``            ``return` `(``double``)a[n / ``2``];``        ``}`` ` `        ``return` `(``double``)(a[(n - ``1``) / ``2``] + a[n / ``2``]) / ``2.0``;``    ``}`` ` `    ``// Function to find the K maximum absolute``    ``// difference with the median of the array``    ``public` `static` `void` `kStrongest(``int``[] arr, ``int` `n, ``int` `k)``    ``{``        ``// Sort the array.``        ``Arrays.sort(arr);`` ` `        ``// Store median``        ``double` `median = findMedian(arr, n);`` ` `        ``int` `i = ``0``;``        ``int` `j = n - ``1``;``        ``while` `(k != ``0``) {`` ` `            ``// if difference of element at i with K is``            ``// greater than element at j``            ``if` `(Math.abs(median - arr[i])``                ``> Math.abs(median - arr[j])) {``                ``System.out.print(arr[i]);``                ``System.out.print(``" "``);``                ``i++;``            ``}``            ``else` `{``                ``System.out.print(arr[j]);``                ``System.out.print(``" "``);``                ``j--;``            ``}``            ``k--;``        ``}``    ``}`` ` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = { ``1``, ``2``, ``3``, ``4``, ``5` `};``        ``int` `k = ``3``;``        ``int` `n = arr.length;`` ` `        ``kStrongest(arr, n, k);``    ``}``}`` ` `// this code is contributed by bhardwajji`

## Python3

 `# C++ implementation to find first K``# elements whose difference with the``# median of array is maximum`` ` `# Function for calculating median``def` `findMedian(a, n):``   ` `      ``# check for even case``    ``if` `n ``%` `2` `!``=` `0``:``        ``return` `a[n``/``/``2``]``    ``return` `(a[(n``-``1``)``/``/``2``] ``+` `a[n``/``/``2``])``/``2`` ` `# Function to find the K maximum absolute``# difference with the median of the array``def` `kStrongest(arr, n, k):``   ` `      ``# sort array``    ``arr.sort()``     ` `    ``# store median``    ``median ``=` `findMedian(arr, n)``    ``i ``=` `0``    ``j ``=` `n ``-` `1``    ``while` `k:``       ` `          ``# if difference of element at i with K is greater than element at j``        ``if` `abs``(median``-``arr[i]) > ``abs``(median``-``arr[j]):``            ``print``(arr[i], end``=``" "``)``            ``i ``+``=` `1``        ``else``:``            ``print``(arr[j], end``=``" "``)``            ``j ``-``=` `1``        ``k ``-``=` `1`` ` `#driver code``arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``]``k ``=` `3``n ``=` `len``(arr)``kStrongest(arr, n, k)`

## C#

 `// C# implementation to find first K``// elements whose difference with the ``// median of array is maximum`` ` `using` `System;`` ` `public` `class` `GFG``{``    ``// Function for calculating median ``    ``static` `double` `FindMedian(``int``[] a, ``int` `n) ``    ``{``        ``// check for even case ``        ``if` `(n % 2 != 0) ``            ``return` `(``double``)a[n / 2]; ``        ``return` `(``double``)(a[(n - 1) / 2] + a[n / 2]) / 2.0; ``    ``} `` ` `    ``// Function to find the K maximum absolute``    ``// difference with the median of the array``    ``static` `void` `KStrongest(``int``[] arr, ``int` `n, ``int` `k)``    ``{``        ``// Sort the array.``        ``Array.Sort(arr);`` ` `        ``// Store median``        ``double` `median = FindMedian(arr, n);`` ` `        ``int` `i = 0, j = n - 1;``        ``while` `(k > 0) {``            ``// if difference of element at i with K is greater than element at j``            ``if` `(Math.Abs(median - arr[i]) > Math.Abs(median - arr[j])) {``                ``Console.Write(arr[i] + ``" "``);``                ``i++;``            ``}``            ``else` `{``                ``Console.Write(arr[j] + ``" "``);``                ``j--;``            ``}``            ``k--;``        ``}``    ``}``     ` `    ``// Driver Code``    ``static` `void` `Main(``string``[] args)``    ``{``        ``int``[] arr = { 1, 2, 3, 4, 5 };``        ``int` `k = 3;``        ``int` `n = arr.Length;`` ` `        ``KStrongest(arr, n, k);``    ``}``}`` ` `//this code is contributed by bhardwajji`

## Javascript

 `// JavaScript implementation to find first K``// elements whose difference with the``// median of array is maximum`` ` `function` `findMedian(a, n) {``// check for even case``if` `(n % 2 !== 0) {``return` `a[(Math.floor(n / 2))];``}``return` `(a[(n - 1) / 2] + a[n / 2]) / 2.0;``}`` ` `function` `kStrongest(arr, n, k) {``// Sort the array.``arr.sort(``function``(a, b) {``return` `a - b;``});``// Store median``var` `median = findMedian(arr, n);`` ` `var` `i = 0;``var` `j = n - 1;``while` `(k !== 0) {`` ` `    ``// if difference of element at i with K is``    ``// greater than element at j``    ``if` `(Math.abs(median - arr[i])``        ``> Math.abs(median - arr[j])) {``        ``console.log(arr[i] + ``" "``);``        ``i++;``    ``}``    ``else` `{``        ``console.log(arr[j] + ``" "``);``        ``j--;``    ``}``    ``k--;``}``}`` ` `// Driver Code``var` `arr = [ 1, 2, 3, 4, 5 ];``var` `k = 3;``var` `n = arr.length;`` ` `kStrongest(arr, n, k);`` ` `// this code is contributed by shivamsharma215`

Output

`5 1 4 `

Time Complexity:- O(NlogN)
Auxiliary Space- O(1)

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