Maximum set of number from the first N natural numbers whose Bitwise AND is positive

Given a positive integer N, the task is to find the maximum set of numbers from the first N natural numbers whose Bitwise AND is positive

Examples:

Input: N = 7
Output: 4
Explanation:
The set of numbers from the first N(= 7) natural numbers whose Bitwise AND is positive is {4, 5, 6, 7}, which is of maximum length.

Input: N = 16
Output: 8

Approach: The given problem can be solved based on the observation that 2^N and (2^N – 1), results in 0. Therefore, the maximum length of the set must not include both 2^N and (2^N – 1) in the same set. The maximum subarray with non-zero AND value can be found out as:

• Find the maximum power of 2 less than or equal to N and if N is a power of 2, the answer should be N/2, for example, when N is 16, the maximum subarray with non-zero AND value is 8.
• Otherwise, the answer is the length between the N and the largest power of 2 less than or equal to N.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the maximum set of
// number whose Bitwise AND is positive
int maximumSizeOfSet(int N)
{
    // Base Case
    if (N == 1)
        return 1;

    // Store the power of 2 less than
    // or equal to N
    int temp = 1;
    while (temp * 2 <= N) {
        temp *= 2;
    }

    // N is power of 2
    if (N & (N - 1) == 0)
        return N / 2;
    else
        return N - temp + 1;
}

// Driver Code
int main()
{
    int N = 7;
    cout << maximumSizeOfSet(N);

    return 0;
}

Java

// Java program for the above approach
class GFG{

// Function to find the maximum set of
// number whose Bitwise AND is positive
public static int maximumSizeOfSet(int N)
{

    // Base Case
    if (N == 1)
        return 1;

    // Store the power of 2 less than
    // or equal to N
    int temp = 1;
    while (temp * 2 <= N) {
        temp *= 2;
    }

    // N is power of 2
    if ((N & (N - 1)) == 0)
        return N / 2;
    else
        return N - temp + 1;
}

// Driver Code
public static void main(String args[])
{
    int N = 7;
    System.out.println(maximumSizeOfSet(N));
}

}

// This code is contributed by gfgking.

Python3

# python program for the above approach

# Function to find the maximum set of
# number whose Bitwise AND is positive
def maximumSizeOfSet(N):

    # Base Case
    if (N == 1):
        return 1

    # Store the power of 2 less than
    # or equal to N
    temp = 1
    while (temp * 2 <= N):
        temp *= 2

    # N is power of 2
    if (N & (N - 1) == 0):
        return N // 2
    else:
        return N - temp + 1

# Driver Code
if __name__ == "__main__":

    N = 7
    print(maximumSizeOfSet(N))

# This code is contributed by rakeshsahni

C#

// C# program for the above approach
using System;

public class GFG {

    static int maximumSizeOfSet(int N)
    {

        // Base Case
        if (N == 1)
            return 1;

        // Store the power of 2 less than
        // or equal to N
        int temp = 1;
        while (temp * 2 <= N) {
            temp *= 2;
        }

        // N is power of 2
        if ((N & (N - 1)) == 0)
            return N / 2;
        else
            return N - temp + 1;
    }

    // Driver Code
    public static void Main(String[] args)
    {
        int N = 7;

        Console.WriteLine(maximumSizeOfSet(N));
    }
}

// This code is contributed by dwivediyash

Javascript

<script>
    // JavaScript program for the above approach

    // Function to find the maximum set of
    // number whose Bitwise AND is positive
    const maximumSizeOfSet = (N) => {
        // Base Case
        if (N == 1)
            return 1;

        // Store the power of 2 less than
        // or equal to N
        let temp = 1;
        while (temp * 2 <= N) {
            temp *= 2;
        }

        // N is power of 2
        if (N & (N - 1) == 0)
            return parseInt(N / 2);
        else
            return N - temp + 1;
    }

    // Driver Code
    let N = 7;
    document.write(maximumSizeOfSet(N));

    // This code is contributed by rakeshsahni

</script>

Output:

4

Time Complexity: O(log N)
Auxiliary Space: O(1)