Check whether bitwise AND of a number with any subset of an array is zero or not

Given an array and a Number N. The task is to check whether there exists any subset of this array such that the bitwise AND of this subset with N is zero.

Examples: 

Input : arr[] = {1, 2, 4}  ;  N = 3
Output : YES
Explanation: The subsets are:
(1, 2 ), (1, 4), (1, 2, 4) 

Input : arr[] = {1, 1, 1}  ;  N = 3
Output : NO

A Simple Approach is to find the bitwise AND of all the subsets of the array and check whether the AND of N with any subset is zero or not.

An Efficient Approach is to observe that the bitwise-AND of any two numbers will always produce a number less than or equal to the smaller number. So our task is to find the subset which has the minimum value of bitwise AND. So as stated earlier the AND of any two numbers will always produce a number less than or equal to the minimum number so the minimum value of AND will be the AND of all the array elements. So the task now reduces to check the bitwise-AND of all the array elements and N and if it is zero we will print YES otherwise NO.

Below is the implementation of the above approach: 

// C++ program to check whether bitwise AND of a number
// with any subset of an array is zero or not
#include <bits/stdc++.h>
using namespace std;

// Function to check whether bitwise AND of a number
// with any subset of an array is zero or not
void isSubsetAndZero(int array[], int length, int N)
{
    // variable to store the
    // AND of all the elements
    int arrAnd = array[0];

    // find the AND of all the elements
    // of the array
    for (int i = 1; i < length; i++) {
        arrAnd = arrAnd & array[i];
    }

    // if the AND of all the array elements
    // and N is equal to zero
    if ((arrAnd & N) == 0)
        cout << "YES" << endl;
    else
        cout << "NO" << endl;
}

// Driver Code
int main()
{
    int array[] = { 1, 2, 4 };
    int length = sizeof(array) / sizeof(int);

    int N = 3;

    isSubsetAndZero(array, length, N);
}

// Java program to check whether bitwise AND of a number
// with any subset of an array is zero or not
import java.io.*;

public class GFG {


// Function to check whether bitwise AND of a number
// with any subset of an array is zero or not
static void isSubsetAndZero(int array[], int length, int N)
{
    // variable to store the
    // AND of all the elements
    int arrAnd = array[0];

    // find the AND of all the elements
    // of the array
    for (int i = 1; i < length; i++) {
        arrAnd = arrAnd & array[i];
    }

    // if the AND of all the array elements
    // and N is equal to zero
    if ((arrAnd & N) == 0)
        System.out.println( "YES");
    else
        System.out.println( "NO");
}

// Driver Code
    public static void main (String[] args) {
        int array[] = { 1, 2, 4 };
    int length = array.length;

    int N = 3;

    isSubsetAndZero(array, length, N);
    }
}
//This code is contributed by shs..

# Python 3 program to check whether
# bitwise AND of a number with any 
# subset of an array is zero or not

# Function to check whether bitwise 
# AND of a number with any subset 
# of an array is zero or not
def isSubsetAndZero(array, length, N):

    # variable to store the
    # AND of all the elements
    arrAnd = array[0]

    # find the AND of all 
    # the elements of the array
    for i in range(1, length) :
        arrAnd = arrAnd & array[i]

    # if the AND of all the array 
    # elements and N is equal to zero
    if ((arrAnd & N) == 0):
        print("YES")
    else:
        print("NO")

# Driver Code
if __name__ == "__main__":
    array = [ 1, 2, 4 ]
    length = len(array)

    N = 3

    isSubsetAndZero(array, length, N)

# This code is contributed 
# by ChitraNayal

// C# program to check whether 
// bitwise AND of a number with 
// any subset of an array is zero or not
using System;

class GFG
{

// Function to check whether bitwise 
// AND of a number with any subset 
// of an array is zero or not
static void isSubsetAndZero(int []array, 
                            int length, int N)
{
    // variable to store the
    // AND of all the elements
    int arrAnd = array[0];

    // find the AND of all the 
    // elements of the array
    for (int i = 1; i < length; i++) 
    {
        arrAnd = arrAnd & array[i];
    }

    // if the AND of all the array 
    // elements and N is equal to zero
    if ((arrAnd & N) == 0)
        Console.WriteLine( "YES");
    else
        Console.WriteLine( "NO");
}

// Driver Code
public static void Main () 
{
    int []array = { 1, 2, 4 };
    int length = array.Length;
    
    int N = 3;
    
    isSubsetAndZero(array, length, N);
}
}

// This code is contributed 
// by inder_verma

<?php
// PHP program to check whether 
// bitwise AND of a number with 
// any subset of an array is zero or not

// Function to check whether 
// bitwise AND of a number with
// any subset of an array is zero or not
function isSubsetAndZero($array, $length, $N)
{
    // variable to store the
    // AND of all the elements
    $arrAnd = $array[0];

    // find the AND of all the
    // elements of the array
    for ($i = 1; $i <$length; $i++) 
    {
        $arrAnd = $arrAnd & $array[$i];
    }

    // if the AND of all the array 
    // elements and N is equal to zero
    if (($arrAnd & $N) == 0)
        echo("YES");
    else
        echo("NO");
}

// Driver Code
$array = array( 1, 2, 4 );
$length = count($array);

$N = 3;

isSubsetAndZero($array, $length, $N);

// This code is contributed 
// by Shashank
?>

<script>

// Javascript implementation of the above approach


// Function to check whether bitwise AND of a number
// with any subset of an array is zero or not
function isSubsetAndZero(array, len, N)
{
    // variable to store the
    // AND of all the elements
    var arrAnd = array[0];

    // find the AND of all the elements
    // of the array
    for (var i = 1; i < len; i++) {
        arrAnd = arrAnd & array[i];
    }

    // if the AND of all the array elements
    // and N is equal to zero
    if ((arrAnd & N) == 0)
        document.write("YES"+"<br>");
    else
        document.write("NO"+"<br>");
}



var array = [1, 2, 4 ];
var len = array.length;
var N = 3;
isSubsetAndZero(array, len, N);

// This code is contributed by SoumikMondal

</script>

YES

Time Complexity: O(N), where N is the length of the array
Auxiliary Space: O(1)

andrew1234

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Article Tags :

• Bit Magic
• Competitive Programming
• DSA
• subset
• Bitwise-AND

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Practice Tags :

• Bit Magic
• subset