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

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.

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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
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[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
        cout << "-1";
}
  
// Driver code
int main()
{
    int arr[] = { 1, 5, 3, 3 };
    int n = sizeof(arr) / sizeof(int);
  
    findArrangement(arr, n);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# 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

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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[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
        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

chevron_right


Output:

3 5 3 1

Time Complexity: O(N)



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.