Print bitwise AND set of a number N

Given a number N, print all the numbers which are a bitwise AND set of the binary representation of N. Bitwise AND set of a number N is all possible numbers x smaller than or equal N such that N & i is equal to x for some number i. 

Examples :

Input : N = 5
Output : 0, 1, 4, 5 
Explanation: 0 & 5 = 0 
 1 & 5 = 1
 2 & 5 = 0
 3 & 5 = 1
 4 & 5 = 4
 5 & 5 = 5 
So we get 0, 1, 4 and 5 in the 
bitwise subsets of N.
Input : N = 9
Output : 0, 1, 8, 9 

Simple Approach: A naive approach is to iterate from all numbers from 0 to N and check if (N&i == i). Print the numbers which satisfy the specified condition. 

Below is the implementation of above idea:  

0 1 8 9 

Time Complexity : O(N)

Efficient Solution: An efficient solution is to use bitwise operators to find the subsets. Instead of iterating for every i, we can simply iterate for the bitwise subsets only. Iterating backward for i=(i-1)&n gives us every bitwise subset, where i starts from n and ends at 1. 

Below is the implementation of above idea:  

9 8 1 0

Output :

9 8 1 0

Time Complexity: O(K), where K is the number of bitwise subsets of N.

Approach: Optimized Bit Manipulation

Steps:

1. Initialize an empty list res with 0 as the first element.
2. Initialize a variable x as 1.
3. While x is less than or equal to N, do the following:
   a. If the x-th bit of N is 1, then for each element r in res, append r | x to res.
   b. Multiply x by 2.
4. Return the final list res.
   

0 1 4 5 

Time Complexity: O(log N)
Auxiliary Space: O(2^log N)