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# Generate an N-length array with sum equal to twice the sum of its absolute difference with same-indexed elements of given array

• Last Updated : 07 Apr, 2021

Given an array arr[] of size N, the task is to construct an array brr[] of size N that satisfies the following conditions:

• In every pair of consecutive elements in the array brr[], one element must be divisible by the other, i.e. brr[i] must be divisible by brr[i + 1] or vice-versa.
• Every ith element in the array brr[] must satisfy brr[i] >= arr[i] / 2.
• The sum of elements of the array arr[] must be greater than or equal to 2 * Σabs(arr[i] – brr[i]).

Examples:

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Input: arr[] = { 11, 5, 7, 3, 2 }
Output: 8 4 4 2 2
Explanation:
abs(11 – 8) + abs(5 – 4) + abs(7 – 4) + abs(3 – 2) + abs(2 – 2) = 8
arr + arr + … + arr = 28
2 * 8 <= 28 and for every ith element brr[i] >= arr[i] / 2.
Therefore, one of the possible values of brr[] are 8 4 4 2 2.

Input: arr[] = { 11, 7, 5 }
Output: { 8, 4, 4 }

Approach: The idea is based on the following observation:

If brr[i] is the nearest power of 2 and is smaller than or equal to arr[i], then brr[i] must be greater than or equal to arr[i] / 2 and also the sum of elements of the array, arr[] must be greater than or equal to 2 * Σabs(arr[i] – brr[i]).

Follow the steps below to solve the problem:

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to construct an array``// with given conditions``void` `constructArray(``int` `arr[], ``int` `N)``{``    ``int` `brr[N] = { 0 };` `    ``// Traverse the array arr[]``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``int` `K = ``log``(arr[i]) / ``log``(2);` `        ``// Stores closest power of 2``        ``// less than or equal to arr[i]``        ``int` `R = ``pow``(2, K);` `        ``// Stores R into brr[i]``        ``brr[i] = R;``    ``}` `    ``// Print array elements``    ``for` `(``int` `i = 0; i < N; i++) {``        ``cout << brr[i] << ``" "``;``    ``}``}` `// Driver Code``int` `main()``{` `    ``// Given array``    ``int` `arr[] = { 11, 5, 7, 3, 2 };` `    ``// Size of the array``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function Call``    ``constructArray(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG{` `// Function to conan array``// with given conditions``static` `void` `constructArray(``int` `arr[], ``int` `N)``{``    ``int` `brr[] = ``new` `int``[N];``    ` `    ``// Traverse the array arr[]``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ``int` `K = (``int``)(Math.log(arr[i]) /``                      ``Math.log(``2``));``        ` `        ``// Stores closest power of 2``        ``// less than or equal to arr[i]``        ``int` `R = (``int``)Math.pow(``2``, K);``        ` `        ``// Stores R into brr[i]``        ``brr[i] = R;``    ``}``    ` `    ``// Print array elements``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ``System.out.print(brr[i] + ``" "``);``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Given array``    ``int` `arr[] = { ``11``, ``5``, ``7``, ``3``, ``2` `};` `    ``// Size of the array``    ``int` `N = arr.length;` `    ``// Function Call``    ``constructArray(arr, N);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program for the above approach``from` `math ``import` `log` `# Function to construct an array``# with given conditions``def` `constructArray(arr, N):``    ``brr ``=` `[``0``]``*``N` `    ``# Traverse the array arr[]``    ``for` `i ``in` `range``(N):``        ``K ``=` `int``(log(arr[i])``/``log(``2``))` `        ``# Stores closest power of 2``        ``# less than or equal to arr[i]``        ``R ``=` `pow``(``2``, K)` `        ``# Stores R into brr[i]``        ``brr[i] ``=` `R` `    ``# Prarray elements``    ``for` `i ``in` `range``(N):``        ``print``(brr[i], end ``=` `" "``)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``  ` `  ``# Given array``    ``arr ``=` `[``11``, ``5``, ``7``, ``3``, ``2``]` `    ``# Size of the array``    ``N ``=` `len``(arr)` `    ``# Function Call``    ``constructArray(arr, N)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program for the above approach   ``using` `System;   ``     ` `class` `GFG{   ``     ` `// Function to construct an array   ``// with given conditions   ``static` `void` `constructArray(``int` `[]arr, ``int` `N)   ``{   ``    ``int``[] brr = ``new` `int``[N];   ``    ``Array.Clear(brr, 0, brr.Length);   ``    ` `    ``// Traverse the array arr[]   ``    ``for``(``int` `i = 0; i < N; i++)``    ``{   ``        ``int` `K = (``int``)(Math.Log(arr[i]) /``                      ``Math.Log(2));   ``                      ` `        ``// Stores closest power of 2   ``        ``// less than or equal to arr[i]   ``        ``int` `R = (``int``)Math.Pow(2, K);   ``        ` `        ``// Stores R into brr[i]   ``        ``brr[i] = R;   ``    ``}   ``     ` `    ``// Print array elements   ``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``Console.Write(brr[i] + ``" "``);   ``    ``}   ``}   ``     ` `// Driver Code   ``public` `static` `void` `Main()   ``{   ``    ` `    ``// Given array   ``    ``int` `[]arr = { 11, 5, 7, 3, 2 };   ``     ` `    ``// Size of the array   ``    ``int` `N = arr.Length;   ``     ` `    ``// Function Call   ``    ``constructArray(arr, N);   ``}   ``}` `// This code is contributed by SURENDRA_GANGWAR`

## Javascript

 ``
Output:
`8 4 4 2 2`

Time Complexity: O(N)
Auxiliary Space: O(N)

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