# Rearrange array elements such that Bitwise AND of first N – 1 elements is equal to last element

• Difficulty Level : Medium
• Last Updated : 09 Nov, 2021

Given an array arr[] of N positive integers, the task is to find an arrangement such that Bitwise AND of the first N – 1 elements is equal to the last element. If no such arrangement is possible then output will be -1.
Examples:

Input: arr[] = {1, 5, 3, 3}
Output: 3 5 3 1
(3 & 5 & 3) = 1 which is equal to the last element.
Input: arr[] = {2, 3, 7}
Output: -1
No such arrangement is possible.

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Approach:

• Let p = x & y then p ≤ min(x, y) which means Bitwise AND is a non-increasing function. If bitwise AND is performed on some elements then the value will be decreasing or remain the same.
• So, it is obvious to put the smallest element at the last index and then check if the last element is equal to the bitwise AND of the first N – 1 elements or not. If yes, then print the required arrangement otherwise print -1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Utility function to print``// the elements of an array``void` `printArr(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i] << ``" "``;``}` `// Function to find the required arrangement``void` `findArrangement(``int` `arr[], ``int` `n)``{` `    ``// There has to be atleast 2 elements``    ``if` `(n < 2) {``        ``cout << ``"-1"``;``        ``return``;``    ``}` `    ``// Minimum element from the array``    ``int` `minVal = *min_element(arr, arr + n);` `    ``// Swap any occurrence of the minimum``    ``// element with the last element``    ``for` `(``int` `i = 0; i < n; i++) {``        ``if` `(arr[i] == minVal) {``            ``swap(arr[i], arr[n - 1]);``            ``break``;``        ``}``    ``}` `    ``// Find the bitwise AND of the``    ``// first (n - 1) elements``    ``int` `andVal = arr;``    ``for` `(``int` `i = 1; i < n - 1; i++) {``        ``andVal &= arr[i];``    ``}` `    ``// If the bitwise AND is equal``    ``// to the last element then``    ``// print the arrangement``    ``if` `(andVal == arr[n - 1])``        ``printArr(arr, n);``    ``else``        ``cout << ``"-1"``;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 5, 3, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``findArrangement(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.*;` `class` `GFG``{` `// Utility function to print``// the elements of an array``static` `void` `printArr(``int` `[]arr, ``int` `n)``{``    ``for` `(``int` `i = ``0``; i < n; i++)``        ``System.out.print(arr[i] + ``" "``);``}` `// Function to find the required arrangement``static` `void` `findArrangement(``int` `arr[], ``int` `n)``{` `    ``// There has to be atleast 2 elements``    ``if` `(n < ``2``)``    ``{``        ``System.out.print(``"-1"``);``        ``return``;``    ``}` `    ``// Minimum element from the array``    ``int` `minVal = Arrays.stream(arr).min().getAsInt();` `    ``// Swap any occurrence of the minimum``    ``// element with the last element``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``if` `(arr[i] == minVal)``        ``{``            ``swap(arr, i, n - ``1``);``            ``break``;``        ``}``    ``}` `    ``// Find the bitwise AND of the``    ``// first (n - 1) elements``    ``int` `andVal = arr[``0``];``    ``for` `(``int` `i = ``1``; i < n - ``1``; i++)``    ``{``        ``andVal &= arr[i];``    ``}` `    ``// If the bitwise AND is equal``    ``// to the last element then``    ``// print the arrangement``    ``if` `(andVal == arr[n - ``1``])``        ``printArr(arr, n);``    ``else``        ``System.out.print(``"-1"``);``}` `static` `int``[] swap(``int` `[]arr, ``int` `i, ``int` `j)``{``    ``int` `temp = arr[i];``    ``arr[i] = arr[j];``    ``arr[j] = temp;``    ``return` `arr;``}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``int` `arr[] = { ``1``, ``5``, ``3``, ``3` `};``    ``int` `n = arr.length;` `    ``findArrangement(arr, n);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implementation of the approach` `# Utility function to print``# the elements of an array``def` `printArr(arr, n) :` `    ``for` `i ``in` `range``(n) :``        ``print``(arr[i], end ``=` `" "``);` `# Function to find the required arrangement``def` `findArrangement(arr, n) :` `    ``# There has to be atleast 2 elements``    ``if` `(n < ``2``) :``        ``print``(``"-1"``, end ``=` `"");``        ``return``;` `    ``# Minimum element from the array``    ``minVal ``=` `min``(arr);` `    ``# Swap any occurrence of the minimum``    ``# element with the last element``    ``for` `i ``in` `range``(n) :``        ``if` `(arr[i] ``=``=` `minVal) :``            ``arr[i], arr[n ``-` `1``] ``=` `arr[n ``-` `1``], arr[i];``            ``break``;``            ` `    ``# Find the bitwise AND of the``    ``# first (n - 1) elements``    ``andVal ``=` `arr[``0``];``    ``for` `i ``in` `range``(``1``, n ``-` `1``) :``        ``andVal &``=` `arr[i];` `    ``# If the bitwise AND is equal``    ``# to the last element then``    ``# print the arrangement``    ``if` `(andVal ``=``=` `arr[n ``-` `1``]) :``        ``printArr(arr, n);``    ``else` `:``        ``print``(``"-1"``);` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[ ``1``, ``5``, ``3``, ``3` `];``    ``n ``=` `len``(arr);` `    ``findArrangement(arr, n);` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;   ``using` `System.Linq;` `class` `GFG``{`` ` `// Utility function to print``// the elements of an array``static` `void` `printArr(``int` `[]arr, ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``Console.Write(arr[i] + ``" "``);``}`` ` `// Function to find the required arrangement``static` `void` `findArrangement(``int` `[]arr, ``int` `n)``{`` ` `    ``// There has to be atleast 2 elements``    ``if` `(n < 2)``    ``{``        ``Console.Write(``"-1"``);``        ``return``;``    ``}`` ` `    ``// Minimum element from the array``    ``int` `minVal = arr.Min();`` ` `    ``// Swap any occurrence of the minimum``    ``// element with the last element``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``if` `(arr[i] == minVal)``        ``{``            ``swap(arr, i, n - 1);``            ``break``;``        ``}``    ``}`` ` `    ``// Find the bitwise AND of the``    ``// first (n - 1) elements``    ``int` `andVal = arr;``    ``for` `(``int` `i = 1; i < n - 1; i++)``    ``{``        ``andVal &= arr[i];``    ``}`` ` `    ``// If the bitwise AND is equal``    ``// to the last element then``    ``// print the arrangement``    ``if` `(andVal == arr[n - 1])``        ``printArr(arr, n);``    ``else``        ``Console.Write(``"-1"``);``}`` ` `static` `int``[] swap(``int` `[]arr, ``int` `i, ``int` `j)``{``    ``int` `temp = arr[i];``    ``arr[i] = arr[j];``    ``arr[j] = temp;``    ``return` `arr;``}`` ` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``int` `[]arr = { 1, 5, 3, 3 };``    ``int` `n = arr.Length;`` ` `    ``findArrangement(arr, n);``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``
Output:
`3 5 3 1`

Time Complexity: O(N)

Auxiliary Space: O(1)

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