Print all submasks of a given mask

Given an integer N, the task is to print all the subsets of the set formed by the set bits present in the binary representation of N.

Examples:

Input: N = 5
Output: 5 4 1 
Explanation:
Binary representation of N is "101", Therefore all the required subsets are {"101", "100", "001", "000"}.

Input: N = 25
Output: 25 24 17 16 9 8 1 
Explanation:
Binary representation of N is "11001". Therefore, all the required subsets are {"11001", "11000", "10001", "10000", "01001", "01000", "0001", "0000"}.

Naive Approach: The simplest approach is to traverse every mask in the range [0, 1 << (count of set bit in N)] and check if no other bits are set in it except for the bits in N. Then, print it. 
Time Complexity: O(2^{(count of set bit in N)})
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized by only traversing the submasks which are the subset of mask N.

• Suppose S is the current submask which is the subset of mask N. Then, it can be observed that by assigning S = (S - 1) & N, the next submask of N can be obtained which is less than S.
• In S - 1, it flips all the bits present on the right of the rightmost set bit including rightmost set bit of S.
• Therefore, after performing Bitwise & with N, a submask of N is obtained.
• Therefore, S = (S - 1) & N gives the next submask of N which is less than S.

Follow the steps below to solve the problem:

• Initialize a variable, say S = N.
• Iterate while S > 0 and in each iteration, print the value of S.
• Assign S = (S - 1) & N.

Below is the implementation of the above approach:

25 24 17 16 9 8 1

Time Complexity: O(2^{(count of set bit in N)})
Auxiliary Space: O(1)