# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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 that 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++

 `// C++ program to check whether bitwise AND of a number ` `// with any subset of an array is zero or not ` `#include ` `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

 `// 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

 `# 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#

 `// 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

 ` `

Output:

```YES
```

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